1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
5240
5241
5242
5243
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
5289
5290
5291
5292
5293
5294
5295
5296
5297
5298
5299
5300
5301
5302
5303
5304
5305
5306
5307
5308
5309
5310
5311
5312
5313
5314
5315
5316
5317
5318
5319
5320
5321
5322
5323
5324
5325
5326
5327
5328
5329
5330
5331
5332
5333
5334
5335
5336
5337
5338
5339
5340
5341
5342
5343
5344
5345
5346
5347
5348
5349
5350
5351
5352
5353
5354
5355
5356
5357
5358
5359
5360
5361
5362
5363
5364
5365
5366
5367
5368
5369
5370
5371
5372
5373
5374
5375
5376
5377
5378
5379
5380
5381
5382
5383
5384
5385
5386
5387
5388
5389
5390
5391
5392
5393
5394
5395
5396
5397
5398
5399
5400
5401
5402
5403
5404
5405
5406
5407
5408
5409
5410
5411
5412
5413
5414
5415
5416
5417
5418
5419
5420
5421
5422
5423
5424
5425
5426
5427
5428
5429
5430
5431
5432
5433
5434
5435
5436
5437
5438
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
5456
5457
5458
5459
5460
5461
5462
5463
5464
5465
5466
5467
5468
5469
5470
5471
5472
5473
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
5489
5490
5491
5492
5493
5494
5495
5496
5497
5498
5499
5500
5501
5502
5503
5504
5505
5506
5507
5508
5509
5510
5511
5512
5513
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
5529
5530
5531
5532
5533
5534
5535
5536
5537
5538
5539
5540
5541
5542
5543
5544
5545
5546
5547
5548
5549
5550
5551
5552
5553
5554
5555
5556
5557
5558
5559
5560
5561
5562
5563
5564
5565
5566
5567
5568
5569
5570
5571
5572
5573
5574
5575
5576
5577
5578
5579
5580
5581
5582
5583
5584
5585
5586
5587
5588
5589
5590
5591
5592
5593
5594
5595
5596
5597
5598
5599
5600
5601
5602
5603
5604
5605
5606
5607
5608
5609
5610
5611
5612
5613
5614
5615
5616
5617
5618
5619
5620
5621
5622
5623
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
5644
5645
5646
5647
5648
5649
5650
5651
5652
5653
5654
5655
5656
5657
5658
5659
5660
5661
5662
5663
5664
5665
5666
5667
5668
5669
5670
5671
5672
5673
5674
5675
5676
5677
5678
5679
5680
5681
5682
5683
5684
5685
5686
5687
5688
5689
5690
5691
5692
5693
5694
5695
5696
5697
5698
5699
5700
5701
5702
5703
5704
5705
5706
5707
5708
5709
5710
5711
5712
5713
5714
5715
5716
5717
5718
5719
5720
5721
5722
5723
5724
5725
5726
5727
5728
5729
5730
5731
5732
5733
5734
5735
5736
5737
5738
5739
5740
5741
5742
5743
5744
5745
5746
5747
5748
5749
5750
5751
5752
5753
5754
5755
5756
5757
5758
5759
5760
5761
5762
5763
5764
5765
5766
5767
5768
5769
5770
5771
5772
5773
5774
5775
5776
5777
5778
5779
5780
5781
5782
5783
5784
5785
5786
5787
5788
5789
5790
5791
5792
5793
5794
5795
5796
5797
5798
5799
5800
5801
5802
5803
5804
5805
5806
5807
5808
5809
5810
5811
5812
5813
5814
5815
5816
5817
5818
5819
5820
5821
5822
5823
5824
5825
5826
5827
5828
5829
5830
5831
5832
5833
5834
5835
5836
5837
5838
5839
5840
5841
5842
5843
5844
5845
5846
5847
5848
5849
5850
5851
5852
5853
5854
5855
5856
5857
5858
5859
5860
5861
5862
5863
5864
5865
5866
5867
5868
5869
5870
5871
5872
5873
5874
5875
5876
5877
5878
5879
5880
5881
5882
5883
5884
5885
5886
5887
5888
5889
5890
5891
5892
5893
5894
5895
5896
5897
5898
5899
5900
5901
5902
5903
5904
5905
5906
5907
5908
5909
5910
5911
5912
5913
5914
5915
5916
5917
5918
5919
5920
5921
5922
5923
5924
5925
5926
5927
5928
5929
5930
5931
5932
5933
5934
5935
5936
5937
5938
5939
5940
5941
5942
5943
5944
5945
5946
5947
5948
5949
5950
5951
5952
5953
5954
5955
5956
5957
5958
5959
5960
5961
5962
5963
5964
5965
5966
5967
5968
5969
5970
5971
5972
5973
5974
5975
5976
5977
5978
5979
5980
5981
5982
5983
5984
5985
5986
5987
5988
5989
5990
5991
5992
5993
5994
5995
5996
5997
5998
5999
6000
6001
6002
6003
6004
6005
6006
6007
6008
6009
6010
6011
6012
6013
6014
6015
6016
6017
6018
6019
6020
6021
6022
6023
6024
6025
6026
6027
6028
6029
6030
6031
6032
6033
6034
6035
6036
6037
6038
6039
6040
6041
6042
6043
6044
6045
6046
6047
6048
6049
6050
6051
6052
6053
6054
6055
6056
6057
6058
6059
6060
6061
6062
6063
6064
6065
6066
6067
6068
6069
6070
6071
6072
6073
6074
6075
6076
6077
6078
6079
6080
6081
6082
6083
6084
6085
6086
6087
6088
6089
6090
6091
6092
6093
6094
6095
6096
6097
6098
6099
6100
6101
6102
6103
6104
6105
6106
6107
6108
6109
6110
6111
6112
6113
6114
6115
6116
6117
6118
6119
6120
6121
6122
6123
6124
6125
6126
6127
6128
6129
6130
6131
6132
6133
6134
6135
6136
6137
6138
6139
6140
6141
6142
6143
6144
6145
6146
6147
6148
6149
6150
6151
6152
6153
6154
6155
6156
6157
6158
6159
6160
6161
6162
6163
6164
6165
6166
6167
6168
6169
6170
6171
6172
6173
6174
6175
6176
6177
6178
6179
6180
6181
6182
6183
6184
6185
6186
6187
6188
6189
6190
6191
6192
6193
6194
6195
6196
6197
6198
6199
6200
6201
6202
6203
6204
6205
6206
6207
6208
6209
6210
6211
6212
6213
6214
6215
6216
6217
6218
6219
6220
6221
6222
6223
6224
6225
6226
6227
6228
6229
6230
6231
6232
6233
6234
6235
6236
6237
6238
6239
6240
6241
6242
6243
6244
6245
6246
6247
6248
6249
6250
6251
6252
6253
6254
6255
6256
6257
6258
6259
6260
6261
6262
6263
6264
6265
6266
6267
6268
6269
6270
6271
6272
6273
6274
6275
6276
6277
6278
6279
6280
6281
6282
6283
6284
6285
6286
6287
6288
6289
6290
6291
6292
6293
6294
6295
6296
6297
6298
6299
6300
6301
6302
6303
6304
6305
6306
6307
6308
6309
6310
6311
6312
6313
6314
6315
6316
6317
6318
6319
6320
6321
6322
6323
6324
6325
6326
6327
6328
6329
6330
6331
6332
6333
6334
6335
6336
6337
6338
6339
6340
6341
6342
6343
6344
6345
6346
6347
6348
6349
6350
6351
6352
6353
6354
6355
6356
6357
6358
6359
6360
6361
6362
6363
6364
6365
6366
6367
6368
6369
6370
6371
6372
6373
6374
6375
6376
6377
6378
6379
6380
6381
6382
6383
6384
6385
6386
6387
6388
6389
6390
6391
6392
6393
6394
6395
6396
6397
6398
6399
6400
6401
6402
6403
6404
6405
6406
6407
6408
6409
6410
6411
6412
6413
6414
6415
6416
6417
6418
6419
6420
6421
6422
6423
6424
6425
6426
6427
6428
6429
6430
6431
6432
6433
6434
6435
6436
6437
6438
6439
6440
6441
6442
6443
6444
6445
6446
6447
6448
6449
6450
6451
6452
6453
6454
6455
6456
6457
6458
6459
6460
6461
6462
6463
6464
6465
6466
6467
6468
6469
6470
6471
6472
6473
6474
6475
6476
6477
6478
6479
6480
6481
6482
6483
6484
6485
6486
6487
6488
6489
6490
6491
6492
6493
6494
6495
6496
6497
6498
6499
6500
6501
6502
6503
6504
6505
6506
6507
6508
6509
6510
6511
6512
6513
6514
6515
6516
6517
6518
6519
6520
6521
6522
6523
6524
6525
6526
6527
6528
6529
6530
6531
6532
6533
6534
6535
6536
6537
6538
6539
6540
6541
6542
6543
6544
6545
6546
6547
6548
6549
6550
6551
6552
6553
6554
6555
6556
6557
6558
6559
6560
6561
6562
6563
6564
6565
6566
6567
6568
6569
6570
6571
6572
6573
6574
6575
6576
6577
6578
6579
6580
6581
6582
6583
6584
6585
6586
6587
6588
6589
6590
6591
6592
6593
6594
6595
6596
6597
6598
6599
6600
6601
6602
6603
6604
6605
6606
6607
6608
6609
6610
6611
6612
6613
6614
6615
6616
6617
6618
6619
6620
6621
6622
6623
6624
6625
6626
6627
6628
6629
6630
6631
6632
6633
6634
6635
6636
6637
6638
6639
6640
6641
6642
6643
6644
6645
6646
6647
6648
6649
6650
6651
6652
6653
6654
6655
6656
6657
6658
6659
6660
6661
6662
6663
6664
6665
6666
6667
6668
6669
6670
6671
6672
6673
6674
6675
6676
6677
6678
6679
6680
6681
6682
6683
6684
6685
6686
6687
6688
6689
6690
6691
6692
6693
6694
6695
6696
6697
6698
6699
6700
6701
6702
6703
6704
6705
6706
6707
6708
6709
6710
6711
6712
6713
6714
6715
6716
6717
6718
6719
6720
6721
6722
6723
6724
6725
6726
6727
6728
6729
6730
6731
6732
6733
6734
6735
6736
6737
6738
6739
6740
6741
6742
6743
6744
6745
6746
6747
6748
6749
6750
6751
6752
6753
6754
6755
6756
6757
6758
6759
6760
6761
6762
6763
6764
6765
6766
6767
6768
6769
6770
6771
6772
6773
6774
6775
6776
6777
6778
6779
6780
6781
6782
6783
6784
6785
6786
6787
6788
6789
6790
6791
6792
6793
6794
6795
6796
6797
6798
6799
6800
6801
6802
6803
6804
6805
6806
6807
6808
6809
6810
6811
6812
6813
6814
6815
6816
6817
6818
6819
6820
6821
6822
6823
6824
6825
6826
6827
6828
6829
6830
6831
6832
6833
6834
6835
6836
6837
6838
6839
6840
6841
6842
6843
6844
6845
6846
6847
6848
6849
6850
6851
6852
6853
6854
6855
6856
6857
6858
6859
6860
6861
6862
6863
6864
6865
6866
6867
6868
6869
6870
6871
6872
6873
6874
6875
6876
6877
6878
6879
6880
6881
6882
6883
6884
6885
6886
6887
6888
6889
6890
6891
6892
6893
6894
6895
6896
6897
6898
6899
6900
6901
6902
6903
6904
6905
6906
6907
6908
6909
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6921
6922
6923
6924
6925
6926
6927
6928
6929
6930
6931
6932
6933
6934
6935
6936
6937
6938
6939
6940
6941
6942
6943
6944
6945
6946
6947
6948
6949
6950
6951
6952
6953
6954
6955
6956
6957
6958
6959
6960
6961
6962
6963
6964
6965
6966
6967
6968
6969
6970
6971
6972
6973
6974
6975
6976
6977
6978
6979
6980
6981
6982
6983
6984
6985
6986
6987
6988
6989
6990
6991
6992
6993
6994
6995
6996
6997
6998
6999
7000
7001
7002
7003
7004
7005
7006
7007
7008
7009
7010
7011
7012
7013
7014
7015
7016
7017
7018
7019
7020
7021
7022
7023
7024
7025
7026
7027
7028
7029
7030
7031
7032
7033
7034
7035
7036
7037
7038
7039
7040
7041
7042
7043
7044
7045
7046
7047
7048
7049
7050
7051
7052
7053
7054
7055
7056
7057
7058
7059
7060
7061
7062
7063
7064
7065
7066
7067
7068
7069
7070
7071
7072
7073
7074
7075
7076
7077
7078
7079
7080
7081
7082
7083
7084
7085
7086
7087
7088
7089
7090
7091
7092
7093
7094
7095
7096
7097
7098
7099
7100
7101
7102
7103
7104
7105
7106
7107
7108
7109
7110
7111
7112
7113
7114
7115
7116
7117
7118
7119
7120
7121
7122
7123
7124
7125
7126
7127
7128
7129
7130
7131
7132
7133
7134
7135
7136
7137
7138
7139
7140
7141
7142
7143
7144
7145
7146
7147
7148
7149
7150
7151
7152
7153
7154
7155
7156
7157
7158
7159
7160
7161
7162
7163
7164
7165
7166
7167
7168
7169
7170
7171
7172
7173
7174
7175
7176
7177
7178
7179
7180
7181
7182
7183
7184
7185
7186
7187
7188
7189
7190
7191
7192
7193
7194
7195
7196
7197
7198
7199
7200
7201
7202
7203
7204
7205
7206
7207
7208
7209
7210
7211
7212
7213
7214
7215
7216
7217
7218
7219
7220
7221
7222
7223
7224
7225
7226
7227
7228
7229
7230
7231
7232
7233
7234
7235
7236
7237
7238
7239
7240
7241
7242
7243
7244
7245
7246
7247
7248
7249
7250
7251
7252
7253
7254
7255
7256
7257
7258
7259
7260
7261
7262
7263
7264
7265
7266
7267
7268
7269
7270
7271
7272
7273
7274
7275
7276
7277
7278
7279
7280
7281
7282
7283
7284
7285
7286
7287
7288
7289
7290
7291
7292
7293
7294
7295
7296
7297
7298
7299
7300
7301
7302
7303
7304
7305
7306
7307
7308
7309
7310
7311
7312
7313
7314
7315
7316
7317
7318
7319
7320
7321
7322
7323
7324
7325
7326
7327
7328
7329
7330
7331
7332
7333
7334
7335
7336
7337
7338
7339
7340
7341
7342
7343
7344
7345
7346
7347
7348
7349
7350
7351
7352
7353
7354
7355
7356
7357
7358
7359
7360
7361
7362
7363
7364
7365
7366
7367
7368
7369
7370
7371
7372
7373
7374
7375
7376
7377
7378
7379
7380
7381
7382
7383
7384
7385
7386
7387
7388
7389
7390
7391
7392
7393
7394
7395
7396
7397
7398
7399
7400
7401
7402
7403
7404
7405
7406
7407
7408
7409
7410
7411
7412
7413
7414
7415
7416
7417
7418
7419
7420
7421
7422
7423
7424
7425
7426
7427
7428
7429
7430
7431
7432
7433
7434
7435
7436
7437
7438
7439
7440
7441
7442
7443
7444
7445
7446
7447
7448
7449
7450
7451
7452
7453
7454
7455
7456
7457
7458
7459
7460
7461
7462
7463
7464
7465
7466
7467
7468
7469
7470
7471
7472
7473
7474
7475
7476
7477
7478
7479
7480
7481
7482
7483
7484
7485
7486
7487
7488
7489
7490
7491
7492
7493
7494
7495
7496
7497
7498
7499
7500
7501
7502
7503
7504
7505
7506
7507
7508
7509
7510
7511
7512
7513
7514
7515
7516
7517
7518
7519
7520
7521
7522
7523
7524
7525
7526
7527
7528
7529
7530
7531
7532
7533
7534
7535
7536
7537
7538
7539
7540
7541
7542
7543
7544
7545
7546
7547
7548
7549
7550
7551
7552
7553
7554
7555
7556
7557
7558
7559
7560
7561
7562
7563
7564
7565
7566
7567
7568
7569
7570
7571
7572
7573
7574
7575
7576
7577
7578
7579
7580
7581
7582
7583
7584
7585
7586
7587
7588
7589
7590
7591
7592
7593
7594
7595
7596
7597
7598
7599
7600
7601
7602
7603
7604
7605
7606
7607
7608
7609
7610
7611
7612
7613
7614
7615
7616
7617
7618
7619
7620
7621
7622
7623
7624
7625
7626
7627
7628
7629
7630
7631
7632
7633
7634
7635
7636
7637
7638
7639
7640
7641
7642
7643
7644
7645
7646
7647
7648
7649
7650
7651
7652
7653
7654
7655
7656
7657
7658
7659
7660
7661
7662
7663
7664
7665
7666
7667
7668
7669
7670
7671
7672
7673
7674
7675
7676
7677
7678
7679
7680
7681
7682
7683
7684
7685
7686
7687
7688
7689
7690
7691
7692
7693
7694
7695
7696
7697
7698
7699
7700
7701
7702
7703
7704
7705
7706
7707
7708
7709
7710
7711
7712
7713
7714
7715
7716
7717
7718
7719
7720
7721
7722
7723
7724
7725
7726
7727
7728
7729
7730
7731
7732
7733
7734
7735
7736
7737
7738
7739
7740
7741
7742
7743
7744
7745
7746
7747
7748
7749
7750
7751
7752
7753
7754
7755
7756
7757
7758
7759
7760
7761
7762
7763
7764
7765
7766
7767
7768
7769
7770
7771
7772
7773
7774
7775
7776
7777
7778
7779
7780
7781
7782
7783
7784
7785
7786
7787
7788
7789
7790
7791
7792
7793
7794
7795
7796
7797
7798
7799
7800
7801
7802
7803
7804
7805
7806
7807
7808
7809
7810
7811
7812
7813
7814
7815
7816
7817
7818
7819
7820
7821
7822
7823
7824
7825
7826
7827
7828
7829
7830
7831
7832
7833
7834
7835
7836
7837
7838
7839
7840
7841
7842
7843
7844
7845
7846
7847
7848
7849
7850
7851
7852
7853
7854
7855
7856
7857
7858
7859
7860
7861
7862
7863
7864
7865
7866
7867
7868
7869
7870
7871
7872
7873
7874
7875
7876
7877
7878
7879
7880
7881
7882
7883
7884
7885
7886
7887
7888
7889
7890
7891
7892
7893
7894
7895
7896
7897
7898
7899
7900
7901
7902
7903
7904
7905
7906
7907
7908
7909
7910
7911
7912
7913
7914
7915
7916
7917
7918
7919
7920
7921
7922
7923
7924
7925
7926
7927
7928
7929
7930
7931
7932
7933
7934
7935
7936
7937
7938
7939
7940
7941
7942
7943
7944
7945
7946
7947
7948
7949
7950
7951
7952
7953
7954
7955
7956
7957
7958
7959
7960
7961
7962
7963
7964
7965
7966
7967
7968
7969
7970
7971
7972
7973
7974
7975
7976
7977
7978
7979
7980
7981
7982
7983
7984
7985
7986
7987
7988
7989
7990
7991
7992
7993
7994
7995
7996
7997
7998
7999
8000
8001
8002
8003
8004
8005
8006
8007
8008
8009
8010
8011
8012
8013
8014
8015
8016
8017
8018
8019
8020
8021
8022
8023
8024
8025
8026
8027
8028
8029
8030
8031
8032
8033
8034
8035
8036
8037
8038
8039
8040
8041
8042
8043
8044
8045
8046
8047
8048
8049
8050
8051
8052
8053
8054
8055
8056
8057
8058
8059
8060
8061
8062
8063
8064
8065
8066
8067
8068
8069
8070
8071
8072
8073
8074
8075
8076
8077
8078
8079
8080
8081
8082
8083
8084
8085
8086
8087
8088
8089
8090
8091
8092
8093
8094
8095
8096
8097
8098
8099
8100
8101
8102
8103
8104
8105
8106
8107
8108
8109
8110
8111
8112
8113
8114
8115
8116
8117
8118
8119
8120
8121
8122
8123
8124
8125
8126
8127
8128
8129
8130
8131
8132
8133
8134
8135
8136
8137
8138
8139
8140
8141
8142
8143
8144
8145
8146
8147
8148
8149
8150
8151
8152
8153
8154
8155
8156
8157
8158
8159
8160
8161
8162
8163
8164
8165
8166
8167
8168
8169
8170
8171
8172
8173
8174
8175
8176
8177
8178
8179
8180
8181
8182
8183
8184
8185
8186
8187
8188
8189
8190
8191
8192
8193
8194
8195
8196
8197
8198
8199
8200
8201
8202
8203
8204
8205
8206
8207
8208
8209
8210
8211
8212
8213
8214
8215
8216
8217
8218
8219
8220
8221
8222
8223
8224
8225
8226
8227
8228
8229
8230
8231
8232
8233
8234
8235
8236
8237
8238
8239
8240
8241
8242
8243
8244
8245
8246
8247
8248
8249
8250
8251
8252
8253
8254
8255
8256
8257
8258
8259
8260
8261
8262
8263
8264
8265
8266
8267
8268
8269
8270
8271
8272
8273
8274
8275
8276
8277
8278
8279
8280
8281
8282
8283
8284
8285
8286
8287
8288
8289
8290
8291
8292
8293
8294
8295
8296
8297
8298
8299
8300
8301
8302
8303
8304
8305
8306
8307
8308
8309
8310
8311
8312
8313
8314
8315
8316
8317
8318
8319
8320
8321
8322
8323
8324
8325
8326
8327
8328
8329
8330
8331
8332
8333
8334
8335
8336
8337
8338
8339
8340
8341
8342
8343
8344
8345
8346
8347
8348
8349
8350
8351
8352
8353
8354
8355
8356
8357
8358
8359
8360
8361
8362
8363
8364
8365
8366
8367
8368
8369
8370
8371
8372
8373
8374
8375
8376
8377
8378
8379
8380
8381
8382
8383
8384
8385
8386
8387
8388
8389
8390
8391
8392
8393
8394
8395
8396
8397
8398
8399
8400
8401
8402
8403
8404
8405
8406
8407
8408
8409
8410
8411
8412
8413
8414
8415
8416
8417
8418
8419
8420
8421
8422
8423
8424
8425
8426
8427
8428
8429
8430
8431
8432
8433
8434
8435
8436
8437
8438
8439
8440
8441
8442
8443
8444
8445
8446
8447
8448
8449
8450
8451
8452
8453
8454
8455
8456
8457
8458
8459
8460
8461
8462
8463
8464
8465
8466
8467
8468
8469
8470
8471
8472
8473
8474
8475
8476
8477
8478
8479
8480
8481
8482
8483
8484
8485
8486
8487
8488
8489
8490
8491
8492
8493
8494
8495
8496
8497
8498
8499
8500
8501
8502
8503
8504
8505
8506
8507
8508
8509
8510
8511
8512
8513
8514
8515
8516
8517
8518
8519
8520
8521
8522
8523
8524
8525
8526
8527
8528
8529
8530
8531
8532
8533
8534
8535
8536
8537
8538
8539
8540
8541
8542
8543
8544
8545
8546
8547
8548
8549
8550
8551
8552
8553
8554
8555
8556
8557
8558
8559
8560
8561
8562
8563
8564
8565
8566
8567
8568
8569
8570
8571
8572
8573
8574
8575
8576
8577
8578
8579
8580
8581
8582
8583
8584
8585
8586
8587
8588
8589
8590
8591
8592
8593
8594
8595
8596
8597
8598
8599
8600
8601
8602
8603
8604
8605
8606
8607
8608
8609
8610
8611
8612
8613
8614
8615
8616
8617
8618
8619
8620
8621
8622
8623
8624
8625
8626
8627
8628
8629
8630
8631
8632
8633
8634
8635
8636
8637
8638
8639
8640
8641
8642
8643
8644
8645
8646
8647
8648
8649
8650
8651
8652
8653
8654
8655
8656
8657
8658
8659
8660
8661
8662
8663
8664
8665
8666
8667
8668
8669
8670
8671
8672
8673
8674
8675
8676
8677
8678
8679
8680
8681
8682
8683
8684
8685
8686
8687
8688
8689
8690
8691
8692
8693
8694
8695
8696
8697
8698
8699
8700
8701
8702
8703
8704
8705
8706
8707
8708
8709
8710
8711
8712
8713
8714
8715
8716
8717
8718
8719
8720
8721
8722
8723
8724
8725
8726
8727
8728
8729
8730
8731
8732
8733
8734
8735
8736
8737
8738
8739
8740
8741
8742
8743
8744
8745
8746
8747
8748
8749
8750
8751
8752
8753
8754
8755
8756
8757
8758
8759
8760
8761
8762
8763
8764
8765
8766
8767
8768
8769
8770
8771
8772
8773
8774
8775
8776
8777
8778
8779
8780
8781
8782
8783
8784
8785
8786
8787
8788
8789
8790
8791
8792
8793
8794
8795
8796
8797
8798
8799
8800
8801
8802
8803
8804
8805
8806
8807
8808
8809
8810
8811
8812
8813
8814
8815
8816
8817
8818
8819
8820
8821
8822
8823
8824
8825
8826
8827
8828
8829
8830
8831
8832
8833
8834
8835
8836
8837
8838
8839
8840
8841
8842
8843
8844
8845
8846
8847
8848
8849
8850
8851
8852
8853
8854
8855
8856
8857
8858
8859
8860
8861
8862
8863
8864
8865
8866
8867
8868
8869
8870
8871
8872
8873
8874
8875
8876
8877
8878
8879
8880
8881
8882
8883
8884
8885
8886
8887
8888
8889
8890
8891
8892
8893
8894
8895
8896
8897
8898
8899
8900
8901
8902
8903
8904
8905
8906
8907
8908
8909
8910
8911
8912
8913
8914
8915
8916
8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
8941
8942
8943
8944
8945
8946
8947
8948
8949
8950
8951
8952
8953
8954
8955
8956
8957
8958
8959
8960
8961
8962
8963
8964
8965
8966
8967
8968
8969
8970
8971
8972
8973
8974
8975
8976
8977
8978
8979
8980
8981
8982
8983
8984
8985
8986
8987
8988
8989
8990
8991
8992
8993
8994
8995
8996
8997
8998
8999
9000
9001
9002
9003
9004
9005
9006
9007
9008
9009
9010
9011
9012
9013
9014
9015
9016
9017
9018
9019
9020
9021
9022
9023
9024
9025
9026
9027
9028
9029
9030
9031
9032
9033
9034
9035
9036
9037
9038
9039
9040
9041
9042
9043
9044
9045
9046
9047
9048
9049
9050
9051
9052
9053
9054
9055
9056
9057
9058
9059
9060
9061
9062
9063
9064
9065
9066
9067
9068
9069
9070
9071
9072
9073
9074
9075
9076
9077
9078
9079
9080
9081
9082
9083
9084
9085
9086
9087
9088
9089
9090
9091
9092
9093
9094
9095
9096
9097
9098
9099
9100
9101
9102
9103
9104
9105
9106
9107
9108
9109
9110
9111
9112
9113
9114
9115
9116
9117
9118
9119
9120
9121
9122
9123
9124
9125
9126
9127
9128
9129
9130
9131
9132
9133
9134
9135
9136
9137
9138
9139
9140
9141
9142
9143
9144
9145
9146
9147
9148
9149
9150
9151
9152
9153
9154
9155
9156
9157
9158
9159
9160
9161
9162
9163
9164
9165
9166
9167
9168
9169
9170
9171
9172
9173
9174
9175
9176
9177
9178
9179
9180
9181
9182
9183
9184
9185
9186
9187
9188
9189
9190
9191
9192
9193
9194
9195
9196
9197
9198
9199
9200
9201
9202
9203
9204
9205
9206
9207
9208
9209
9210
9211
9212
9213
9214
9215
9216
9217
9218
9219
9220
9221
9222
9223
9224
9225
9226
9227
9228
9229
9230
9231
9232
9233
9234
9235
9236
9237
9238
9239
9240
9241
9242
9243
9244
9245
9246
9247
9248
9249
9250
9251
9252
9253
9254
9255
9256
9257
9258
9259
9260
9261
9262
9263
9264
9265
9266
9267
9268
9269
9270
9271
9272
9273
9274
9275
9276
9277
9278
9279
9280
9281
9282
9283
9284
9285
9286
9287
9288
9289
9290
9291
9292
9293
9294
9295
9296
9297
9298
9299
9300
9301
9302
9303
9304
9305
9306
9307
9308
9309
9310
9311
9312
9313
9314
9315
9316
9317
9318
9319
9320
9321
9322
9323
9324
9325
9326
9327
9328
9329
9330
9331
9332
9333
9334
9335
9336
9337
9338
9339
9340
9341
9342
9343
9344
9345
9346
9347
9348
9349
9350
9351
9352
9353
9354
9355
9356
9357
9358
9359
9360
9361
9362
9363
9364
9365
9366
9367
9368
9369
9370
9371
9372
9373
9374
9375
9376
9377
9378
9379
9380
9381
9382
9383
9384
9385
9386
9387
9388
9389
9390
9391
9392
9393
9394
9395
9396
9397
9398
9399
9400
9401
9402
9403
9404
9405
9406
9407
9408
9409
9410
9411
9412
9413
9414
9415
9416
9417
9418
9419
9420
9421
9422
9423
9424
9425
9426
9427
9428
9429
9430
9431
9432
9433
9434
9435
9436
9437
9438
9439
9440
9441
9442
9443
9444
9445
9446
9447
9448
9449
9450
9451
9452
9453
9454
9455
9456
9457
9458
9459
9460
9461
9462
9463
9464
9465
9466
9467
9468
9469
9470
9471
9472
9473
9474
9475
9476
9477
9478
9479
9480
9481
9482
9483
9484
9485
9486
9487
9488
9489
9490
9491
9492
9493
9494
9495
9496
9497
9498
9499
9500
9501
9502
9503
9504
9505
9506
9507
9508
9509
9510
9511
9512
9513
9514
9515
9516
9517
9518
9519
9520
9521
9522
9523
9524
9525
9526
9527
9528
9529
9530
9531
9532
9533
9534
9535
9536
9537
9538
9539
9540
9541
9542
9543
9544
9545
9546
9547
9548
9549
9550
9551
9552
9553
9554
9555
9556
9557
9558
9559
9560
9561
9562
9563
9564
9565
9566
9567
9568
9569
9570
9571
9572
9573
9574
9575
9576
9577
9578
9579
9580
9581
9582
9583
9584
9585
9586
9587
9588
9589
9590
9591
9592
9593
9594
9595
9596
9597
9598
9599
9600
9601
9602
9603
9604
9605
9606
9607
9608
9609
9610
9611
9612
9613
9614
9615
9616
9617
9618
9619
9620
9621
9622
9623
9624
9625
9626
9627
9628
9629
9630
9631
9632
9633
9634
9635
9636
9637
9638
9639
9640
9641
9642
9643
9644
9645
9646
9647
9648
9649
9650
9651
9652
9653
9654
9655
9656
9657
9658
9659
9660
9661
9662
9663
9664
9665
9666
9667
9668
9669
9670
9671
9672
9673
9674
9675
9676
9677
9678
9679
9680
9681
9682
9683
9684
9685
9686
9687
9688
9689
9690
9691
9692
9693
9694
9695
9696
9697
9698
9699
9700
9701
9702
9703
9704
9705
9706
9707
9708
9709
9710
9711
9712
9713
9714
9715
9716
9717
9718
9719
9720
9721
9722
9723
9724
9725
9726
9727
9728
9729
9730
9731
9732
9733
9734
9735
9736
9737
9738
9739
9740
9741
9742
9743
9744
9745
9746
9747
9748
9749
9750
9751
9752
9753
9754
9755
9756
9757
9758
9759
9760
9761
9762
9763
9764
9765
9766
9767
9768
9769
9770
9771
9772
9773
9774
9775
9776
9777
9778
9779
9780
9781
9782
9783
9784
9785
9786
9787
9788
9789
9790
9791
9792
9793
9794
9795
9796
9797
9798
9799
9800
9801
9802
9803
9804
9805
9806
9807
9808
9809
9810
9811
9812
9813
9814
9815
9816
9817
9818
9819
9820
9821
9822
9823
9824
9825
9826
9827
9828
9829
9830
9831
9832
9833
9834
9835
9836
9837
9838
9839
9840
9841
9842
9843
9844
9845
9846
9847
9848
9849
9850
9851
9852
9853
9854
9855
9856
9857
9858
9859
9860
9861
9862
9863
9864
9865
9866
9867
9868
9869
9870
9871
9872
9873
9874
9875
9876
9877
9878
9879
9880
9881
9882
9883
9884
9885
9886
9887
9888
9889
9890
9891
9892
9893
9894
9895
9896
9897
9898
9899
9900
9901
9902
9903
9904
9905
9906
9907
9908
9909
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921
9922
9923
9924
9925
9926
9927
9928
9929
9930
9931
9932
9933
9934
9935
9936
9937
9938
9939
9940
9941
9942
9943
9944
9945
9946
9947
9948
9949
9950
9951
9952
9953
9954
9955
9956
9957
9958
9959
9960
9961
9962
9963
9964
9965
9966
9967
9968
9969
9970
9971
9972
9973
9974
9975
9976
9977
9978
9979
9980
9981
9982
9983
9984
9985
9986
9987
9988
9989
9990
9991
9992
9993
9994
9995
9996
9997
9998
9999
10000
10001
10002
10003
10004
10005
10006
10007
10008
10009
10010
10011
10012
10013
10014
10015
10016
10017
10018
10019
10020
10021
10022
10023
10024
10025
10026
10027
10028
10029
10030
10031
10032
10033
10034
10035
10036
10037
10038
10039
10040
10041
10042
10043
10044
10045
10046
10047
10048
10049
10050
10051
10052
10053
10054
10055
10056
10057
10058
10059
10060
10061
10062
10063
10064
10065
10066
10067
10068
10069
10070
10071
10072
10073
10074
10075
10076
10077
10078
10079
10080
10081
10082
10083
10084
10085
10086
10087
10088
10089
10090
10091
10092
10093
10094
10095
10096
10097
10098
10099
10100
10101
10102
10103
10104
10105
10106
10107
10108
10109
10110
10111
10112
10113
10114
10115
10116
10117
10118
10119
10120
10121
10122
10123
10124
10125
10126
10127
10128
10129
10130
10131
10132
10133
10134
10135
10136
10137
10138
10139
10140
10141
10142
10143
10144
10145
10146
10147
10148
10149
10150
10151
10152
10153
10154
10155
10156
10157
10158
10159
10160
10161
10162
10163
10164
10165
10166
10167
10168
10169
10170
10171
10172
10173
10174
10175
10176
10177
10178
10179
10180
10181
10182
10183
10184
10185
10186
10187
10188
10189
10190
10191
10192
10193
10194
10195
10196
10197
10198
10199
10200
10201
10202
10203
10204
10205
10206
10207
10208
10209
10210
10211
10212
10213
10214
10215
10216
10217
10218
10219
10220
10221
10222
10223
10224
10225
10226
10227
10228
10229
10230
10231
10232
10233
10234
10235
10236
10237
10238
10239
10240
10241
10242
10243
10244
10245
10246
10247
10248
10249
10250
10251
10252
10253
10254
10255
10256
10257
10258
10259
10260
10261
10262
10263
10264
10265
10266
10267
10268
10269
10270
10271
10272
10273
10274
10275
10276
10277
10278
10279
10280
10281
10282
10283
10284
10285
10286
10287
10288
10289
10290
10291
10292
10293
10294
10295
10296
10297
10298
10299
10300
10301
10302
10303
10304
10305
10306
10307
10308
10309
10310
10311
10312
10313
10314
10315
10316
10317
10318
10319
10320
10321
10322
10323
10324
10325
10326
10327
10328
10329
10330
10331
10332
10333
10334
10335
10336
10337
10338
10339
10340
10341
10342
10343
10344
10345
10346
10347
10348
10349
10350
10351
10352
10353
10354
10355
10356
10357
10358
10359
10360
10361
10362
10363
10364
10365
10366
10367
10368
10369
10370
10371
10372
10373
10374
10375
10376
10377
10378
10379
10380
10381
10382
10383
10384
10385
10386
10387
10388
10389
10390
10391
10392
10393
10394
10395
10396
10397
10398
10399
10400
10401
10402
10403
10404
10405
10406
10407
10408
10409
10410
10411
10412
10413
10414
10415
10416
10417
10418
10419
10420
10421
10422
10423
10424
10425
10426
10427
10428
10429
10430
10431
10432
10433
10434
10435
10436
10437
10438
10439
10440
10441
10442
10443
10444
10445
10446
10447
10448
10449
10450
10451
10452
10453
10454
10455
10456
10457
10458
10459
10460
10461
10462
10463
10464
10465
10466
10467
10468
10469
10470
10471
10472
10473
10474
10475
10476
10477
10478
10479
10480
10481
10482
10483
10484
10485
10486
10487
10488
10489
10490
10491
10492
10493
10494
10495
10496
10497
10498
10499
10500
10501
10502
10503
10504
10505
10506
10507
10508
10509
10510
10511
10512
10513
10514
10515
10516
10517
10518
10519
10520
10521
10522
10523
10524
10525
10526
10527
10528
10529
10530
10531
10532
10533
10534
10535
10536
10537
10538
10539
10540
10541
10542
10543
10544
10545
10546
10547
10548
10549
10550
10551
10552
10553
10554
10555
10556
10557
10558
10559
10560
10561
10562
10563
10564
10565
10566
10567
10568
10569
10570
10571
10572
10573
10574
10575
10576
10577
10578
10579
10580
10581
10582
10583
10584
10585
10586
10587
10588
10589
10590
10591
10592
10593
10594
10595
10596
10597
10598
10599
10600
10601
10602
10603
10604
10605
10606
10607
10608
10609
10610
10611
10612
10613
10614
10615
10616
10617
10618
10619
10620
10621
10622
10623
10624
10625
10626
10627
10628
10629
10630
10631
10632
10633
10634
10635
10636
10637
10638
10639
10640
10641
10642
10643
10644
10645
10646
10647
10648
10649
10650
10651
10652
10653
10654
10655
10656
10657
10658
10659
10660
10661
10662
10663
10664
10665
10666
10667
10668
10669
10670
10671
10672
10673
10674
10675
10676
10677
10678
10679
10680
10681
10682
10683
10684
10685
10686
10687
10688
10689
10690
10691
10692
10693
10694
10695
10696
10697
10698
10699
10700
10701
10702
10703
10704
10705
10706
10707
10708
10709
10710
10711
10712
10713
10714
10715
10716
10717
10718
10719
10720
10721
10722
10723
10724
10725
10726
10727
10728
10729
10730
10731
10732
10733
10734
10735
10736
10737
10738
10739
10740
10741
10742
10743
10744
10745
10746
10747
10748
10749
10750
10751
10752
10753
10754
10755
10756
10757
10758
10759
10760
10761
10762
10763
10764
10765
10766
10767
10768
10769
10770
10771
10772
10773
10774
10775
10776
10777
10778
10779
10780
10781
10782
10783
10784
10785
10786
10787
10788
10789
10790
10791
10792
10793
10794
10795
10796
10797
10798
10799
10800
10801
10802
10803
10804
10805
10806
10807
10808
10809
10810
10811
10812
10813
10814
10815
10816
10817
10818
10819
10820
10821
10822
10823
10824
10825
10826
10827
10828
10829
10830
10831
10832
10833
10834
10835
10836
10837
10838
10839
10840
10841
10842
10843
10844
10845
10846
10847
10848
10849
10850
10851
10852
10853
10854
10855
10856
10857
10858
10859
10860
10861
10862
10863
10864
10865
10866
10867
10868
10869
10870
10871
10872
10873
10874
10875
10876
10877
10878
10879
10880
10881
10882
10883
10884
10885
10886
10887
10888
10889
10890
10891
10892
10893
10894
10895
10896
10897
10898
10899
10900
10901
10902
10903
10904
10905
10906
10907
10908
10909
10910
10911
10912
10913
10914
10915
10916
10917
10918
10919
10920
10921
10922
10923
10924
10925
10926
10927
10928
10929
10930
10931
10932
10933
10934
10935
10936
10937
10938
10939
10940
10941
10942
10943
10944
10945
10946
10947
10948
10949
10950
10951
10952
10953
10954
10955
10956
10957
10958
10959
10960
10961
10962
10963
10964
10965
10966
10967
10968
10969
10970
10971
10972
10973
10974
10975
10976
10977
10978
10979
10980
10981
10982
10983
10984
10985
10986
10987
10988
10989
10990
10991
10992
10993
10994
10995
10996
10997
10998
10999
11000
11001
11002
11003
11004
11005
11006
11007
11008
11009
11010
11011
11012
11013
11014
11015
11016
11017
11018
11019
11020
11021
11022
11023
11024
11025
11026
11027
11028
11029
11030
11031
11032
11033
11034
11035
11036
11037
11038
11039
11040
11041
11042
11043
11044
11045
11046
11047
11048
11049
11050
11051
11052
11053
11054
11055
11056
11057
11058
11059
11060
11061
11062
11063
11064
11065
11066
11067
11068
11069
11070
11071
11072
11073
11074
11075
11076
11077
11078
11079
11080
11081
11082
11083
11084
11085
11086
11087
11088
11089
11090
11091
11092
11093
11094
11095
11096
11097
11098
11099
11100
11101
11102
11103
11104
11105
11106
11107
11108
11109
11110
11111
11112
11113
11114
11115
11116
11117
11118
11119
11120
11121
11122
11123
11124
11125
11126
11127
11128
11129
11130
11131
11132
11133
11134
11135
11136
11137
11138
11139
11140
11141
11142
11143
11144
11145
11146
11147
11148
11149
11150
11151
11152
11153
11154
11155
11156
11157
11158
11159
11160
11161
11162
11163
11164
11165
11166
11167
11168
11169
11170
11171
11172
11173
11174
11175
11176
11177
11178
11179
11180
11181
11182
11183
11184
11185
11186
11187
11188
11189
11190
11191
11192
11193
11194
11195
11196
11197
11198
11199
11200
11201
11202
11203
11204
11205
11206
11207
11208
11209
11210
11211
11212
11213
11214
11215
11216
11217
11218
11219
11220
11221
11222
11223
11224
11225
11226
11227
11228
11229
11230
11231
11232
11233
11234
11235
11236
11237
11238
11239
11240
11241
11242
11243
11244
11245
11246
11247
11248
11249
11250
11251
11252
11253
11254
11255
11256
11257
11258
11259
11260
11261
11262
11263
11264
11265
11266
11267
11268
11269
11270
11271
11272
11273
11274
11275
11276
11277
11278
11279
11280
11281
11282
11283
11284
11285
11286
11287
11288
11289
11290
11291
11292
11293
11294
11295
11296
11297
11298
11299
11300
11301
11302
11303
11304
11305
11306
11307
11308
11309
11310
11311
11312
11313
11314
11315
11316
11317
11318
11319
11320
11321
11322
11323
11324
11325
11326
11327
11328
11329
11330
11331
11332
11333
11334
11335
11336
11337
11338
11339
11340
11341
11342
11343
11344
11345
11346
11347
11348
11349
11350
11351
11352
11353
11354
11355
11356
11357
11358
11359
11360
11361
11362
11363
11364
11365
11366
11367
11368
11369
11370
11371
11372
11373
11374
11375
11376
11377
11378
11379
11380
11381
11382
11383
11384
11385
11386
11387
11388
11389
11390
11391
11392
11393
11394
11395
11396
11397
11398
11399
11400
11401
11402
11403
11404
11405
11406
11407
11408
11409
11410
11411
11412
11413
11414
11415
11416
11417
11418
11419
11420
11421
11422
11423
11424
11425
11426
11427
11428
11429
11430
11431
11432
11433
11434
11435
11436
11437
11438
11439
11440
11441
11442
11443
11444
11445
11446
11447
11448
11449
11450
11451
11452
11453
11454
11455
11456
11457
11458
11459
11460
11461
11462
11463
11464
11465
11466
11467
11468
11469
11470
11471
11472
11473
11474
11475
11476
11477
11478
11479
11480
11481
11482
11483
11484
11485
11486
11487
11488
11489
11490
11491
11492
11493
11494
11495
11496
11497
11498
11499
11500
11501
11502
11503
11504
11505
11506
11507
11508
11509
11510
11511
11512
11513
11514
11515
11516
11517
11518
11519
11520
11521
11522
11523
11524
11525
11526
11527
11528
11529
11530
11531
11532
11533
11534
11535
11536
11537
11538
11539
11540
11541
11542
11543
11544
11545
11546
11547
11548
11549
11550
11551
11552
11553
11554
11555
11556
11557
11558
11559
11560
11561
11562
11563
11564
11565
11566
11567
11568
11569
11570
11571
11572
11573
11574
11575
11576
11577
11578
11579
11580
11581
11582
11583
11584
11585
11586
11587
11588
11589
11590
11591
11592
11593
11594
11595
11596
11597
11598
11599
11600
11601
11602
11603
11604
11605
11606
11607
11608
11609
11610
11611
11612
11613
11614
11615
11616
11617
11618
11619
11620
11621
11622
11623
11624
11625
11626
11627
11628
11629
11630
11631
11632
11633
11634
11635
11636
11637
11638
11639
11640
11641
11642
11643
11644
11645
11646
11647
11648
11649
11650
11651
11652
11653
11654
11655
11656
11657
11658
11659
11660
11661
11662
11663
11664
11665
11666
11667
11668
11669
11670
11671
11672
11673
11674
11675
11676
11677
11678
11679
11680
11681
11682
11683
11684
11685
11686
11687
11688
11689
11690
11691
11692
11693
11694
11695
11696
11697
11698
11699
11700
11701
11702
11703
11704
11705
11706
11707
11708
11709
11710
11711
11712
11713
11714
11715
11716
11717
11718
11719
11720
11721
11722
11723
11724
11725
11726
11727
11728
11729
11730
11731
11732
11733
11734
11735
11736
11737
11738
11739
11740
11741
11742
11743
11744
11745
11746
11747
11748
11749
11750
11751
11752
11753
11754
11755
11756
11757
11758
11759
11760
11761
11762
11763
11764
11765
11766
11767
11768
11769
11770
11771
11772
11773
11774
11775
11776
11777
11778
11779
11780
11781
11782
11783
11784
11785
11786
11787
11788
11789
11790
11791
11792
11793
11794
11795
11796
11797
11798
11799
11800
11801
11802
11803
11804
11805
11806
11807
11808
11809
11810
11811
11812
11813
11814
11815
11816
11817
11818
11819
11820
11821
11822
11823
11824
11825
11826
11827
11828
11829
11830
11831
11832
11833
11834
11835
11836
11837
11838
11839
11840
11841
11842
11843
11844
11845
11846
11847
11848
11849
11850
11851
11852
11853
11854
11855
11856
11857
11858
11859
11860
11861
11862
11863
11864
11865
11866
11867
11868
11869
11870
11871
11872
11873
11874
11875
11876
11877
11878
11879
11880
11881
11882
11883
11884
11885
11886
11887
11888
11889
11890
11891
11892
11893
11894
11895
11896
11897
11898
11899
11900
11901
11902
11903
11904
11905
11906
11907
11908
11909
11910
11911
11912
11913
11914
11915
11916
11917
11918
11919
11920
11921
11922
11923
11924
11925
11926
11927
11928
11929
11930
11931
11932
11933
11934
11935
11936
11937
11938
11939
11940
11941
11942
11943
11944
11945
11946
11947
11948
11949
11950
11951
11952
11953
11954
11955
11956
11957
11958
11959
11960
11961
11962
11963
11964
11965
11966
11967
11968
11969
11970
11971
11972
11973
11974
11975
11976
11977
11978
11979
11980
11981
11982
11983
11984
11985
11986
11987
11988
11989
11990
11991
11992
11993
11994
11995
11996
11997
11998
11999
12000
12001
12002
12003
12004
12005
12006
12007
12008
12009
12010
12011
12012
12013
12014
12015
12016
12017
12018
12019
12020
12021
12022
12023
12024
12025
12026
12027
12028
12029
12030
12031
12032
12033
12034
12035
12036
12037
12038
12039
12040
12041
12042
12043
12044
12045
12046
12047
12048
12049
12050
12051
12052
12053
12054
12055
12056
12057
12058
12059
12060
12061
12062
12063
12064
12065
12066
12067
12068
12069
12070
12071
12072
12073
12074
12075
12076
12077
12078
12079
12080
12081
12082
12083
12084
12085
12086
12087
12088
12089
12090
12091
12092
12093
12094
12095
12096
12097
12098
12099
12100
12101
12102
12103
12104
12105
12106
12107
12108
12109
12110
12111
12112
12113
12114
12115
12116
12117
12118
12119
12120
12121
12122
12123
12124
12125
12126
12127
12128
12129
12130
12131
12132
12133
12134
12135
12136
12137
12138
12139
12140
12141
12142
12143
12144
12145
12146
12147
12148
12149
12150
12151
12152
12153
12154
12155
12156
12157
12158
12159
12160
12161
12162
12163
12164
12165
12166
12167
12168
12169
12170
12171
12172
12173
12174
12175
12176
12177
12178
12179
12180
12181
12182
12183
12184
12185
12186
12187
12188
12189
12190
12191
12192
12193
12194
12195
12196
12197
12198
12199
12200
12201
12202
12203
12204
12205
12206
12207
12208
12209
12210
12211
12212
12213
12214
12215
12216
12217
12218
12219
12220
12221
12222
12223
12224
12225
12226
12227
12228
12229
12230
12231
12232
12233
12234
12235
12236
12237
12238
12239
12240
12241
12242
12243
12244
12245
12246
12247
12248
12249
12250
12251
12252
12253
12254
12255
12256
12257
12258
12259
12260
12261
12262
12263
12264
12265
12266
12267
12268
12269
12270
12271
12272
12273
12274
12275
12276
12277
12278
12279
12280
12281
12282
12283
12284
12285
12286
12287
12288
12289
12290
12291
12292
12293
12294
12295
12296
12297
12298
12299
12300
12301
12302
12303
12304
12305
12306
12307
12308
12309
12310
12311
12312
12313
12314
12315
12316
12317
12318
12319
12320
12321
12322
12323
12324
12325
12326
12327
12328
12329
12330
12331
12332
12333
12334
12335
12336
12337
12338
12339
12340
12341
12342
12343
12344
12345
12346
12347
12348
12349
12350
12351
12352
12353
12354
12355
12356
12357
12358
12359
12360
12361
12362
12363
12364
12365
12366
12367
12368
12369
12370
12371
12372
12373
12374
12375
12376
12377
12378
12379
12380
12381
12382
12383
12384
12385
12386
12387
12388
12389
12390
12391
12392
12393
12394
12395
12396
12397
12398
12399
12400
12401
12402
12403
12404
12405
12406
12407
12408
12409
12410
12411
12412
12413
12414
12415
12416
12417
12418
12419
12420
12421
12422
12423
12424
12425
12426
12427
12428
12429
12430
12431
12432
12433
12434
12435
12436
12437
12438
12439
12440
12441
12442
12443
12444
12445
12446
12447
12448
12449
12450
12451
12452
12453
12454
12455
12456
12457
12458
12459
12460
12461
12462
12463
12464
12465
12466
12467
12468
12469
12470
12471
12472
12473
12474
12475
12476
12477
12478
12479
12480
12481
12482
12483
12484
12485
12486
12487
12488
12489
12490
12491
12492
12493
12494
12495
12496
12497
12498
12499
12500
12501
12502
12503
12504
12505
12506
12507
12508
12509
12510
12511
12512
12513
12514
12515
12516
12517
12518
12519
12520
12521
12522
12523
12524
12525
12526
12527
12528
12529
12530
12531
12532
12533
12534
12535
12536
12537
12538
12539
12540
12541
12542
12543
12544
12545
12546
12547
12548
12549
12550
12551
12552
12553
12554
12555
12556
12557
12558
12559
12560
12561
12562
12563
12564
12565
12566
12567
12568
12569
12570
12571
12572
12573
12574
12575
12576
12577
12578
12579
12580
12581
12582
12583
12584
12585
12586
12587
12588
12589
12590
12591
12592
12593
12594
12595
12596
12597
12598
12599
12600
12601
12602
12603
12604
12605
12606
12607
12608
12609
12610
12611
12612
12613
12614
12615
12616
12617
12618
12619
12620
12621
12622
12623
12624
12625
12626
12627
12628
12629
12630
12631
12632
12633
12634
12635
12636
12637
12638
12639
12640
12641
12642
12643
12644
12645
12646
12647
12648
12649
12650
12651
12652
12653
12654
12655
12656
12657
12658
12659
12660
12661
12662
12663
12664
12665
12666
12667
12668
12669
12670
12671
12672
12673
12674
12675
12676
12677
12678
12679
12680
12681
12682
12683
12684
12685
12686
12687
12688
12689
12690
12691
12692
12693
12694
12695
12696
12697
12698
12699
12700
12701
12702
12703
12704
12705
12706
12707
12708
12709
12710
12711
12712
12713
12714
12715
12716
12717
12718
12719
12720
12721
12722
12723
12724
12725
12726
12727
12728
12729
12730
12731
12732
12733
12734
12735
12736
12737
12738
12739
12740
12741
12742
12743
12744
12745
12746
12747
12748
12749
12750
12751
12752
12753
12754
12755
12756
12757
12758
12759
12760
12761
12762
12763
12764
12765
12766
12767
12768
12769
12770
12771
12772
12773
12774
12775
12776
12777
12778
12779
12780
12781
12782
12783
12784
12785
12786
12787
12788
12789
12790
12791
12792
12793
12794
12795
12796
12797
12798
12799
12800
12801
12802
12803
12804
12805
12806
12807
12808
12809
12810
12811
12812
12813
12814
12815
12816
12817
12818
12819
12820
12821
12822
12823
12824
12825
12826
12827
12828
12829
12830
12831
12832
12833
12834
12835
12836
12837
12838
12839
12840
12841
12842
12843
12844
12845
12846
12847
12848
12849
12850
12851
12852
12853
12854
12855
12856
12857
12858
12859
12860
12861
12862
12863
12864
12865
12866
12867
12868
12869
12870
12871
12872
12873
12874
12875
12876
12877
12878
12879
12880
12881
12882
12883
12884
12885
12886
12887
12888
12889
12890
12891
12892
12893
12894
12895
12896
12897
12898
12899
12900
12901
12902
12903
12904
12905
12906
12907
12908
12909
12910
12911
12912
12913
12914
12915
12916
12917
12918
12919
12920
12921
12922
12923
12924
12925
12926
12927
12928
12929
12930
12931
12932
12933
12934
12935
12936
12937
12938
12939
12940
12941
12942
12943
12944
12945
12946
12947
12948
12949
12950
12951
12952
12953
12954
12955
12956
12957
12958
12959
12960
12961
12962
12963
12964
12965
12966
12967
12968
12969
12970
12971
12972
12973
12974
12975
12976
12977
12978
12979
12980
12981
12982
12983
12984
12985
12986
12987
12988
12989
12990
12991
12992
12993
12994
12995
12996
12997
12998
12999
13000
13001
13002
13003
13004
13005
13006
13007
13008
13009
13010
13011
13012
13013
13014
13015
13016
13017
13018
13019
13020
13021
13022
13023
13024
13025
13026
13027
13028
13029
13030
13031
13032
13033
13034
13035
13036
13037
13038
13039
13040
13041
13042
13043
13044
13045
13046
13047
13048
13049
13050
13051
13052
13053
13054
13055
13056
13057
13058
13059
13060
13061
13062
13063
13064
13065
13066
13067
13068
13069
13070
13071
13072
13073
13074
13075
13076
13077
13078
13079
13080
13081
13082
13083
13084
13085
13086
13087
13088
13089
13090
13091
13092
13093
13094
13095
13096
13097
13098
13099
13100
13101
13102
13103
13104
13105
13106
13107
13108
13109
13110
13111
13112
13113
13114
13115
13116
13117
13118
13119
13120
13121
13122
13123
13124
13125
13126
13127
13128
13129
13130
13131
13132
13133
13134
13135
13136
13137
13138
13139
13140
13141
13142
13143
13144
13145
13146
13147
13148
13149
13150
13151
13152
13153
13154
13155
13156
13157
13158
13159
13160
13161
13162
13163
13164
13165
13166
13167
13168
13169
13170
13171
13172
13173
13174
13175
13176
13177
13178
13179
13180
13181
13182
13183
13184
13185
13186
13187
13188
13189
13190
13191
13192
13193
13194
13195
13196
13197
13198
13199
13200
13201
13202
13203
13204
13205
13206
13207
13208
13209
13210
13211
13212
13213
13214
13215
13216
13217
13218
13219
13220
13221
13222
13223
13224
13225
13226
13227
13228
13229
13230
13231
13232
13233
13234
13235
13236
13237
13238
13239
13240
13241
13242
13243
13244
13245
13246
13247
13248
13249
13250
13251
13252
13253
13254
13255
13256
13257
13258
13259
13260
13261
13262
13263
13264
13265
13266
13267
13268
13269
13270
13271
13272
13273
13274
13275
13276
13277
13278
13279
13280
13281
13282
13283
13284
13285
13286
13287
13288
13289
13290
13291
13292
13293
13294
13295
13296
13297
13298
13299
13300
13301
13302
13303
13304
13305
13306
13307
13308
13309
13310
13311
13312
13313
13314
13315
13316
13317
13318
13319
13320
13321
13322
13323
13324
13325
13326
13327
13328
13329
13330
13331
13332
13333
13334
13335
13336
13337
13338
13339
13340
13341
13342
13343
13344
13345
13346
13347
13348
13349
13350
13351
13352
13353
13354
13355
13356
13357
13358
13359
13360
13361
13362
13363
13364
13365
13366
13367
13368
13369
13370
13371
13372
13373
13374
13375
13376
13377
13378
13379
13380
13381
13382
13383
13384
13385
13386
13387
13388
13389
13390
13391
13392
13393
13394
13395
13396
13397
13398
13399
13400
13401
13402
13403
13404
13405
13406
13407
13408
13409
13410
13411
13412
13413
13414
13415
13416
13417
13418
13419
13420
13421
13422
13423
13424
13425
13426
13427
13428
13429
13430
13431
13432
13433
13434
13435
13436
13437
13438
13439
13440
13441
13442
13443
13444
13445
13446
13447
13448
13449
13450
13451
13452
13453
13454
13455
13456
13457
13458
13459
13460
13461
13462
13463
13464
13465
13466
13467
13468
13469
13470
13471
13472
13473
13474
13475
13476
13477
13478
13479
13480
13481
13482
13483
13484
13485
13486
13487
13488
13489
13490
13491
13492
13493
13494
13495
13496
13497
13498
13499
13500
13501
13502
13503
13504
13505
13506
13507
13508
13509
13510
13511
13512
13513
13514
13515
13516
13517
13518
13519
13520
13521
13522
13523
13524
13525
13526
13527
13528
13529
13530
13531
13532
13533
13534
13535
13536
13537
13538
13539
13540
13541
13542
13543
13544
13545
13546
13547
13548
13549
13550
13551
13552
13553
13554
13555
13556
13557
13558
13559
13560
13561
13562
13563
13564
13565
13566
13567
13568
13569
13570
13571
13572
13573
13574
13575
13576
13577
13578
13579
13580
13581
13582
13583
13584
13585
13586
13587
13588
13589
13590
13591
13592
13593
13594
13595
13596
13597
13598
13599
13600
13601
13602
13603
13604
13605
13606
13607
13608
13609
13610
13611
13612
13613
13614
13615
13616
13617
13618
13619
13620
13621
13622
13623
13624
13625
13626
13627
13628
13629
13630
13631
13632
13633
13634
13635
13636
13637
13638
13639
13640
13641
13642
13643
13644
13645
13646
13647
13648
13649
13650
13651
13652
13653
13654
13655
13656
13657
13658
13659
13660
13661
13662
13663
13664
13665
13666
13667
13668
13669
13670
13671
13672
13673
13674
13675
13676
13677
13678
13679
13680
13681
13682
13683
13684
13685
13686
13687
13688
13689
13690
13691
13692
13693
13694
13695
13696
13697
13698
13699
13700
13701
13702
13703
13704
13705
13706
13707
13708
13709
13710
13711
13712
13713
13714
13715
13716
13717
13718
13719
13720
13721
13722
13723
13724
13725
13726
13727
13728
13729
13730
13731
13732
13733
13734
13735
13736
13737
13738
13739
13740
13741
13742
13743
13744
13745
13746
13747
13748
13749
13750
13751
13752
13753
13754
13755
13756
13757
13758
13759
13760
13761
13762
13763
13764
13765
13766
13767
13768
13769
13770
13771
13772
13773
13774
13775
13776
13777
13778
13779
13780
13781
13782
13783
13784
13785
13786
13787
13788
13789
13790
13791
13792
13793
13794
13795
13796
13797
13798
13799
13800
13801
13802
13803
13804
13805
13806
13807
13808
13809
13810
13811
13812
13813
13814
13815
13816
13817
13818
13819
13820
13821
13822
13823
13824
13825
13826
13827
13828
13829
13830
13831
13832
13833
13834
13835
13836
13837
13838
13839
13840
13841
13842
13843
13844
13845
13846
13847
13848
13849
13850
13851
13852
13853
13854
13855
13856
13857
13858
13859
13860
13861
13862
13863
13864
13865
13866
13867
13868
13869
13870
13871
13872
13873
13874
13875
13876
13877
13878
13879
13880
13881
13882
13883
13884
13885
13886
13887
13888
13889
13890
13891
13892
13893
13894
13895
13896
13897
13898
13899
13900
13901
13902
13903
13904
13905
13906
13907
13908
13909
13910
13911
13912
13913
13914
13915
13916
13917
13918
13919
13920
13921
13922
13923
13924
13925
13926
13927
13928
13929
13930
13931
13932
13933
13934
13935
13936
13937
13938
13939
13940
13941
13942
13943
13944
13945
13946
13947
13948
13949
13950
13951
13952
13953
13954
13955
13956
13957
13958
13959
13960
13961
13962
13963
13964
13965
13966
13967
13968
13969
13970
13971
13972
13973
13974
13975
13976
13977
13978
13979
13980
13981
13982
13983
13984
13985
13986
13987
13988
13989
13990
13991
13992
13993
13994
13995
13996
13997
13998
13999
14000
14001
14002
14003
14004
14005
14006
14007
14008
14009
14010
14011
14012
14013
14014
14015
14016
14017
14018
14019
14020
14021
14022
14023
14024
14025
14026
14027
14028
14029
14030
14031
14032
14033
14034
14035
14036
14037
14038
14039
14040
14041
14042
14043
14044
14045
14046
14047
14048
14049
14050
14051
14052
14053
14054
14055
14056
14057
14058
14059
14060
14061
14062
14063
14064
14065
14066
14067
14068
14069
14070
14071
14072
14073
14074
14075
14076
14077
14078
14079
14080
14081
14082
14083
14084
14085
14086
14087
14088
14089
14090
14091
14092
14093
14094
14095
14096
14097
14098
14099
14100
14101
14102
14103
14104
14105
14106
14107
14108
14109
14110
14111
14112
14113
14114
14115
14116
14117
14118
14119
14120
14121
14122
14123
14124
14125
14126
14127
14128
14129
14130
14131
14132
14133
14134
14135
14136
14137
14138
14139
14140
14141
14142
14143
14144
14145
14146
14147
14148
14149
14150
14151
14152
14153
14154
14155
14156
14157
14158
14159
14160
14161
14162
14163
14164
14165
14166
14167
14168
14169
14170
14171
14172
14173
14174
14175
14176
14177
14178
14179
14180
14181
14182
14183
14184
14185
14186
14187
14188
14189
14190
14191
14192
14193
14194
14195
14196
14197
14198
14199
14200
14201
14202
14203
14204
14205
14206
14207
14208
14209
14210
14211
14212
14213
14214
14215
14216
14217
14218
14219
14220
14221
14222
14223
14224
14225
14226
14227
14228
14229
14230
14231
14232
14233
14234
14235
14236
14237
14238
14239
14240
14241
14242
14243
14244
14245
14246
14247
14248
14249
14250
14251
14252
14253
14254
14255
14256
14257
14258
14259
14260
14261
14262
14263
14264
14265
14266
14267
14268
14269
14270
14271
14272
14273
14274
14275
14276
14277
14278
14279
14280
14281
14282
14283
14284
14285
14286
14287
14288
14289
14290
14291
14292
14293
14294
14295
14296
14297
14298
14299
14300
14301
14302
14303
14304
14305
14306
14307
14308
14309
14310
14311
14312
14313
14314
14315
14316
14317
14318
14319
14320
14321
14322
14323
14324
14325
14326
14327
14328
14329
14330
14331
14332
14333
14334
14335
14336
14337
14338
14339
14340
14341
14342
14343
14344
14345
14346
14347
14348
14349
14350
14351
14352
14353
14354
14355
14356
14357
14358
14359
14360
14361
14362
14363
14364
14365
14366
14367
14368
14369
14370
14371
14372
14373
14374
14375
14376
14377
14378
14379
14380
14381
14382
14383
14384
14385
14386
14387
14388
14389
14390
14391
14392
14393
14394
14395
14396
14397
14398
14399
14400
14401
14402
14403
14404
14405
14406
14407
14408
14409
14410
14411
14412
14413
14414
14415
14416
14417
14418
14419
14420
14421
14422
14423
14424
14425
14426
14427
14428
14429
14430
14431
14432
14433
14434
14435
14436
14437
14438
14439
14440
14441
14442
14443
14444
14445
14446
14447
14448
14449
14450
14451
14452
14453
14454
14455
14456
14457
14458
14459
14460
14461
14462
14463
14464
14465
14466
14467
14468
14469
14470
14471
14472
14473
14474
14475
14476
14477
14478
14479
14480
14481
14482
14483
14484
14485
14486
14487
14488
14489
14490
14491
14492
14493
14494
14495
14496
14497
14498
14499
14500
14501
14502
14503
14504
14505
14506
14507
14508
14509
14510
14511
14512
14513
14514
14515
14516
14517
14518
14519
14520
14521
14522
14523
14524
14525
14526
14527
14528
14529
14530
14531
14532
14533
14534
14535
14536
14537
14538
14539
14540
14541
14542
14543
14544
14545
14546
14547
14548
14549
14550
14551
14552
14553
14554
14555
14556
14557
14558
14559
14560
14561
14562
14563
14564
14565
14566
14567
14568
14569
14570
14571
14572
14573
14574
14575
14576
14577
14578
14579
14580
14581
14582
14583
14584
14585
14586
14587
14588
14589
14590
14591
14592
14593
14594
14595
14596
14597
14598
14599
14600
14601
14602
14603
14604
14605
14606
14607
14608
14609
14610
14611
14612
14613
14614
14615
14616
14617
14618
14619
14620
14621
14622
14623
14624
14625
14626
14627
14628
14629
14630
14631
14632
14633
14634
14635
14636
14637
14638
14639
14640
14641
14642
14643
14644
14645
14646
14647
14648
14649
14650
14651
14652
14653
14654
14655
14656
14657
14658
14659
14660
14661
14662
14663
14664
14665
14666
14667
14668
14669
14670
14671
14672
14673
14674
14675
14676
14677
14678
14679
14680
14681
14682
14683
14684
14685
14686
14687
14688
14689
14690
14691
14692
14693
14694
14695
14696
14697
14698
14699
14700
14701
14702
14703
14704
14705
14706
14707
14708
14709
14710
14711
14712
14713
14714
14715
14716
14717
14718
14719
14720
14721
14722
14723
14724
14725
14726
14727
14728
14729
14730
14731
14732
14733
14734
14735
14736
14737
14738
14739
14740
14741
14742
14743
14744
14745
14746
14747
14748
14749
14750
14751
14752
14753
14754
14755
14756
14757
14758
14759
14760
14761
14762
14763
14764
14765
14766
14767
14768
14769
14770
14771
14772
14773
14774
14775
14776
14777
14778
14779
14780
14781
14782
14783
14784
14785
14786
14787
14788
14789
14790
14791
14792
14793
14794
14795
14796
14797
14798
14799
14800
14801
14802
14803
14804
14805
14806
14807
14808
14809
14810
14811
14812
14813
14814
14815
14816
14817
14818
14819
14820
14821
14822
14823
14824
14825
14826
14827
14828
14829
14830
14831
14832
14833
14834
14835
14836
14837
14838
14839
14840
14841
14842
14843
14844
14845
14846
14847
14848
14849
14850
14851
14852
14853
14854
14855
14856
14857
14858
14859
14860
14861
14862
14863
14864
14865
14866
14867
14868
14869
14870
14871
14872
14873
14874
14875
14876
14877
14878
14879
14880
14881
14882
14883
14884
14885
14886
14887
14888
14889
14890
14891
14892
14893
14894
14895
14896
14897
14898
14899
14900
14901
14902
14903
14904
14905
14906
14907
14908
14909
14910
14911
14912
14913
14914
14915
14916
14917
14918
14919
14920
14921
14922
14923
14924
14925
14926
14927
14928
14929
14930
14931
14932
14933
14934
14935
14936
14937
14938
14939
14940
14941
14942
14943
14944
14945
14946
14947
14948
14949
14950
14951
14952
14953
14954
14955
14956
14957
14958
14959
14960
14961
14962
14963
14964
14965
14966
14967
14968
14969
14970
14971
14972
14973
14974
14975
14976
14977
14978
14979
14980
14981
14982
14983
14984
14985
14986
14987
14988
14989
14990
14991
14992
14993
14994
14995
14996
14997
14998
14999
15000
15001
15002
15003
15004
15005
15006
15007
15008
15009
15010
15011
15012
15013
15014
15015
15016
15017
15018
15019
15020
15021
15022
15023
15024
15025
15026
15027
15028
15029
15030
15031
15032
15033
15034
15035
15036
15037
15038
15039
15040
15041
15042
15043
15044
15045
15046
15047
15048
15049
15050
15051
15052
15053
15054
15055
15056
15057
15058
15059
15060
15061
15062
15063
15064
15065
15066
15067
15068
15069
15070
15071
15072
15073
15074
15075
15076
15077
15078
15079
15080
15081
15082
15083
15084
15085
15086
15087
15088
15089
15090
15091
15092
15093
15094
15095
15096
15097
15098
15099
15100
15101
15102
15103
15104
15105
15106
15107
15108
15109
15110
15111
15112
15113
15114
15115
15116
15117
15118
15119
15120
15121
15122
15123
15124
15125
15126
15127
15128
15129
15130
15131
15132
15133
15134
15135
15136
15137
15138
15139
15140
15141
15142
15143
15144
15145
15146
15147
15148
15149
15150
15151
15152
15153
15154
15155
15156
15157
15158
15159
15160
15161
15162
15163
15164
15165
15166
15167
15168
15169
15170
15171
15172
15173
15174
15175
15176
15177
15178
15179
15180
15181
15182
15183
15184
15185
15186
15187
15188
15189
15190
15191
15192
15193
15194
15195
15196
15197
15198
15199
15200
15201
15202
15203
15204
15205
15206
15207
15208
15209
15210
15211
15212
15213
15214
15215
15216
15217
15218
15219
15220
15221
15222
15223
15224
15225
15226
15227
15228
15229
15230
15231
15232
15233
15234
15235
15236
15237
15238
15239
15240
15241
15242
15243
15244
15245
15246
15247
15248
15249
15250
15251
15252
15253
15254
15255
15256
15257
15258
15259
15260
15261
15262
15263
15264
15265
15266
15267
15268
15269
15270
15271
15272
15273
15274
15275
15276
15277
15278
15279
15280
15281
15282
15283
15284
15285
15286
15287
15288
15289
15290
15291
15292
15293
15294
15295
15296
15297
15298
15299
15300
15301
15302
15303
15304
15305
15306
15307
15308
15309
15310
15311
15312
15313
15314
15315
15316
15317
15318
15319
15320
15321
15322
15323
15324
15325
15326
15327
15328
15329
15330
15331
15332
15333
15334
15335
15336
15337
15338
15339
15340
15341
15342
15343
15344
15345
15346
15347
15348
15349
15350
15351
15352
15353
15354
15355
15356
15357
15358
15359
15360
15361
15362
15363
15364
15365
15366
15367
15368
15369
15370
15371
15372
15373
15374
15375
15376
15377
15378
15379
15380
15381
15382
15383
15384
15385
15386
15387
15388
15389
15390
15391
15392
15393
15394
15395
15396
15397
15398
15399
15400
15401
15402
15403
15404
15405
15406
15407
15408
15409
15410
15411
15412
15413
15414
15415
15416
15417
15418
15419
15420
15421
15422
15423
15424
15425
15426
15427
15428
15429
15430
15431
15432
15433
15434
15435
15436
15437
15438
15439
15440
15441
15442
15443
15444
15445
15446
15447
15448
15449
15450
15451
15452
15453
15454
15455
15456
15457
15458
15459
15460
15461
15462
15463
15464
15465
15466
15467
15468
15469
15470
15471
15472
15473
15474
15475
15476
15477
15478
15479
15480
15481
15482
15483
15484
15485
15486
15487
15488
15489
15490
15491
15492
15493
15494
15495
15496
15497
15498
15499
15500
15501
15502
15503
15504
15505
15506
15507
15508
15509
15510
15511
15512
15513
15514
15515
15516
15517
15518
15519
15520
15521
15522
15523
15524
15525
15526
15527
15528
15529
15530
15531
15532
15533
15534
15535
15536
15537
15538
15539
15540
15541
15542
15543
15544
15545
15546
15547
15548
15549
15550
15551
15552
15553
15554
15555
15556
15557
15558
15559
15560
15561
15562
15563
15564
15565
15566
15567
15568
15569
15570
15571
15572
15573
15574
15575
15576
15577
15578
15579
15580
15581
15582
15583
15584
15585
15586
15587
15588
15589
15590
15591
15592
15593
15594
15595
15596
15597
15598
15599
15600
15601
15602
15603
15604
15605
15606
15607
15608
15609
15610
15611
15612
15613
15614
15615
15616
15617
15618
15619
15620
15621
15622
15623
15624
15625
15626
15627
15628
15629
15630
15631
15632
15633
15634
15635
15636
15637
15638
15639
15640
15641
15642
15643
15644
15645
15646
15647
15648
15649
15650
15651
15652
15653
15654
15655
15656
15657
15658
15659
15660
15661
15662
15663
15664
15665
15666
15667
15668
15669
15670
15671
15672
15673
15674
15675
15676
15677
15678
15679
15680
15681
15682
15683
15684
15685
15686
15687
15688
15689
15690
15691
15692
15693
15694
15695
15696
15697
15698
15699
15700
15701
15702
15703
15704
15705
15706
15707
15708
15709
15710
15711
15712
15713
15714
15715
15716
15717
15718
15719
15720
15721
15722
15723
15724
15725
15726
15727
15728
15729
15730
15731
15732
15733
15734
15735
15736
15737
15738
15739
15740
15741
15742
15743
15744
15745
15746
15747
15748
15749
15750
15751
15752
15753
15754
15755
15756
15757
15758
15759
15760
15761
15762
15763
15764
15765
15766
15767
15768
15769
15770
15771
15772
15773
15774
15775
15776
15777
15778
15779
15780
15781
15782
15783
15784
15785
15786
15787
15788
15789
15790
15791
15792
15793
15794
15795
15796
15797
15798
15799
15800
15801
15802
15803
15804
15805
15806
15807
15808
15809
15810
15811
15812
15813
15814
15815
15816
15817
15818
15819
15820
15821
15822
15823
15824
15825
15826
15827
15828
15829
15830
15831
15832
15833
15834
15835
15836
15837
15838
15839
15840
15841
15842
15843
15844
15845
15846
15847
15848
15849
15850
15851
15852
15853
15854
15855
15856
15857
15858
15859
15860
15861
15862
15863
15864
15865
15866
15867
15868
15869
15870
15871
15872
15873
15874
15875
15876
15877
15878
15879
15880
15881
15882
15883
15884
15885
15886
15887
15888
15889
15890
15891
15892
15893
15894
15895
15896
15897
15898
15899
15900
15901
15902
15903
15904
15905
15906
15907
15908
15909
15910
15911
15912
15913
15914
15915
15916
15917
15918
15919
15920
15921
15922
15923
15924
15925
15926
15927
15928
15929
15930
15931
15932
15933
15934
15935
15936
15937
15938
15939
15940
15941
15942
15943
15944
15945
15946
15947
15948
15949
15950
15951
15952
15953
15954
15955
15956
15957
15958
15959
15960
15961
15962
15963
15964
15965
15966
15967
15968
15969
15970
15971
15972
15973
15974
15975
15976
15977
15978
15979
15980
15981
15982
15983
15984
15985
15986
15987
15988
15989
15990
15991
15992
15993
15994
15995
15996
15997
15998
15999
16000
16001
16002
16003
16004
16005
16006
16007
16008
16009
16010
16011
16012
16013
16014
16015
16016
16017
16018
16019
16020
16021
16022
16023
16024
16025
16026
16027
16028
16029
16030
16031
16032
16033
16034
16035
16036
16037
16038
16039
16040
16041
16042
16043
16044
16045
16046
16047
16048
16049
16050
16051
16052
16053
16054
16055
16056
16057
16058
16059
16060
16061
16062
16063
16064
16065
16066
16067
16068
16069
16070
16071
16072
16073
16074
16075
16076
16077
16078
16079
16080
16081
16082
16083
16084
16085
16086
16087
16088
16089
16090
16091
16092
16093
16094
16095
16096
16097
16098
16099
16100
16101
16102
16103
16104
16105
16106
16107
16108
16109
16110
16111
16112
16113
16114
16115
16116
16117
16118
16119
16120
16121
16122
16123
16124
16125
16126
16127
16128
16129
16130
16131
16132
16133
16134
16135
16136
16137
16138
16139
16140
16141
16142
16143
16144
16145
16146
16147
16148
16149
16150
16151
16152
16153
16154
16155
16156
16157
16158
16159
16160
16161
16162
16163
16164
16165
16166
16167
16168
16169
16170
16171
16172
16173
16174
16175
16176
16177
16178
16179
16180
16181
16182
16183
16184
16185
16186
16187
16188
16189
16190
16191
16192
16193
16194
16195
16196
16197
16198
16199
16200
16201
16202
16203
16204
16205
16206
16207
16208
16209
16210
16211
16212
16213
16214
16215
16216
16217
16218
16219
16220
16221
16222
16223
16224
16225
16226
16227
16228
16229
16230
16231
16232
16233
16234
16235
16236
16237
16238
16239
16240
16241
16242
16243
16244
16245
16246
16247
16248
16249
16250
16251
16252
16253
16254
16255
16256
16257
16258
16259
16260
16261
16262
16263
16264
16265
16266
16267
16268
16269
16270
16271
16272
16273
16274
16275
16276
16277
16278
16279
16280
16281
16282
16283
16284
16285
16286
16287
16288
16289
16290
16291
16292
16293
16294
16295
16296
16297
16298
16299
16300
16301
16302
16303
16304
16305
16306
16307
16308
16309
16310
16311
16312
16313
16314
16315
16316
16317
16318
16319
16320
16321
16322
16323
16324
16325
16326
16327
16328
16329
16330
16331
16332
16333
16334
16335
16336
16337
16338
16339
16340
16341
16342
16343
16344
16345
16346
16347
16348
16349
16350
16351
16352
16353
16354
16355
16356
16357
16358
16359
16360
16361
16362
16363
16364
16365
16366
16367
16368
16369
16370
16371
16372
16373
16374
16375
16376
16377
16378
16379
16380
16381
16382
16383
16384
16385
16386
16387
16388
16389
16390
16391
16392
16393
16394
16395
16396
16397
16398
16399
16400
16401
16402
16403
16404
16405
16406
16407
16408
16409
16410
16411
16412
16413
16414
16415
16416
16417
16418
16419
16420
16421
16422
16423
16424
16425
16426
16427
16428
16429
16430
16431
16432
16433
16434
16435
16436
16437
16438
16439
16440
16441
16442
16443
16444
16445
16446
16447
16448
16449
16450
16451
16452
16453
16454
16455
16456
16457
16458
16459
16460
16461
16462
16463
16464
16465
16466
16467
16468
16469
16470
16471
16472
16473
16474
16475
16476
16477
16478
16479
16480
16481
16482
16483
16484
16485
16486
16487
16488
16489
16490
16491
16492
16493
16494
16495
16496
16497
16498
16499
16500
16501
16502
16503
16504
16505
16506
16507
16508
16509
16510
16511
16512
16513
16514
16515
16516
16517
16518
16519
16520
16521
16522
16523
16524
16525
16526
16527
16528
16529
16530
16531
16532
16533
16534
16535
16536
16537
16538
16539
16540
16541
16542
16543
16544
16545
16546
16547
16548
16549
16550
16551
16552
16553
16554
16555
16556
16557
16558
16559
16560
16561
16562
16563
16564
16565
16566
16567
16568
16569
16570
16571
16572
16573
16574
16575
16576
16577
16578
16579
16580
16581
16582
16583
16584
16585
16586
16587
16588
16589
16590
16591
16592
16593
16594
16595
16596
16597
16598
16599
16600
16601
16602
16603
16604
16605
16606
16607
16608
16609
16610
16611
16612
16613
16614
16615
16616
16617
16618
16619
16620
16621
16622
16623
16624
16625
16626
16627
16628
16629
16630
16631
16632
16633
16634
16635
16636
16637
16638
16639
16640
16641
16642
16643
16644
16645
16646
16647
16648
16649
16650
16651
16652
16653
16654
16655
16656
16657
16658
16659
16660
16661
16662
16663
16664
16665
16666
16667
16668
16669
16670
16671
16672
16673
16674
16675
16676
16677
16678
16679
16680
16681
16682
16683
16684
16685
16686
16687
16688
16689
16690
16691
16692
16693
16694
16695
16696
16697
16698
16699
16700
16701
16702
16703
16704
16705
16706
16707
16708
16709
16710
16711
16712
16713
16714
16715
16716
16717
16718
16719
16720
16721
16722
16723
16724
16725
16726
16727
16728
16729
16730
16731
16732
16733
16734
16735
16736
16737
16738
16739
16740
16741
16742
16743
16744
16745
16746
16747
16748
16749
16750
16751
16752
16753
16754
16755
16756
16757
16758
16759
16760
16761
16762
16763
16764
16765
16766
16767
16768
16769
16770
16771
16772
16773
16774
16775
16776
16777
16778
16779
16780
16781
16782
16783
16784
16785
16786
16787
16788
16789
16790
16791
16792
16793
16794
16795
16796
16797
16798
16799
16800
16801
16802
16803
16804
16805
16806
16807
16808
16809
16810
16811
16812
16813
16814
16815
16816
16817
16818
16819
16820
16821
16822
16823
16824
16825
16826
16827
16828
16829
16830
16831
16832
16833
16834
16835
16836
16837
16838
16839
16840
16841
16842
16843
16844
16845
16846
16847
16848
16849
16850
16851
16852
16853
16854
16855
16856
16857
16858
16859
16860
16861
16862
16863
16864
16865
16866
16867
16868
16869
16870
16871
16872
16873
16874
16875
16876
16877
16878
16879
16880
16881
16882
16883
16884
16885
16886
16887
16888
16889
16890
16891
16892
16893
16894
16895
16896
16897
16898
16899
16900
16901
16902
16903
16904
16905
16906
16907
16908
16909
16910
16911
16912
16913
16914
16915
16916
16917
16918
16919
16920
16921
16922
16923
16924
16925
16926
16927
16928
16929
16930
16931
16932
16933
16934
16935
16936
16937
16938
16939
16940
16941
16942
16943
16944
16945
16946
16947
16948
16949
16950
16951
16952
16953
16954
16955
16956
16957
16958
16959
16960
16961
16962
16963
16964
16965
16966
16967
16968
16969
16970
16971
16972
16973
16974
16975
16976
16977
16978
16979
16980
16981
16982
16983
16984
16985
16986
16987
16988
16989
16990
16991
16992
16993
16994
16995
16996
16997
16998
16999
17000
17001
17002
17003
17004
17005
17006
17007
17008
17009
17010
17011
17012
17013
17014
17015
17016
17017
17018
17019
17020
17021
17022
17023
17024
17025
17026
17027
17028
17029
17030
17031
17032
17033
17034
17035
17036
17037
17038
17039
17040
17041
17042
17043
17044
17045
17046
17047
17048
17049
17050
17051
17052
17053
17054
17055
17056
17057
17058
17059
17060
17061
17062
17063
17064
17065
17066
17067
17068
17069
17070
17071
17072
17073
17074
17075
17076
17077
17078
17079
17080
17081
17082
17083
17084
17085
17086
17087
17088
17089
17090
17091
17092
17093
17094
17095
17096
17097
17098
17099
17100
17101
17102
17103
17104
17105
17106
17107
17108
17109
17110
17111
17112
17113
17114
17115
17116
17117
17118
17119
17120
17121
17122
17123
17124
17125
17126
17127
17128
17129
17130
17131
17132
17133
17134
17135
17136
17137
17138
17139
17140
17141
17142
17143
17144
17145
17146
17147
17148
17149
17150
17151
17152
17153
17154
17155
17156
17157
17158
17159
17160
17161
17162
17163
17164
17165
17166
17167
17168
17169
17170
17171
17172
17173
17174
17175
17176
17177
17178
17179
17180
17181
17182
17183
17184
17185
17186
17187
17188
17189
17190
17191
17192
17193
17194
17195
17196
17197
17198
17199
17200
17201
17202
17203
17204
17205
17206
17207
17208
17209
17210
17211
17212
17213
17214
17215
17216
17217
17218
17219
17220
17221
17222
17223
17224
17225
17226
17227
17228
17229
17230
17231
17232
17233
17234
17235
17236
17237
17238
17239
17240
17241
17242
17243
17244
17245
17246
17247
17248
17249
17250
17251
17252
17253
17254
17255
17256
17257
17258
17259
17260
17261
17262
17263
17264
17265
17266
17267
17268
17269
17270
17271
17272
17273
17274
17275
17276
17277
17278
17279
17280
17281
17282
17283
17284
17285
17286
17287
17288
17289
17290
17291
17292
17293
17294
17295
17296
17297
17298
17299
17300
17301
17302
17303
17304
17305
17306
17307
17308
17309
17310
17311
17312
17313
17314
17315
17316
17317
17318
17319
17320
17321
17322
17323
17324
17325
17326
17327
17328
17329
17330
17331
17332
17333
17334
17335
17336
17337
17338
17339
17340
17341
17342
17343
17344
17345
17346
17347
17348
17349
17350
17351
17352
17353
17354
17355
17356
17357
17358
17359
17360
17361
17362
17363
17364
17365
17366
17367
17368
17369
17370
17371
17372
17373
17374
17375
17376
17377
17378
17379
17380
17381
17382
17383
17384
17385
17386
17387
17388
17389
17390
17391
17392
17393
17394
17395
17396
17397
17398
17399
17400
17401
17402
17403
17404
17405
17406
17407
17408
17409
17410
17411
17412
17413
17414
17415
17416
17417
17418
17419
17420
17421
17422
17423
17424
17425
17426
17427
17428
17429
17430
17431
17432
17433
17434
17435
17436
17437
17438
17439
17440
17441
17442
17443
17444
17445
17446
17447
17448
17449
17450
17451
17452
17453
17454
17455
17456
17457
17458
17459
17460
17461
17462
17463
17464
17465
17466
17467
17468
17469
17470
17471
17472
17473
17474
17475
17476
17477
17478
17479
17480
17481
17482
17483
17484
17485
17486
17487
17488
17489
17490
17491
17492
17493
17494
17495
17496
17497
17498
17499
17500
17501
17502
17503
17504
17505
17506
17507
17508
17509
17510
17511
17512
17513
17514
17515
17516
17517
17518
17519
17520
17521
17522
17523
17524
17525
17526
17527
17528
17529
17530
17531
17532
17533
17534
17535
17536
17537
17538
17539
17540
17541
17542
17543
17544
17545
17546
17547
17548
17549
17550
17551
17552
17553
17554
17555
17556
17557
17558
17559
17560
17561
17562
17563
17564
17565
17566
17567
17568
17569
17570
17571
17572
17573
17574
17575
17576
17577
17578
17579
17580
17581
17582
17583
17584
17585
17586
17587
17588
17589
17590
17591
17592
17593
17594
17595
17596
17597
17598
17599
17600
17601
17602
17603
17604
17605
17606
17607
17608
17609
17610
17611
17612
17613
17614
17615
17616
17617
17618
17619
17620
17621
17622
17623
17624
17625
17626
17627
17628
17629
17630
17631
17632
17633
17634
17635
17636
17637
17638
17639
17640
17641
17642
17643
17644
17645
17646
17647
17648
17649
17650
17651
17652
17653
17654
17655
17656
17657
17658
17659
17660
17661
17662
17663
17664
17665
17666
17667
17668
17669
17670
17671
17672
17673
17674
17675
17676
17677
17678
17679
17680
17681
17682
17683
17684
17685
17686
17687
17688
17689
17690
17691
17692
17693
17694
17695
17696
17697
17698
17699
17700
17701
17702
17703
17704
17705
17706
17707
17708
17709
17710
17711
17712
17713
17714
17715
17716
17717
17718
17719
17720
17721
17722
17723
17724
17725
17726
17727
17728
17729
17730
17731
17732
17733
17734
17735
17736
17737
17738
17739
17740
17741
17742
17743
17744
17745
17746
17747
17748
17749
17750
17751
17752
17753
17754
17755
17756
17757
17758
17759
17760
17761
17762
17763
17764
17765
17766
17767
17768
17769
17770
17771
17772
17773
17774
17775
17776
17777
17778
17779
17780
17781
17782
17783
17784
17785
17786
17787
17788
17789
17790
17791
17792
17793
17794
17795
17796
17797
17798
17799
17800
17801
17802
17803
17804
17805
17806
17807
17808
17809
17810
17811
17812
17813
17814
17815
17816
17817
17818
17819
17820
17821
17822
17823
17824
17825
17826
17827
17828
17829
17830
17831
17832
17833
17834
17835
17836
17837
17838
17839
17840
17841
17842
17843
17844
17845
17846
17847
17848
17849
17850
17851
17852
17853
17854
17855
17856
17857
17858
17859
17860
17861
17862
17863
17864
17865
17866
17867
17868
17869
17870
17871
17872
17873
17874
17875
17876
17877
17878
17879
17880
17881
17882
17883
17884
17885
17886
17887
17888
17889
17890
17891
17892
17893
17894
17895
17896
17897
17898
17899
17900
17901
17902
17903
17904
17905
17906
17907
17908
17909
17910
17911
17912
17913
17914
17915
17916
17917
17918
17919
17920
17921
17922
17923
17924
17925
17926
17927
17928
17929
17930
17931
17932
17933
17934
17935
17936
17937
17938
17939
17940
17941
17942
17943
17944
17945
17946
17947
17948
17949
17950
17951
17952
17953
17954
17955
17956
17957
17958
17959
17960
17961
17962
17963
17964
17965
17966
17967
17968
17969
17970
17971
17972
17973
17974
17975
17976
17977
17978
17979
17980
17981
17982
17983
17984
17985
17986
17987
17988
17989
17990
17991
17992
17993
17994
17995
17996
17997
17998
17999
18000
18001
18002
18003
18004
18005
18006
18007
18008
18009
18010
18011
18012
18013
18014
18015
18016
18017
18018
18019
18020
18021
18022
18023
18024
18025
18026
18027
18028
18029
18030
18031
18032
18033
18034
18035
18036
18037
18038
18039
18040
18041
18042
18043
18044
18045
18046
18047
18048
18049
18050
18051
18052
18053
18054
18055
18056
18057
18058
18059
18060
18061
18062
18063
18064
18065
18066
18067
18068
18069
18070
18071
18072
18073
18074
18075
18076
18077
18078
18079
18080
18081
18082
18083
18084
18085
18086
18087
18088
18089
18090
18091
18092
18093
18094
18095
18096
18097
18098
18099
18100
18101
18102
18103
18104
18105
18106
18107
18108
18109
18110
18111
18112
18113
18114
18115
18116
18117
18118
18119
18120
18121
18122
18123
18124
18125
18126
18127
18128
18129
18130
18131
18132
18133
18134
18135
18136
18137
18138
18139
18140
18141
18142
18143
18144
18145
18146
18147
18148
18149
18150
18151
18152
18153
18154
18155
18156
18157
18158
18159
18160
18161
18162
18163
18164
18165
18166
18167
18168
18169
18170
18171
18172
18173
18174
18175
18176
18177
18178
18179
18180
18181
18182
18183
18184
18185
18186
18187
18188
18189
18190
18191
18192
18193
18194
18195
18196
18197
18198
18199
18200
18201
18202
18203
18204
18205
18206
18207
18208
18209
18210
18211
18212
18213
18214
18215
18216
18217
18218
18219
18220
18221
18222
18223
18224
18225
18226
18227
18228
18229
18230
18231
18232
18233
18234
18235
18236
18237
18238
18239
18240
18241
18242
18243
18244
18245
18246
18247
18248
18249
18250
18251
18252
18253
18254
18255
18256
18257
18258
18259
18260
18261
18262
18263
18264
18265
18266
18267
18268
18269
18270
18271
18272
18273
18274
18275
18276
18277
18278
18279
18280
18281
18282
18283
18284
18285
18286
18287
18288
18289
18290
18291
18292
18293
18294
18295
18296
18297
18298
18299
18300
18301
18302
18303
18304
18305
18306
18307
18308
18309
18310
18311
18312
18313
18314
18315
18316
18317
18318
18319
18320
18321
18322
18323
18324
18325
18326
18327
18328
18329
18330
18331
18332
18333
18334
18335
18336
18337
18338
18339
18340
18341
18342
18343
18344
18345
18346
18347
18348
18349
18350
18351
18352
18353
18354
18355
18356
18357
18358
18359
18360
18361
18362
18363
18364
18365
18366
18367
18368
18369
18370
18371
18372
18373
18374
18375
18376
18377
18378
18379
18380
18381
18382
18383
18384
18385
18386
18387
18388
18389
18390
18391
18392
18393
18394
18395
18396
18397
18398
18399
18400
18401
18402
18403
18404
18405
18406
18407
18408
18409
18410
18411
18412
18413
18414
18415
18416
18417
18418
18419
18420
18421
18422
18423
18424
18425
18426
18427
18428
18429
18430
18431
18432
18433
18434
18435
18436
18437
18438
18439
18440
18441
18442
18443
18444
18445
18446
18447
18448
18449
18450
18451
18452
18453
18454
18455
18456
18457
18458
18459
18460
18461
18462
18463
18464
18465
18466
18467
18468
18469
18470
18471
18472
18473
18474
18475
18476
18477
18478
18479
18480
18481
18482
18483
18484
18485
18486
18487
18488
18489
18490
18491
18492
18493
18494
18495
18496
18497
18498
18499
18500
18501
18502
18503
18504
18505
18506
18507
18508
18509
18510
18511
18512
18513
18514
18515
18516
18517
18518
18519
18520
18521
18522
18523
18524
18525
18526
18527
18528
18529
18530
18531
18532
18533
18534
18535
18536
18537
18538
18539
18540
18541
18542
18543
18544
18545
18546
18547
18548
18549
18550
18551
18552
18553
18554
18555
18556
18557
18558
18559
18560
18561
18562
18563
18564
18565
18566
18567
18568
18569
18570
18571
18572
18573
18574
18575
18576
18577
18578
18579
18580
18581
18582
18583
18584
18585
18586
18587
18588
18589
18590
18591
18592
18593
18594
18595
18596
18597
18598
18599
18600
18601
18602
18603
18604
18605
18606
18607
18608
18609
18610
18611
18612
18613
18614
18615
18616
18617
18618
18619
18620
18621
18622
18623
18624
18625
18626
18627
18628
18629
18630
18631
18632
18633
18634
18635
18636
18637
18638
18639
18640
18641
18642
18643
18644
18645
18646
18647
18648
18649
18650
18651
18652
18653
18654
18655
18656
18657
18658
18659
18660
18661
18662
18663
18664
18665
18666
18667
18668
18669
18670
18671
18672
18673
18674
18675
18676
18677
18678
18679
18680
18681
18682
18683
18684
18685
18686
18687
18688
18689
18690
18691
18692
18693
18694
18695
18696
18697
18698
18699
18700
18701
18702
18703
18704
18705
18706
18707
18708
18709
18710
18711
18712
18713
18714
18715
18716
18717
18718
18719
18720
18721
18722
18723
18724
18725
18726
18727
18728
18729
18730
18731
18732
18733
18734
18735
18736
18737
18738
18739
18740
18741
18742
18743
18744
18745
18746
18747
18748
18749
18750
18751
18752
18753
18754
18755
18756
18757
18758
18759
18760
18761
18762
18763
18764
18765
18766
18767
18768
18769
18770
18771
18772
18773
18774
18775
18776
18777
18778
18779
18780
18781
18782
18783
18784
18785
18786
18787
18788
18789
18790
18791
18792
18793
18794
18795
18796
18797
18798
18799
18800
18801
18802
18803
18804
18805
18806
18807
18808
18809
18810
18811
18812
18813
18814
18815
18816
18817
18818
18819
18820
18821
18822
18823
18824
18825
18826
18827
18828
18829
18830
18831
18832
18833
18834
18835
18836
18837
18838
18839
18840
18841
18842
18843
18844
18845
18846
18847
18848
18849
18850
18851
18852
18853
18854
18855
18856
18857
18858
18859
18860
18861
18862
18863
18864
18865
18866
18867
18868
18869
18870
18871
18872
18873
18874
18875
18876
18877
18878
18879
18880
18881
18882
18883
18884
18885
18886
18887
18888
18889
18890
18891
18892
18893
18894
18895
18896
18897
18898
18899
18900
18901
18902
18903
18904
18905
18906
18907
18908
18909
18910
18911
18912
18913
18914
18915
18916
18917
18918
18919
18920
18921
18922
18923
18924
18925
18926
18927
18928
18929
18930
18931
18932
18933
18934
18935
18936
18937
18938
18939
18940
18941
18942
18943
18944
18945
18946
18947
18948
18949
18950
18951
18952
18953
18954
18955
18956
18957
18958
18959
18960
18961
18962
18963
18964
18965
18966
18967
18968
18969
18970
18971
18972
18973
18974
18975
18976
18977
18978
18979
18980
18981
18982
18983
18984
18985
18986
18987
18988
18989
18990
18991
18992
18993
18994
18995
18996
18997
18998
18999
19000
19001
19002
19003
19004
19005
19006
19007
19008
19009
19010
19011
19012
19013
19014
19015
19016
19017
19018
19019
19020
19021
19022
19023
19024
19025
19026
19027
19028
19029
19030
19031
19032
19033
19034
19035
19036
19037
19038
19039
19040
19041
19042
19043
19044
19045
19046
19047
19048
19049
19050
19051
19052
19053
19054
19055
19056
19057
19058
19059
19060
19061
19062
19063
19064
19065
19066
19067
19068
19069
19070
19071
19072
19073
19074
19075
19076
19077
19078
19079
19080
19081
19082
19083
19084
19085
19086
19087
19088
19089
19090
19091
19092
19093
19094
19095
19096
19097
19098
19099
19100
19101
19102
19103
19104
19105
19106
19107
19108
19109
19110
19111
19112
19113
19114
19115
19116
19117
19118
19119
19120
19121
19122
19123
19124
19125
19126
19127
19128
19129
19130
19131
19132
19133
19134
19135
19136
19137
19138
19139
19140
19141
19142
19143
19144
19145
19146
19147
19148
19149
19150
19151
19152
19153
19154
19155
19156
19157
19158
19159
19160
19161
19162
19163
19164
19165
19166
19167
19168
19169
19170
19171
19172
19173
19174
19175
19176
19177
19178
19179
19180
19181
19182
19183
19184
19185
19186
19187
19188
19189
19190
19191
19192
19193
19194
19195
19196
19197
19198
19199
19200
19201
19202
19203
19204
19205
19206
19207
19208
19209
19210
19211
19212
19213
19214
19215
19216
19217
19218
19219
19220
19221
19222
19223
19224
19225
19226
19227
19228
19229
19230
19231
19232
19233
19234
19235
19236
19237
19238
19239
19240
19241
19242
19243
19244
19245
19246
19247
19248
19249
19250
19251
19252
19253
19254
19255
19256
19257
19258
19259
19260
19261
19262
19263
19264
19265
19266
19267
19268
19269
19270
19271
19272
19273
19274
19275
19276
19277
19278
19279
19280
19281
19282
19283
19284
19285
19286
19287
19288
19289
19290
19291
19292
19293
19294
19295
19296
19297
19298
19299
19300
19301
19302
19303
19304
19305
19306
19307
19308
19309
19310
19311
19312
19313
19314
19315
19316
19317
19318
19319
19320
19321
19322
19323
19324
19325
19326
19327
19328
19329
19330
19331
19332
19333
19334
19335
19336
19337
19338
19339
19340
19341
19342
19343
19344
19345
19346
19347
19348
19349
19350
19351
19352
19353
19354
19355
19356
19357
19358
19359
19360
19361
19362
19363
19364
19365
19366
19367
19368
19369
19370
19371
19372
19373
19374
19375
19376
19377
19378
19379
19380
19381
19382
19383
19384
19385
19386
19387
19388
19389
19390
19391
19392
19393
19394
19395
19396
19397
19398
19399
19400
19401
19402
19403
19404
19405
19406
19407
19408
19409
19410
19411
19412
19413
19414
19415
19416
19417
19418
19419
19420
19421
19422
19423
19424
19425
19426
19427
19428
19429
19430
19431
19432
19433
19434
19435
19436
19437
19438
19439
19440
19441
19442
19443
19444
19445
19446
19447
19448
19449
19450
19451
19452
19453
19454
19455
19456
19457
19458
19459
19460
19461
19462
19463
19464
19465
19466
19467
19468
19469
19470
19471
19472
19473
19474
19475
19476
19477
19478
19479
19480
19481
19482
19483
19484
19485
19486
19487
19488
19489
19490
19491
19492
19493
19494
19495
19496
19497
19498
19499
19500
19501
19502
19503
19504
19505
19506
19507
19508
19509
19510
19511
19512
19513
19514
19515
19516
19517
19518
19519
19520
19521
19522
19523
19524
19525
19526
19527
19528
19529
19530
19531
19532
19533
19534
19535
19536
19537
19538
19539
19540
19541
19542
19543
19544
19545
19546
19547
19548
19549
19550
19551
19552
19553
19554
19555
19556
19557
19558
19559
19560
19561
19562
19563
19564
19565
19566
19567
19568
19569
19570
19571
19572
19573
19574
19575
19576
19577
19578
19579
19580
19581
19582
19583
19584
19585
19586
19587
19588
19589
19590
19591
19592
19593
19594
19595
19596
19597
19598
19599
19600
19601
19602
19603
19604
19605
19606
19607
19608
19609
19610
19611
19612
19613
19614
19615
19616
19617
19618
19619
19620
19621
19622
19623
19624
19625
19626
19627
19628
19629
19630
19631
19632
19633
19634
19635
19636
19637
19638
19639
19640
19641
19642
19643
19644
19645
19646
19647
19648
19649
19650
19651
19652
19653
19654
19655
19656
19657
19658
19659
19660
19661
19662
19663
19664
19665
19666
19667
19668
19669
19670
19671
19672
19673
19674
19675
19676
19677
19678
19679
19680
19681
19682
19683
19684
19685
19686
19687
19688
19689
19690
19691
19692
19693
19694
19695
19696
19697
19698
19699
19700
19701
19702
19703
19704
19705
19706
19707
19708
19709
19710
19711
19712
19713
19714
19715
19716
19717
19718
19719
19720
19721
19722
19723
19724
19725
19726
19727
19728
19729
19730
19731
19732
19733
19734
19735
19736
19737
19738
19739
19740
19741
19742
19743
19744
19745
19746
19747
19748
19749
19750
19751
19752
19753
19754
19755
19756
19757
19758
19759
19760
19761
19762
19763
19764
19765
19766
19767
19768
19769
19770
19771
19772
19773
19774
19775
19776
19777
19778
19779
19780
19781
19782
19783
19784
19785
19786
19787
19788
19789
19790
19791
19792
19793
19794
19795
19796
19797
19798
19799
19800
19801
19802
19803
19804
19805
19806
19807
19808
19809
19810
19811
19812
19813
19814
19815
19816
19817
19818
19819
19820
19821
19822
19823
19824
19825
19826
19827
19828
19829
19830
19831
19832
19833
19834
19835
19836
19837
19838
19839
19840
19841
19842
19843
19844
19845
19846
19847
19848
19849
19850
19851
19852
19853
19854
19855
19856
19857
19858
19859
19860
19861
19862
19863
19864
19865
19866
19867
19868
19869
19870
19871
19872
19873
19874
19875
19876
19877
19878
19879
19880
19881
19882
19883
19884
19885
19886
19887
19888
19889
19890
19891
19892
19893
19894
19895
19896
19897
19898
19899
19900
19901
19902
19903
19904
19905
19906
19907
19908
19909
19910
19911
19912
19913
19914
19915
19916
19917
19918
19919
19920
19921
19922
19923
19924
19925
19926
19927
19928
19929
19930
19931
19932
19933
19934
19935
19936
19937
19938
19939
19940
19941
19942
19943
19944
19945
19946
19947
19948
19949
19950
19951
19952
19953
19954
19955
19956
19957
19958
19959
19960
19961
19962
19963
19964
19965
19966
19967
19968
19969
19970
19971
19972
19973
19974
19975
19976
19977
19978
19979
19980
19981
19982
19983
19984
19985
19986
19987
19988
19989
19990
19991
19992
19993
19994
19995
19996
19997
19998
19999
20000
20001
20002
20003
20004
20005
20006
20007
20008
20009
20010
20011
20012
20013
20014
20015
20016
20017
20018
20019
20020
20021
20022
20023
20024
20025
20026
20027
20028
20029
20030
20031
20032
20033
20034
20035
20036
20037
20038
20039
20040
20041
20042
20043
20044
20045
20046
20047
20048
20049
20050
20051
20052
20053
20054
20055
20056
20057
20058
20059
20060
20061
20062
20063
20064
20065
20066
20067
20068
20069
20070
20071
20072
20073
20074
20075
20076
20077
20078
20079
20080
20081
20082
20083
20084
20085
20086
20087
20088
20089
20090
20091
20092
20093
20094
20095
20096
20097
20098
20099
20100
20101
20102
20103
20104
20105
20106
20107
20108
20109
20110
20111
20112
20113
20114
20115
20116
20117
20118
20119
20120
20121
20122
20123
20124
20125
20126
20127
20128
20129
20130
20131
20132
20133
20134
20135
20136
20137
20138
20139
20140
20141
20142
20143
20144
20145
20146
20147
20148
20149
20150
20151
20152
20153
20154
20155
20156
20157
20158
20159
20160
20161
20162
20163
20164
20165
20166
20167
20168
20169
20170
20171
20172
20173
20174
20175
20176
20177
20178
20179
20180
20181
20182
20183
20184
20185
20186
20187
20188
20189
20190
20191
20192
20193
20194
20195
20196
20197
20198
20199
20200
20201
20202
20203
20204
20205
20206
20207
20208
20209
20210
20211
20212
20213
20214
20215
20216
20217
20218
20219
20220
20221
20222
20223
20224
20225
20226
20227
20228
20229
20230
20231
20232
20233
20234
20235
20236
20237
20238
20239
20240
20241
20242
20243
20244
20245
20246
20247
20248
20249
20250
20251
20252
20253
20254
20255
20256
20257
20258
20259
20260
20261
20262
20263
20264
20265
20266
20267
20268
20269
20270
20271
20272
20273
20274
20275
20276
20277
20278
20279
20280
20281
20282
20283
20284
20285
20286
20287
20288
20289
20290
20291
20292
20293
20294
20295
20296
20297
20298
20299
20300
20301
20302
20303
20304
20305
20306
20307
20308
20309
20310
20311
20312
20313
20314
20315
20316
20317
20318
20319
20320
20321
20322
20323
20324
20325
20326
20327
20328
20329
20330
20331
20332
20333
20334
20335
20336
20337
20338
20339
20340
20341
20342
20343
20344
20345
20346
20347
20348
20349
20350
20351
20352
20353
20354
20355
20356
20357
20358
20359
20360
20361
20362
20363
20364
20365
20366
20367
20368
20369
20370
20371
20372
20373
20374
20375
20376
20377
20378
20379
20380
20381
20382
20383
20384
20385
20386
20387
20388
20389
20390
20391
20392
20393
20394
20395
20396
20397
20398
20399
20400
20401
20402
20403
20404
20405
20406
20407
20408
20409
20410
20411
20412
20413
20414
20415
20416
20417
20418
20419
20420
20421
20422
20423
20424
20425
20426
20427
20428
20429
20430
20431
20432
20433
20434
20435
20436
20437
20438
20439
20440
20441
20442
20443
20444
20445
20446
20447
20448
20449
20450
20451
20452
20453
20454
20455
20456
20457
20458
20459
20460
20461
20462
20463
20464
20465
20466
20467
20468
20469
20470
20471
20472
20473
20474
20475
20476
20477
20478
20479
20480
20481
20482
20483
20484
20485
20486
20487
20488
20489
20490
20491
20492
20493
20494
20495
20496
20497
20498
20499
20500
20501
20502
20503
20504
20505
20506
20507
20508
20509
20510
20511
20512
20513
20514
20515
20516
20517
20518
20519
20520
20521
20522
20523
20524
20525
20526
20527
20528
20529
20530
20531
20532
20533
20534
20535
20536
20537
20538
20539
20540
20541
20542
20543
20544
20545
20546
20547
20548
20549
20550
20551
20552
20553
20554
20555
20556
20557
20558
20559
20560
20561
20562
20563
20564
20565
20566
20567
20568
20569
20570
20571
20572
20573
20574
20575
20576
20577
20578
20579
20580
20581
20582
20583
20584
20585
20586
20587
20588
20589
20590
20591
20592
20593
20594
20595
20596
20597
20598
20599
20600
20601
20602
20603
20604
20605
20606
20607
20608
20609
20610
20611
20612
20613
20614
20615
20616
20617
20618
20619
20620
20621
20622
20623
20624
20625
20626
20627
20628
20629
20630
20631
20632
20633
20634
20635
20636
20637
20638
20639
20640
20641
20642
20643
20644
20645
20646
20647
20648
20649
20650
20651
20652
20653
20654
20655
20656
20657
20658
20659
20660
20661
20662
20663
20664
20665
20666
20667
20668
20669
20670
20671
20672
20673
20674
20675
20676
20677
20678
20679
20680
20681
20682
20683
20684
20685
20686
20687
20688
20689
20690
20691
20692
20693
20694
20695
20696
20697
20698
20699
20700
20701
20702
20703
20704
20705
20706
20707
20708
20709
20710
20711
20712
20713
20714
20715
20716
20717
20718
20719
20720
20721
20722
20723
20724
20725
20726
20727
20728
20729
20730
20731
20732
20733
20734
20735
20736
20737
20738
20739
20740
20741
20742
20743
20744
20745
20746
20747
20748
20749
20750
20751
20752
20753
20754
20755
20756
20757
20758
20759
20760
20761
20762
20763
20764
20765
20766
20767
20768
20769
20770
20771
20772
20773
20774
20775
20776
20777
20778
20779
20780
20781
20782
20783
20784
20785
20786
20787
20788
20789
20790
20791
20792
20793
20794
20795
20796
20797
20798
20799
20800
20801
20802
20803
20804
20805
20806
20807
20808
20809
20810
20811
20812
20813
20814
20815
20816
20817
20818
20819
20820
20821
20822
20823
20824
20825
20826
20827
20828
20829
20830
20831
20832
20833
20834
20835
20836
20837
20838
20839
20840
20841
20842
20843
20844
20845
20846
20847
20848
20849
20850
20851
20852
20853
20854
20855
20856
20857
20858
20859
20860
20861
20862
20863
20864
20865
20866
20867
20868
20869
20870
20871
20872
20873
20874
20875
20876
20877
20878
20879
20880
20881
20882
20883
20884
20885
20886
20887
20888
20889
20890
20891
20892
20893
20894
20895
20896
20897
20898
20899
20900
20901
20902
20903
20904
20905
20906
20907
20908
20909
20910
20911
20912
20913
20914
20915
20916
20917
20918
20919
20920
20921
20922
20923
20924
20925
20926
20927
20928
20929
20930
20931
20932
20933
20934
20935
20936
20937
20938
20939
20940
20941
20942
20943
20944
20945
20946
20947
20948
20949
20950
20951
20952
20953
20954
20955
20956
20957
20958
20959
20960
20961
20962
20963
20964
20965
20966
20967
20968
20969
20970
20971
20972
20973
20974
20975
20976
20977
20978
20979
20980
20981
20982
20983
20984
20985
20986
20987
20988
20989
20990
20991
20992
20993
20994
20995
20996
20997
20998
20999
21000
21001
21002
21003
21004
21005
21006
21007
21008
21009
21010
21011
21012
21013
21014
21015
21016
21017
21018
21019
21020
21021
21022
21023
21024
21025
21026
21027
21028
21029
21030
21031
21032
21033
21034
21035
21036
21037
21038
21039
21040
21041
21042
21043
21044
21045
21046
21047
21048
21049
21050
21051
21052
21053
21054
21055
21056
21057
21058
21059
21060
21061
21062
21063
21064
21065
21066
21067
21068
21069
21070
21071
21072
21073
21074
21075
21076
21077
21078
21079
21080
21081
21082
21083
21084
21085
21086
21087
21088
21089
21090
21091
21092
21093
21094
21095
21096
21097
21098
21099
21100
21101
21102
21103
21104
21105
21106
21107
21108
21109
21110
21111
21112
21113
21114
21115
21116
21117
21118
21119
21120
21121
21122
21123
21124
21125
21126
21127
21128
21129
21130
21131
21132
21133
21134
21135
21136
21137
21138
21139
21140
21141
21142
21143
21144
21145
21146
21147
21148
21149
21150
21151
21152
21153
21154
21155
21156
21157
21158
21159
21160
21161
21162
21163
21164
21165
21166
21167
21168
21169
21170
21171
21172
21173
21174
21175
21176
21177
21178
21179
21180
21181
21182
21183
21184
21185
21186
21187
21188
21189
21190
21191
21192
21193
21194
21195
21196
21197
21198
21199
21200
21201
21202
21203
21204
21205
21206
21207
21208
21209
21210
21211
21212
21213
21214
21215
21216
21217
21218
21219
21220
21221
21222
21223
21224
21225
21226
21227
21228
21229
21230
21231
21232
21233
21234
21235
21236
21237
21238
21239
21240
21241
21242
21243
21244
21245
21246
21247
21248
21249
21250
21251
21252
21253
21254
21255
21256
21257
21258
21259
21260
21261
21262
21263
21264
21265
21266
21267
21268
21269
21270
21271
21272
21273
21274
21275
21276
21277
21278
21279
21280
21281
21282
21283
21284
21285
21286
21287
21288
21289
21290
21291
21292
21293
21294
21295
21296
21297
21298
21299
21300
21301
21302
21303
21304
21305
21306
21307
21308
21309
21310
21311
21312
21313
21314
21315
21316
21317
21318
21319
21320
21321
21322
21323
21324
21325
21326
21327
21328
21329
21330
21331
21332
21333
21334
21335
21336
21337
21338
21339
21340
21341
21342
21343
21344
21345
21346
21347
21348
21349
21350
21351
21352
21353
21354
21355
21356
21357
21358
21359
21360
21361
21362
21363
21364
21365
21366
21367
21368
21369
21370
21371
21372
21373
21374
21375
21376
21377
21378
21379
21380
21381
21382
21383
21384
21385
21386
21387
21388
21389
21390
21391
21392
21393
21394
21395
21396
21397
21398
21399
21400
21401
21402
21403
21404
21405
21406
21407
21408
21409
21410
21411
21412
21413
21414
21415
21416
21417
21418
21419
21420
21421
21422
21423
21424
21425
21426
21427
21428
21429
21430
21431
21432
21433
21434
21435
21436
21437
21438
21439
21440
21441
21442
21443
21444
21445
21446
21447
21448
21449
21450
21451
21452
21453
21454
21455
21456
21457
21458
21459
21460
21461
21462
21463
21464
21465
21466
21467
21468
21469
21470
21471
21472
21473
21474
21475
21476
21477
21478
21479
21480
21481
21482
21483
21484
21485
21486
21487
21488
21489
21490
21491
21492
21493
21494
21495
21496
21497
21498
21499
21500
21501
21502
21503
21504
21505
21506
21507
21508
21509
21510
21511
21512
21513
21514
21515
21516
21517
21518
21519
21520
21521
21522
21523
21524
21525
21526
21527
21528
21529
21530
21531
21532
21533
21534
21535
21536
21537
21538
21539
21540
21541
21542
21543
21544
21545
21546
21547
21548
21549
21550
21551
21552
21553
21554
21555
21556
21557
21558
21559
21560
21561
21562
21563
21564
21565
21566
21567
21568
21569
21570
21571
21572
21573
21574
21575
21576
21577
21578
21579
21580
21581
21582
21583
21584
21585
21586
21587
21588
21589
21590
21591
21592
21593
21594
21595
21596
21597
21598
21599
21600
21601
21602
21603
21604
21605
21606
21607
21608
21609
21610
21611
21612
21613
21614
21615
21616
21617
21618
21619
21620
21621
21622
21623
21624
21625
21626
21627
21628
21629
21630
21631
21632
21633
21634
21635
21636
21637
21638
21639
21640
21641
21642
21643
21644
21645
21646
21647
21648
21649
21650
21651
21652
21653
21654
21655
21656
21657
21658
21659
21660
21661
21662
21663
21664
21665
21666
21667
21668
21669
21670
21671
21672
21673
21674
21675
21676
21677
21678
21679
21680
21681
21682
21683
21684
21685
21686
21687
21688
21689
21690
21691
21692
21693
21694
21695
21696
21697
21698
21699
21700
21701
21702
21703
21704
21705
21706
21707
21708
21709
21710
21711
21712
21713
21714
21715
21716
21717
21718
21719
21720
21721
21722
21723
21724
21725
21726
21727
21728
21729
21730
21731
21732
21733
21734
21735
21736
21737
21738
21739
21740
21741
21742
21743
21744
21745
21746
21747
21748
21749
21750
21751
21752
21753
21754
21755
21756
21757
21758
21759
21760
21761
21762
21763
21764
21765
21766
21767
21768
21769
21770
21771
21772
21773
21774
21775
21776
21777
21778
21779
21780
21781
21782
21783
21784
21785
21786
21787
21788
21789
21790
21791
21792
21793
21794
21795
21796
21797
21798
21799
21800
21801
21802
21803
21804
21805
21806
21807
21808
21809
21810
21811
21812
21813
21814
21815
21816
21817
21818
21819
21820
21821
21822
21823
21824
21825
21826
21827
21828
21829
21830
21831
21832
21833
21834
21835
21836
21837
21838
21839
21840
21841
21842
21843
21844
21845
21846
21847
21848
21849
21850
21851
21852
21853
21854
21855
21856
21857
21858
21859
21860
21861
21862
21863
21864
21865
21866
21867
21868
21869
21870
21871
21872
21873
21874
21875
21876
21877
21878
21879
21880
21881
21882
21883
21884
21885
21886
21887
21888
21889
21890
21891
21892
21893
21894
21895
21896
21897
21898
21899
21900
21901
21902
21903
21904
21905
21906
21907
21908
21909
21910
21911
21912
21913
21914
21915
21916
21917
21918
21919
21920
21921
21922
21923
21924
21925
21926
21927
21928
21929
21930
21931
21932
21933
21934
21935
21936
21937
21938
21939
21940
21941
21942
21943
21944
21945
21946
21947
21948
21949
21950
21951
21952
21953
21954
21955
21956
21957
21958
21959
21960
21961
21962
21963
21964
21965
21966
21967
21968
21969
21970
21971
21972
21973
21974
21975
21976
21977
21978
21979
21980
21981
21982
21983
21984
21985
21986
21987
21988
21989
21990
21991
21992
21993
21994
21995
21996
21997
21998
21999
22000
22001
22002
22003
22004
22005
22006
22007
22008
22009
22010
22011
22012
22013
22014
22015
22016
22017
22018
22019
22020
22021
22022
22023
22024
22025
22026
22027
22028
22029
22030
22031
22032
22033
22034
22035
22036
22037
22038
22039
22040
22041
22042
22043
22044
22045
22046
22047
22048
22049
22050
22051
22052
22053
22054
22055
22056
22057
22058
22059
22060
22061
22062
22063
22064
22065
22066
22067
22068
22069
22070
22071
22072
22073
22074
22075
22076
22077
22078
22079
22080
22081
22082
22083
22084
22085
22086
22087
22088
22089
22090
22091
22092
22093
22094
22095
22096
22097
22098
22099
22100
22101
22102
22103
22104
22105
22106
22107
22108
22109
22110
22111
22112
22113
22114
22115
22116
22117
22118
22119
22120
22121
22122
22123
22124
22125
22126
22127
22128
22129
22130
22131
22132
22133
22134
22135
22136
22137
22138
22139
22140
22141
22142
22143
22144
22145
22146
22147
22148
22149
22150
22151
22152
22153
22154
22155
22156
22157
22158
22159
22160
22161
22162
22163
22164
22165
22166
22167
22168
22169
22170
22171
22172
22173
22174
22175
22176
22177
22178
22179
22180
22181
22182
22183
22184
22185
22186
22187
22188
22189
22190
22191
22192
22193
22194
22195
22196
22197
22198
22199
22200
22201
22202
22203
22204
22205
22206
22207
22208
22209
22210
22211
22212
22213
22214
22215
22216
22217
22218
22219
22220
22221
22222
22223
22224
22225
22226
22227
22228
22229
22230
22231
22232
22233
22234
22235
22236
22237
22238
22239
22240
22241
22242
22243
22244
22245
22246
22247
22248
22249
22250
22251
22252
22253
22254
22255
22256
22257
22258
22259
22260
22261
22262
22263
22264
22265
22266
22267
22268
22269
22270
22271
22272
22273
22274
22275
22276
22277
22278
22279
22280
22281
22282
22283
22284
22285
22286
22287
22288
22289
22290
22291
22292
22293
22294
22295
22296
22297
22298
22299
22300
22301
22302
22303
22304
22305
22306
22307
22308
22309
22310
22311
22312
22313
22314
22315
22316
22317
22318
22319
22320
22321
22322
22323
22324
22325
22326
22327
22328
22329
22330
22331
22332
22333
22334
22335
22336
22337
22338
22339
22340
22341
22342
22343
22344
22345
22346
22347
22348
22349
22350
22351
22352
22353
22354
22355
22356
22357
22358
22359
22360
22361
22362
22363
22364
22365
22366
22367
22368
22369
22370
22371
22372
22373
22374
22375
22376
22377
22378
22379
22380
22381
22382
22383
22384
22385
22386
22387
22388
22389
22390
22391
22392
22393
22394
22395
22396
22397
22398
22399
22400
22401
22402
22403
22404
22405
22406
22407
22408
22409
22410
22411
22412
22413
22414
22415
22416
22417
22418
22419
22420
22421
22422
22423
22424
22425
22426
22427
22428
22429
22430
22431
22432
22433
22434
22435
22436
22437
22438
22439
22440
22441
22442
22443
22444
22445
22446
22447
22448
22449
22450
22451
22452
22453
22454
22455
22456
22457
22458
22459
22460
22461
22462
22463
22464
22465
22466
22467
22468
22469
22470
22471
22472
22473
22474
22475
22476
22477
22478
22479
22480
22481
22482
22483
22484
22485
22486
22487
22488
22489
22490
22491
22492
22493
22494
22495
22496
22497
22498
22499
22500
22501
22502
22503
22504
22505
22506
22507
22508
22509
22510
22511
22512
22513
22514
22515
22516
22517
22518
22519
22520
22521
22522
22523
22524
22525
22526
22527
22528
22529
22530
22531
22532
22533
22534
22535
22536
22537
22538
22539
22540
22541
22542
22543
22544
22545
22546
22547
22548
22549
22550
22551
22552
22553
22554
22555
22556
22557
22558
22559
22560
22561
22562
22563
22564
22565
22566
22567
22568
22569
22570
22571
22572
22573
22574
22575
22576
22577
22578
22579
22580
22581
22582
22583
22584
22585
22586
22587
22588
22589
22590
22591
22592
22593
22594
22595
22596
22597
22598
22599
22600
22601
22602
22603
22604
22605
22606
22607
22608
22609
22610
22611
22612
22613
22614
22615
22616
22617
22618
22619
22620
22621
22622
22623
22624
22625
22626
22627
22628
22629
22630
22631
22632
22633
22634
22635
22636
22637
22638
22639
22640
22641
22642
22643
22644
22645
22646
22647
22648
22649
22650
22651
22652
22653
22654
22655
22656
22657
22658
22659
22660
22661
22662
22663
22664
22665
22666
22667
22668
22669
22670
22671
22672
22673
22674
22675
22676
22677
22678
22679
22680
22681
22682
22683
22684
22685
22686
22687
22688
22689
22690
22691
22692
22693
22694
22695
22696
22697
22698
22699
22700
22701
22702
22703
22704
22705
22706
22707
22708
22709
22710
22711
22712
22713
22714
22715
22716
22717
22718
22719
22720
22721
22722
22723
22724
22725
22726
22727
22728
22729
22730
22731
22732
22733
22734
22735
22736
22737
22738
22739
22740
22741
22742
22743
22744
22745
22746
22747
22748
22749
22750
22751
22752
22753
22754
22755
22756
22757
22758
22759
22760
22761
22762
22763
22764
22765
22766
22767
22768
22769
22770
22771
22772
22773
22774
22775
22776
22777
22778
22779
22780
22781
22782
22783
22784
22785
22786
22787
22788
22789
22790
22791
22792
22793
22794
22795
22796
22797
22798
22799
22800
22801
22802
22803
22804
22805
22806
22807
22808
22809
22810
22811
22812
22813
22814
22815
22816
22817
22818
22819
22820
22821
22822
22823
22824
22825
22826
22827
22828
22829
22830
22831
22832
22833
22834
22835
22836
22837
22838
22839
22840
22841
22842
22843
22844
22845
22846
22847
22848
22849
22850
22851
22852
22853
22854
22855
22856
22857
22858
22859
22860
22861
22862
22863
22864
22865
22866
22867
22868
22869
22870
22871
22872
22873
22874
22875
22876
22877
22878
22879
22880
22881
22882
22883
22884
22885
22886
22887
22888
22889
22890
22891
22892
22893
22894
22895
22896
22897
22898
22899
22900
22901
22902
22903
22904
22905
22906
22907
22908
22909
22910
22911
22912
22913
22914
22915
22916
22917
22918
22919
22920
22921
22922
22923
22924
22925
22926
22927
22928
22929
22930
22931
22932
22933
22934
22935
22936
22937
22938
22939
22940
22941
22942
22943
22944
22945
22946
22947
22948
22949
22950
22951
22952
22953
22954
22955
22956
22957
22958
22959
22960
22961
22962
22963
22964
22965
22966
22967
22968
22969
22970
22971
22972
22973
22974
22975
22976
22977
22978
22979
22980
22981
22982
22983
22984
22985
22986
22987
22988
22989
22990
22991
22992
22993
22994
22995
22996
22997
22998
22999
23000
23001
23002
23003
23004
23005
23006
23007
23008
23009
23010
23011
23012
23013
23014
23015
23016
23017
23018
23019
23020
23021
23022
23023
23024
23025
23026
23027
23028
23029
23030
23031
23032
23033
23034
23035
23036
23037
23038
23039
23040
23041
23042
23043
23044
23045
23046
23047
23048
23049
23050
23051
23052
23053
23054
23055
23056
23057
23058
23059
23060
23061
23062
23063
23064
23065
23066
23067
23068
23069
23070
23071
23072
23073
23074
23075
23076
23077
23078
23079
23080
23081
23082
23083
23084
23085
23086
23087
23088
23089
23090
23091
23092
23093
23094
23095
23096
23097
23098
23099
23100
23101
23102
23103
23104
23105
23106
23107
23108
23109
23110
23111
23112
23113
23114
23115
23116
23117
23118
23119
23120
23121
23122
23123
23124
23125
23126
23127
23128
23129
23130
23131
23132
23133
23134
23135
23136
23137
23138
23139
23140
23141
23142
23143
23144
23145
23146
23147
23148
23149
23150
23151
23152
23153
23154
23155
23156
23157
23158
23159
23160
23161
23162
23163
23164
23165
23166
23167
23168
23169
23170
23171
23172
23173
23174
23175
23176
23177
23178
23179
23180
23181
23182
23183
23184
23185
23186
23187
23188
23189
23190
23191
23192
23193
23194
23195
23196
23197
23198
23199
23200
23201
23202
23203
23204
23205
23206
23207
23208
23209
23210
23211
23212
23213
23214
23215
23216
23217
23218
23219
23220
23221
23222
23223
23224
23225
23226
23227
23228
23229
23230
23231
23232
23233
23234
23235
23236
23237
23238
23239
23240
23241
23242
23243
23244
23245
23246
23247
23248
23249
23250
23251
23252
23253
23254
23255
23256
23257
23258
23259
23260
23261
23262
23263
23264
23265
23266
23267
23268
23269
23270
23271
23272
23273
23274
23275
23276
23277
23278
23279
23280
23281
23282
23283
23284
23285
23286
23287
23288
23289
23290
23291
23292
23293
23294
23295
23296
23297
23298
23299
23300
23301
23302
23303
23304
23305
23306
23307
23308
23309
23310
23311
23312
23313
23314
23315
23316
23317
23318
23319
23320
23321
23322
23323
23324
23325
23326
23327
23328
23329
23330
23331
23332
23333
23334
23335
23336
23337
23338
23339
23340
23341
23342
23343
23344
23345
23346
23347
23348
23349
23350
23351
23352
23353
23354
23355
23356
23357
23358
23359
23360
23361
23362
23363
23364
23365
23366
23367
23368
23369
23370
23371
23372
23373
23374
23375
23376
23377
23378
23379
23380
23381
23382
23383
23384
23385
23386
23387
23388
23389
23390
23391
23392
23393
23394
23395
23396
23397
23398
23399
23400
23401
23402
23403
23404
23405
23406
23407
23408
23409
23410
23411
23412
23413
23414
23415
23416
23417
23418
23419
23420
23421
23422
23423
23424
23425
23426
23427
23428
23429
23430
23431
23432
23433
23434
23435
23436
23437
23438
23439
23440
23441
23442
23443
23444
23445
23446
23447
23448
23449
23450
23451
23452
23453
23454
23455
23456
23457
23458
23459
23460
23461
23462
23463
23464
23465
23466
23467
23468
23469
23470
23471
23472
23473
23474
23475
23476
23477
23478
23479
23480
23481
23482
23483
23484
23485
23486
23487
23488
23489
23490
23491
23492
23493
23494
23495
23496
23497
23498
23499
23500
23501
23502
23503
23504
23505
23506
23507
23508
23509
23510
23511
23512
23513
23514
23515
23516
23517
23518
23519
23520
23521
23522
23523
23524
23525
23526
23527
23528
23529
23530
23531
23532
23533
23534
23535
23536
23537
23538
23539
23540
23541
23542
23543
23544
23545
23546
23547
23548
23549
23550
23551
23552
23553
23554
23555
23556
23557
23558
23559
23560
23561
23562
23563
23564
23565
23566
23567
23568
23569
23570
23571
23572
23573
23574
23575
23576
23577
23578
23579
23580
23581
23582
23583
23584
23585
23586
23587
23588
23589
23590
23591
23592
23593
23594
23595
23596
23597
23598
23599
23600
23601
23602
23603
23604
23605
23606
23607
23608
23609
23610
23611
23612
23613
23614
23615
23616
23617
23618
23619
23620
23621
23622
23623
23624
23625
23626
23627
23628
23629
23630
23631
23632
23633
23634
23635
23636
23637
23638
23639
23640
23641
23642
23643
23644
23645
23646
23647
23648
23649
23650
23651
23652
23653
23654
23655
23656
23657
23658
23659
23660
23661
23662
23663
23664
23665
23666
23667
23668
23669
23670
23671
23672
23673
23674
23675
23676
23677
23678
23679
23680
23681
23682
23683
23684
23685
23686
23687
23688
23689
23690
23691
23692
23693
23694
23695
23696
23697
23698
23699
23700
23701
23702
23703
23704
23705
23706
23707
23708
23709
23710
23711
23712
23713
23714
23715
23716
23717
23718
23719
23720
23721
23722
23723
23724
23725
23726
23727
23728
23729
23730
23731
23732
23733
23734
23735
23736
23737
23738
23739
23740
23741
23742
23743
23744
23745
23746
23747
23748
23749
23750
23751
23752
23753
23754
23755
23756
23757
23758
23759
23760
23761
23762
23763
23764
23765
23766
23767
23768
23769
23770
23771
23772
23773
23774
23775
23776
23777
23778
23779
23780
23781
23782
23783
23784
23785
23786
23787
23788
23789
23790
23791
23792
23793
23794
23795
23796
23797
23798
23799
23800
23801
23802
23803
23804
23805
23806
23807
23808
23809
23810
23811
23812
23813
23814
23815
23816
23817
23818
23819
23820
23821
23822
23823
23824
23825
23826
23827
23828
23829
23830
23831
23832
23833
23834
23835
23836
23837
23838
23839
23840
23841
23842
23843
23844
23845
23846
23847
23848
23849
23850
23851
23852
23853
23854
23855
23856
23857
23858
23859
23860
23861
23862
23863
23864
23865
23866
23867
23868
23869
23870
23871
23872
23873
23874
23875
23876
23877
23878
23879
23880
23881
23882
23883
23884
23885
23886
23887
23888
23889
23890
23891
23892
23893
23894
23895
23896
23897
23898
23899
23900
23901
23902
23903
23904
23905
23906
23907
23908
23909
23910
23911
23912
23913
23914
23915
23916
23917
23918
23919
23920
23921
23922
23923
23924
23925
23926
23927
23928
23929
23930
23931
23932
23933
23934
23935
23936
23937
23938
23939
23940
23941
23942
23943
23944
23945
23946
23947
23948
23949
23950
23951
23952
23953
23954
23955
23956
23957
23958
23959
23960
23961
23962
23963
23964
23965
23966
23967
23968
23969
23970
23971
23972
23973
23974
23975
23976
23977
23978
23979
23980
23981
23982
23983
23984
23985
23986
23987
23988
23989
23990
23991
23992
23993
23994
23995
23996
23997
23998
23999
24000
24001
24002
24003
24004
24005
24006
24007
24008
24009
24010
24011
24012
24013
24014
24015
24016
24017
24018
24019
24020
24021
24022
24023
24024
24025
24026
24027
24028
24029
24030
24031
24032
24033
24034
24035
24036
24037
24038
24039
24040
24041
24042
24043
24044
24045
24046
24047
24048
24049
24050
24051
24052
24053
24054
24055
24056
24057
24058
24059
24060
24061
24062
24063
24064
24065
24066
24067
24068
24069
24070
24071
24072
24073
24074
24075
24076
24077
24078
24079
24080
24081
24082
24083
24084
24085
24086
24087
24088
24089
24090
24091
24092
24093
24094
24095
24096
24097
24098
24099
24100
24101
24102
24103
24104
24105
24106
24107
24108
24109
24110
24111
24112
24113
24114
24115
24116
24117
24118
24119
24120
24121
24122
24123
24124
24125
24126
24127
24128
24129
24130
24131
24132
24133
24134
24135
24136
24137
24138
24139
24140
24141
24142
24143
24144
24145
24146
24147
24148
24149
24150
24151
24152
24153
24154
24155
24156
24157
24158
24159
24160
24161
24162
24163
24164
24165
24166
24167
24168
24169
24170
24171
24172
24173
24174
24175
24176
24177
24178
24179
24180
24181
24182
24183
24184
24185
24186
24187
24188
24189
24190
24191
24192
24193
24194
24195
24196
24197
24198
24199
24200
24201
24202
24203
24204
24205
24206
24207
24208
24209
24210
24211
24212
24213
24214
24215
24216
24217
24218
24219
24220
24221
24222
24223
24224
24225
24226
24227
24228
24229
24230
24231
24232
24233
24234
24235
24236
24237
24238
24239
24240
24241
24242
24243
24244
24245
24246
24247
24248
24249
24250
24251
24252
24253
24254
24255
24256
24257
24258
24259
24260
24261
24262
24263
24264
24265
24266
24267
24268
24269
24270
24271
24272
24273
24274
24275
24276
24277
24278
24279
24280
24281
24282
24283
24284
24285
24286
24287
24288
24289
24290
24291
24292
24293
24294
24295
24296
24297
24298
24299
24300
24301
24302
24303
24304
24305
24306
24307
24308
24309
24310
24311
24312
24313
24314
24315
24316
24317
24318
24319
24320
24321
24322
24323
24324
24325
24326
24327
24328
24329
24330
24331
24332
24333
24334
24335
24336
24337
24338
24339
24340
24341
24342
24343
24344
24345
24346
24347
24348
24349
24350
24351
24352
24353
24354
24355
24356
24357
24358
24359
24360
24361
24362
24363
24364
24365
24366
24367
24368
24369
24370
24371
24372
24373
24374
24375
24376
24377
24378
24379
24380
24381
24382
24383
24384
24385
24386
24387
24388
24389
24390
24391
24392
24393
24394
24395
24396
24397
24398
24399
24400
24401
24402
24403
24404
24405
24406
24407
24408
24409
24410
24411
24412
24413
24414
24415
24416
24417
24418
24419
24420
24421
24422
24423
24424
24425
24426
24427
24428
24429
24430
24431
24432
24433
24434
24435
24436
24437
24438
24439
24440
24441
24442
24443
24444
24445
24446
24447
24448
24449
24450
24451
24452
24453
24454
24455
24456
24457
24458
24459
24460
24461
24462
24463
24464
24465
24466
24467
24468
24469
24470
24471
24472
24473
24474
24475
24476
24477
24478
24479
24480
24481
24482
24483
24484
24485
24486
24487
24488
24489
24490
24491
24492
24493
24494
24495
24496
24497
24498
24499
24500
24501
24502
24503
24504
24505
24506
24507
24508
24509
24510
24511
24512
24513
24514
24515
24516
24517
24518
24519
24520
24521
24522
24523
24524
24525
24526
24527
24528
24529
24530
24531
24532
24533
24534
24535
24536
24537
24538
24539
24540
24541
24542
24543
24544
24545
24546
24547
24548
24549
24550
24551
24552
24553
24554
24555
24556
24557
24558
24559
24560
24561
24562
24563
24564
24565
24566
24567
24568
24569
24570
24571
24572
24573
24574
24575
24576
24577
24578
24579
24580
24581
24582
24583
24584
24585
24586
24587
24588
24589
24590
24591
24592
24593
24594
24595
24596
24597
24598
24599
24600
24601
24602
24603
24604
24605
24606
24607
24608
24609
24610
24611
24612
24613
24614
24615
24616
24617
24618
24619
24620
24621
24622
24623
24624
24625
24626
24627
24628
24629
24630
24631
24632
24633
24634
24635
24636
24637
24638
24639
24640
24641
24642
24643
24644
24645
24646
24647
24648
24649
24650
24651
24652
24653
24654
24655
24656
24657
24658
24659
24660
24661
24662
24663
24664
24665
24666
24667
24668
24669
24670
24671
24672
24673
24674
24675
24676
24677
24678
24679
24680
24681
24682
24683
24684
24685
24686
24687
24688
24689
24690
24691
24692
24693
24694
24695
24696
24697
24698
24699
24700
24701
24702
24703
24704
24705
24706
24707
24708
24709
24710
24711
24712
24713
24714
24715
24716
24717
24718
24719
24720
24721
24722
24723
24724
24725
24726
24727
24728
24729
24730
24731
24732
24733
24734
24735
24736
24737
24738
24739
24740
24741
24742
24743
24744
24745
24746
24747
24748
24749
24750
24751
24752
24753
24754
24755
24756
24757
24758
24759
24760
24761
24762
24763
24764
24765
24766
24767
24768
24769
24770
24771
24772
24773
24774
24775
24776
24777
24778
24779
24780
24781
24782
24783
24784
24785
24786
24787
24788
24789
24790
24791
24792
24793
24794
24795
|
#
# $OpenBSD: fpsp.s,v 1.3 2001/09/20 17:02:30 mpech Exp $
# $NetBSD: fpsp.s,v 1.2 1996/05/15 19:48:03 is Exp $
#
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
# M68000 Hi-Performance Microprocessor Division
# M68060 Software Package Production Release
#
# M68060 Software Package Copyright (C) 1993, 1994, 1995, 1996 Motorola Inc.
# All rights reserved.
#
# THE SOFTWARE is provided on an "AS IS" basis and without warranty.
# To the maximum extent permitted by applicable law,
# MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
# INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS
# FOR A PARTICULAR PURPOSE and any warranty against infringement with
# regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
# and any accompanying written materials.
#
# To the maximum extent permitted by applicable law,
# IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
# (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS PROFITS,
# BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR OTHER PECUNIARY LOSS)
# ARISING OF THE USE OR INABILITY TO USE THE SOFTWARE.
#
# Motorola assumes no responsibility for the maintenance and support
# of the SOFTWARE.
#
# You are hereby granted a copyright license to use, modify, and distribute the
# SOFTWARE so long as this entire notice is retained without alteration
# in any modified and/or redistributed versions, and that such modified
# versions are clearly identified as such.
# No licenses are granted by implication, estoppel or otherwise under any
# patents or trademarks of Motorola, Inc.
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# freal.s:
# This file is appended to the top of the 060FPSP package
# and contains the entry points into the package. The user, in
# effect, branches to one of the branch table entries located
# after _060FPSP_TABLE.
# Also, subroutine stubs exist in this file (_fpsp_done for
# example) that are referenced by the FPSP package itself in order
# to call a given routine. The stub routine actually performs the
# callout. The FPSP code does a "bsr" to the stub routine. This
# extra layer of hierarchy adds a slight performance penalty but
# it makes the FPSP code easier to read and more mainatinable.
#
set _off_bsun, 0x00
set _off_snan, 0x04
set _off_operr, 0x08
set _off_ovfl, 0x0c
set _off_unfl, 0x10
set _off_dz, 0x14
set _off_inex, 0x18
set _off_fline, 0x1c
set _off_fpu_dis, 0x20
set _off_trap, 0x24
set _off_trace, 0x28
set _off_access, 0x2c
set _off_done, 0x30
set _off_imr, 0x40
set _off_dmr, 0x44
set _off_dmw, 0x48
set _off_irw, 0x4c
set _off_irl, 0x50
set _off_drb, 0x54
set _off_drw, 0x58
set _off_drl, 0x5c
set _off_dwb, 0x60
set _off_dww, 0x64
set _off_dwl, 0x68
_060FPSP_TABLE:
###############################################################
# Here's the table of ENTRY POINTS for those linking the package.
bra.l _fpsp_snan
short 0x0000
bra.l _fpsp_operr
short 0x0000
bra.l _fpsp_ovfl
short 0x0000
bra.l _fpsp_unfl
short 0x0000
bra.l _fpsp_dz
short 0x0000
bra.l _fpsp_inex
short 0x0000
bra.l _fpsp_fline
short 0x0000
bra.l _fpsp_unsupp
short 0x0000
bra.l _fpsp_effadd
short 0x0000
space 56
###############################################################
global _fpsp_done
_fpsp_done:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_done,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_ovfl
_real_ovfl:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_ovfl,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_unfl
_real_unfl:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_unfl,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_inex
_real_inex:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_inex,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_bsun
_real_bsun:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_bsun,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_operr
_real_operr:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_operr,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_snan
_real_snan:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_snan,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_dz
_real_dz:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_dz,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_fline
_real_fline:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_fline,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_fpu_disabled
_real_fpu_disabled:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_fpu_dis,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_trap
_real_trap:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_trap,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_trace
_real_trace:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_trace,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _real_access
_real_access:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_access,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
#######################################
global _imem_read
_imem_read:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_imr,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_read
_dmem_read:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_dmr,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_write
_dmem_write:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_dmw,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _imem_read_word
_imem_read_word:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_irw,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _imem_read_long
_imem_read_long:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_irl,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_read_byte
_dmem_read_byte:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_drb,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_read_word
_dmem_read_word:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_drw,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_read_long
_dmem_read_long:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_drl,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_write_byte
_dmem_write_byte:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_dwb,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_write_word
_dmem_write_word:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_dww,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
global _dmem_write_long
_dmem_write_long:
mov.l %d0,-(%sp)
mov.l (_060FPSP_TABLE-0x80+_off_dwl,%pc),%d0
pea.l (_060FPSP_TABLE-0x80,%pc,%d0)
mov.l 0x4(%sp),%d0
rtd &0x4
#
# This file contains a set of define statements for constants
# in order to promote readability within the corecode itself.
#
set LOCAL_SIZE, 192 # stack frame size(bytes)
set LV, -LOCAL_SIZE # stack offset
set EXC_SR, 0x4 # stack status register
set EXC_PC, 0x6 # stack pc
set EXC_VOFF, 0xa # stacked vector offset
set EXC_EA, 0xc # stacked <ea>
set EXC_FP, 0x0 # frame pointer
set EXC_AREGS, -68 # offset of all address regs
set EXC_DREGS, -100 # offset of all data regs
set EXC_FPREGS, -36 # offset of all fp regs
set EXC_A7, EXC_AREGS+(7*4) # offset of saved a7
set OLD_A7, EXC_AREGS+(6*4) # extra copy of saved a7
set EXC_A6, EXC_AREGS+(6*4) # offset of saved a6
set EXC_A5, EXC_AREGS+(5*4)
set EXC_A4, EXC_AREGS+(4*4)
set EXC_A3, EXC_AREGS+(3*4)
set EXC_A2, EXC_AREGS+(2*4)
set EXC_A1, EXC_AREGS+(1*4)
set EXC_A0, EXC_AREGS+(0*4)
set EXC_D7, EXC_DREGS+(7*4)
set EXC_D6, EXC_DREGS+(6*4)
set EXC_D5, EXC_DREGS+(5*4)
set EXC_D4, EXC_DREGS+(4*4)
set EXC_D3, EXC_DREGS+(3*4)
set EXC_D2, EXC_DREGS+(2*4)
set EXC_D1, EXC_DREGS+(1*4)
set EXC_D0, EXC_DREGS+(0*4)
set EXC_FP0, EXC_FPREGS+(0*12) # offset of saved fp0
set EXC_FP1, EXC_FPREGS+(1*12) # offset of saved fp1
set EXC_FP2, EXC_FPREGS+(2*12) # offset of saved fp2 (not used)
set FP_SCR1, LV+80 # fp scratch 1
set FP_SCR1_EX, FP_SCR1+0
set FP_SCR1_SGN, FP_SCR1+2
set FP_SCR1_HI, FP_SCR1+4
set FP_SCR1_LO, FP_SCR1+8
set FP_SCR0, LV+68 # fp scratch 0
set FP_SCR0_EX, FP_SCR0+0
set FP_SCR0_SGN, FP_SCR0+2
set FP_SCR0_HI, FP_SCR0+4
set FP_SCR0_LO, FP_SCR0+8
set FP_DST, LV+56 # fp destination operand
set FP_DST_EX, FP_DST+0
set FP_DST_SGN, FP_DST+2
set FP_DST_HI, FP_DST+4
set FP_DST_LO, FP_DST+8
set FP_SRC, LV+44 # fp source operand
set FP_SRC_EX, FP_SRC+0
set FP_SRC_SGN, FP_SRC+2
set FP_SRC_HI, FP_SRC+4
set FP_SRC_LO, FP_SRC+8
set USER_FPIAR, LV+40 # FP instr address register
set USER_FPSR, LV+36 # FP status register
set FPSR_CC, USER_FPSR+0 # FPSR condition codes
set FPSR_QBYTE, USER_FPSR+1 # FPSR qoutient byte
set FPSR_EXCEPT, USER_FPSR+2 # FPSR exception status byte
set FPSR_AEXCEPT, USER_FPSR+3 # FPSR accrued exception byte
set USER_FPCR, LV+32 # FP control register
set FPCR_ENABLE, USER_FPCR+2 # FPCR exception enable
set FPCR_MODE, USER_FPCR+3 # FPCR rounding mode control
set L_SCR3, LV+28 # integer scratch 3
set L_SCR2, LV+24 # integer scratch 2
set L_SCR1, LV+20 # integer scratch 1
set STORE_FLG, LV+19 # flag: operand store (ie. not fcmp/ftst)
set EXC_TEMP2, LV+24 # temporary space
set EXC_TEMP, LV+16 # temporary space
set DTAG, LV+15 # destination operand type
set STAG, LV+14 # source operand type
set SPCOND_FLG, LV+10 # flag: special case (see below)
set EXC_CC, LV+8 # saved condition codes
set EXC_EXTWPTR, LV+4 # saved current PC (active)
set EXC_EXTWORD, LV+2 # saved extension word
set EXC_CMDREG, LV+2 # saved extension word
set EXC_OPWORD, LV+0 # saved operation word
################################
# Helpful macros
set FTEMP, 0 # offsets within an
set FTEMP_EX, 0 # extended precision
set FTEMP_SGN, 2 # value saved in memory.
set FTEMP_HI, 4
set FTEMP_LO, 8
set FTEMP_GRS, 12
set LOCAL, 0 # offsets within an
set LOCAL_EX, 0 # extended precision
set LOCAL_SGN, 2 # value saved in memory.
set LOCAL_HI, 4
set LOCAL_LO, 8
set LOCAL_GRS, 12
set DST, 0 # offsets within an
set DST_EX, 0 # extended precision
set DST_HI, 4 # value saved in memory.
set DST_LO, 8
set SRC, 0 # offsets within an
set SRC_EX, 0 # extended precision
set SRC_HI, 4 # value saved in memory.
set SRC_LO, 8
set SGL_LO, 0x3f81 # min sgl prec exponent
set SGL_HI, 0x407e # max sgl prec exponent
set DBL_LO, 0x3c01 # min dbl prec exponent
set DBL_HI, 0x43fe # max dbl prec exponent
set EXT_LO, 0x0 # min ext prec exponent
set EXT_HI, 0x7ffe # max ext prec exponent
set EXT_BIAS, 0x3fff # extended precision bias
set SGL_BIAS, 0x007f # single precision bias
set DBL_BIAS, 0x03ff # double precision bias
set NORM, 0x00 # operand type for STAG/DTAG
set ZERO, 0x01 # operand type for STAG/DTAG
set INF, 0x02 # operand type for STAG/DTAG
set QNAN, 0x03 # operand type for STAG/DTAG
set DENORM, 0x04 # operand type for STAG/DTAG
set SNAN, 0x05 # operand type for STAG/DTAG
set UNNORM, 0x06 # operand type for STAG/DTAG
##################
# FPSR/FPCR bits #
##################
set neg_bit, 0x3 # negative result
set z_bit, 0x2 # zero result
set inf_bit, 0x1 # infinite result
set nan_bit, 0x0 # NAN result
set q_sn_bit, 0x7 # sign bit of quotient byte
set bsun_bit, 7 # branch on unordered
set snan_bit, 6 # signalling NAN
set operr_bit, 5 # operand error
set ovfl_bit, 4 # overflow
set unfl_bit, 3 # underflow
set dz_bit, 2 # divide by zero
set inex2_bit, 1 # inexact result 2
set inex1_bit, 0 # inexact result 1
set aiop_bit, 7 # accrued inexact operation bit
set aovfl_bit, 6 # accrued overflow bit
set aunfl_bit, 5 # accrued underflow bit
set adz_bit, 4 # accrued dz bit
set ainex_bit, 3 # accrued inexact bit
#############################
# FPSR individual bit masks #
#############################
set neg_mask, 0x08000000 # negative bit mask (lw)
set inf_mask, 0x02000000 # infinity bit mask (lw)
set z_mask, 0x04000000 # zero bit mask (lw)
set nan_mask, 0x01000000 # nan bit mask (lw)
set neg_bmask, 0x08 # negative bit mask (byte)
set inf_bmask, 0x02 # infinity bit mask (byte)
set z_bmask, 0x04 # zero bit mask (byte)
set nan_bmask, 0x01 # nan bit mask (byte)
set bsun_mask, 0x00008000 # bsun exception mask
set snan_mask, 0x00004000 # snan exception mask
set operr_mask, 0x00002000 # operr exception mask
set ovfl_mask, 0x00001000 # overflow exception mask
set unfl_mask, 0x00000800 # underflow exception mask
set dz_mask, 0x00000400 # dz exception mask
set inex2_mask, 0x00000200 # inex2 exception mask
set inex1_mask, 0x00000100 # inex1 exception mask
set aiop_mask, 0x00000080 # accrued illegal operation
set aovfl_mask, 0x00000040 # accrued overflow
set aunfl_mask, 0x00000020 # accrued underflow
set adz_mask, 0x00000010 # accrued divide by zero
set ainex_mask, 0x00000008 # accrued inexact
######################################
# FPSR combinations used in the FPSP #
######################################
set dzinf_mask, inf_mask+dz_mask+adz_mask
set opnan_mask, nan_mask+operr_mask+aiop_mask
set nzi_mask, 0x01ffffff #clears N, Z, and I
set unfinx_mask, unfl_mask+inex2_mask+aunfl_mask+ainex_mask
set unf2inx_mask, unfl_mask+inex2_mask+ainex_mask
set ovfinx_mask, ovfl_mask+inex2_mask+aovfl_mask+ainex_mask
set inx1a_mask, inex1_mask+ainex_mask
set inx2a_mask, inex2_mask+ainex_mask
set snaniop_mask, nan_mask+snan_mask+aiop_mask
set snaniop2_mask, snan_mask+aiop_mask
set naniop_mask, nan_mask+aiop_mask
set neginf_mask, neg_mask+inf_mask
set infaiop_mask, inf_mask+aiop_mask
set negz_mask, neg_mask+z_mask
set opaop_mask, operr_mask+aiop_mask
set unfl_inx_mask, unfl_mask+aunfl_mask+ainex_mask
set ovfl_inx_mask, ovfl_mask+aovfl_mask+ainex_mask
#########
# misc. #
#########
set rnd_stky_bit, 29 # stky bit pos in longword
set sign_bit, 0x7 # sign bit
set signan_bit, 0x6 # signalling nan bit
set sgl_thresh, 0x3f81 # minimum sgl exponent
set dbl_thresh, 0x3c01 # minimum dbl exponent
set x_mode, 0x0 # extended precision
set s_mode, 0x4 # single precision
set d_mode, 0x8 # double precision
set rn_mode, 0x0 # round-to-nearest
set rz_mode, 0x1 # round-to-zero
set rm_mode, 0x2 # round-tp-minus-infinity
set rp_mode, 0x3 # round-to-plus-infinity
set mantissalen, 64 # length of mantissa in bits
set BYTE, 1 # len(byte) == 1 byte
set WORD, 2 # len(word) == 2 bytes
set LONG, 4 # len(longword) == 2 bytes
set BSUN_VEC, 0xc0 # bsun vector offset
set INEX_VEC, 0xc4 # inexact vector offset
set DZ_VEC, 0xc8 # dz vector offset
set UNFL_VEC, 0xcc # unfl vector offset
set OPERR_VEC, 0xd0 # operr vector offset
set OVFL_VEC, 0xd4 # ovfl vector offset
set SNAN_VEC, 0xd8 # snan vector offset
###########################
# SPecial CONDition FLaGs #
###########################
set ftrapcc_flg, 0x01 # flag bit: ftrapcc exception
set fbsun_flg, 0x02 # flag bit: bsun exception
set mia7_flg, 0x04 # flag bit: (a7)+ <ea>
set mda7_flg, 0x08 # flag bit: -(a7) <ea>
set fmovm_flg, 0x40 # flag bit: fmovm instruction
set immed_flg, 0x80 # flag bit: &<data> <ea>
set ftrapcc_bit, 0x0
set fbsun_bit, 0x1
set mia7_bit, 0x2
set mda7_bit, 0x3
set immed_bit, 0x7
##################################
# TRANSCENDENTAL "LAST-OP" FLAGS #
##################################
set FMUL_OP, 0x0 # fmul instr performed last
set FDIV_OP, 0x1 # fdiv performed last
set FADD_OP, 0x2 # fadd performed last
set FMOV_OP, 0x3 # fmov performed last
#############
# CONSTANTS #
#############
T1: long 0x40C62D38,0xD3D64634 # 16381 LOG2 LEAD
T2: long 0x3D6F90AE,0xB1E75CC7 # 16381 LOG2 TRAIL
PI: long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
PIBY2: long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
TWOBYPI:
long 0x3FE45F30,0x6DC9C883
#########################################################################
# XDEF **************************************************************** #
# _fpsp_ovfl(): 060FPSP entry point for FP Overflow exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Overflow exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _fpsp_done() - "callout" for 060FPSP exit (all work done!) #
# _real_ovfl() - "callout" for Overflow exception enabled code #
# _real_inex() - "callout" for Inexact exception enabled code #
# _real_trace() - "callout" for Trace exception code #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Ovfl exception stack frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# Overflow Exception enabled: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# Overflow Exception disabled: #
# - The system stack is unchanged #
# - The "exception present" flag in the fsave frame is cleared #
# #
# ALGORITHM *********************************************************** #
# On the 060, if an FP overflow is present as the result of any #
# instruction, the 060 will take an overflow exception whether the #
# exception is enabled or disabled in the FPCR. For the disabled case, #
# This handler emulates the instruction to determine what the correct #
# default result should be for the operation. This default result is #
# then stored in either the FP regfile, data regfile, or memory. #
# Finally, the handler exits through the "callout" _fpsp_done() #
# denoting that no exceptional conditions exist within the machine. #
# If the exception is enabled, then this handler must create the #
# exceptional operand and plave it in the fsave state frame, and store #
# the default result (only if the instruction is opclass 3). For #
# exceptions enabled, this handler must exit through the "callout" #
# _real_ovfl() so that the operating system enabled overflow handler #
# can handle this case. #
# Two other conditions exist. First, if overflow was disabled #
# but the inexact exception was enabled, this handler must exit #
# through the "callout" _real_inex() regardless of whether the result #
# was inexact. #
# Also, in the case of an opclass three instruction where #
# overflow was disabled and the trace exception was enabled, this #
# handler must exit through the "callout" _real_trace(). #
# #
#########################################################################
global _fpsp_ovfl
_fpsp_ovfl:
#$# sub.l &24,%sp # make room for src/dst
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
##############################################################################
btst &0x5,EXC_CMDREG(%a6) # is instr an fmove out?
bne.w fovfl_out
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
# since, I believe, only NORMs and DENORMs can come through here,
# maybe we can avoid the subroutine call.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # maybe NORM,DENORM
# bit five of the fp extension word separates the monadic and dyadic operations
# that can pass through fpsp_ovfl(). remember that fcmp, ftst, and fsincos
# will never take this exception.
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b fovfl_extract # monadic
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fovfl_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fovfl_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
fovfl_extract:
#$# mov.l FP_SRC_EX(%a6),TRAP_SRCOP_EX(%a6)
#$# mov.l FP_SRC_HI(%a6),TRAP_SRCOP_HI(%a6)
#$# mov.l FP_SRC_LO(%a6),TRAP_SRCOP_LO(%a6)
#$# mov.l FP_DST_EX(%a6),TRAP_DSTOP_EX(%a6)
#$# mov.l FP_DST_HI(%a6),TRAP_DSTOP_HI(%a6)
#$# mov.l FP_DST_LO(%a6),TRAP_DSTOP_LO(%a6)
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec/mode
mov.b 1+EXC_CMDREG(%a6),%d1
andi.w &0x007f,%d1 # extract extension
andi.l &0x00ff01ff,USER_FPSR(%a6) # zero all but accured field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
# maybe we can make these entry points ONLY the OVFL entry points of each routine.
mov.l (tbl_unsupp.l,%pc,%d1.w*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
# the operation has been emulated. the result is in fp0.
# the EXOP, if an exception occurred, is in fp1.
# we must save the default result regardless of whether
# traps are enabled or disabled.
bfextu EXC_CMDREG(%a6){&6:&3},%d0
bsr.l store_fpreg
# the exceptional possibilities we have left ourselves with are ONLY overflow
# and inexact. and, the inexact is such that overflow occurred and was disabled
# but inexact was enabled.
btst &ovfl_bit,FPCR_ENABLE(%a6)
bne.b fovfl_ovfl_on
btst &inex2_bit,FPCR_ENABLE(%a6)
bne.b fovfl_inex_on
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
#$# add.l &24,%sp
bra.l _fpsp_done
# overflow is enabled AND overflow, of course, occurred. so, we have the EXOP
# in fp1. now, simply jump to _real_ovfl()!
fovfl_ovfl_on:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP (fp1) to stack
mov.w &0xe005,2+FP_SRC(%a6) # save exc status
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # do this after fmovm,other f<op>s!
unlk %a6
bra.l _real_ovfl
# overflow occurred but is disabled. meanwhile, inexact is enabled. therefore,
# we must jump to real_inex().
fovfl_inex_on:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP (fp1) to stack
mov.b &0xc4,1+EXC_VOFF(%a6) # vector offset = 0xc4
mov.w &0xe001,2+FP_SRC(%a6) # save exc status
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # do this after fmovm,other f<op>s!
unlk %a6
bra.l _real_inex
########################################################################
fovfl_out:
#$# mov.l FP_SRC_EX(%a6),TRAP_SRCOP_EX(%a6)
#$# mov.l FP_SRC_HI(%a6),TRAP_SRCOP_HI(%a6)
#$# mov.l FP_SRC_LO(%a6),TRAP_SRCOP_LO(%a6)
# the src operand is definitely a NORM(!), so tag it as such
mov.b &NORM,STAG(%a6) # set src optype tag
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec/mode
and.l &0xffff00ff,USER_FPSR(%a6) # zero all but accured field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0 # pass ptr to src operand
bsr.l fout
btst &ovfl_bit,FPCR_ENABLE(%a6)
bne.w fovfl_ovfl_on
btst &inex2_bit,FPCR_ENABLE(%a6)
bne.w fovfl_inex_on
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
#$# add.l &24,%sp
btst &0x7,(%sp) # is trace on?
beq.l _fpsp_done # no
fmov.l %fpiar,0x8(%sp) # "Current PC" is in FPIAR
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x024
bra.l _real_trace
#########################################################################
# XDEF **************************************************************** #
# _fpsp_unfl(): 060FPSP entry point for FP Underflow exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Underflow exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _fpsp_done() - "callout" for 060FPSP exit (all work done!) #
# _real_ovfl() - "callout" for Overflow exception enabled code #
# _real_inex() - "callout" for Inexact exception enabled code #
# _real_trace() - "callout" for Trace exception code #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Unfl exception stack frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# Underflow Exception enabled: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# Underflow Exception disabled: #
# - The system stack is unchanged #
# - The "exception present" flag in the fsave frame is cleared #
# #
# ALGORITHM *********************************************************** #
# On the 060, if an FP underflow is present as the result of any #
# instruction, the 060 will take an underflow exception whether the #
# exception is enabled or disabled in the FPCR. For the disabled case, #
# This handler emulates the instruction to determine what the correct #
# default result should be for the operation. This default result is #
# then stored in either the FP regfile, data regfile, or memory. #
# Finally, the handler exits through the "callout" _fpsp_done() #
# denoting that no exceptional conditions exist within the machine. #
# If the exception is enabled, then this handler must create the #
# exceptional operand and plave it in the fsave state frame, and store #
# the default result (only if the instruction is opclass 3). For #
# exceptions enabled, this handler must exit through the "callout" #
# _real_unfl() so that the operating system enabled overflow handler #
# can handle this case. #
# Two other conditions exist. First, if underflow was disabled #
# but the inexact exception was enabled and the result was inexact, #
# this handler must exit through the "callout" _real_inex(). #
# was inexact. #
# Also, in the case of an opclass three instruction where #
# underflow was disabled and the trace exception was enabled, this #
# handler must exit through the "callout" _real_trace(). #
# #
#########################################################################
global _fpsp_unfl
_fpsp_unfl:
#$# sub.l &24,%sp # make room for src/dst
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
##############################################################################
btst &0x5,EXC_CMDREG(%a6) # is instr an fmove out?
bne.w funfl_out
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # maybe NORM,DENORM
# bit five of the fp ext word separates the monadic and dyadic operations
# that can pass through fpsp_unfl(). remember that fcmp, and ftst
# will never take this exception.
btst &0x5,1+EXC_CMDREG(%a6) # is op monadic or dyadic?
beq.b funfl_extract # monadic
# now, what's left that's not dyadic is fsincos. we can distinguish it
# from all dyadics by the '0110xxx pattern
btst &0x4,1+EXC_CMDREG(%a6) # is op an fsincos?
bne.b funfl_extract # yes
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b funfl_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
funfl_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
funfl_extract:
#$# mov.l FP_SRC_EX(%a6),TRAP_SRCOP_EX(%a6)
#$# mov.l FP_SRC_HI(%a6),TRAP_SRCOP_HI(%a6)
#$# mov.l FP_SRC_LO(%a6),TRAP_SRCOP_LO(%a6)
#$# mov.l FP_DST_EX(%a6),TRAP_DSTOP_EX(%a6)
#$# mov.l FP_DST_HI(%a6),TRAP_DSTOP_HI(%a6)
#$# mov.l FP_DST_LO(%a6),TRAP_DSTOP_LO(%a6)
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec/mode
mov.b 1+EXC_CMDREG(%a6),%d1
andi.w &0x007f,%d1 # extract extension
andi.l &0x00ff01ff,USER_FPSR(%a6)
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
# maybe we can make these entry points ONLY the OVFL entry points of each routine.
mov.l (tbl_unsupp.l,%pc,%d1.w*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
bfextu EXC_CMDREG(%a6){&6:&3},%d0
bsr.l store_fpreg
# The `060 FPU multiplier hardware is such that if the result of a
# multiply operation is the smallest possible normalized number
# (0x00000000_80000000_00000000), then the machine will take an
# underflow exception. Since this is incorrect, we need to check
# if our emulation, after re-doing the operation, decided that
# no underflow was called for. We do these checks only in
# funfl_{unfl,inex}_on() because w/ both exceptions disabled, this
# special case will simply exit gracefully with the correct result.
# the exceptional possibilities we have left ourselves with are ONLY overflow
# and inexact. and, the inexact is such that overflow occurred and was disabled
# but inexact was enabled.
btst &unfl_bit,FPCR_ENABLE(%a6)
bne.b funfl_unfl_on
funfl_chkinex:
btst &inex2_bit,FPCR_ENABLE(%a6)
bne.b funfl_inex_on
funfl_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
#$# add.l &24,%sp
bra.l _fpsp_done
# overflow is enabled AND overflow, of course, occurred. so, we have the EXOP
# in fp1 (don't forget to save fp0). what to do now?
# well, we simply have to get to go to _real_unfl()!
funfl_unfl_on:
# The `060 FPU multiplier hardware is such that if the result of a
# multiply operation is the smallest possible normalized number
# (0x00000000_80000000_00000000), then the machine will take an
# underflow exception. Since this is incorrect, we check here to see
# if our emulation, after re-doing the operation, decided that
# no underflow was called for.
btst &unfl_bit,FPSR_EXCEPT(%a6)
beq.w funfl_chkinex
funfl_unfl_on2:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP (fp1) to stack
mov.w &0xe003,2+FP_SRC(%a6) # save exc status
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # do this after fmovm,other f<op>s!
unlk %a6
bra.l _real_unfl
# undeflow occurred but is disabled. meanwhile, inexact is enabled. therefore,
# we must jump to real_inex().
funfl_inex_on:
# The `060 FPU multiplier hardware is such that if the result of a
# multiply operation is the smallest possible normalized number
# (0x00000000_80000000_00000000), then the machine will take an
# underflow exception.
# But, whether bogus or not, if inexact is enabled AND it occurred,
# then we have to branch to real_inex.
btst &inex2_bit,FPSR_EXCEPT(%a6)
beq.w funfl_exit
funfl_inex_on2:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to stack
mov.b &0xc4,1+EXC_VOFF(%a6) # vector offset = 0xc4
mov.w &0xe001,2+FP_SRC(%a6) # save exc status
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # do this after fmovm,other f<op>s!
unlk %a6
bra.l _real_inex
#######################################################################
funfl_out:
#$# mov.l FP_SRC_EX(%a6),TRAP_SRCOP_EX(%a6)
#$# mov.l FP_SRC_HI(%a6),TRAP_SRCOP_HI(%a6)
#$# mov.l FP_SRC_LO(%a6),TRAP_SRCOP_LO(%a6)
# the src operand is definitely a NORM(!), so tag it as such
mov.b &NORM,STAG(%a6) # set src optype tag
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec/mode
and.l &0xffff00ff,USER_FPSR(%a6) # zero all but accured field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0 # pass ptr to src operand
bsr.l fout
btst &unfl_bit,FPCR_ENABLE(%a6)
bne.w funfl_unfl_on2
btst &inex2_bit,FPCR_ENABLE(%a6)
bne.w funfl_inex_on2
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
#$# add.l &24,%sp
btst &0x7,(%sp) # is trace on?
beq.l _fpsp_done # no
fmov.l %fpiar,0x8(%sp) # "Current PC" is in FPIAR
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x024
bra.l _real_trace
#########################################################################
# XDEF **************************************************************** #
# _fpsp_unsupp(): 060FPSP entry point for FP "Unimplemented #
# Data Type" exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Unimplemented Data Type exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_{word,long}() - read instruction word/longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# load_fpn1() - load src operand from FP regfile #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _real_inex() - "callout" to operating system inexact handler #
# _fpsp_done() - "callout" for exit; work all done #
# _real_trace() - "callout" for Trace enabled exception #
# funimp_skew() - adjust fsave src ops to "incorrect" value #
# _real_snan() - "callout" for SNAN exception #
# _real_operr() - "callout" for OPERR exception #
# _real_ovfl() - "callout" for OVFL exception #
# _real_unfl() - "callout" for UNFL exception #
# get_packed() - fetch packed operand from memory #
# #
# INPUT *************************************************************** #
# - The system stack contains the "Unimp Data Type" stk frame #
# - The fsave frame contains the ssrc op (for UNNORM/DENORM) #
# #
# OUTPUT ************************************************************** #
# If Inexact exception (opclass 3): #
# - The system stack is changed to an Inexact exception stk frame #
# If SNAN exception (opclass 3): #
# - The system stack is changed to an SNAN exception stk frame #
# If OPERR exception (opclass 3): #
# - The system stack is changed to an OPERR exception stk frame #
# If OVFL exception (opclass 3): #
# - The system stack is changed to an OVFL exception stk frame #
# If UNFL exception (opclass 3): #
# - The system stack is changed to an UNFL exception stack frame #
# If Trace exception enabled: #
# - The system stack is changed to a Trace exception stack frame #
# Else: (normal case) #
# - Correct result has been stored as appropriate #
# #
# ALGORITHM *********************************************************** #
# Two main instruction types can enter here: (1) DENORM or UNNORM #
# unimplemented data types. These can be either opclass 0,2 or 3 #
# instructions, and (2) PACKED unimplemented data format instructions #
# also of opclasses 0,2, or 3. #
# For UNNORM/DENORM opclass 0 and 2, the handler fetches the src #
# operand from the fsave state frame and the dst operand (if dyadic) #
# from the FP register file. The instruction is then emulated by #
# choosing an emulation routine from a table of routines indexed by #
# instruction type. Once the instruction has been emulated and result #
# saved, then we check to see if any enabled exceptions resulted from #
# instruction emulation. If none, then we exit through the "callout" #
# _fpsp_done(). If there is an enabled FP exception, then we insert #
# this exception into the FPU in the fsave state frame and then exit #
# through _fpsp_done(). #
# PACKED opclass 0 and 2 is similar in how the instruction is #
# emulated and exceptions handled. The differences occur in how the #
# handler loads the packed op (by calling get_packed() routine) and #
# by the fact that a Trace exception could be pending for PACKED ops. #
# If a Trace exception is pending, then the current exception stack #
# frame is changed to a Trace exception stack frame and an exit is #
# made through _real_trace(). #
# For UNNORM/DENORM opclass 3, the actual move out to memory is #
# performed by calling the routine fout(). If no exception should occur #
# as the result of emulation, then an exit either occurs through #
# _fpsp_done() or through _real_trace() if a Trace exception is pending #
# (a Trace stack frame must be created here, too). If an FP exception #
# should occur, then we must create an exception stack frame of that #
# type and jump to either _real_snan(), _real_operr(), _real_inex(), #
# _real_unfl(), or _real_ovfl() as appropriate. PACKED opclass 3 #
# emulation is performed in a similar manner. #
# #
#########################################################################
#
# (1) DENORM and UNNORM (unimplemented) data types:
#
# post-instruction
# *****************
# * EA *
# pre-instruction * *
# ***************** *****************
# * 0x0 * 0x0dc * * 0x3 * 0x0dc *
# ***************** *****************
# * Next * * Next *
# * PC * * PC *
# ***************** *****************
# * SR * * SR *
# ***************** *****************
#
# (2) PACKED format (unsupported) opclasses two and three:
# *****************
# * EA *
# * *
# *****************
# * 0x2 * 0x0dc *
# *****************
# * Next *
# * PC *
# *****************
# * SR *
# *****************
#
global _fpsp_unsupp
_fpsp_unsupp:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # save fp state
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
btst &0x5,EXC_SR(%a6) # user or supervisor mode?
bne.b fu_s
fu_u:
mov.l %usp,%a0 # fetch user stack pointer
mov.l %a0,EXC_A7(%a6) # save on stack
bra.b fu_cont
# if the exception is an opclass zero or two unimplemented data type
# exception, then the a7' calculated here is wrong since it doesn't
# stack an ea. however, we don't need an a7' for this case anyways.
fu_s:
lea 0x4+EXC_EA(%a6),%a0 # load old a7'
mov.l %a0,EXC_A7(%a6) # save on stack
fu_cont:
# the FPIAR holds the "current PC" of the faulting instruction
# the FPIAR should be set correctly for ALL exceptions passing through
# this point.
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6) # store OPWORD and EXTWORD
############################
clr.b SPCOND_FLG(%a6) # clear special condition flag
# Separate opclass three (fpn-to-mem) ops since they have a different
# stack frame and protocol.
btst &0x5,EXC_CMDREG(%a6) # is it an fmove out?
bne.w fu_out # yes
# Separate packed opclass two instructions.
bfextu EXC_CMDREG(%a6){&0:&6},%d0
cmpi.b %d0,&0x13
beq.w fu_in_pack
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field
andi.l &0x00ff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
# Opclass two w/ memory-to-fpn operation will have an incorrect extended
# precision format if the src format was single or double and the
# source data type was an INF, NAN, DENORM, or UNNORM
lea FP_SRC(%a6),%a0 # pass ptr to input
bsr.l fix_skewed_ops
# we don't know whether the src operand or the dst operand (or both) is the
# UNNORM or DENORM. call the function that tags the operand type. if the
# input is an UNNORM, then convert it to a NORM, DENORM, or ZERO.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2 # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2:
mov.b %d0,STAG(%a6) # save src optype tag
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
# bit five of the fp extension word separates the monadic and dyadic operations
# at this point
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b fu_extract # monadic
cmpi.b 1+EXC_CMDREG(%a6),&0x3a # is operation an ftst?
beq.b fu_extract # yes, so it's monadic, too
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
fu_extract:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # fetch rnd mode/prec
bfextu 1+EXC_CMDREG(%a6){&1:&7},%d1 # extract extension
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
mov.l (tbl_unsupp.l,%pc,%d1.l*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
#
# Exceptions in order of precedence:
# BSUN : none
# SNAN : all dyadic ops
# OPERR : fsqrt(-NORM)
# OVFL : all except ftst,fcmp
# UNFL : all except ftst,fcmp
# DZ : fdiv
# INEX2 : all except ftst,fcmp
# INEX1 : none (packed doesn't go through here)
#
# we determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions set
bne.b fu_in_ena # some are enabled
fu_in_cont:
# fcmp and ftst do not store any result.
mov.b 1+EXC_CMDREG(%a6),%d0 # fetch extension
andi.b &0x38,%d0 # extract bits 3-5
cmpi.b %d0,&0x38 # is instr fcmp or ftst?
beq.b fu_in_exit # yes
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l store_fpreg # store the result
fu_in_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
bra.l _fpsp_done
fu_in_ena:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b fu_in_exc # there is at least one set
#
# No exceptions occurred that were also enabled. Now:
#
# if (OVFL && ovfl_disabled && inexact_enabled) {
# branch to _real_inex() (even if the result was exact!);
# } else {
# save the result in the proper fp reg (unless the op is fcmp or ftst);
# return;
# }
#
btst &ovfl_bit,FPSR_EXCEPT(%a6) # was overflow set?
beq.b fu_in_cont # no
fu_in_ovflchk:
btst &inex2_bit,FPCR_ENABLE(%a6) # was inexact enabled?
beq.b fu_in_cont # no
bra.w fu_in_exc_ovfl # go insert overflow frame
#
# An exception occurred and that exception was enabled:
#
# shift enabled exception field into lo byte of d0;
# if (((INEX2 || INEX1) && inex_enabled && OVFL && ovfl_disabled) ||
# ((INEX2 || INEX1) && inex_enabled && UNFL && unfl_disabled)) {
# /*
# * this is the case where we must call _real_inex() now or else
# * there will be no other way to pass it the exceptional operand
# */
# call _real_inex();
# } else {
# restore exc state (SNAN||OPERR||OVFL||UNFL||DZ||INEX) into the FPU;
# }
#
fu_in_exc:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX? (6)
bne.b fu_in_exc_exit # no
# the enabled exception was inexact
btst &unfl_bit,FPSR_EXCEPT(%a6) # did disabled underflow occur?
bne.w fu_in_exc_unfl # yes
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did disabled overflow occur?
bne.w fu_in_exc_ovfl # yes
# here, we insert the correct fsave status value into the fsave frame for the
# corresponding exception. the operand in the fsave frame should be the original
# src operand.
fu_in_exc_exit:
mov.l %d0,-(%sp) # save d0
bsr.l funimp_skew # skew sgl or dbl inputs
mov.l (%sp)+,%d0 # restore d0
mov.w (tbl_except.b,%pc,%d0.w*2),2+FP_SRC(%a6) # create exc status
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # restore src op
unlk %a6
bra.l _fpsp_done
tbl_except:
short 0xe000,0xe006,0xe004,0xe005
short 0xe003,0xe002,0xe001,0xe001
fu_in_exc_unfl:
mov.w &0x4,%d0
bra.b fu_in_exc_exit
fu_in_exc_ovfl:
mov.w &0x03,%d0
bra.b fu_in_exc_exit
# If the input operand to this operation was opclass two and a single
# or double precision denorm, inf, or nan, the operand needs to be
# "corrected" in order to have the proper equivalent extended precision
# number.
global fix_skewed_ops
fix_skewed_ops:
bfextu EXC_CMDREG(%a6){&0:&6},%d0 # extract opclass,src fmt
cmpi.b %d0,&0x11 # is class = 2 & fmt = sgl?
beq.b fso_sgl # yes
cmpi.b %d0,&0x15 # is class = 2 & fmt = dbl?
beq.b fso_dbl # yes
rts # no
fso_sgl:
mov.w LOCAL_EX(%a0),%d0 # fetch src exponent
andi.w &0x7fff,%d0 # strip sign
cmpi.w %d0,&0x3f80 # is |exp| == $3f80?
beq.b fso_sgl_dnrm_zero # yes
cmpi.w %d0,&0x407f # no; is |exp| == $407f?
beq.b fso_infnan # yes
rts # no
fso_sgl_dnrm_zero:
andi.l &0x7fffffff,LOCAL_HI(%a0) # clear j-bit
beq.b fso_zero # it's a skewed zero
fso_sgl_dnrm:
# here, we count on norm not to alter a0...
bsr.l norm # normalize mantissa
neg.w %d0 # -shft amt
addi.w &0x3f81,%d0 # adjust new exponent
andi.w &0x8000,LOCAL_EX(%a0) # clear old exponent
or.w %d0,LOCAL_EX(%a0) # insert new exponent
rts
fso_zero:
andi.w &0x8000,LOCAL_EX(%a0) # clear bogus exponent
rts
fso_infnan:
andi.b &0x7f,LOCAL_HI(%a0) # clear j-bit
ori.w &0x7fff,LOCAL_EX(%a0) # make exponent = $7fff
rts
fso_dbl:
mov.w LOCAL_EX(%a0),%d0 # fetch src exponent
andi.w &0x7fff,%d0 # strip sign
cmpi.w %d0,&0x3c00 # is |exp| == $3c00?
beq.b fso_dbl_dnrm_zero # yes
cmpi.w %d0,&0x43ff # no; is |exp| == $43ff?
beq.b fso_infnan # yes
rts # no
fso_dbl_dnrm_zero:
andi.l &0x7fffffff,LOCAL_HI(%a0) # clear j-bit
bne.b fso_dbl_dnrm # it's a skewed denorm
tst.l LOCAL_LO(%a0) # is it a zero?
beq.b fso_zero # yes
fso_dbl_dnrm:
# here, we count on norm not to alter a0...
bsr.l norm # normalize mantissa
neg.w %d0 # -shft amt
addi.w &0x3c01,%d0 # adjust new exponent
andi.w &0x8000,LOCAL_EX(%a0) # clear old exponent
or.w %d0,LOCAL_EX(%a0) # insert new exponent
rts
#################################################################
# fmove out took an unimplemented data type exception.
# the src operand is in FP_SRC. Call _fout() to write out the result and
# to determine which exceptions, if any, to take.
fu_out:
# Separate packed move outs from the UNNORM and DENORM move outs.
bfextu EXC_CMDREG(%a6){&3:&3},%d0
cmpi.b %d0,&0x3
beq.w fu_out_pack
cmpi.b %d0,&0x7
beq.w fu_out_pack
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field.
# fmove out doesn't affect ccodes.
and.l &0xffff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
# the src can ONLY be a DENORM or an UNNORM! so, don't make any big subroutine
# call here. just figure out what it is...
mov.w FP_SRC_EX(%a6),%d0 # get exponent
andi.w &0x7fff,%d0 # strip sign
beq.b fu_out_denorm # it's a DENORM
lea FP_SRC(%a6),%a0
bsr.l unnorm_fix # yes; fix it
mov.b %d0,STAG(%a6)
bra.b fu_out_cont
fu_out_denorm:
mov.b &DENORM,STAG(%a6)
fu_out_cont:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # fetch rnd mode/prec
lea FP_SRC(%a6),%a0 # pass ptr to src operand
mov.l (%a6),EXC_A6(%a6) # in case a6 changes
bsr.l fout # call fmove out routine
# Exceptions in order of precedence:
# BSUN : none
# SNAN : none
# OPERR : fmove.{b,w,l} out of large UNNORM
# OVFL : fmove.{s,d}
# UNFL : fmove.{s,d,x}
# DZ : none
# INEX2 : all
# INEX1 : none (packed doesn't travel through here)
# determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w fu_out_ena # some are enabled
fu_out_done:
mov.l EXC_A6(%a6),(%a6) # in case a6 changed
# on extended precision opclass three instructions using pre-decrement or
# post-increment addressing mode, the address register is not updated. is the
# address register was the stack pointer used from user mode, then let's update
# it here. if it was used from supervisor mode, then we have to handle this
# as a special case.
btst &0x5,EXC_SR(%a6)
bne.b fu_out_done_s
mov.l EXC_A7(%a6),%a0 # restore a7
mov.l %a0,%usp
fu_out_done_cont:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
btst &0x7,(%sp) # is trace on?
bne.b fu_out_trace # yes
bra.l _fpsp_done
# is the ea mode pre-decrement of the stack pointer from supervisor mode?
# ("fmov.x fpm,-(a7)") if so,
fu_out_done_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg
bne.b fu_out_done_cont
# the extended precision result is still in fp0. but, we need to save it
# somewhere on the stack until we can copy it to its final resting place.
# here, we're counting on the top of the stack to be the old place-holders
# for fp0/fp1 which have already been restored. that way, we can write
# over those destinations with the shifted stack frame.
fmovm.x &0x80,FP_SRC(%a6) # put answer on stack
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.l (%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+2+EXC_PC(%sp),LOCAL_SIZE+2+EXC_PC-0xc(%sp)
# now, copy the result to the proper place on the stack
mov.l LOCAL_SIZE+FP_SRC_EX(%sp),LOCAL_SIZE+EXC_SR+0x0(%sp)
mov.l LOCAL_SIZE+FP_SRC_HI(%sp),LOCAL_SIZE+EXC_SR+0x4(%sp)
mov.l LOCAL_SIZE+FP_SRC_LO(%sp),LOCAL_SIZE+EXC_SR+0x8(%sp)
add.l &LOCAL_SIZE-0x8,%sp
btst &0x7,(%sp)
bne.b fu_out_trace
bra.l _fpsp_done
fu_out_ena:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b fu_out_exc # there is at least one set
# no exceptions were set.
# if a disabled overflow occurred and inexact was enabled but the result
# was exact, then a branch to _real_inex() is made.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # was overflow set?
beq.w fu_out_done # no
fu_out_ovflchk:
btst &inex2_bit,FPCR_ENABLE(%a6) # was inexact enabled?
beq.w fu_out_done # no
bra.w fu_inex # yes
#
# The fp move out that took the "Unimplemented Data Type" exception was
# being traced. Since the stack frames are similar, get the "current" PC
# from FPIAR and put it in the trace stack frame then jump to _real_trace().
#
# UNSUPP FRAME TRACE FRAME
# ***************** *****************
# * EA * * Current *
# * * * PC *
# ***************** *****************
# * 0x3 * 0x0dc * * 0x2 * 0x024 *
# ***************** *****************
# * Next * * Next *
# * PC * * PC *
# ***************** *****************
# * SR * * SR *
# ***************** *****************
#
fu_out_trace:
mov.w &0x2024,0x6(%sp)
fmov.l %fpiar,0x8(%sp)
bra.l _real_trace
# an exception occurred and that exception was enabled.
fu_out_exc:
subi.l &24,%d0 # fix offset to be 0-8
# we don't mess with the existing fsave frame. just re-insert it and
# jump to the "_real_{}()" handler...
mov.w (tbl_fu_out.b,%pc,%d0.w*2),%d0
jmp (tbl_fu_out.b,%pc,%d0.w*1)
swbeg &0x8
tbl_fu_out:
short tbl_fu_out - tbl_fu_out # BSUN can't happen
short tbl_fu_out - tbl_fu_out # SNAN can't happen
short fu_operr - tbl_fu_out # OPERR
short fu_ovfl - tbl_fu_out # OVFL
short fu_unfl - tbl_fu_out # UNFL
short tbl_fu_out - tbl_fu_out # DZ can't happen
short fu_inex - tbl_fu_out # INEX2
short tbl_fu_out - tbl_fu_out # INEX1 won't make it here
# for snan,operr,ovfl,unfl, src op is still in FP_SRC so just
# frestore it.
fu_snan:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d8,EXC_VOFF(%a6) # vector offset = 0xd8
mov.w &0xe006,2+FP_SRC(%a6)
frestore FP_SRC(%a6)
unlk %a6
bra.l _real_snan
fu_operr:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d0,EXC_VOFF(%a6) # vector offset = 0xd0
mov.w &0xe004,2+FP_SRC(%a6)
frestore FP_SRC(%a6)
unlk %a6
bra.l _real_operr
fu_ovfl:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to the stack
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d4,EXC_VOFF(%a6) # vector offset = 0xd4
mov.w &0xe005,2+FP_SRC(%a6)
frestore FP_SRC(%a6) # restore EXOP
unlk %a6
bra.l _real_ovfl
# underflow can happen for extended precision. extended precision opclass
# three instruction exceptions don't update the stack pointer. so, if the
# exception occurred from user mode, then simply update a7 and exit normally.
# if the exception occurred from supervisor mode, check if
fu_unfl:
mov.l EXC_A6(%a6),(%a6) # restore a6
btst &0x5,EXC_SR(%a6)
bne.w fu_unfl_s
mov.l EXC_A7(%a6),%a0 # restore a7 whether we need
mov.l %a0,%usp # to or not...
fu_unfl_cont:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to the stack
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30cc,EXC_VOFF(%a6) # vector offset = 0xcc
mov.w &0xe003,2+FP_SRC(%a6)
frestore FP_SRC(%a6) # restore EXOP
unlk %a6
bra.l _real_unfl
fu_unfl_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg # was the <ea> mode -(sp)?
bne.b fu_unfl_cont
# the extended precision result is still in fp0. but, we need to save it
# somewhere on the stack until we can copy it to its final resting place
# (where the exc frame is currently). make sure it's not at the top of the
# frame or it will get overwritten when the exc stack frame is shifted "down".
fmovm.x &0x80,FP_SRC(%a6) # put answer on stack
fmovm.x &0x40,FP_DST(%a6) # put EXOP on stack
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30cc,EXC_VOFF(%a6) # vector offset = 0xcc
mov.w &0xe003,2+FP_DST(%a6)
frestore FP_DST(%a6) # restore EXOP
mov.l (%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+2+EXC_PC(%sp),LOCAL_SIZE+2+EXC_PC-0xc(%sp)
mov.l LOCAL_SIZE+EXC_EA(%sp),LOCAL_SIZE+EXC_EA-0xc(%sp)
# now, copy the result to the proper place on the stack
mov.l LOCAL_SIZE+FP_SRC_EX(%sp),LOCAL_SIZE+EXC_SR+0x0(%sp)
mov.l LOCAL_SIZE+FP_SRC_HI(%sp),LOCAL_SIZE+EXC_SR+0x4(%sp)
mov.l LOCAL_SIZE+FP_SRC_LO(%sp),LOCAL_SIZE+EXC_SR+0x8(%sp)
add.l &LOCAL_SIZE-0x8,%sp
bra.l _real_unfl
# fmove in and out enter here.
fu_inex:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to the stack
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30c4,EXC_VOFF(%a6) # vector offset = 0xc4
mov.w &0xe001,2+FP_SRC(%a6)
frestore FP_SRC(%a6) # restore EXOP
unlk %a6
bra.l _real_inex
#########################################################################
#########################################################################
fu_in_pack:
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field
andi.l &0x0ff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
bsr.l get_packed # fetch packed src operand
lea FP_SRC(%a6),%a0 # pass ptr to src
bsr.l set_tag_x # set src optype tag
mov.b %d0,STAG(%a6) # save src optype tag
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
# bit five of the fp extension word separates the monadic and dyadic operations
# at this point
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b fu_extract_p # monadic
cmpi.b 1+EXC_CMDREG(%a6),&0x3a # is operation an ftst?
beq.b fu_extract_p # yes, so it's monadic, too
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2_done_p # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2_done_p:
mov.b %d0,DTAG(%a6) # save dst optype tag
fu_extract_p:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # fetch rnd mode/prec
bfextu 1+EXC_CMDREG(%a6){&1:&7},%d1 # extract extension
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
mov.l (tbl_unsupp.l,%pc,%d1.l*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
#
# Exceptions in order of precedence:
# BSUN : none
# SNAN : all dyadic ops
# OPERR : fsqrt(-NORM)
# OVFL : all except ftst,fcmp
# UNFL : all except ftst,fcmp
# DZ : fdiv
# INEX2 : all except ftst,fcmp
# INEX1 : all
#
# we determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w fu_in_ena_p # some are enabled
fu_in_cont_p:
# fcmp and ftst do not store any result.
mov.b 1+EXC_CMDREG(%a6),%d0 # fetch extension
andi.b &0x38,%d0 # extract bits 3-5
cmpi.b %d0,&0x38 # is instr fcmp or ftst?
beq.b fu_in_exit_p # yes
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l store_fpreg # store the result
fu_in_exit_p:
btst &0x5,EXC_SR(%a6) # user or supervisor?
bne.w fu_in_exit_s_p # supervisor
mov.l EXC_A7(%a6),%a0 # update user a7
mov.l %a0,%usp
fu_in_exit_cont_p:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6 # unravel stack frame
btst &0x7,(%sp) # is trace on?
bne.w fu_trace_p # yes
bra.l _fpsp_done # exit to os
# the exception occurred in supervisor mode. check to see if the
# addressing mode was (a7)+. if so, we'll need to shift the
# stack frame "up".
fu_in_exit_s_p:
btst &mia7_bit,SPCOND_FLG(%a6) # was ea mode (a7)+
beq.b fu_in_exit_cont_p # no
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6 # unravel stack frame
# shift the stack frame "up". we don't really care about the <ea> field.
mov.l 0x4(%sp),0x10(%sp)
mov.l 0x0(%sp),0xc(%sp)
add.l &0xc,%sp
btst &0x7,(%sp) # is trace on?
bne.w fu_trace_p # yes
bra.l _fpsp_done # exit to os
fu_in_ena_p:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled & set
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b fu_in_exc_p # at least one was set
#
# No exceptions occurred that were also enabled. Now:
#
# if (OVFL && ovfl_disabled && inexact_enabled) {
# branch to _real_inex() (even if the result was exact!);
# } else {
# save the result in the proper fp reg (unless the op is fcmp or ftst);
# return;
# }
#
btst &ovfl_bit,FPSR_EXCEPT(%a6) # was overflow set?
beq.w fu_in_cont_p # no
fu_in_ovflchk_p:
btst &inex2_bit,FPCR_ENABLE(%a6) # was inexact enabled?
beq.w fu_in_cont_p # no
bra.w fu_in_exc_ovfl_p # do _real_inex() now
#
# An exception occurred and that exception was enabled:
#
# shift enabled exception field into lo byte of d0;
# if (((INEX2 || INEX1) && inex_enabled && OVFL && ovfl_disabled) ||
# ((INEX2 || INEX1) && inex_enabled && UNFL && unfl_disabled)) {
# /*
# * this is the case where we must call _real_inex() now or else
# * there will be no other way to pass it the exceptional operand
# */
# call _real_inex();
# } else {
# restore exc state (SNAN||OPERR||OVFL||UNFL||DZ||INEX) into the FPU;
# }
#
fu_in_exc_p:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX? (6 or 7)
blt.b fu_in_exc_exit_p # no
# the enabled exception was inexact
btst &unfl_bit,FPSR_EXCEPT(%a6) # did disabled underflow occur?
bne.w fu_in_exc_unfl_p # yes
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did disabled overflow occur?
bne.w fu_in_exc_ovfl_p # yes
# here, we insert the correct fsave status value into the fsave frame for the
# corresponding exception. the operand in the fsave frame should be the original
# src operand.
# as a reminder for future predicted pain and agony, we are passing in fsave the
# "non-skewed" operand for cases of sgl and dbl src INFs,NANs, and DENORMs.
# this is INCORRECT for enabled SNAN which would give to the user the skewed SNAN!!!
fu_in_exc_exit_p:
btst &0x5,EXC_SR(%a6) # user or supervisor?
bne.w fu_in_exc_exit_s_p # supervisor
mov.l EXC_A7(%a6),%a0 # update user a7
mov.l %a0,%usp
fu_in_exc_exit_cont_p:
mov.w (tbl_except_p.b,%pc,%d0.w*2),2+FP_SRC(%a6)
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # restore src op
unlk %a6
btst &0x7,(%sp) # is trace enabled?
bne.w fu_trace_p # yes
bra.l _fpsp_done
tbl_except_p:
short 0xe000,0xe006,0xe004,0xe005
short 0xe003,0xe002,0xe001,0xe001
fu_in_exc_ovfl_p:
mov.w &0x3,%d0
bra.w fu_in_exc_exit_p
fu_in_exc_unfl_p:
mov.w &0x4,%d0
bra.w fu_in_exc_exit_p
fu_in_exc_exit_s_p:
btst &mia7_bit,SPCOND_FLG(%a6)
beq.b fu_in_exc_exit_cont_p
mov.w (tbl_except_p.b,%pc,%d0.w*2),2+FP_SRC(%a6)
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # restore src op
unlk %a6 # unravel stack frame
# shift stack frame "up". who cares about <ea> field.
mov.l 0x4(%sp),0x10(%sp)
mov.l 0x0(%sp),0xc(%sp)
add.l &0xc,%sp
btst &0x7,(%sp) # is trace on?
bne.b fu_trace_p # yes
bra.l _fpsp_done # exit to os
#
# The opclass two PACKED instruction that took an "Unimplemented Data Type"
# exception was being traced. Make the "current" PC the FPIAR and put it in the
# trace stack frame then jump to _real_trace().
#
# UNSUPP FRAME TRACE FRAME
# ***************** *****************
# * EA * * Current *
# * * * PC *
# ***************** *****************
# * 0x2 * 0x0dc * * 0x2 * 0x024 *
# ***************** *****************
# * Next * * Next *
# * PC * * PC *
# ***************** *****************
# * SR * * SR *
# ***************** *****************
fu_trace_p:
mov.w &0x2024,0x6(%sp)
fmov.l %fpiar,0x8(%sp)
bra.l _real_trace
#########################################################
#########################################################
fu_out_pack:
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field.
# fmove out doesn't affect ccodes.
and.l &0xffff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
bfextu EXC_CMDREG(%a6){&6:&3},%d0
bsr.l load_fpn1
# unlike other opclass 3, unimplemented data type exceptions, packed must be
# able to detect all operand types.
lea FP_SRC(%a6),%a0
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2_p # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2_p:
mov.b %d0,STAG(%a6) # save src optype tag
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # fetch rnd mode/prec
lea FP_SRC(%a6),%a0 # pass ptr to src operand
mov.l (%a6),EXC_A6(%a6) # in case a6 changes
bsr.l fout # call fmove out routine
# Exceptions in order of precedence:
# BSUN : no
# SNAN : yes
# OPERR : if ((k_factor > +17) || (dec. exp exceeds 3 digits))
# OVFL : no
# UNFL : no
# DZ : no
# INEX2 : yes
# INEX1 : no
# determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w fu_out_ena_p # some are enabled
fu_out_exit_p:
mov.l EXC_A6(%a6),(%a6) # restore a6
btst &0x5,EXC_SR(%a6) # user or supervisor?
bne.b fu_out_exit_s_p # supervisor
mov.l EXC_A7(%a6),%a0 # update user a7
mov.l %a0,%usp
fu_out_exit_cont_p:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6 # unravel stack frame
btst &0x7,(%sp) # is trace on?
bne.w fu_trace_p # yes
bra.l _fpsp_done # exit to os
# the exception occurred in supervisor mode. check to see if the
# addressing mode was -(a7). if so, we'll need to shift the
# stack frame "down".
fu_out_exit_s_p:
btst &mda7_bit,SPCOND_FLG(%a6) # was ea mode -(a7)
beq.b fu_out_exit_cont_p # no
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.l (%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+2+EXC_PC(%sp),LOCAL_SIZE+2+EXC_PC-0xc(%sp)
# now, copy the result to the proper place on the stack
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+EXC_SR+0x0(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+EXC_SR+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+EXC_SR+0x8(%sp)
add.l &LOCAL_SIZE-0x8,%sp
btst &0x7,(%sp)
bne.w fu_trace_p
bra.l _fpsp_done
fu_out_ena_p:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled
bfffo %d0{&24:&8},%d0 # find highest priority exception
beq.w fu_out_exit_p
mov.l EXC_A6(%a6),(%a6) # restore a6
# an exception occurred and that exception was enabled.
# the only exception possible on packed move out are INEX, OPERR, and SNAN.
fu_out_exc_p:
cmpi.b %d0,&0x1a
bgt.w fu_inex_p2
beq.w fu_operr_p
fu_snan_p:
btst &0x5,EXC_SR(%a6)
bne.b fu_snan_s_p
mov.l EXC_A7(%a6),%a0
mov.l %a0,%usp
bra.w fu_snan
fu_snan_s_p:
cmpi.b SPCOND_FLG(%a6),&mda7_flg
bne.w fu_snan
# the instruction was "fmove.p fpn,-(a7)" from supervisor mode.
# the strategy is to move the exception frame "down" 12 bytes. then, we
# can store the default result where the exception frame was.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d8,EXC_VOFF(%a6) # vector offset = 0xd0
mov.w &0xe006,2+FP_SRC(%a6) # set fsave status
frestore FP_SRC(%a6) # restore src operand
mov.l (%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+2+EXC_PC(%sp),LOCAL_SIZE+2+EXC_PC-0xc(%sp)
mov.l LOCAL_SIZE+EXC_EA(%sp),LOCAL_SIZE+EXC_EA-0xc(%sp)
# now, we copy the default result to it's proper location
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+0x8(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+0xc(%sp)
add.l &LOCAL_SIZE-0x8,%sp
bra.l _real_snan
fu_operr_p:
btst &0x5,EXC_SR(%a6)
bne.w fu_operr_p_s
mov.l EXC_A7(%a6),%a0
mov.l %a0,%usp
bra.w fu_operr
fu_operr_p_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg
bne.w fu_operr
# the instruction was "fmove.p fpn,-(a7)" from supervisor mode.
# the strategy is to move the exception frame "down" 12 bytes. then, we
# can store the default result where the exception frame was.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d0,EXC_VOFF(%a6) # vector offset = 0xd0
mov.w &0xe004,2+FP_SRC(%a6) # set fsave status
frestore FP_SRC(%a6) # restore src operand
mov.l (%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+2+EXC_PC(%sp),LOCAL_SIZE+2+EXC_PC-0xc(%sp)
mov.l LOCAL_SIZE+EXC_EA(%sp),LOCAL_SIZE+EXC_EA-0xc(%sp)
# now, we copy the default result to it's proper location
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+0x8(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+0xc(%sp)
add.l &LOCAL_SIZE-0x8,%sp
bra.l _real_operr
fu_inex_p2:
btst &0x5,EXC_SR(%a6)
bne.w fu_inex_s_p2
mov.l EXC_A7(%a6),%a0
mov.l %a0,%usp
bra.w fu_inex
fu_inex_s_p2:
cmpi.b SPCOND_FLG(%a6),&mda7_flg
bne.w fu_inex
# the instruction was "fmove.p fpn,-(a7)" from supervisor mode.
# the strategy is to move the exception frame "down" 12 bytes. then, we
# can store the default result where the exception frame was.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30c4,EXC_VOFF(%a6) # vector offset = 0xc4
mov.w &0xe001,2+FP_SRC(%a6) # set fsave status
frestore FP_SRC(%a6) # restore src operand
mov.l (%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+2+EXC_PC(%sp),LOCAL_SIZE+2+EXC_PC-0xc(%sp)
mov.l LOCAL_SIZE+EXC_EA(%sp),LOCAL_SIZE+EXC_EA-0xc(%sp)
# now, we copy the default result to it's proper location
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+0x8(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+0xc(%sp)
add.l &LOCAL_SIZE-0x8,%sp
bra.l _real_inex
#########################################################################
#
# if we're stuffing a source operand back into an fsave frame then we
# have to make sure that for single or double source operands that the
# format stuffed is as weird as the hardware usually makes it.
#
global funimp_skew
funimp_skew:
bfextu EXC_EXTWORD(%a6){&3:&3},%d0 # extract src specifier
cmpi.b %d0,&0x1 # was src sgl?
beq.b funimp_skew_sgl # yes
cmpi.b %d0,&0x5 # was src dbl?
beq.b funimp_skew_dbl # yes
rts
funimp_skew_sgl:
mov.w FP_SRC_EX(%a6),%d0 # fetch DENORM exponent
andi.w &0x7fff,%d0 # strip sign
beq.b funimp_skew_sgl_not
cmpi.w %d0,&0x3f80
bgt.b funimp_skew_sgl_not
neg.w %d0 # make exponent negative
addi.w &0x3f81,%d0 # find amt to shift
mov.l FP_SRC_HI(%a6),%d1 # fetch DENORM hi(man)
lsr.l %d0,%d1 # shift it
bset &31,%d1 # set j-bit
mov.l %d1,FP_SRC_HI(%a6) # insert new hi(man)
andi.w &0x8000,FP_SRC_EX(%a6) # clear old exponent
ori.w &0x3f80,FP_SRC_EX(%a6) # insert new "skewed" exponent
funimp_skew_sgl_not:
rts
funimp_skew_dbl:
mov.w FP_SRC_EX(%a6),%d0 # fetch DENORM exponent
andi.w &0x7fff,%d0 # strip sign
beq.b funimp_skew_dbl_not
cmpi.w %d0,&0x3c00
bgt.b funimp_skew_dbl_not
tst.b FP_SRC_EX(%a6) # make "internal format"
smi.b 0x2+FP_SRC(%a6)
mov.w %d0,FP_SRC_EX(%a6) # insert exponent with cleared sign
clr.l %d0 # clear g,r,s
lea FP_SRC(%a6),%a0 # pass ptr to src op
mov.w &0x3c01,%d1 # pass denorm threshold
bsr.l dnrm_lp # denorm it
mov.w &0x3c00,%d0 # new exponent
tst.b 0x2+FP_SRC(%a6) # is sign set?
beq.b fss_dbl_denorm_done # no
bset &15,%d0 # set sign
fss_dbl_denorm_done:
bset &0x7,FP_SRC_HI(%a6) # set j-bit
mov.w %d0,FP_SRC_EX(%a6) # insert new exponent
funimp_skew_dbl_not:
rts
#########################################################################
global _mem_write2
_mem_write2:
btst &0x5,EXC_SR(%a6)
beq.l _dmem_write
mov.l 0x0(%a0),FP_DST_EX(%a6)
mov.l 0x4(%a0),FP_DST_HI(%a6)
mov.l 0x8(%a0),FP_DST_LO(%a6)
clr.l %d1
rts
#########################################################################
# XDEF **************************************************************** #
# _fpsp_effadd(): 060FPSP entry point for FP "Unimplemented #
# effective address" exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Unimplemented Effective Address exception in an operating #
# system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# decbin() - convert packed data to FP binary data #
# _real_fpu_disabled() - "callout" for "FPU disabled" exception #
# _real_access() - "callout" for access error exception #
# _mem_read() - read extended immediate operand from memory #
# _fpsp_done() - "callout" for exit; work all done #
# _real_trace() - "callout" for Trace enabled exception #
# fmovm_dynamic() - emulate dynamic fmovm instruction #
# fmovm_ctrl() - emulate fmovm control instruction #
# #
# INPUT *************************************************************** #
# - The system stack contains the "Unimplemented <ea>" stk frame #
# #
# OUTPUT ************************************************************** #
# If access error: #
# - The system stack is changed to an access error stack frame #
# If FPU disabled: #
# - The system stack is changed to an FPU disabled stack frame #
# If Trace exception enabled: #
# - The system stack is changed to a Trace exception stack frame #
# Else: (normal case) #
# - None (correct result has been stored as appropriate) #
# #
# ALGORITHM *********************************************************** #
# This exception handles 3 types of operations: #
# (1) FP Instructions using extended precision or packed immediate #
# addressing mode. #
# (2) The "fmovm.x" instruction w/ dynamic register specification. #
# (3) The "fmovm.l" instruction w/ 2 or 3 control registers. #
# #
# For immediate data operations, the data is read in w/ a #
# _mem_read() "callout", converted to FP binary (if packed), and used #
# as the source operand to the instruction specified by the instruction #
# word. If no FP exception should be reported ads a result of the #
# emulation, then the result is stored to the destination register and #
# the handler exits through _fpsp_done(). If an enabled exc has been #
# signalled as a result of emulation, then an fsave state frame #
# corresponding to the FP exception type must be entered into the 060 #
# FPU before exiting. In either the enabled or disabled cases, we #
# must also check if a Trace exception is pending, in which case, we #
# must create a Trace exception stack frame from the current exception #
# stack frame. If no Trace is pending, we simply exit through #
# _fpsp_done(). #
# For "fmovm.x", call the routine fmovm_dynamic() which will #
# decode and emulate the instruction. No FP exceptions can be pending #
# as a result of this operation emulation. A Trace exception can be #
# pending, though, which means the current stack frame must be changed #
# to a Trace stack frame and an exit made through _real_trace(). #
# For the case of "fmovm.x Dn,-(a7)", where the offending instruction #
# was executed from supervisor mode, this handler must store the FP #
# register file values to the system stack by itself since #
# fmovm_dynamic() can't handle this. A normal exit is made through #
# fpsp_done(). #
# For "fmovm.l", fmovm_ctrl() is used to emulate the instruction. #
# Again, a Trace exception may be pending and an exit made through #
# _real_trace(). Else, a normal exit is made through _fpsp_done(). #
# #
# Before any of the above is attempted, it must be checked to #
# see if the FPU is disabled. Since the "Unimp <ea>" exception is taken #
# before the "FPU disabled" exception, but the "FPU disabled" exception #
# has higher priority, we check the disabled bit in the PCR. If set, #
# then we must create an 8 word "FPU disabled" exception stack frame #
# from the current 4 word exception stack frame. This includes #
# reproducing the effective address of the instruction to put on the #
# new stack frame. #
# #
# In the process of all emulation work, if a _mem_read() #
# "callout" returns a failing result indicating an access error, then #
# we must create an access error stack frame from the current stack #
# frame. This information includes a faulting address and a fault- #
# status-longword. These are created within this handler. #
# #
#########################################################################
global _fpsp_effadd
_fpsp_effadd:
# This exception type takes priority over the "Line F Emulator"
# exception. Therefore, the FPU could be disabled when entering here.
# So, we must check to see if it's disabled and handle that case separately.
mov.l %d0,-(%sp) # save d0
movc %pcr,%d0 # load proc cr
btst &0x1,%d0 # is FPU disabled?
bne.w iea_disabled # yes
mov.l (%sp)+,%d0 # restore d0
link %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# PC of instruction that took the exception is the PC in the frame
mov.l EXC_PC(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6) # store OPWORD and EXTWORD
#########################################################################
tst.w %d0 # is operation fmovem?
bmi.w iea_fmovm # yes
#
# here, we will have:
# fabs fdabs fsabs facos fmod
# fadd fdadd fsadd fasin frem
# fcmp fatan fscale
# fdiv fddiv fsdiv fatanh fsin
# fint fcos fsincos
# fintrz fcosh fsinh
# fmove fdmove fsmove fetox ftan
# fmul fdmul fsmul fetoxm1 ftanh
# fneg fdneg fsneg fgetexp ftentox
# fsgldiv fgetman ftwotox
# fsglmul flog10
# fsqrt flog2
# fsub fdsub fssub flogn
# ftst flognp1
# which can all use f<op>.{x,p}
# so, now it's immediate data extended precision AND PACKED FORMAT!
#
iea_op:
andi.l &0x00ff00ff,USER_FPSR(%a6)
btst &0xa,%d0 # is src fmt x or p?
bne.b iea_op_pack # packed
mov.l EXC_EXTWPTR(%a6),%a0 # pass: ptr to #<data>
lea FP_SRC(%a6),%a1 # pass: ptr to super addr
mov.l &0xc,%d0 # pass: 12 bytes
bsr.l _imem_read # read extended immediate
tst.l %d1 # did ifetch fail?
bne.w iea_iacc # yes
bra.b iea_op_setsrc
iea_op_pack:
mov.l EXC_EXTWPTR(%a6),%a0 # pass: ptr to #<data>
lea FP_SRC(%a6),%a1 # pass: ptr to super dst
mov.l &0xc,%d0 # pass: 12 bytes
bsr.l _imem_read # read packed operand
tst.l %d1 # did ifetch fail?
bne.w iea_iacc # yes
# The packed operand is an INF or a NAN if the exponent field is all ones.
bfextu FP_SRC(%a6){&1:&15},%d0 # get exp
cmpi.w %d0,&0x7fff # INF or NAN?
beq.b iea_op_setsrc # operand is an INF or NAN
# The packed operand is a zero if the mantissa is all zero, else it's
# a normal packed op.
mov.b 3+FP_SRC(%a6),%d0 # get byte 4
andi.b &0x0f,%d0 # clear all but last nybble
bne.b iea_op_gp_not_spec # not a zero
tst.l FP_SRC_HI(%a6) # is lw 2 zero?
bne.b iea_op_gp_not_spec # not a zero
tst.l FP_SRC_LO(%a6) # is lw 3 zero?
beq.b iea_op_setsrc # operand is a ZERO
iea_op_gp_not_spec:
lea FP_SRC(%a6),%a0 # pass: ptr to packed op
bsr.l decbin # convert to extended
fmovm.x &0x80,FP_SRC(%a6) # make this the srcop
iea_op_setsrc:
addi.l &0xc,EXC_EXTWPTR(%a6) # update extension word pointer
# FP_SRC now holds the src operand.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # could be ANYTHING!!!
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b iea_op_getdst # no
bsr.l unnorm_fix # yes; convert to NORM/DENORM/ZERO
mov.b %d0,STAG(%a6) # set new optype tag
iea_op_getdst:
clr.b STORE_FLG(%a6) # clear "store result" boolean
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b iea_op_extract # monadic
btst &0x4,1+EXC_CMDREG(%a6) # is operation fsincos,ftst,fcmp?
bne.b iea_op_spec # yes
iea_op_loaddst:
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # fetch dst regno
bsr.l load_fpn2 # load dst operand
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
mov.b %d0,DTAG(%a6) # could be ANYTHING!!!
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b iea_op_extract # no
bsr.l unnorm_fix # yes; convert to NORM/DENORM/ZERO
mov.b %d0,DTAG(%a6) # set new optype tag
bra.b iea_op_extract
# the operation is fsincos, ftst, or fcmp. only fcmp is dyadic
iea_op_spec:
btst &0x3,1+EXC_CMDREG(%a6) # is operation fsincos?
beq.b iea_op_extract # yes
# now, we're left with ftst and fcmp. so, first let's tag them so that they don't
# store a result. then, only fcmp will branch back and pick up a dst operand.
st STORE_FLG(%a6) # don't store a final result
btst &0x1,1+EXC_CMDREG(%a6) # is operation fcmp?
beq.b iea_op_loaddst # yes
iea_op_extract:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass: rnd mode,prec
mov.b 1+EXC_CMDREG(%a6),%d1
andi.w &0x007f,%d1 # extract extension
fmov.l &0x0,%fpcr
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
mov.l (tbl_unsupp.l,%pc,%d1.w*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
#
# Exceptions in order of precedence:
# BSUN : none
# SNAN : all operations
# OPERR : all reg-reg or mem-reg operations that can normally operr
# OVFL : same as OPERR
# UNFL : same as OPERR
# DZ : same as OPERR
# INEX2 : same as OPERR
# INEX1 : all packed immediate operations
#
# we determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.b iea_op_ena # some are enabled
# now, we save the result, unless, of course, the operation was ftst or fcmp.
# these don't save results.
iea_op_save:
tst.b STORE_FLG(%a6) # does this op store a result?
bne.b iea_op_exit1 # exit with no frestore
iea_op_store:
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # fetch dst regno
bsr.l store_fpreg # store the result
iea_op_exit1:
mov.l EXC_PC(%a6),USER_FPIAR(%a6) # set FPIAR to "Current PC"
mov.l EXC_EXTWPTR(%a6),EXC_PC(%a6) # set "Next PC" in exc frame
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6 # unravel the frame
btst &0x7,(%sp) # is trace on?
bne.w iea_op_trace # yes
bra.l _fpsp_done # exit to os
iea_op_ena:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enable and set
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b iea_op_exc # at least one was set
# no exception occurred. now, did a disabled, exact overflow occur with inexact
# enabled? if so, then we have to stuff an overflow frame into the FPU.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
beq.b iea_op_save
iea_op_ovfl:
btst &inex2_bit,FPCR_ENABLE(%a6) # is inexact enabled?
beq.b iea_op_store # no
bra.b iea_op_exc_ovfl # yes
# an enabled exception occurred. we have to insert the exception type back into
# the machine.
iea_op_exc:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX?
bne.b iea_op_exc_force # no
# the enabled exception was inexact. so, if it occurs with an overflow
# or underflow that was disabled, then we have to force an overflow or
# underflow frame.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
bne.b iea_op_exc_ovfl # yes
btst &unfl_bit,FPSR_EXCEPT(%a6) # did underflow occur?
bne.b iea_op_exc_unfl # yes
iea_op_exc_force:
mov.w (tbl_iea_except.b,%pc,%d0.w*2),2+FP_SRC(%a6)
bra.b iea_op_exit2 # exit with frestore
tbl_iea_except:
short 0xe002, 0xe006, 0xe004, 0xe005
short 0xe003, 0xe002, 0xe001, 0xe001
iea_op_exc_ovfl:
mov.w &0xe005,2+FP_SRC(%a6)
bra.b iea_op_exit2
iea_op_exc_unfl:
mov.w &0xe003,2+FP_SRC(%a6)
iea_op_exit2:
mov.l EXC_PC(%a6),USER_FPIAR(%a6) # set FPIAR to "Current PC"
mov.l EXC_EXTWPTR(%a6),EXC_PC(%a6) # set "Next PC" in exc frame
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # restore exceptional state
unlk %a6 # unravel the frame
btst &0x7,(%sp) # is trace on?
bne.b iea_op_trace # yes
bra.l _fpsp_done # exit to os
#
# The opclass two instruction that took an "Unimplemented Effective Address"
# exception was being traced. Make the "current" PC the FPIAR and put it in
# the trace stack frame then jump to _real_trace().
#
# UNIMP EA FRAME TRACE FRAME
# ***************** *****************
# * 0x0 * 0x0f0 * * Current *
# ***************** * PC *
# * Current * *****************
# * PC * * 0x2 * 0x024 *
# ***************** *****************
# * SR * * Next *
# ***************** * PC *
# *****************
# * SR *
# *****************
iea_op_trace:
mov.l (%sp),-(%sp) # shift stack frame "down"
mov.w 0x8(%sp),0x4(%sp)
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x024
fmov.l %fpiar,0x8(%sp) # "Current PC" is in FPIAR
bra.l _real_trace
#########################################################################
iea_fmovm:
btst &14,%d0 # ctrl or data reg
beq.w iea_fmovm_ctrl
iea_fmovm_data:
btst &0x5,EXC_SR(%a6) # user or supervisor mode
bne.b iea_fmovm_data_s
iea_fmovm_data_u:
mov.l %usp,%a0
mov.l %a0,EXC_A7(%a6) # store current a7
bsr.l fmovm_dynamic # do dynamic fmovm
mov.l EXC_A7(%a6),%a0 # load possibly new a7
mov.l %a0,%usp # update usp
bra.w iea_fmovm_exit
iea_fmovm_data_s:
clr.b SPCOND_FLG(%a6)
lea 0x2+EXC_VOFF(%a6),%a0
mov.l %a0,EXC_A7(%a6)
bsr.l fmovm_dynamic # do dynamic fmovm
cmpi.b SPCOND_FLG(%a6),&mda7_flg
beq.w iea_fmovm_data_predec
cmpi.b SPCOND_FLG(%a6),&mia7_flg
bne.w iea_fmovm_exit
# right now, d0 = the size.
# the data has been fetched from the supervisor stack, but we have not
# incremented the stack pointer by the appropriate number of bytes.
# do it here.
iea_fmovm_data_postinc:
btst &0x7,EXC_SR(%a6)
bne.b iea_fmovm_data_pi_trace
mov.w EXC_SR(%a6),(EXC_SR,%a6,%d0)
mov.l EXC_EXTWPTR(%a6),(EXC_PC,%a6,%d0)
mov.w &0x00f0,(EXC_VOFF,%a6,%d0)
lea (EXC_SR,%a6,%d0),%a0
mov.l %a0,EXC_SR(%a6)
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
mov.l (%sp)+,%sp
bra.l _fpsp_done
iea_fmovm_data_pi_trace:
mov.w EXC_SR(%a6),(EXC_SR-0x4,%a6,%d0)
mov.l EXC_EXTWPTR(%a6),(EXC_PC-0x4,%a6,%d0)
mov.w &0x2024,(EXC_VOFF-0x4,%a6,%d0)
mov.l EXC_PC(%a6),(EXC_VOFF+0x2-0x4,%a6,%d0)
lea (EXC_SR-0x4,%a6,%d0),%a0
mov.l %a0,EXC_SR(%a6)
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
mov.l (%sp)+,%sp
bra.l _real_trace
# right now, d1 = size and d0 = the strg.
iea_fmovm_data_predec:
mov.b %d1,EXC_VOFF(%a6) # store strg
mov.b %d0,0x1+EXC_VOFF(%a6) # store size
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.l (%a6),-(%sp) # make a copy of a6
mov.l %d0,-(%sp) # save d0
mov.l %d1,-(%sp) # save d1
mov.l EXC_EXTWPTR(%a6),-(%sp) # make a copy of Next PC
clr.l %d0
mov.b 0x1+EXC_VOFF(%a6),%d0 # fetch size
neg.l %d0 # get negative of size
btst &0x7,EXC_SR(%a6) # is trace enabled?
beq.b iea_fmovm_data_p2
mov.w EXC_SR(%a6),(EXC_SR-0x4,%a6,%d0)
mov.l EXC_PC(%a6),(EXC_VOFF-0x2,%a6,%d0)
mov.l (%sp)+,(EXC_PC-0x4,%a6,%d0)
mov.w &0x2024,(EXC_VOFF-0x4,%a6,%d0)
pea (%a6,%d0) # create final sp
bra.b iea_fmovm_data_p3
iea_fmovm_data_p2:
mov.w EXC_SR(%a6),(EXC_SR,%a6,%d0)
mov.l (%sp)+,(EXC_PC,%a6,%d0)
mov.w &0x00f0,(EXC_VOFF,%a6,%d0)
pea (0x4,%a6,%d0) # create final sp
iea_fmovm_data_p3:
clr.l %d1
mov.b EXC_VOFF(%a6),%d1 # fetch strg
tst.b %d1
bpl.b fm_1
fmovm.x &0x80,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_1:
lsl.b &0x1,%d1
bpl.b fm_2
fmovm.x &0x40,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_2:
lsl.b &0x1,%d1
bpl.b fm_3
fmovm.x &0x20,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_3:
lsl.b &0x1,%d1
bpl.b fm_4
fmovm.x &0x10,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_4:
lsl.b &0x1,%d1
bpl.b fm_5
fmovm.x &0x08,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_5:
lsl.b &0x1,%d1
bpl.b fm_6
fmovm.x &0x04,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_6:
lsl.b &0x1,%d1
bpl.b fm_7
fmovm.x &0x02,(0x4+0x8,%a6,%d0)
addi.l &0xc,%d0
fm_7:
lsl.b &0x1,%d1
bpl.b fm_end
fmovm.x &0x01,(0x4+0x8,%a6,%d0)
fm_end:
mov.l 0x4(%sp),%d1
mov.l 0x8(%sp),%d0
mov.l 0xc(%sp),%a6
mov.l (%sp)+,%sp
btst &0x7,(%sp) # is trace enabled?
beq.l _fpsp_done
bra.l _real_trace
#########################################################################
iea_fmovm_ctrl:
bsr.l fmovm_ctrl # load ctrl regs
iea_fmovm_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
btst &0x7,EXC_SR(%a6) # is trace on?
bne.b iea_fmovm_trace # yes
mov.l EXC_EXTWPTR(%a6),EXC_PC(%a6) # set Next PC
unlk %a6 # unravel the frame
bra.l _fpsp_done # exit to os
#
# The control reg instruction that took an "Unimplemented Effective Address"
# exception was being traced. The "Current PC" for the trace frame is the
# PC stacked for Unimp EA. The "Next PC" is in EXC_EXTWPTR.
# After fixing the stack frame, jump to _real_trace().
#
# UNIMP EA FRAME TRACE FRAME
# ***************** *****************
# * 0x0 * 0x0f0 * * Current *
# ***************** * PC *
# * Current * *****************
# * PC * * 0x2 * 0x024 *
# ***************** *****************
# * SR * * Next *
# ***************** * PC *
# *****************
# * SR *
# *****************
# this ain't a pretty solution, but it works:
# -restore a6 (not with unlk)
# -shift stack frame down over where old a6 used to be
# -add LOCAL_SIZE to stack pointer
iea_fmovm_trace:
mov.l (%a6),%a6 # restore frame pointer
mov.w EXC_SR+LOCAL_SIZE(%sp),0x0+LOCAL_SIZE(%sp)
mov.l EXC_PC+LOCAL_SIZE(%sp),0x8+LOCAL_SIZE(%sp)
mov.l EXC_EXTWPTR+LOCAL_SIZE(%sp),0x2+LOCAL_SIZE(%sp)
mov.w &0x2024,0x6+LOCAL_SIZE(%sp) # stk fmt = 0x2; voff = 0x024
add.l &LOCAL_SIZE,%sp # clear stack frame
bra.l _real_trace
#########################################################################
# The FPU is disabled and so we should really have taken the "Line
# F Emulator" exception. So, here we create an 8-word stack frame
# from our 4-word stack frame. This means we must calculate the length
# the the faulting instruction to get the "next PC". This is trivial for
# immediate operands but requires some extra work for fmovm dynamic
# which can use most addressing modes.
iea_disabled:
mov.l (%sp)+,%d0 # restore d0
link %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
# PC of instruction that took the exception is the PC in the frame
mov.l EXC_PC(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6) # store OPWORD and EXTWORD
tst.w %d0 # is instr fmovm?
bmi.b iea_dis_fmovm # yes
# instruction is using an extended precision immediate operand. therefore,
# the total instruction length is 16 bytes.
iea_dis_immed:
mov.l &0x10,%d0 # 16 bytes of instruction
bra.b iea_dis_cont
iea_dis_fmovm:
btst &0xe,%d0 # is instr fmovm ctrl
bne.b iea_dis_fmovm_data # no
# the instruction is a fmovm.l with 2 or 3 registers.
bfextu %d0{&19:&3},%d1
mov.l &0xc,%d0
cmpi.b %d1,&0x7 # move all regs?
bne.b iea_dis_cont
addq.l &0x4,%d0
bra.b iea_dis_cont
# the instruction is an fmovm.x dynamic which can use many addressing
# modes and thus can have several different total instruction lengths.
# call fmovm_calc_ea which will go through the ea calc process and,
# as a by-product, will tell us how long the instruction is.
iea_dis_fmovm_data:
clr.l %d0
bsr.l fmovm_calc_ea
mov.l EXC_EXTWPTR(%a6),%d0
sub.l EXC_PC(%a6),%d0
iea_dis_cont:
mov.w %d0,EXC_VOFF(%a6) # store stack shift value
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
# here, we actually create the 8-word frame from the 4-word frame,
# with the "next PC" as additional info.
# the <ea> field is let as undefined.
subq.l &0x8,%sp # make room for new stack
mov.l %d0,-(%sp) # save d0
mov.w 0xc(%sp),0x4(%sp) # move SR
mov.l 0xe(%sp),0x6(%sp) # move Current PC
clr.l %d0
mov.w 0x12(%sp),%d0
mov.l 0x6(%sp),0x10(%sp) # move Current PC
add.l %d0,0x6(%sp) # make Next PC
mov.w &0x402c,0xa(%sp) # insert offset,frame format
mov.l (%sp)+,%d0 # restore d0
bra.l _real_fpu_disabled
##########
iea_iacc:
movc %pcr,%d0
btst &0x1,%d0
bne.b iea_iacc_cont
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1 on stack
iea_iacc_cont:
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
subq.w &0x8,%sp # make stack frame bigger
mov.l 0x8(%sp),(%sp) # store SR,hi(PC)
mov.w 0xc(%sp),0x4(%sp) # store lo(PC)
mov.w &0x4008,0x6(%sp) # store voff
mov.l 0x2(%sp),0x8(%sp) # store ea
mov.l &0x09428001,0xc(%sp) # store fslw
iea_acc_done:
btst &0x5,(%sp) # user or supervisor mode?
beq.b iea_acc_done2 # user
bset &0x2,0xd(%sp) # set supervisor TM bit
iea_acc_done2:
bra.l _real_access
iea_dacc:
lea -LOCAL_SIZE(%a6),%sp
movc %pcr,%d1
btst &0x1,%d1
bne.b iea_dacc_cont
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1 on stack
fmovm.l LOCAL_SIZE+USER_FPCR(%sp),%fpcr,%fpsr,%fpiar # restore ctrl regs
iea_dacc_cont:
mov.l (%a6),%a6
mov.l 0x4+LOCAL_SIZE(%sp),-0x8+0x4+LOCAL_SIZE(%sp)
mov.w 0x8+LOCAL_SIZE(%sp),-0x8+0x8+LOCAL_SIZE(%sp)
mov.w &0x4008,-0x8+0xa+LOCAL_SIZE(%sp)
mov.l %a0,-0x8+0xc+LOCAL_SIZE(%sp)
mov.w %d0,-0x8+0x10+LOCAL_SIZE(%sp)
mov.w &0x0001,-0x8+0x12+LOCAL_SIZE(%sp)
movm.l LOCAL_SIZE+EXC_DREGS(%sp),&0x0303 # restore d0-d1/a0-a1
add.w &LOCAL_SIZE-0x4,%sp
bra.b iea_acc_done
#########################################################################
# XDEF **************************************************************** #
# _fpsp_operr(): 060FPSP entry point for FP Operr exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Operand Error exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# _real_operr() - "callout" to operating system operr handler #
# _dmem_write_{byte,word,long}() - store data to mem (opclass 3) #
# store_dreg_{b,w,l}() - store data to data regfile (opclass 3) #
# facc_out_{b,w,l}() - store to memory took access error (opcl 3) #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Operr exception frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# No access error: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# #
# ALGORITHM *********************************************************** #
# In a system where the FP Operr exception is enabled, the goal #
# is to get to the handler specified at _real_operr(). But, on the 060, #
# for opclass zero and two instruction taking this exception, the #
# input operand in the fsave frame may be incorrect for some cases #
# and needs to be corrected. This handler calls fix_skewed_ops() to #
# do just this and then exits through _real_operr(). #
# For opclass 3 instructions, the 060 doesn't store the default #
# operr result out to memory or data register file as it should. #
# This code must emulate the move out before finally exiting through #
# _real_inex(). The move out, if to memory, is performed using #
# _mem_write() "callout" routines that may return a failing result. #
# In this special case, the handler must exit through facc_out() #
# which creates an access error stack frame from the current operr #
# stack frame. #
# #
#########################################################################
global _fpsp_operr
_fpsp_operr:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
##############################################################################
btst &13,%d0 # is instr an fmove out?
bne.b foperr_out # fmove out
# here, we simply see if the operand in the fsave frame needs to be "unskewed".
# this would be the case for opclass two operations with a source infinity or
# denorm operand in the sgl or dbl format. NANs also become skewed, but can't
# cause an operr so we don't need to check for them here.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
foperr_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6)
unlk %a6
bra.l _real_operr
########################################################################
#
# the hardware does not save the default result to memory on enabled
# operand error exceptions. we do this here before passing control to
# the user operand error handler.
#
# byte, word, and long destination format operations can pass
# through here. we simply need to test the sign of the src
# operand and save the appropriate minimum or maximum integer value
# to the effective address as pointed to by the stacked effective address.
#
# although packed opclass three operations can take operand error
# exceptions, they won't pass through here since they are caught
# first by the unsupported data format exception handler. that handler
# sends them directly to _real_operr() if necessary.
#
foperr_out:
mov.w FP_SRC_EX(%a6),%d1 # fetch exponent
andi.w &0x7fff,%d1
cmpi.w %d1,&0x7fff
bne.b foperr_out_not_qnan
# the operand is either an infinity or a QNAN.
tst.l FP_SRC_LO(%a6)
bne.b foperr_out_qnan
mov.l FP_SRC_HI(%a6),%d1
andi.l &0x7fffffff,%d1
beq.b foperr_out_not_qnan
foperr_out_qnan:
mov.l FP_SRC_HI(%a6),L_SCR1(%a6)
bra.b foperr_out_jmp
foperr_out_not_qnan:
mov.l &0x7fffffff,%d1
tst.b FP_SRC_EX(%a6)
bpl.b foperr_out_not_qnan2
addq.l &0x1,%d1
foperr_out_not_qnan2:
mov.l %d1,L_SCR1(%a6)
foperr_out_jmp:
bfextu %d0{&19:&3},%d0 # extract dst format field
mov.b 1+EXC_OPWORD(%a6),%d1 # extract <ea> mode,reg
mov.w (tbl_operr.b,%pc,%d0.w*2),%a0
jmp (tbl_operr.b,%pc,%a0)
tbl_operr:
short foperr_out_l - tbl_operr # long word integer
short tbl_operr - tbl_operr # sgl prec shouldn't happen
short tbl_operr - tbl_operr # ext prec shouldn't happen
short foperr_exit - tbl_operr # packed won't enter here
short foperr_out_w - tbl_operr # word integer
short tbl_operr - tbl_operr # dbl prec shouldn't happen
short foperr_out_b - tbl_operr # byte integer
short tbl_operr - tbl_operr # packed won't enter here
foperr_out_b:
mov.b L_SCR1(%a6),%d0 # load positive default result
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b foperr_out_b_save_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_byte # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_b # yes
bra.w foperr_exit
foperr_out_b_save_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_b # store result to regfile
bra.w foperr_exit
foperr_out_w:
mov.w L_SCR1(%a6),%d0 # load positive default result
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b foperr_out_w_save_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_word # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_w # yes
bra.w foperr_exit
foperr_out_w_save_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_w # store result to regfile
bra.w foperr_exit
foperr_out_l:
mov.l L_SCR1(%a6),%d0 # load positive default result
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b foperr_out_l_save_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_long # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.w foperr_exit
foperr_out_l_save_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_l # store result to regfile
bra.w foperr_exit
#########################################################################
# XDEF **************************************************************** #
# _fpsp_snan(): 060FPSP entry point for FP SNAN exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Signalling NAN exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# _real_snan() - "callout" to operating system SNAN handler #
# _dmem_write_{byte,word,long}() - store data to mem (opclass 3) #
# store_dreg_{b,w,l}() - store data to data regfile (opclass 3) #
# facc_out_{b,w,l,d,x}() - store to mem took acc error (opcl 3) #
# _calc_ea_fout() - fix An if <ea> is -() or ()+; also get <ea> #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP SNAN exception frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# No access error: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# #
# ALGORITHM *********************************************************** #
# In a system where the FP SNAN exception is enabled, the goal #
# is to get to the handler specified at _real_snan(). But, on the 060, #
# for opclass zero and two instructions taking this exception, the #
# input operand in the fsave frame may be incorrect for some cases #
# and needs to be corrected. This handler calls fix_skewed_ops() to #
# do just this and then exits through _real_snan(). #
# For opclass 3 instructions, the 060 doesn't store the default #
# SNAN result out to memory or data register file as it should. #
# This code must emulate the move out before finally exiting through #
# _real_snan(). The move out, if to memory, is performed using #
# _mem_write() "callout" routines that may return a failing result. #
# In this special case, the handler must exit through facc_out() #
# which creates an access error stack frame from the current SNAN #
# stack frame. #
# For the case of an extended precision opclass 3 instruction, #
# if the effective addressing mode was -() or ()+, then the address #
# register must get updated by calling _calc_ea_fout(). If the <ea> #
# was -(a7) from supervisor mode, then the exception frame currently #
# on the system stack must be carefully moved "down" to make room #
# for the operand being moved. #
# #
#########################################################################
global _fpsp_snan
_fpsp_snan:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
##############################################################################
btst &13,%d0 # is instr an fmove out?
bne.w fsnan_out # fmove out
# here, we simply see if the operand in the fsave frame needs to be "unskewed".
# this would be the case for opclass two operations with a source infinity or
# denorm operand in the sgl or dbl format. NANs also become skewed and must be
# fixed here.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
fsnan_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6)
unlk %a6
bra.l _real_snan
########################################################################
#
# the hardware does not save the default result to memory on enabled
# snan exceptions. we do this here before passing control to
# the user snan handler.
#
# byte, word, long, and packed destination format operations can pass
# through here. since packed format operations already were handled by
# fpsp_unsupp(), then we need to do nothing else for them here.
# for byte, word, and long, we simply need to test the sign of the src
# operand and save the appropriate minimum or maximum integer value
# to the effective address as pointed to by the stacked effective address.
#
fsnan_out:
bfextu %d0{&19:&3},%d0 # extract dst format field
mov.b 1+EXC_OPWORD(%a6),%d1 # extract <ea> mode,reg
mov.w (tbl_snan.b,%pc,%d0.w*2),%a0
jmp (tbl_snan.b,%pc,%a0)
tbl_snan:
short fsnan_out_l - tbl_snan # long word integer
short fsnan_out_s - tbl_snan # sgl prec shouldn't happen
short fsnan_out_x - tbl_snan # ext prec shouldn't happen
short tbl_snan - tbl_snan # packed needs no help
short fsnan_out_w - tbl_snan # word integer
short fsnan_out_d - tbl_snan # dbl prec shouldn't happen
short fsnan_out_b - tbl_snan # byte integer
short tbl_snan - tbl_snan # packed needs no help
fsnan_out_b:
mov.b FP_SRC_HI(%a6),%d0 # load upper byte of SNAN
bset &6,%d0 # set SNAN bit
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_b_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_byte # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_b # yes
bra.w fsnan_exit
fsnan_out_b_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_b # store result to regfile
bra.w fsnan_exit
fsnan_out_w:
mov.w FP_SRC_HI(%a6),%d0 # load upper word of SNAN
bset &14,%d0 # set SNAN bit
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_w_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_word # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_w # yes
bra.w fsnan_exit
fsnan_out_w_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_w # store result to regfile
bra.w fsnan_exit
fsnan_out_l:
mov.l FP_SRC_HI(%a6),%d0 # load upper longword of SNAN
bset &30,%d0 # set SNAN bit
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_l_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_long # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.w fsnan_exit
fsnan_out_l_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_l # store result to regfile
bra.w fsnan_exit
fsnan_out_s:
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_d_dn # yes
mov.l FP_SRC_EX(%a6),%d0 # fetch SNAN sign
andi.l &0x80000000,%d0 # keep sign
ori.l &0x7fc00000,%d0 # insert new exponent,SNAN bit
mov.l FP_SRC_HI(%a6),%d1 # load mantissa
lsr.l &0x8,%d1 # shift mantissa for sgl
or.l %d1,%d0 # create sgl SNAN
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_long # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.w fsnan_exit
fsnan_out_d_dn:
mov.l FP_SRC_EX(%a6),%d0 # fetch SNAN sign
andi.l &0x80000000,%d0 # keep sign
ori.l &0x7fc00000,%d0 # insert new exponent,SNAN bit
mov.l %d1,-(%sp)
mov.l FP_SRC_HI(%a6),%d1 # load mantissa
lsr.l &0x8,%d1 # shift mantissa for sgl
or.l %d1,%d0 # create sgl SNAN
mov.l (%sp)+,%d1
andi.w &0x0007,%d1
bsr.l store_dreg_l # store result to regfile
bra.w fsnan_exit
fsnan_out_d:
mov.l FP_SRC_EX(%a6),%d0 # fetch SNAN sign
andi.l &0x80000000,%d0 # keep sign
ori.l &0x7ff80000,%d0 # insert new exponent,SNAN bit
mov.l FP_SRC_HI(%a6),%d1 # load hi mantissa
mov.l %d0,FP_SCR0_EX(%a6) # store to temp space
mov.l &11,%d0 # load shift amt
lsr.l %d0,%d1
or.l %d1,FP_SCR0_EX(%a6) # create dbl hi
mov.l FP_SRC_HI(%a6),%d1 # load hi mantissa
andi.l &0x000007ff,%d1
ror.l %d0,%d1
mov.l %d1,FP_SCR0_HI(%a6) # store to temp space
mov.l FP_SRC_LO(%a6),%d1 # load lo mantissa
lsr.l %d0,%d1
or.l %d1,FP_SCR0_HI(%a6) # create dbl lo
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
mov.l EXC_EA(%a6),%a1 # pass: dst addr
movq.l &0x8,%d0 # pass: size of 8 bytes
bsr.l _dmem_write # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_d # yes
bra.w fsnan_exit
# for extended precision, if the addressing mode is pre-decrement or
# post-increment, then the address register did not get updated.
# in addition, for pre-decrement, the stacked <ea> is incorrect.
fsnan_out_x:
clr.b SPCOND_FLG(%a6) # clear special case flag
mov.w FP_SRC_EX(%a6),FP_SCR0_EX(%a6)
clr.w 2+FP_SCR0(%a6)
mov.l FP_SRC_HI(%a6),%d0
bset &30,%d0
mov.l %d0,FP_SCR0_HI(%a6)
mov.l FP_SRC_LO(%a6),FP_SCR0_LO(%a6)
btst &0x5,EXC_SR(%a6) # supervisor mode exception?
bne.b fsnan_out_x_s # yes
mov.l %usp,%a0 # fetch user stack pointer
mov.l %a0,EXC_A7(%a6) # save on stack for calc_ea()
mov.l (%a6),EXC_A6(%a6)
bsr.l _calc_ea_fout # find the correct ea,update An
mov.l %a0,%a1
mov.l %a0,EXC_EA(%a6) # stack correct <ea>
mov.l EXC_A7(%a6),%a0
mov.l %a0,%usp # restore user stack pointer
mov.l EXC_A6(%a6),(%a6)
fsnan_out_x_save:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
movq.l &0xc,%d0 # pass: size of extended
bsr.l _dmem_write # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_x # yes
bra.w fsnan_exit
fsnan_out_x_s:
mov.l (%a6),EXC_A6(%a6)
bsr.l _calc_ea_fout # find the correct ea,update An
mov.l %a0,%a1
mov.l %a0,EXC_EA(%a6) # stack correct <ea>
mov.l EXC_A6(%a6),(%a6)
cmpi.b SPCOND_FLG(%a6),&mda7_flg # is <ea> mode -(a7)?
bne.b fsnan_out_x_save # no
# the operation was "fmove.x SNAN,-(a7)" from supervisor mode.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6)
mov.l EXC_A6(%a6),%a6 # restore frame pointer
mov.l LOCAL_SIZE+EXC_SR(%sp),LOCAL_SIZE+EXC_SR-0xc(%sp)
mov.l LOCAL_SIZE+EXC_PC+0x2(%sp),LOCAL_SIZE+EXC_PC+0x2-0xc(%sp)
mov.l LOCAL_SIZE+EXC_EA(%sp),LOCAL_SIZE+EXC_EA-0xc(%sp)
mov.l LOCAL_SIZE+FP_SCR0_EX(%sp),LOCAL_SIZE+EXC_SR(%sp)
mov.l LOCAL_SIZE+FP_SCR0_HI(%sp),LOCAL_SIZE+EXC_PC+0x2(%sp)
mov.l LOCAL_SIZE+FP_SCR0_LO(%sp),LOCAL_SIZE+EXC_EA(%sp)
add.l &LOCAL_SIZE-0x8,%sp
bra.l _real_snan
#########################################################################
# XDEF **************************************************************** #
# _fpsp_inex(): 060FPSP entry point for FP Inexact exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Inexact exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# smovcr() - emulate an "fmovcr" instruction #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _real_inex() - "callout" to operating system inexact handler #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Inexact exception frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# #
# ALGORITHM *********************************************************** #
# In a system where the FP Inexact exception is enabled, the goal #
# is to get to the handler specified at _real_inex(). But, on the 060, #
# for opclass zero and two instruction taking this exception, the #
# hardware doesn't store the correct result to the destination FP #
# register as did the '040 and '881/2. This handler must emulate the #
# instruction in order to get this value and then store it to the #
# correct register before calling _real_inex(). #
# For opclass 3 instructions, the 060 doesn't store the default #
# inexact result out to memory or data register file as it should. #
# This code must emulate the move out by calling fout() before finally #
# exiting through _real_inex(). #
# #
#########################################################################
global _fpsp_inex
_fpsp_inex:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
##############################################################################
btst &13,%d0 # is instr an fmove out?
bne.w finex_out # fmove out
# the hardware, for "fabs" and "fneg" w/ a long source format, puts the
# longword integer directly into the upper longword of the mantissa along
# w/ an exponent value of 0x401e. we convert this to extended precision here.
bfextu %d0{&19:&3},%d0 # fetch instr size
bne.b finex_cont # instr size is not long
cmpi.w FP_SRC_EX(%a6),&0x401e # is exponent 0x401e?
bne.b finex_cont # no
fmov.l &0x0,%fpcr
fmov.l FP_SRC_HI(%a6),%fp0 # load integer src
fmov.x %fp0,FP_SRC(%a6) # store integer as extended precision
mov.w &0xe001,0x2+FP_SRC(%a6)
finex_cont:
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
# Here, we zero the ccode and exception byte field since we're going to
# emulate the whole instruction. Notice, though, that we don't kill the
# INEX1 bit. This is because a packed op has long since been converted
# to extended before arriving here. Therefore, we need to retain the
# INEX1 bit from when the operand was first converted.
andi.l &0x00ff01ff,USER_FPSR(%a6) # zero all but accured field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
bfextu EXC_EXTWORD(%a6){&0:&6},%d1 # extract upper 6 of cmdreg
cmpi.b %d1,&0x17 # is op an fmovecr?
beq.w finex_fmovcr # yes
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # maybe NORM,DENORM
# bits four and five of the fp extension word separate the monadic and dyadic
# operations that can pass through fpsp_inex(). remember that fcmp and ftst
# will never take this exception, but fsincos will.
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b finex_extract # monadic
btst &0x4,1+EXC_CMDREG(%a6) # is operation an fsincos?
bne.b finex_extract # yes
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b finex_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
finex_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
finex_extract:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec/mode
mov.b 1+EXC_CMDREG(%a6),%d1
andi.w &0x007f,%d1 # extract extension
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
mov.l (tbl_unsupp.l,%pc,%d1.w*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
# the operation has been emulated. the result is in fp0.
finex_save:
bfextu EXC_CMDREG(%a6){&6:&3},%d0
bsr.l store_fpreg
finex_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6)
unlk %a6
bra.l _real_inex
finex_fmovcr:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec,mode
mov.b 1+EXC_CMDREG(%a6),%d1
andi.l &0x0000007f,%d1 # pass rom offset
bsr.l smovcr
bra.b finex_save
########################################################################
#
# the hardware does not save the default result to memory on enabled
# inexact exceptions. we do this here before passing control to
# the user inexact handler.
#
# byte, word, and long destination format operations can pass
# through here. so can double and single precision.
# although packed opclass three operations can take inexact
# exceptions, they won't pass through here since they are caught
# first by the unsupported data format exception handler. that handler
# sends them directly to _real_inex() if necessary.
#
finex_out:
mov.b &NORM,STAG(%a6) # src is a NORM
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # pass rnd prec,mode
andi.l &0xffff00ff,USER_FPSR(%a6) # zero exception field
lea FP_SRC(%a6),%a0 # pass ptr to src operand
bsr.l fout # store the default result
bra.b finex_exit
#########################################################################
# XDEF **************************************************************** #
# _fpsp_dz(): 060FPSP entry point for FP DZ exception. #
# #
# This handler should be the first code executed upon taking #
# the FP DZ exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword from memory #
# fix_skewed_ops() - adjust fsave operand #
# _real_dz() - "callout" exit point from FP DZ handler #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP DZ exception stack. #
# - The fsave frame contains the source operand. #
# #
# OUTPUT ************************************************************** #
# - The system stack contains the FP DZ exception stack. #
# - The fsave frame contains the adjusted source operand. #
# #
# ALGORITHM *********************************************************** #
# In a system where the DZ exception is enabled, the goal is to #
# get to the handler specified at _real_dz(). But, on the 060, when the #
# exception is taken, the input operand in the fsave state frame may #
# be incorrect for some cases and need to be adjusted. So, this package #
# adjusts the operand using fix_skewed_ops() and then branches to #
# _real_dz(). #
# #
#########################################################################
global _fpsp_dz
_fpsp_dz:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
##############################################################################
# here, we simply see if the operand in the fsave frame needs to be "unskewed".
# this would be the case for opclass two operations with a source zero
# in the sgl or dbl format.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
fdz_exit:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6)
unlk %a6
bra.l _real_dz
#########################################################################
# XDEF **************************************************************** #
# _fpsp_fline(): 060FPSP entry point for "Line F emulator" exc. #
# #
# This handler should be the first code executed upon taking the #
# "Line F Emulator" exception in an operating system. #
# #
# XREF **************************************************************** #
# _fpsp_unimp() - handle "FP Unimplemented" exceptions #
# _real_fpu_disabled() - handle "FPU disabled" exceptions #
# _real_fline() - handle "FLINE" exceptions #
# _imem_read_long() - read instruction longword #
# #
# INPUT *************************************************************** #
# - The system stack contains a "Line F Emulator" exception #
# stack frame. #
# #
# OUTPUT ************************************************************** #
# - The system stack is unchanged #
# #
# ALGORITHM *********************************************************** #
# When a "Line F Emulator" exception occurs, there are 3 possible #
# exception types, denoted by the exception stack frame format number: #
# (1) FPU unimplemented instruction (6 word stack frame) #
# (2) FPU disabled (8 word stack frame) #
# (3) Line F (4 word stack frame) #
# #
# This module determines which and forks the flow off to the #
# appropriate "callout" (for "disabled" and "Line F") or to the #
# correct emulation code (for "FPU unimplemented"). #
# This code also must check for "fmovecr" instructions w/ a #
# non-zero <ea> field. These may get flagged as "Line F" but should #
# really be flagged as "FPU Unimplemented". (This is a "feature" on #
# the '060. #
# #
#########################################################################
global _fpsp_fline
_fpsp_fline:
# check to see if this exception is a "FP Unimplemented Instruction"
# exception. if so, branch directly to that handler's entry point.
cmpi.w 0x6(%sp),&0x202c
beq.l _fpsp_unimp
# check to see if the FPU is disabled. if so, jump to the OS entry
# point for that condition.
cmpi.w 0x6(%sp),&0x402c
beq.l _real_fpu_disabled
# the exception was an "F-Line Illegal" exception. we check to see
# if the F-Line instruction is an "fmovecr" w/ a non-zero <ea>. if
# so, convert the F-Line exception stack frame to an FP Unimplemented
# Instruction exception stack frame else branch to the OS entry
# point for the F-Line exception handler.
link.w %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
mov.l EXC_PC(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch instruction words
bfextu %d0{&0:&10},%d1 # is it an fmovecr?
cmpi.w %d1,&0x03c8
bne.b fline_fline # no
bfextu %d0{&16:&6},%d1 # is it an fmovecr?
cmpi.b %d1,&0x17
bne.b fline_fline # no
# it's an fmovecr w/ a non-zero <ea> that has entered through
# the F-Line Illegal exception.
# so, we need to convert the F-Line exception stack frame into an
# FP Unimplemented Instruction stack frame and jump to that entry
# point.
#
# but, if the FPU is disabled, then we need to jump to the FPU diabled
# entry point.
movc %pcr,%d0
btst &0x1,%d0
beq.b fline_fmovcr
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
sub.l &0x8,%sp # make room for "Next PC", <ea>
mov.w 0x8(%sp),(%sp)
mov.l 0xa(%sp),0x2(%sp) # move "Current PC"
mov.w &0x402c,0x6(%sp)
mov.l 0x2(%sp),0xc(%sp)
addq.l &0x4,0x2(%sp) # set "Next PC"
bra.l _real_fpu_disabled
fline_fmovcr:
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
fmov.l 0x2(%sp),%fpiar # set current PC
addq.l &0x4,0x2(%sp) # set Next PC
mov.l (%sp),-(%sp)
mov.l 0x8(%sp),0x4(%sp)
mov.b &0x20,0x6(%sp)
bra.l _fpsp_unimp
fline_fline:
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
bra.l _real_fline
#########################################################################
# XDEF **************************************************************** #
# _fpsp_unimp(): 060FPSP entry point for FP "Unimplemented #
# Instruction" exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Unimplemented Instruction exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_{word,long}() - read instruction word/longword #
# load_fop() - load src/dst ops from memory and/or FP regfile #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# tbl_trans - addr of table of emulation routines for trnscndls #
# _real_access() - "callout" for access error exception #
# _fpsp_done() - "callout" for exit; work all done #
# _real_trace() - "callout" for Trace enabled exception #
# smovcr() - emulate "fmovecr" instruction #
# funimp_skew() - adjust fsave src ops to "incorrect" value #
# _ftrapcc() - emulate an "ftrapcc" instruction #
# _fdbcc() - emulate an "fdbcc" instruction #
# _fscc() - emulate an "fscc" instruction #
# _real_trap() - "callout" for Trap exception #
# _real_bsun() - "callout" for enabled Bsun exception #
# #
# INPUT *************************************************************** #
# - The system stack contains the "Unimplemented Instr" stk frame #
# #
# OUTPUT ************************************************************** #
# If access error: #
# - The system stack is changed to an access error stack frame #
# If Trace exception enabled: #
# - The system stack is changed to a Trace exception stack frame #
# Else: (normal case) #
# - Correct result has been stored as appropriate #
# #
# ALGORITHM *********************************************************** #
# There are two main cases of instructions that may enter here to #
# be emulated: (1) the FPgen instructions, most of which were also #
# unimplemented on the 040, and (2) "ftrapcc", "fscc", and "fdbcc". #
# For the first set, this handler calls the routine load_fop() #
# to load the source and destination (for dyadic) operands to be used #
# for instruction emulation. The correct emulation routine is then #
# chosen by decoding the instruction type and indexing into an #
# emulation subroutine index table. After emulation returns, this #
# handler checks to see if an exception should occur as a result of the #
# FP instruction emulation. If so, then an FP exception of the correct #
# type is inserted into the FPU state frame using the "frestore" #
# instruction before exiting through _fpsp_done(). In either the #
# exceptional or non-exceptional cases, we must check to see if the #
# Trace exception is enabled. If so, then we must create a Trace #
# exception frame from the current exception frame and exit through #
# _real_trace(). #
# For "fdbcc", "ftrapcc", and "fscc", the emulation subroutines #
# _fdbcc(), _ftrapcc(), and _fscc() respectively are used. All three #
# may flag that a BSUN exception should be taken. If so, then the #
# current exception stack frame is converted into a BSUN exception #
# stack frame and an exit is made through _real_bsun(). If the #
# instruction was "ftrapcc" and a Trap exception should result, a Trap #
# exception stack frame is created from the current frame and an exit #
# is made through _real_trap(). If a Trace exception is pending, then #
# a Trace exception frame is created from the current frame and a jump #
# is made to _real_trace(). Finally, if none of these conditions exist, #
# then the handler exits though the callout _fpsp_done(). #
# #
# In any of the above scenarios, if a _mem_read() or _mem_write() #
# "callout" returns a failing value, then an access error stack frame #
# is created from the current stack frame and an exit is made through #
# _real_access(). #
# #
#########################################################################
#
# FP UNIMPLEMENTED INSTRUCTION STACK FRAME:
#
# *****************
# * * => <ea> of fp unimp instr.
# - EA -
# * *
# *****************
# * 0x2 * 0x02c * => frame format and vector offset(vector #11)
# *****************
# * *
# - Next PC - => PC of instr to execute after exc handling
# * *
# *****************
# * SR * => SR at the time the exception was taken
# *****************
#
# Note: the !NULL bit does not get set in the fsave frame when the
# machine encounters an fp unimp exception. Therefore, it must be set
# before leaving this handler.
#
global _fpsp_unimp
_fpsp_unimp:
link.w %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1
btst &0x5,EXC_SR(%a6) # user mode exception?
bne.b funimp_s # no; supervisor mode
# save the value of the user stack pointer onto the stack frame
funimp_u:
mov.l %usp,%a0 # fetch user stack pointer
mov.l %a0,EXC_A7(%a6) # store in stack frame
bra.b funimp_cont
# store the value of the supervisor stack pointer BEFORE the exc occurred.
# old_sp is address just above stacked effective address.
funimp_s:
lea 4+EXC_EA(%a6),%a0 # load old a7'
mov.l %a0,EXC_A7(%a6) # store a7'
mov.l %a0,OLD_A7(%a6) # make a copy
funimp_cont:
# the FPIAR holds the "current PC" of the faulting instruction.
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
############################################################################
fmov.l &0x0,%fpcr # clear FPCR
fmov.l &0x0,%fpsr # clear FPSR
clr.b SPCOND_FLG(%a6) # clear "special case" flag
# Divide the fp instructions into 8 types based on the TYPE field in
# bits 6-8 of the opword(classes 6,7 are undefined).
# (for the '060, only two types can take this exception)
# bftst %d0{&7:&3} # test TYPE
btst &22,%d0 # type 0 or 1 ?
bne.w funimp_misc # type 1
#########################################
# TYPE == 0: General instructions #
#########################################
funimp_gen:
clr.b STORE_FLG(%a6) # clear "store result" flag
# clear the ccode byte and exception status byte
andi.l &0x00ff00ff,USER_FPSR(%a6)
bfextu %d0{&16:&6},%d1 # extract upper 6 of cmdreg
cmpi.b %d1,&0x17 # is op an fmovecr?
beq.w funimp_fmovcr # yes
funimp_gen_op:
bsr.l _load_fop # load
clr.l %d0
mov.b FPCR_MODE(%a6),%d0 # fetch rnd mode
mov.b 1+EXC_CMDREG(%a6),%d1
andi.w &0x003f,%d1 # extract extension bits
lsl.w &0x3,%d1 # shift right 3 bits
or.b STAG(%a6),%d1 # insert src optag bits
lea FP_DST(%a6),%a1 # pass dst ptr in a1
lea FP_SRC(%a6),%a0 # pass src ptr in a0
mov.w (tbl_trans.w,%pc,%d1.w*2),%d1
jsr (tbl_trans.w,%pc,%d1.w*1) # emulate
funimp_fsave:
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w funimp_ena # some are enabled
funimp_store:
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # fetch Dn
bsr.l store_fpreg # store result to fp regfile
funimp_gen_exit:
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
funimp_gen_exit_cmp:
cmpi.b SPCOND_FLG(%a6),&mia7_flg # was the ea mode (sp)+ ?
beq.b funimp_gen_exit_a7 # yes
cmpi.b SPCOND_FLG(%a6),&mda7_flg # was the ea mode -(sp) ?
beq.b funimp_gen_exit_a7 # yes
funimp_gen_exit_cont:
unlk %a6
funimp_gen_exit_cont2:
btst &0x7,(%sp) # is trace on?
beq.l _fpsp_done # no
# this catches a problem with the case where an exception will be re-inserted
# into the machine. the frestore has already been executed...so, the fmov.l
# alone of the control register would trigger an unwanted exception.
# until I feel like fixing this, we'll sidestep the exception.
fsave -(%sp)
fmov.l %fpiar,0x14(%sp) # "Current PC" is in FPIAR
frestore (%sp)+
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x24
bra.l _real_trace
funimp_gen_exit_a7:
btst &0x5,EXC_SR(%a6) # supervisor or user mode?
bne.b funimp_gen_exit_a7_s # supervisor
mov.l %a0,-(%sp)
mov.l EXC_A7(%a6),%a0
mov.l %a0,%usp
mov.l (%sp)+,%a0
bra.b funimp_gen_exit_cont
# if the instruction was executed from supervisor mode and the addressing
# mode was (a7)+, then the stack frame for the rte must be shifted "up"
# "n" bytes where "n" is the size of the src operand type.
# f<op>.{b,w,l,s,d,x,p}
funimp_gen_exit_a7_s:
mov.l %d0,-(%sp) # save d0
mov.l EXC_A7(%a6),%d0 # load new a7'
sub.l OLD_A7(%a6),%d0 # subtract old a7'
mov.l 0x2+EXC_PC(%a6),(0x2+EXC_PC,%a6,%d0) # shift stack frame
mov.l EXC_SR(%a6),(EXC_SR,%a6,%d0) # shift stack frame
mov.w %d0,EXC_SR(%a6) # store incr number
mov.l (%sp)+,%d0 # restore d0
unlk %a6
add.w (%sp),%sp # stack frame shifted
bra.b funimp_gen_exit_cont2
######################
# fmovecr.x #ccc,fpn #
######################
funimp_fmovcr:
clr.l %d0
mov.b FPCR_MODE(%a6),%d0
mov.b 1+EXC_CMDREG(%a6),%d1
andi.l &0x0000007f,%d1 # pass rom offset in d1
bsr.l smovcr
bra.w funimp_fsave
#########################################################################
#
# the user has enabled some exceptions. we figure not to see this too
# often so that's why it gets lower priority.
#
funimp_ena:
# was an exception set that was also enabled?
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled and set
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b funimp_exc # at least one was set
# no exception that was enabled was set BUT if we got an exact overflow
# and overflow wasn't enabled but inexact was (yech!) then this is
# an inexact exception; otherwise, return to normal non-exception flow.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
beq.w funimp_store # no; return to normal flow
# the overflow w/ exact result happened but was inexact set in the FPCR?
funimp_ovfl:
btst &inex2_bit,FPCR_ENABLE(%a6) # is inexact enabled?
beq.w funimp_store # no; return to normal flow
bra.b funimp_exc_ovfl # yes
# some exception happened that was actually enabled.
# we'll insert this new exception into the FPU and then return.
funimp_exc:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX?
bne.b funimp_exc_force # no
# the enabled exception was inexact. so, if it occurs with an overflow
# or underflow that was disabled, then we have to force an overflow or
# underflow frame. the eventual overflow or underflow handler will see that
# it's actually an inexact and act appropriately. this is the only easy
# way to have the EXOP available for the enabled inexact handler when
# a disabled overflow or underflow has also happened.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
bne.b funimp_exc_ovfl # yes
btst &unfl_bit,FPSR_EXCEPT(%a6) # did underflow occur?
bne.b funimp_exc_unfl # yes
# force the fsave exception status bits to signal an exception of the
# appropriate type. don't forget to "skew" the source operand in case we
# "unskewed" the one the hardware initially gave us.
funimp_exc_force:
mov.l %d0,-(%sp) # save d0
bsr.l funimp_skew # check for special case
mov.l (%sp)+,%d0 # restore d0
mov.w (tbl_funimp_except.b,%pc,%d0.w*2),2+FP_SRC(%a6)
bra.b funimp_gen_exit2 # exit with frestore
tbl_funimp_except:
short 0xe002, 0xe006, 0xe004, 0xe005
short 0xe003, 0xe002, 0xe001, 0xe001
# insert an overflow frame
funimp_exc_ovfl:
bsr.l funimp_skew # check for special case
mov.w &0xe005,2+FP_SRC(%a6)
bra.b funimp_gen_exit2
# insert an underflow frame
funimp_exc_unfl:
bsr.l funimp_skew # check for special case
mov.w &0xe003,2+FP_SRC(%a6)
# this is the general exit point for an enabled exception that will be
# restored into the machine for the instruction just emulated.
funimp_gen_exit2:
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # insert exceptional status
bra.w funimp_gen_exit_cmp
############################################################################
#
# TYPE == 1: FDB<cc>, FS<cc>, FTRAP<cc>
#
# These instructions were implemented on the '881/2 and '040 in hardware but
# are emulated in software on the '060.
#
funimp_misc:
bfextu %d0{&10:&3},%d1 # extract mode field
cmpi.b %d1,&0x1 # is it an fdb<cc>?
beq.w funimp_fdbcc # yes
cmpi.b %d1,&0x7 # is it an fs<cc>?
bne.w funimp_fscc # yes
bfextu %d0{&13:&3},%d1
cmpi.b %d1,&0x2 # is it an fs<cc>?
blt.w funimp_fscc # yes
#########################
# ftrap<cc> #
# ftrap<cc>.w #<data> #
# ftrap<cc>.l #<data> #
#########################
funimp_ftrapcc:
bsr.l _ftrapcc # FTRAP<cc>()
cmpi.b SPCOND_FLG(%a6),&fbsun_flg # is enabled bsun occurring?
beq.w funimp_bsun # yes
cmpi.b SPCOND_FLG(%a6),&ftrapcc_flg # should a trap occur?
bne.w funimp_done # no
# FP UNIMP FRAME TRAP FRAME
# ***************** *****************
# ** <EA> ** ** Current PC **
# ***************** *****************
# * 0x2 * 0x02c * * 0x2 * 0x01c *
# ***************** *****************
# ** Next PC ** ** Next PC **
# ***************** *****************
# * SR * * SR *
# ***************** *****************
# (6 words) (6 words)
#
# the ftrapcc instruction should take a trap. so, here we must create a
# trap stack frame from an unimplemented fp instruction stack frame and
# jump to the user supplied entry point for the trap exception
funimp_ftrapcc_tp:
mov.l USER_FPIAR(%a6),EXC_EA(%a6) # Address = Current PC
mov.w &0x201c,EXC_VOFF(%a6) # Vector Offset = 0x01c
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
bra.l _real_trap
#########################
# fdb<cc> Dn,<label> #
#########################
funimp_fdbcc:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word # read displacement
tst.l %d1 # did ifetch fail?
bne.w funimp_iacc # yes
ext.l %d0 # sign extend displacement
bsr.l _fdbcc # FDB<cc>()
cmpi.b SPCOND_FLG(%a6),&fbsun_flg # is enabled bsun occurring?
beq.w funimp_bsun
bra.w funimp_done # branch to finish
#################
# fs<cc>.b <ea> #
#################
funimp_fscc:
bsr.l _fscc # FS<cc>()
# I am assuming here that an "fs<cc>.b -(An)" or "fs<cc>.b (An)+" instruction
# does not need to update "An" before taking a bsun exception.
cmpi.b SPCOND_FLG(%a6),&fbsun_flg # is enabled bsun occurring?
beq.w funimp_bsun
btst &0x5,EXC_SR(%a6) # yes; is it a user mode exception?
bne.b funimp_fscc_s # no
funimp_fscc_u:
mov.l EXC_A7(%a6),%a0 # yes; set new USP
mov.l %a0,%usp
bra.w funimp_done # branch to finish
# remember, I'm assuming that post-increment is bogus...(it IS!!!)
# so, the least significant WORD of the stacked effective address got
# overwritten by the "fs<cc> -(An)". We must shift the stack frame "down"
# so that the rte will work correctly without destroying the result.
# even though the operation size is byte, the stack ptr is decr by 2.
#
# remember, also, this instruction may be traced.
funimp_fscc_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg # was a7 modified?
bne.w funimp_done # no
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
btst &0x7,(%sp) # is trace enabled?
bne.b funimp_fscc_s_trace # yes
subq.l &0x2,%sp
mov.l 0x2(%sp),(%sp) # shift SR,hi(PC) "down"
mov.l 0x6(%sp),0x4(%sp) # shift lo(PC),voff "down"
bra.l _fpsp_done
funimp_fscc_s_trace:
subq.l &0x2,%sp
mov.l 0x2(%sp),(%sp) # shift SR,hi(PC) "down"
mov.w 0x6(%sp),0x4(%sp) # shift lo(PC)
mov.w &0x2024,0x6(%sp) # fmt/voff = $2024
fmov.l %fpiar,0x8(%sp) # insert "current PC"
bra.l _real_trace
#
# The ftrap<cc>, fs<cc>, or fdb<cc> is to take an enabled bsun. we must convert
# the fp unimplemented instruction exception stack frame into a bsun stack frame,
# restore a bsun exception into the machine, and branch to the user
# supplied bsun hook.
#
# FP UNIMP FRAME BSUN FRAME
# ***************** *****************
# ** <EA> ** * 0x0 * 0x0c0 *
# ***************** *****************
# * 0x2 * 0x02c * ** Current PC **
# ***************** *****************
# ** Next PC ** * SR *
# ***************** *****************
# * SR * (4 words)
# *****************
# (6 words)
#
funimp_bsun:
mov.w &0x00c0,2+EXC_EA(%a6) # Fmt = 0x0; Vector Offset = 0x0c0
mov.l USER_FPIAR(%a6),EXC_VOFF(%a6) # PC = Current PC
mov.w EXC_SR(%a6),2+EXC_PC(%a6) # shift SR "up"
mov.w &0xe000,2+FP_SRC(%a6) # bsun exception enabled
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
frestore FP_SRC(%a6) # restore bsun exception
unlk %a6
addq.l &0x4,%sp # erase sludge
bra.l _real_bsun # branch to user bsun hook
#
# all ftrapcc/fscc/fdbcc processing has been completed. unwind the stack frame
# and return.
#
# as usual, we have to check for trace mode being on here. since instructions
# modifying the supervisor stack frame don't pass through here, this is a
# relatively easy task.
#
funimp_done:
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
btst &0x7,(%sp) # is trace enabled?
bne.b funimp_trace # yes
bra.l _fpsp_done
# FP UNIMP FRAME TRACE FRAME
# ***************** *****************
# ** <EA> ** ** Current PC **
# ***************** *****************
# * 0x2 * 0x02c * * 0x2 * 0x024 *
# ***************** *****************
# ** Next PC ** ** Next PC **
# ***************** *****************
# * SR * * SR *
# ***************** *****************
# (6 words) (6 words)
#
# the fscc instruction should take a trace trap. so, here we must create a
# trace stack frame from an unimplemented fp instruction stack frame and
# jump to the user supplied entry point for the trace exception
funimp_trace:
fmov.l %fpiar,0x8(%sp) # current PC is in fpiar
mov.b &0x24,0x7(%sp) # vector offset = 0x024
bra.l _real_trace
################################################################
global tbl_trans
swbeg &0x1c0
tbl_trans:
short tbl_trans - tbl_trans # $00-0 fmovecr all
short tbl_trans - tbl_trans # $00-1 fmovecr all
short tbl_trans - tbl_trans # $00-2 fmovecr all
short tbl_trans - tbl_trans # $00-3 fmovecr all
short tbl_trans - tbl_trans # $00-4 fmovecr all
short tbl_trans - tbl_trans # $00-5 fmovecr all
short tbl_trans - tbl_trans # $00-6 fmovecr all
short tbl_trans - tbl_trans # $00-7 fmovecr all
short tbl_trans - tbl_trans # $01-0 fint norm
short tbl_trans - tbl_trans # $01-1 fint zero
short tbl_trans - tbl_trans # $01-2 fint inf
short tbl_trans - tbl_trans # $01-3 fint qnan
short tbl_trans - tbl_trans # $01-5 fint denorm
short tbl_trans - tbl_trans # $01-4 fint snan
short tbl_trans - tbl_trans # $01-6 fint unnorm
short tbl_trans - tbl_trans # $01-7 ERROR
short ssinh - tbl_trans # $02-0 fsinh norm
short src_zero - tbl_trans # $02-1 fsinh zero
short src_inf - tbl_trans # $02-2 fsinh inf
short src_qnan - tbl_trans # $02-3 fsinh qnan
short ssinhd - tbl_trans # $02-5 fsinh denorm
short src_snan - tbl_trans # $02-4 fsinh snan
short tbl_trans - tbl_trans # $02-6 fsinh unnorm
short tbl_trans - tbl_trans # $02-7 ERROR
short tbl_trans - tbl_trans # $03-0 fintrz norm
short tbl_trans - tbl_trans # $03-1 fintrz zero
short tbl_trans - tbl_trans # $03-2 fintrz inf
short tbl_trans - tbl_trans # $03-3 fintrz qnan
short tbl_trans - tbl_trans # $03-5 fintrz denorm
short tbl_trans - tbl_trans # $03-4 fintrz snan
short tbl_trans - tbl_trans # $03-6 fintrz unnorm
short tbl_trans - tbl_trans # $03-7 ERROR
short tbl_trans - tbl_trans # $04-0 fsqrt norm
short tbl_trans - tbl_trans # $04-1 fsqrt zero
short tbl_trans - tbl_trans # $04-2 fsqrt inf
short tbl_trans - tbl_trans # $04-3 fsqrt qnan
short tbl_trans - tbl_trans # $04-5 fsqrt denorm
short tbl_trans - tbl_trans # $04-4 fsqrt snan
short tbl_trans - tbl_trans # $04-6 fsqrt unnorm
short tbl_trans - tbl_trans # $04-7 ERROR
short tbl_trans - tbl_trans # $05-0 ERROR
short tbl_trans - tbl_trans # $05-1 ERROR
short tbl_trans - tbl_trans # $05-2 ERROR
short tbl_trans - tbl_trans # $05-3 ERROR
short tbl_trans - tbl_trans # $05-4 ERROR
short tbl_trans - tbl_trans # $05-5 ERROR
short tbl_trans - tbl_trans # $05-6 ERROR
short tbl_trans - tbl_trans # $05-7 ERROR
short slognp1 - tbl_trans # $06-0 flognp1 norm
short src_zero - tbl_trans # $06-1 flognp1 zero
short sopr_inf - tbl_trans # $06-2 flognp1 inf
short src_qnan - tbl_trans # $06-3 flognp1 qnan
short slognp1d - tbl_trans # $06-5 flognp1 denorm
short src_snan - tbl_trans # $06-4 flognp1 snan
short tbl_trans - tbl_trans # $06-6 flognp1 unnorm
short tbl_trans - tbl_trans # $06-7 ERROR
short tbl_trans - tbl_trans # $07-0 ERROR
short tbl_trans - tbl_trans # $07-1 ERROR
short tbl_trans - tbl_trans # $07-2 ERROR
short tbl_trans - tbl_trans # $07-3 ERROR
short tbl_trans - tbl_trans # $07-4 ERROR
short tbl_trans - tbl_trans # $07-5 ERROR
short tbl_trans - tbl_trans # $07-6 ERROR
short tbl_trans - tbl_trans # $07-7 ERROR
short setoxm1 - tbl_trans # $08-0 fetoxm1 norm
short src_zero - tbl_trans # $08-1 fetoxm1 zero
short setoxm1i - tbl_trans # $08-2 fetoxm1 inf
short src_qnan - tbl_trans # $08-3 fetoxm1 qnan
short setoxm1d - tbl_trans # $08-5 fetoxm1 denorm
short src_snan - tbl_trans # $08-4 fetoxm1 snan
short tbl_trans - tbl_trans # $08-6 fetoxm1 unnorm
short tbl_trans - tbl_trans # $08-7 ERROR
short stanh - tbl_trans # $09-0 ftanh norm
short src_zero - tbl_trans # $09-1 ftanh zero
short src_one - tbl_trans # $09-2 ftanh inf
short src_qnan - tbl_trans # $09-3 ftanh qnan
short stanhd - tbl_trans # $09-5 ftanh denorm
short src_snan - tbl_trans # $09-4 ftanh snan
short tbl_trans - tbl_trans # $09-6 ftanh unnorm
short tbl_trans - tbl_trans # $09-7 ERROR
short satan - tbl_trans # $0a-0 fatan norm
short src_zero - tbl_trans # $0a-1 fatan zero
short spi_2 - tbl_trans # $0a-2 fatan inf
short src_qnan - tbl_trans # $0a-3 fatan qnan
short satand - tbl_trans # $0a-5 fatan denorm
short src_snan - tbl_trans # $0a-4 fatan snan
short tbl_trans - tbl_trans # $0a-6 fatan unnorm
short tbl_trans - tbl_trans # $0a-7 ERROR
short tbl_trans - tbl_trans # $0b-0 ERROR
short tbl_trans - tbl_trans # $0b-1 ERROR
short tbl_trans - tbl_trans # $0b-2 ERROR
short tbl_trans - tbl_trans # $0b-3 ERROR
short tbl_trans - tbl_trans # $0b-4 ERROR
short tbl_trans - tbl_trans # $0b-5 ERROR
short tbl_trans - tbl_trans # $0b-6 ERROR
short tbl_trans - tbl_trans # $0b-7 ERROR
short sasin - tbl_trans # $0c-0 fasin norm
short src_zero - tbl_trans # $0c-1 fasin zero
short t_operr - tbl_trans # $0c-2 fasin inf
short src_qnan - tbl_trans # $0c-3 fasin qnan
short sasind - tbl_trans # $0c-5 fasin denorm
short src_snan - tbl_trans # $0c-4 fasin snan
short tbl_trans - tbl_trans # $0c-6 fasin unnorm
short tbl_trans - tbl_trans # $0c-7 ERROR
short satanh - tbl_trans # $0d-0 fatanh norm
short src_zero - tbl_trans # $0d-1 fatanh zero
short t_operr - tbl_trans # $0d-2 fatanh inf
short src_qnan - tbl_trans # $0d-3 fatanh qnan
short satanhd - tbl_trans # $0d-5 fatanh denorm
short src_snan - tbl_trans # $0d-4 fatanh snan
short tbl_trans - tbl_trans # $0d-6 fatanh unnorm
short tbl_trans - tbl_trans # $0d-7 ERROR
short ssin - tbl_trans # $0e-0 fsin norm
short src_zero - tbl_trans # $0e-1 fsin zero
short t_operr - tbl_trans # $0e-2 fsin inf
short src_qnan - tbl_trans # $0e-3 fsin qnan
short ssind - tbl_trans # $0e-5 fsin denorm
short src_snan - tbl_trans # $0e-4 fsin snan
short tbl_trans - tbl_trans # $0e-6 fsin unnorm
short tbl_trans - tbl_trans # $0e-7 ERROR
short stan - tbl_trans # $0f-0 ftan norm
short src_zero - tbl_trans # $0f-1 ftan zero
short t_operr - tbl_trans # $0f-2 ftan inf
short src_qnan - tbl_trans # $0f-3 ftan qnan
short stand - tbl_trans # $0f-5 ftan denorm
short src_snan - tbl_trans # $0f-4 ftan snan
short tbl_trans - tbl_trans # $0f-6 ftan unnorm
short tbl_trans - tbl_trans # $0f-7 ERROR
short setox - tbl_trans # $10-0 fetox norm
short ld_pone - tbl_trans # $10-1 fetox zero
short szr_inf - tbl_trans # $10-2 fetox inf
short src_qnan - tbl_trans # $10-3 fetox qnan
short setoxd - tbl_trans # $10-5 fetox denorm
short src_snan - tbl_trans # $10-4 fetox snan
short tbl_trans - tbl_trans # $10-6 fetox unnorm
short tbl_trans - tbl_trans # $10-7 ERROR
short stwotox - tbl_trans # $11-0 ftwotox norm
short ld_pone - tbl_trans # $11-1 ftwotox zero
short szr_inf - tbl_trans # $11-2 ftwotox inf
short src_qnan - tbl_trans # $11-3 ftwotox qnan
short stwotoxd - tbl_trans # $11-5 ftwotox denorm
short src_snan - tbl_trans # $11-4 ftwotox snan
short tbl_trans - tbl_trans # $11-6 ftwotox unnorm
short tbl_trans - tbl_trans # $11-7 ERROR
short stentox - tbl_trans # $12-0 ftentox norm
short ld_pone - tbl_trans # $12-1 ftentox zero
short szr_inf - tbl_trans # $12-2 ftentox inf
short src_qnan - tbl_trans # $12-3 ftentox qnan
short stentoxd - tbl_trans # $12-5 ftentox denorm
short src_snan - tbl_trans # $12-4 ftentox snan
short tbl_trans - tbl_trans # $12-6 ftentox unnorm
short tbl_trans - tbl_trans # $12-7 ERROR
short tbl_trans - tbl_trans # $13-0 ERROR
short tbl_trans - tbl_trans # $13-1 ERROR
short tbl_trans - tbl_trans # $13-2 ERROR
short tbl_trans - tbl_trans # $13-3 ERROR
short tbl_trans - tbl_trans # $13-4 ERROR
short tbl_trans - tbl_trans # $13-5 ERROR
short tbl_trans - tbl_trans # $13-6 ERROR
short tbl_trans - tbl_trans # $13-7 ERROR
short slogn - tbl_trans # $14-0 flogn norm
short t_dz2 - tbl_trans # $14-1 flogn zero
short sopr_inf - tbl_trans # $14-2 flogn inf
short src_qnan - tbl_trans # $14-3 flogn qnan
short slognd - tbl_trans # $14-5 flogn denorm
short src_snan - tbl_trans # $14-4 flogn snan
short tbl_trans - tbl_trans # $14-6 flogn unnorm
short tbl_trans - tbl_trans # $14-7 ERROR
short slog10 - tbl_trans # $15-0 flog10 norm
short t_dz2 - tbl_trans # $15-1 flog10 zero
short sopr_inf - tbl_trans # $15-2 flog10 inf
short src_qnan - tbl_trans # $15-3 flog10 qnan
short slog10d - tbl_trans # $15-5 flog10 denorm
short src_snan - tbl_trans # $15-4 flog10 snan
short tbl_trans - tbl_trans # $15-6 flog10 unnorm
short tbl_trans - tbl_trans # $15-7 ERROR
short slog2 - tbl_trans # $16-0 flog2 norm
short t_dz2 - tbl_trans # $16-1 flog2 zero
short sopr_inf - tbl_trans # $16-2 flog2 inf
short src_qnan - tbl_trans # $16-3 flog2 qnan
short slog2d - tbl_trans # $16-5 flog2 denorm
short src_snan - tbl_trans # $16-4 flog2 snan
short tbl_trans - tbl_trans # $16-6 flog2 unnorm
short tbl_trans - tbl_trans # $16-7 ERROR
short tbl_trans - tbl_trans # $17-0 ERROR
short tbl_trans - tbl_trans # $17-1 ERROR
short tbl_trans - tbl_trans # $17-2 ERROR
short tbl_trans - tbl_trans # $17-3 ERROR
short tbl_trans - tbl_trans # $17-4 ERROR
short tbl_trans - tbl_trans # $17-5 ERROR
short tbl_trans - tbl_trans # $17-6 ERROR
short tbl_trans - tbl_trans # $17-7 ERROR
short tbl_trans - tbl_trans # $18-0 fabs norm
short tbl_trans - tbl_trans # $18-1 fabs zero
short tbl_trans - tbl_trans # $18-2 fabs inf
short tbl_trans - tbl_trans # $18-3 fabs qnan
short tbl_trans - tbl_trans # $18-5 fabs denorm
short tbl_trans - tbl_trans # $18-4 fabs snan
short tbl_trans - tbl_trans # $18-6 fabs unnorm
short tbl_trans - tbl_trans # $18-7 ERROR
short scosh - tbl_trans # $19-0 fcosh norm
short ld_pone - tbl_trans # $19-1 fcosh zero
short ld_pinf - tbl_trans # $19-2 fcosh inf
short src_qnan - tbl_trans # $19-3 fcosh qnan
short scoshd - tbl_trans # $19-5 fcosh denorm
short src_snan - tbl_trans # $19-4 fcosh snan
short tbl_trans - tbl_trans # $19-6 fcosh unnorm
short tbl_trans - tbl_trans # $19-7 ERROR
short tbl_trans - tbl_trans # $1a-0 fneg norm
short tbl_trans - tbl_trans # $1a-1 fneg zero
short tbl_trans - tbl_trans # $1a-2 fneg inf
short tbl_trans - tbl_trans # $1a-3 fneg qnan
short tbl_trans - tbl_trans # $1a-5 fneg denorm
short tbl_trans - tbl_trans # $1a-4 fneg snan
short tbl_trans - tbl_trans # $1a-6 fneg unnorm
short tbl_trans - tbl_trans # $1a-7 ERROR
short tbl_trans - tbl_trans # $1b-0 ERROR
short tbl_trans - tbl_trans # $1b-1 ERROR
short tbl_trans - tbl_trans # $1b-2 ERROR
short tbl_trans - tbl_trans # $1b-3 ERROR
short tbl_trans - tbl_trans # $1b-4 ERROR
short tbl_trans - tbl_trans # $1b-5 ERROR
short tbl_trans - tbl_trans # $1b-6 ERROR
short tbl_trans - tbl_trans # $1b-7 ERROR
short sacos - tbl_trans # $1c-0 facos norm
short ld_ppi2 - tbl_trans # $1c-1 facos zero
short t_operr - tbl_trans # $1c-2 facos inf
short src_qnan - tbl_trans # $1c-3 facos qnan
short sacosd - tbl_trans # $1c-5 facos denorm
short src_snan - tbl_trans # $1c-4 facos snan
short tbl_trans - tbl_trans # $1c-6 facos unnorm
short tbl_trans - tbl_trans # $1c-7 ERROR
short scos - tbl_trans # $1d-0 fcos norm
short ld_pone - tbl_trans # $1d-1 fcos zero
short t_operr - tbl_trans # $1d-2 fcos inf
short src_qnan - tbl_trans # $1d-3 fcos qnan
short scosd - tbl_trans # $1d-5 fcos denorm
short src_snan - tbl_trans # $1d-4 fcos snan
short tbl_trans - tbl_trans # $1d-6 fcos unnorm
short tbl_trans - tbl_trans # $1d-7 ERROR
short sgetexp - tbl_trans # $1e-0 fgetexp norm
short src_zero - tbl_trans # $1e-1 fgetexp zero
short t_operr - tbl_trans # $1e-2 fgetexp inf
short src_qnan - tbl_trans # $1e-3 fgetexp qnan
short sgetexpd - tbl_trans # $1e-5 fgetexp denorm
short src_snan - tbl_trans # $1e-4 fgetexp snan
short tbl_trans - tbl_trans # $1e-6 fgetexp unnorm
short tbl_trans - tbl_trans # $1e-7 ERROR
short sgetman - tbl_trans # $1f-0 fgetman norm
short src_zero - tbl_trans # $1f-1 fgetman zero
short t_operr - tbl_trans # $1f-2 fgetman inf
short src_qnan - tbl_trans # $1f-3 fgetman qnan
short sgetmand - tbl_trans # $1f-5 fgetman denorm
short src_snan - tbl_trans # $1f-4 fgetman snan
short tbl_trans - tbl_trans # $1f-6 fgetman unnorm
short tbl_trans - tbl_trans # $1f-7 ERROR
short tbl_trans - tbl_trans # $20-0 fdiv norm
short tbl_trans - tbl_trans # $20-1 fdiv zero
short tbl_trans - tbl_trans # $20-2 fdiv inf
short tbl_trans - tbl_trans # $20-3 fdiv qnan
short tbl_trans - tbl_trans # $20-5 fdiv denorm
short tbl_trans - tbl_trans # $20-4 fdiv snan
short tbl_trans - tbl_trans # $20-6 fdiv unnorm
short tbl_trans - tbl_trans # $20-7 ERROR
short smod_snorm - tbl_trans # $21-0 fmod norm
short smod_szero - tbl_trans # $21-1 fmod zero
short smod_sinf - tbl_trans # $21-2 fmod inf
short sop_sqnan - tbl_trans # $21-3 fmod qnan
short smod_sdnrm - tbl_trans # $21-5 fmod denorm
short sop_ssnan - tbl_trans # $21-4 fmod snan
short tbl_trans - tbl_trans # $21-6 fmod unnorm
short tbl_trans - tbl_trans # $21-7 ERROR
short tbl_trans - tbl_trans # $22-0 fadd norm
short tbl_trans - tbl_trans # $22-1 fadd zero
short tbl_trans - tbl_trans # $22-2 fadd inf
short tbl_trans - tbl_trans # $22-3 fadd qnan
short tbl_trans - tbl_trans # $22-5 fadd denorm
short tbl_trans - tbl_trans # $22-4 fadd snan
short tbl_trans - tbl_trans # $22-6 fadd unnorm
short tbl_trans - tbl_trans # $22-7 ERROR
short tbl_trans - tbl_trans # $23-0 fmul norm
short tbl_trans - tbl_trans # $23-1 fmul zero
short tbl_trans - tbl_trans # $23-2 fmul inf
short tbl_trans - tbl_trans # $23-3 fmul qnan
short tbl_trans - tbl_trans # $23-5 fmul denorm
short tbl_trans - tbl_trans # $23-4 fmul snan
short tbl_trans - tbl_trans # $23-6 fmul unnorm
short tbl_trans - tbl_trans # $23-7 ERROR
short tbl_trans - tbl_trans # $24-0 fsgldiv norm
short tbl_trans - tbl_trans # $24-1 fsgldiv zero
short tbl_trans - tbl_trans # $24-2 fsgldiv inf
short tbl_trans - tbl_trans # $24-3 fsgldiv qnan
short tbl_trans - tbl_trans # $24-5 fsgldiv denorm
short tbl_trans - tbl_trans # $24-4 fsgldiv snan
short tbl_trans - tbl_trans # $24-6 fsgldiv unnorm
short tbl_trans - tbl_trans # $24-7 ERROR
short srem_snorm - tbl_trans # $25-0 frem norm
short srem_szero - tbl_trans # $25-1 frem zero
short srem_sinf - tbl_trans # $25-2 frem inf
short sop_sqnan - tbl_trans # $25-3 frem qnan
short srem_sdnrm - tbl_trans # $25-5 frem denorm
short sop_ssnan - tbl_trans # $25-4 frem snan
short tbl_trans - tbl_trans # $25-6 frem unnorm
short tbl_trans - tbl_trans # $25-7 ERROR
short sscale_snorm - tbl_trans # $26-0 fscale norm
short sscale_szero - tbl_trans # $26-1 fscale zero
short sscale_sinf - tbl_trans # $26-2 fscale inf
short sop_sqnan - tbl_trans # $26-3 fscale qnan
short sscale_sdnrm - tbl_trans # $26-5 fscale denorm
short sop_ssnan - tbl_trans # $26-4 fscale snan
short tbl_trans - tbl_trans # $26-6 fscale unnorm
short tbl_trans - tbl_trans # $26-7 ERROR
short tbl_trans - tbl_trans # $27-0 fsglmul norm
short tbl_trans - tbl_trans # $27-1 fsglmul zero
short tbl_trans - tbl_trans # $27-2 fsglmul inf
short tbl_trans - tbl_trans # $27-3 fsglmul qnan
short tbl_trans - tbl_trans # $27-5 fsglmul denorm
short tbl_trans - tbl_trans # $27-4 fsglmul snan
short tbl_trans - tbl_trans # $27-6 fsglmul unnorm
short tbl_trans - tbl_trans # $27-7 ERROR
short tbl_trans - tbl_trans # $28-0 fsub norm
short tbl_trans - tbl_trans # $28-1 fsub zero
short tbl_trans - tbl_trans # $28-2 fsub inf
short tbl_trans - tbl_trans # $28-3 fsub qnan
short tbl_trans - tbl_trans # $28-5 fsub denorm
short tbl_trans - tbl_trans # $28-4 fsub snan
short tbl_trans - tbl_trans # $28-6 fsub unnorm
short tbl_trans - tbl_trans # $28-7 ERROR
short tbl_trans - tbl_trans # $29-0 ERROR
short tbl_trans - tbl_trans # $29-1 ERROR
short tbl_trans - tbl_trans # $29-2 ERROR
short tbl_trans - tbl_trans # $29-3 ERROR
short tbl_trans - tbl_trans # $29-4 ERROR
short tbl_trans - tbl_trans # $29-5 ERROR
short tbl_trans - tbl_trans # $29-6 ERROR
short tbl_trans - tbl_trans # $29-7 ERROR
short tbl_trans - tbl_trans # $2a-0 ERROR
short tbl_trans - tbl_trans # $2a-1 ERROR
short tbl_trans - tbl_trans # $2a-2 ERROR
short tbl_trans - tbl_trans # $2a-3 ERROR
short tbl_trans - tbl_trans # $2a-4 ERROR
short tbl_trans - tbl_trans # $2a-5 ERROR
short tbl_trans - tbl_trans # $2a-6 ERROR
short tbl_trans - tbl_trans # $2a-7 ERROR
short tbl_trans - tbl_trans # $2b-0 ERROR
short tbl_trans - tbl_trans # $2b-1 ERROR
short tbl_trans - tbl_trans # $2b-2 ERROR
short tbl_trans - tbl_trans # $2b-3 ERROR
short tbl_trans - tbl_trans # $2b-4 ERROR
short tbl_trans - tbl_trans # $2b-5 ERROR
short tbl_trans - tbl_trans # $2b-6 ERROR
short tbl_trans - tbl_trans # $2b-7 ERROR
short tbl_trans - tbl_trans # $2c-0 ERROR
short tbl_trans - tbl_trans # $2c-1 ERROR
short tbl_trans - tbl_trans # $2c-2 ERROR
short tbl_trans - tbl_trans # $2c-3 ERROR
short tbl_trans - tbl_trans # $2c-4 ERROR
short tbl_trans - tbl_trans # $2c-5 ERROR
short tbl_trans - tbl_trans # $2c-6 ERROR
short tbl_trans - tbl_trans # $2c-7 ERROR
short tbl_trans - tbl_trans # $2d-0 ERROR
short tbl_trans - tbl_trans # $2d-1 ERROR
short tbl_trans - tbl_trans # $2d-2 ERROR
short tbl_trans - tbl_trans # $2d-3 ERROR
short tbl_trans - tbl_trans # $2d-4 ERROR
short tbl_trans - tbl_trans # $2d-5 ERROR
short tbl_trans - tbl_trans # $2d-6 ERROR
short tbl_trans - tbl_trans # $2d-7 ERROR
short tbl_trans - tbl_trans # $2e-0 ERROR
short tbl_trans - tbl_trans # $2e-1 ERROR
short tbl_trans - tbl_trans # $2e-2 ERROR
short tbl_trans - tbl_trans # $2e-3 ERROR
short tbl_trans - tbl_trans # $2e-4 ERROR
short tbl_trans - tbl_trans # $2e-5 ERROR
short tbl_trans - tbl_trans # $2e-6 ERROR
short tbl_trans - tbl_trans # $2e-7 ERROR
short tbl_trans - tbl_trans # $2f-0 ERROR
short tbl_trans - tbl_trans # $2f-1 ERROR
short tbl_trans - tbl_trans # $2f-2 ERROR
short tbl_trans - tbl_trans # $2f-3 ERROR
short tbl_trans - tbl_trans # $2f-4 ERROR
short tbl_trans - tbl_trans # $2f-5 ERROR
short tbl_trans - tbl_trans # $2f-6 ERROR
short tbl_trans - tbl_trans # $2f-7 ERROR
short ssincos - tbl_trans # $30-0 fsincos norm
short ssincosz - tbl_trans # $30-1 fsincos zero
short ssincosi - tbl_trans # $30-2 fsincos inf
short ssincosqnan - tbl_trans # $30-3 fsincos qnan
short ssincosd - tbl_trans # $30-5 fsincos denorm
short ssincossnan - tbl_trans # $30-4 fsincos snan
short tbl_trans - tbl_trans # $30-6 fsincos unnorm
short tbl_trans - tbl_trans # $30-7 ERROR
short ssincos - tbl_trans # $31-0 fsincos norm
short ssincosz - tbl_trans # $31-1 fsincos zero
short ssincosi - tbl_trans # $31-2 fsincos inf
short ssincosqnan - tbl_trans # $31-3 fsincos qnan
short ssincosd - tbl_trans # $31-5 fsincos denorm
short ssincossnan - tbl_trans # $31-4 fsincos snan
short tbl_trans - tbl_trans # $31-6 fsincos unnorm
short tbl_trans - tbl_trans # $31-7 ERROR
short ssincos - tbl_trans # $32-0 fsincos norm
short ssincosz - tbl_trans # $32-1 fsincos zero
short ssincosi - tbl_trans # $32-2 fsincos inf
short ssincosqnan - tbl_trans # $32-3 fsincos qnan
short ssincosd - tbl_trans # $32-5 fsincos denorm
short ssincossnan - tbl_trans # $32-4 fsincos snan
short tbl_trans - tbl_trans # $32-6 fsincos unnorm
short tbl_trans - tbl_trans # $32-7 ERROR
short ssincos - tbl_trans # $33-0 fsincos norm
short ssincosz - tbl_trans # $33-1 fsincos zero
short ssincosi - tbl_trans # $33-2 fsincos inf
short ssincosqnan - tbl_trans # $33-3 fsincos qnan
short ssincosd - tbl_trans # $33-5 fsincos denorm
short ssincossnan - tbl_trans # $33-4 fsincos snan
short tbl_trans - tbl_trans # $33-6 fsincos unnorm
short tbl_trans - tbl_trans # $33-7 ERROR
short ssincos - tbl_trans # $34-0 fsincos norm
short ssincosz - tbl_trans # $34-1 fsincos zero
short ssincosi - tbl_trans # $34-2 fsincos inf
short ssincosqnan - tbl_trans # $34-3 fsincos qnan
short ssincosd - tbl_trans # $34-5 fsincos denorm
short ssincossnan - tbl_trans # $34-4 fsincos snan
short tbl_trans - tbl_trans # $34-6 fsincos unnorm
short tbl_trans - tbl_trans # $34-7 ERROR
short ssincos - tbl_trans # $35-0 fsincos norm
short ssincosz - tbl_trans # $35-1 fsincos zero
short ssincosi - tbl_trans # $35-2 fsincos inf
short ssincosqnan - tbl_trans # $35-3 fsincos qnan
short ssincosd - tbl_trans # $35-5 fsincos denorm
short ssincossnan - tbl_trans # $35-4 fsincos snan
short tbl_trans - tbl_trans # $35-6 fsincos unnorm
short tbl_trans - tbl_trans # $35-7 ERROR
short ssincos - tbl_trans # $36-0 fsincos norm
short ssincosz - tbl_trans # $36-1 fsincos zero
short ssincosi - tbl_trans # $36-2 fsincos inf
short ssincosqnan - tbl_trans # $36-3 fsincos qnan
short ssincosd - tbl_trans # $36-5 fsincos denorm
short ssincossnan - tbl_trans # $36-4 fsincos snan
short tbl_trans - tbl_trans # $36-6 fsincos unnorm
short tbl_trans - tbl_trans # $36-7 ERROR
short ssincos - tbl_trans # $37-0 fsincos norm
short ssincosz - tbl_trans # $37-1 fsincos zero
short ssincosi - tbl_trans # $37-2 fsincos inf
short ssincosqnan - tbl_trans # $37-3 fsincos qnan
short ssincosd - tbl_trans # $37-5 fsincos denorm
short ssincossnan - tbl_trans # $37-4 fsincos snan
short tbl_trans - tbl_trans # $37-6 fsincos unnorm
short tbl_trans - tbl_trans # $37-7 ERROR
##########
# the instruction fetch access for the displacement word for the
# fdbcc emulation failed. here, we create an access error frame
# from the current frame and branch to _real_access().
funimp_iacc:
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
mov.l USER_FPIAR(%a6),EXC_PC(%a6) # store current PC
unlk %a6
mov.l (%sp),-(%sp) # store SR,hi(PC)
mov.w 0x8(%sp),0x4(%sp) # store lo(PC)
mov.w &0x4008,0x6(%sp) # store voff
mov.l 0x2(%sp),0x8(%sp) # store EA
mov.l &0x09428001,0xc(%sp) # store FSLW
btst &0x5,(%sp) # user or supervisor mode?
beq.b funimp_iacc_end # user
bset &0x2,0xd(%sp) # set supervisor TM bit
funimp_iacc_end:
bra.l _real_access
#########################################################################
# ssin(): computes the sine of a normalized input #
# ssind(): computes the sine of a denormalized input #
# scos(): computes the cosine of a normalized input #
# scosd(): computes the cosine of a denormalized input #
# ssincos(): computes the sine and cosine of a normalized input #
# ssincosd(): computes the sine and cosine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = sin(X) or cos(X) #
# #
# For ssincos(X): #
# fp0 = sin(X) #
# fp1 = cos(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 1 ulp in 64 significant bit, i.e. #
# within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# SIN and COS: #
# 1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1. #
# #
# 2. If |X| >= 15Pi or |X| < 2**(-40), go to 7. #
# #
# 3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let #
# k = N mod 4, so in particular, k = 0,1,2,or 3. #
# Overwrite k by k := k + AdjN. #
# #
# 4. If k is even, go to 6. #
# #
# 5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. #
# Return sgn*cos(r) where cos(r) is approximated by an #
# even polynomial in r, 1 + r*r*(B1+s*(B2+ ... + s*B8)), #
# s = r*r. #
# Exit. #
# #
# 6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r) #
# where sin(r) is approximated by an odd polynomial in r #
# r + r*s*(A1+s*(A2+ ... + s*A7)), s = r*r. #
# Exit. #
# #
# 7. If |X| > 1, go to 9. #
# #
# 8. (|X|<2**(-40)) If SIN is invoked, return X; #
# otherwise return 1. #
# #
# 9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, #
# go back to 3. #
# #
# SINCOS: #
# 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. #
# #
# 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let #
# k = N mod 4, so in particular, k = 0,1,2,or 3. #
# #
# 3. If k is even, go to 5. #
# #
# 4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), ie. #
# j1 exclusive or with the l.s.b. of k. #
# sgn1 := (-1)**j1, sgn2 := (-1)**j2. #
# SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where #
# sin(r) and cos(r) are computed as odd and even #
# polynomials in r, respectively. Exit #
# #
# 5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1. #
# SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where #
# sin(r) and cos(r) are computed as odd and even #
# polynomials in r, respectively. Exit #
# #
# 6. If |X| > 1, go to 8. #
# #
# 7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit. #
# #
# 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, #
# go back to 2. #
# #
#########################################################################
SINA7: long 0xBD6AAA77,0xCCC994F5
SINA6: long 0x3DE61209,0x7AAE8DA1
SINA5: long 0xBE5AE645,0x2A118AE4
SINA4: long 0x3EC71DE3,0xA5341531
SINA3: long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
SINA2: long 0x3FF80000,0x88888888,0x888859AF,0x00000000
SINA1: long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
COSB8: long 0x3D2AC4D0,0xD6011EE3
COSB7: long 0xBDA9396F,0x9F45AC19
COSB6: long 0x3E21EED9,0x0612C972
COSB5: long 0xBE927E4F,0xB79D9FCF
COSB4: long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
COSB3: long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
COSB2: long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
COSB1: long 0xBF000000
set INARG,FP_SCR0
set X,FP_SCR0
# set XDCARE,X+2
set XFRAC,X+4
set RPRIME,FP_SCR0
set SPRIME,FP_SCR1
set POSNEG1,L_SCR1
set TWOTO63,L_SCR1
set ENDFLAG,L_SCR2
set INT,L_SCR2
set ADJN,L_SCR3
############################################
global ssin
ssin:
mov.l &0,ADJN(%a6) # yes; SET ADJN TO 0
bra.b SINBGN
############################################
global scos
scos:
mov.l &1,ADJN(%a6) # yes; SET ADJN TO 1
############################################
SINBGN:
#--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE
fmov.x (%a0),%fp0 # LOAD INPUT
fmov.x %fp0,X(%a6) # save input at X
# "COMPACTIFY" X
mov.l (%a0),%d1 # put exp in hi word
mov.w 4(%a0),%d1 # fetch hi(man)
and.l &0x7FFFFFFF,%d1 # strip sign
cmpi.l %d1,&0x3FD78000 # is |X| >= 2**(-40)?
bge.b SOK1 # no
bra.w SINSM # yes; input is very small
SOK1:
cmp.l %d1,&0x4004BC7E # is |X| < 15 PI?
blt.b SINMAIN # no
bra.w SREDUCEX # yes; input is very large
#--THIS IS THE USUAL CASE, |X| <= 15 PI.
#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
SINMAIN:
fmov.x %fp0,%fp1
fmul.d TWOBYPI(%pc),%fp1 # X*2/PI
lea PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32
fmov.l %fp1,INT(%a6) # CONVERT TO INTEGER
mov.l INT(%a6),%d1 # make a copy of N
asl.l &4,%d1 # N *= 16
add.l %d1,%a1 # tbl_addr = a1 + (N*16)
# A1 IS THE ADDRESS OF N*PIBY2
# ...WHICH IS IN TWO PIECES Y1 & Y2
fsub.x (%a1)+,%fp0 # X-Y1
fsub.s (%a1),%fp0 # fp0 = R = (X-Y1)-Y2
SINCONT:
#--continuation from REDUCEX
#--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED
mov.l INT(%a6),%d1
add.l ADJN(%a6),%d1 # SEE IF D0 IS ODD OR EVEN
ror.l &1,%d1 # D0 WAS ODD IFF D0 IS NEGATIVE
cmp.l %d1,&0
blt.w COSPOLY
#--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
#--THEN WE RETURN SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY
#--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE
#--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS
#--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])
#--WHERE T=S*S.
#--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION
#--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.
SINPOLY:
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmov.x %fp0,X(%a6) # X IS R
fmul.x %fp0,%fp0 # FP0 IS S
fmov.d SINA7(%pc),%fp3
fmov.d SINA6(%pc),%fp2
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS T
ror.l &1,%d1
and.l &0x80000000,%d1
# ...LEAST SIG. BIT OF D0 IN SIGN POSITION
eor.l %d1,X(%a6) # X IS NOW R'= SGN*R
fmul.x %fp1,%fp3 # TA7
fmul.x %fp1,%fp2 # TA6
fadd.d SINA5(%pc),%fp3 # A5+TA7
fadd.d SINA4(%pc),%fp2 # A4+TA6
fmul.x %fp1,%fp3 # T(A5+TA7)
fmul.x %fp1,%fp2 # T(A4+TA6)
fadd.d SINA3(%pc),%fp3 # A3+T(A5+TA7)
fadd.x SINA2(%pc),%fp2 # A2+T(A4+TA6)
fmul.x %fp3,%fp1 # T(A3+T(A5+TA7))
fmul.x %fp0,%fp2 # S(A2+T(A4+TA6))
fadd.x SINA1(%pc),%fp1 # A1+T(A3+T(A5+TA7))
fmul.x X(%a6),%fp0 # R'*S
fadd.x %fp2,%fp1 # [A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
fmul.x %fp1,%fp0 # SIN(R')-R'
fmovm.x (%sp)+,&0x30 # restore fp2/fp3
fmov.l %d0,%fpcr # restore users round mode,prec
fadd.x X(%a6),%fp0 # last inst - possible exception set
bra t_inx2
#--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
#--THEN WE RETURN SGN*COS(R). SGN*COS(R) IS COMPUTED BY
#--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE
#--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS
#--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])
#--WHERE T=S*S.
#--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION
#--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2
#--AND IS THEREFORE STORED AS SINGLE PRECISION.
COSPOLY:
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmul.x %fp0,%fp0 # FP0 IS S
fmov.d COSB8(%pc),%fp2
fmov.d COSB7(%pc),%fp3
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS T
fmov.x %fp0,X(%a6) # X IS S
ror.l &1,%d1
and.l &0x80000000,%d1
# ...LEAST SIG. BIT OF D0 IN SIGN POSITION
fmul.x %fp1,%fp2 # TB8
eor.l %d1,X(%a6) # X IS NOW S'= SGN*S
and.l &0x80000000,%d1
fmul.x %fp1,%fp3 # TB7
or.l &0x3F800000,%d1 # D0 IS SGN IN SINGLE
mov.l %d1,POSNEG1(%a6)
fadd.d COSB6(%pc),%fp2 # B6+TB8
fadd.d COSB5(%pc),%fp3 # B5+TB7
fmul.x %fp1,%fp2 # T(B6+TB8)
fmul.x %fp1,%fp3 # T(B5+TB7)
fadd.d COSB4(%pc),%fp2 # B4+T(B6+TB8)
fadd.x COSB3(%pc),%fp3 # B3+T(B5+TB7)
fmul.x %fp1,%fp2 # T(B4+T(B6+TB8))
fmul.x %fp3,%fp1 # T(B3+T(B5+TB7))
fadd.x COSB2(%pc),%fp2 # B2+T(B4+T(B6+TB8))
fadd.s COSB1(%pc),%fp1 # B1+T(B3+T(B5+TB7))
fmul.x %fp2,%fp0 # S(B2+T(B4+T(B6+TB8)))
fadd.x %fp1,%fp0
fmul.x X(%a6),%fp0
fmovm.x (%sp)+,&0x30 # restore fp2/fp3
fmov.l %d0,%fpcr # restore users round mode,prec
fadd.s POSNEG1(%a6),%fp0 # last inst - possible exception set
bra t_inx2
##############################################
# SINe: Big OR Small?
#--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
#--IF |X| < 2**(-40), RETURN X OR 1.
SINBORS:
cmp.l %d1,&0x3FFF8000
bgt.l SREDUCEX
SINSM:
mov.l ADJN(%a6),%d1
cmp.l %d1,&0
bgt.b COSTINY
# here, the operation may underflow iff the precision is sgl or dbl.
# extended denorms are handled through another entry point.
SINTINY:
# mov.w &0x0000,XDCARE(%a6) # JUST IN CASE
fmov.l %d0,%fpcr # restore users round mode,prec
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0 # last inst - possible exception set
bra t_catch
COSTINY:
fmov.s &0x3F800000,%fp0 # fp0 = 1.0
fmov.l %d0,%fpcr # restore users round mode,prec
fadd.s &0x80800000,%fp0 # last inst - possible exception set
bra t_pinx2
################################################
global ssind
#--SIN(X) = X FOR DENORMALIZED X
ssind:
bra t_extdnrm
############################################
global scosd
#--COS(X) = 1 FOR DENORMALIZED X
scosd:
fmov.s &0x3F800000,%fp0 # fp0 = 1.0
bra t_pinx2
##################################################
global ssincos
ssincos:
#--SET ADJN TO 4
mov.l &4,ADJN(%a6)
fmov.x (%a0),%fp0 # LOAD INPUT
fmov.x %fp0,X(%a6)
mov.l (%a0),%d1
mov.w 4(%a0),%d1
and.l &0x7FFFFFFF,%d1 # COMPACTIFY X
cmp.l %d1,&0x3FD78000 # |X| >= 2**(-40)?
bge.b SCOK1
bra.w SCSM
SCOK1:
cmp.l %d1,&0x4004BC7E # |X| < 15 PI?
blt.b SCMAIN
bra.w SREDUCEX
#--THIS IS THE USUAL CASE, |X| <= 15 PI.
#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
SCMAIN:
fmov.x %fp0,%fp1
fmul.d TWOBYPI(%pc),%fp1 # X*2/PI
lea PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32
fmov.l %fp1,INT(%a6) # CONVERT TO INTEGER
mov.l INT(%a6),%d1
asl.l &4,%d1
add.l %d1,%a1 # ADDRESS OF N*PIBY2, IN Y1, Y2
fsub.x (%a1)+,%fp0 # X-Y1
fsub.s (%a1),%fp0 # FP0 IS R = (X-Y1)-Y2
SCCONT:
#--continuation point from REDUCEX
mov.l INT(%a6),%d1
ror.l &1,%d1
cmp.l %d1,&0 # D0 < 0 IFF N IS ODD
bge.w NEVEN
SNODD:
#--REGISTERS SAVED SO FAR: D0, A0, FP2.
fmovm.x &0x04,-(%sp) # save fp2
fmov.x %fp0,RPRIME(%a6)
fmul.x %fp0,%fp0 # FP0 IS S = R*R
fmov.d SINA7(%pc),%fp1 # A7
fmov.d COSB8(%pc),%fp2 # B8
fmul.x %fp0,%fp1 # SA7
fmul.x %fp0,%fp2 # SB8
mov.l %d2,-(%sp)
mov.l %d1,%d2
ror.l &1,%d2
and.l &0x80000000,%d2
eor.l %d1,%d2
and.l &0x80000000,%d2
fadd.d SINA6(%pc),%fp1 # A6+SA7
fadd.d COSB7(%pc),%fp2 # B7+SB8
fmul.x %fp0,%fp1 # S(A6+SA7)
eor.l %d2,RPRIME(%a6)
mov.l (%sp)+,%d2
fmul.x %fp0,%fp2 # S(B7+SB8)
ror.l &1,%d1
and.l &0x80000000,%d1
mov.l &0x3F800000,POSNEG1(%a6)
eor.l %d1,POSNEG1(%a6)
fadd.d SINA5(%pc),%fp1 # A5+S(A6+SA7)
fadd.d COSB6(%pc),%fp2 # B6+S(B7+SB8)
fmul.x %fp0,%fp1 # S(A5+S(A6+SA7))
fmul.x %fp0,%fp2 # S(B6+S(B7+SB8))
fmov.x %fp0,SPRIME(%a6)
fadd.d SINA4(%pc),%fp1 # A4+S(A5+S(A6+SA7))
eor.l %d1,SPRIME(%a6)
fadd.d COSB5(%pc),%fp2 # B5+S(B6+S(B7+SB8))
fmul.x %fp0,%fp1 # S(A4+...)
fmul.x %fp0,%fp2 # S(B5+...)
fadd.d SINA3(%pc),%fp1 # A3+S(A4+...)
fadd.d COSB4(%pc),%fp2 # B4+S(B5+...)
fmul.x %fp0,%fp1 # S(A3+...)
fmul.x %fp0,%fp2 # S(B4+...)
fadd.x SINA2(%pc),%fp1 # A2+S(A3+...)
fadd.x COSB3(%pc),%fp2 # B3+S(B4+...)
fmul.x %fp0,%fp1 # S(A2+...)
fmul.x %fp0,%fp2 # S(B3+...)
fadd.x SINA1(%pc),%fp1 # A1+S(A2+...)
fadd.x COSB2(%pc),%fp2 # B2+S(B3+...)
fmul.x %fp0,%fp1 # S(A1+...)
fmul.x %fp2,%fp0 # S(B2+...)
fmul.x RPRIME(%a6),%fp1 # R'S(A1+...)
fadd.s COSB1(%pc),%fp0 # B1+S(B2...)
fmul.x SPRIME(%a6),%fp0 # S'(B1+S(B2+...))
fmovm.x (%sp)+,&0x20 # restore fp2
fmov.l %d0,%fpcr
fadd.x RPRIME(%a6),%fp1 # COS(X)
bsr sto_cos # store cosine result
fadd.s POSNEG1(%a6),%fp0 # SIN(X)
bra t_inx2
NEVEN:
#--REGISTERS SAVED SO FAR: FP2.
fmovm.x &0x04,-(%sp) # save fp2
fmov.x %fp0,RPRIME(%a6)
fmul.x %fp0,%fp0 # FP0 IS S = R*R
fmov.d COSB8(%pc),%fp1 # B8
fmov.d SINA7(%pc),%fp2 # A7
fmul.x %fp0,%fp1 # SB8
fmov.x %fp0,SPRIME(%a6)
fmul.x %fp0,%fp2 # SA7
ror.l &1,%d1
and.l &0x80000000,%d1
fadd.d COSB7(%pc),%fp1 # B7+SB8
fadd.d SINA6(%pc),%fp2 # A6+SA7
eor.l %d1,RPRIME(%a6)
eor.l %d1,SPRIME(%a6)
fmul.x %fp0,%fp1 # S(B7+SB8)
or.l &0x3F800000,%d1
mov.l %d1,POSNEG1(%a6)
fmul.x %fp0,%fp2 # S(A6+SA7)
fadd.d COSB6(%pc),%fp1 # B6+S(B7+SB8)
fadd.d SINA5(%pc),%fp2 # A5+S(A6+SA7)
fmul.x %fp0,%fp1 # S(B6+S(B7+SB8))
fmul.x %fp0,%fp2 # S(A5+S(A6+SA7))
fadd.d COSB5(%pc),%fp1 # B5+S(B6+S(B7+SB8))
fadd.d SINA4(%pc),%fp2 # A4+S(A5+S(A6+SA7))
fmul.x %fp0,%fp1 # S(B5+...)
fmul.x %fp0,%fp2 # S(A4+...)
fadd.d COSB4(%pc),%fp1 # B4+S(B5+...)
fadd.d SINA3(%pc),%fp2 # A3+S(A4+...)
fmul.x %fp0,%fp1 # S(B4+...)
fmul.x %fp0,%fp2 # S(A3+...)
fadd.x COSB3(%pc),%fp1 # B3+S(B4+...)
fadd.x SINA2(%pc),%fp2 # A2+S(A3+...)
fmul.x %fp0,%fp1 # S(B3+...)
fmul.x %fp0,%fp2 # S(A2+...)
fadd.x COSB2(%pc),%fp1 # B2+S(B3+...)
fadd.x SINA1(%pc),%fp2 # A1+S(A2+...)
fmul.x %fp0,%fp1 # S(B2+...)
fmul.x %fp2,%fp0 # s(a1+...)
fadd.s COSB1(%pc),%fp1 # B1+S(B2...)
fmul.x RPRIME(%a6),%fp0 # R'S(A1+...)
fmul.x SPRIME(%a6),%fp1 # S'(B1+S(B2+...))
fmovm.x (%sp)+,&0x20 # restore fp2
fmov.l %d0,%fpcr
fadd.s POSNEG1(%a6),%fp1 # COS(X)
bsr sto_cos # store cosine result
fadd.x RPRIME(%a6),%fp0 # SIN(X)
bra t_inx2
################################################
SCBORS:
cmp.l %d1,&0x3FFF8000
bgt.w SREDUCEX
################################################
SCSM:
# mov.w &0x0000,XDCARE(%a6)
fmov.s &0x3F800000,%fp1
fmov.l %d0,%fpcr
fsub.s &0x00800000,%fp1
bsr sto_cos # store cosine result
fmov.l %fpcr,%d0 # d0 must have fpcr,too
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0
bra t_catch
##############################################
global ssincosd
#--SIN AND COS OF X FOR DENORMALIZED X
ssincosd:
mov.l %d0,-(%sp) # save d0
fmov.s &0x3F800000,%fp1
bsr sto_cos # store cosine result
mov.l (%sp)+,%d0 # restore d0
bra t_extdnrm
############################################
#--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
#--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
#--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
SREDUCEX:
fmovm.x &0x3c,-(%sp) # save {fp2-fp5}
mov.l %d2,-(%sp) # save d2
fmov.s &0x00000000,%fp1 # fp1 = 0
#--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
#--there is a danger of unwanted overflow in first LOOP iteration. In this
#--case, reduce argument by one remainder step to make subsequent reduction
#--safe.
cmp.l %d1,&0x7ffeffff # is arg dangerously large?
bne.b SLOOP # no
# yes; create 2**16383*PI/2
mov.w &0x7ffe,FP_SCR0_EX(%a6)
mov.l &0xc90fdaa2,FP_SCR0_HI(%a6)
clr.l FP_SCR0_LO(%a6)
# create low half of 2**16383*PI/2 at FP_SCR1
mov.w &0x7fdc,FP_SCR1_EX(%a6)
mov.l &0x85a308d3,FP_SCR1_HI(%a6)
clr.l FP_SCR1_LO(%a6)
ftest.x %fp0 # test sign of argument
fblt.w sred_neg
or.b &0x80,FP_SCR0_EX(%a6) # positive arg
or.b &0x80,FP_SCR1_EX(%a6)
sred_neg:
fadd.x FP_SCR0(%a6),%fp0 # high part of reduction is exact
fmov.x %fp0,%fp1 # save high result in fp1
fadd.x FP_SCR1(%a6),%fp0 # low part of reduction
fsub.x %fp0,%fp1 # determine low component of result
fadd.x FP_SCR1(%a6),%fp1 # fp0/fp1 are reduced argument.
#--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
#--integer quotient will be stored in N
#--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)
SLOOP:
fmov.x %fp0,INARG(%a6) # +-2**K * F, 1 <= F < 2
mov.w INARG(%a6),%d1
mov.l %d1,%a1 # save a copy of D0
and.l &0x00007FFF,%d1
sub.l &0x00003FFF,%d1 # d0 = K
cmp.l %d1,&28
ble.b SLASTLOOP
SCONTLOOP:
sub.l &27,%d1 # d0 = L := K-27
mov.b &0,ENDFLAG(%a6)
bra.b SWORK
SLASTLOOP:
clr.l %d1 # d0 = L := 0
mov.b &1,ENDFLAG(%a6)
SWORK:
#--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
#--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
#--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
#--2**L * (PIby2_1), 2**L * (PIby2_2)
mov.l &0x00003FFE,%d2 # BIASED EXP OF 2/PI
sub.l %d1,%d2 # BIASED EXP OF 2**(-L)*(2/PI)
mov.l &0xA2F9836E,FP_SCR0_HI(%a6)
mov.l &0x4E44152A,FP_SCR0_LO(%a6)
mov.w %d2,FP_SCR0_EX(%a6) # FP_SCR0 = 2**(-L)*(2/PI)
fmov.x %fp0,%fp2
fmul.x FP_SCR0(%a6),%fp2 # fp2 = X * 2**(-L)*(2/PI)
#--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
#--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
#--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
#--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
#--US THE DESIRED VALUE IN FLOATING POINT.
mov.l %a1,%d2
swap %d2
and.l &0x80000000,%d2
or.l &0x5F000000,%d2 # d2 = SIGN(INARG)*2**63 IN SGL
mov.l %d2,TWOTO63(%a6)
fadd.s TWOTO63(%a6),%fp2 # THE FRACTIONAL PART OF FP1 IS ROUNDED
fsub.s TWOTO63(%a6),%fp2 # fp2 = N
# fint.x %fp2
#--CREATING 2**(L)*Piby2_1 and 2**(L)*Piby2_2
mov.l %d1,%d2 # d2 = L
add.l &0x00003FFF,%d2 # BIASED EXP OF 2**L * (PI/2)
mov.w %d2,FP_SCR0_EX(%a6)
mov.l &0xC90FDAA2,FP_SCR0_HI(%a6)
clr.l FP_SCR0_LO(%a6) # FP_SCR0 = 2**(L) * Piby2_1
add.l &0x00003FDD,%d1
mov.w %d1,FP_SCR1_EX(%a6)
mov.l &0x85A308D3,FP_SCR1_HI(%a6)
clr.l FP_SCR1_LO(%a6) # FP_SCR1 = 2**(L) * Piby2_2
mov.b ENDFLAG(%a6),%d1
#--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
#--P2 = 2**(L) * Piby2_2
fmov.x %fp2,%fp4 # fp4 = N
fmul.x FP_SCR0(%a6),%fp4 # fp4 = W = N*P1
fmov.x %fp2,%fp5 # fp5 = N
fmul.x FP_SCR1(%a6),%fp5 # fp5 = w = N*P2
fmov.x %fp4,%fp3 # fp3 = W = N*P1
#--we want P+p = W+w but |p| <= half ulp of P
#--Then, we need to compute A := R-P and a := r-p
fadd.x %fp5,%fp3 # fp3 = P
fsub.x %fp3,%fp4 # fp4 = W-P
fsub.x %fp3,%fp0 # fp0 = A := R - P
fadd.x %fp5,%fp4 # fp4 = p = (W-P)+w
fmov.x %fp0,%fp3 # fp3 = A
fsub.x %fp4,%fp1 # fp1 = a := r - p
#--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
#--|r| <= half ulp of R.
fadd.x %fp1,%fp0 # fp0 = R := A+a
#--No need to calculate r if this is the last loop
cmp.b %d1,&0
bgt.w SRESTORE
#--Need to calculate r
fsub.x %fp0,%fp3 # fp3 = A-R
fadd.x %fp3,%fp1 # fp1 = r := (A-R)+a
bra.w SLOOP
SRESTORE:
fmov.l %fp2,INT(%a6)
mov.l (%sp)+,%d2 # restore d2
fmovm.x (%sp)+,&0x3c # restore {fp2-fp5}
mov.l ADJN(%a6),%d1
cmp.l %d1,&4
blt.w SINCONT
bra.w SCCONT
#########################################################################
# stan(): computes the tangent of a normalized input #
# stand(): computes the tangent of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = tan(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulp in 64 significant bit, i.e. #
# within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. #
# #
# 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let #
# k = N mod 2, so in particular, k = 0 or 1. #
# #
# 3. If k is odd, go to 5. #
# #
# 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a #
# rational function U/V where #
# U = r + r*s*(P1 + s*(P2 + s*P3)), and #
# V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r. #
# Exit. #
# #
# 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by #
# a rational function U/V where #
# U = r + r*s*(P1 + s*(P2 + s*P3)), and #
# V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r, #
# -Cot(r) = -V/U. Exit. #
# #
# 6. If |X| > 1, go to 8. #
# #
# 7. (|X|<2**(-40)) Tan(X) = X. Exit. #
# #
# 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back #
# to 2. #
# #
#########################################################################
TANQ4:
long 0x3EA0B759,0xF50F8688
TANP3:
long 0xBEF2BAA5,0xA8924F04
TANQ3:
long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000
TANP2:
long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000
TANQ2:
long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000
TANP1:
long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000
TANQ1:
long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000
INVTWOPI:
long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000
TWOPI1:
long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
TWOPI2:
long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
#--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
#--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
#--MOST 69 BITS LONG.
# global PITBL
PITBL:
long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000
long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000
long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000
long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000
long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000
long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000
long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000
long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000
long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000
long 0xC0040000,0x90836524,0x88034B96,0x20B00000
long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000
long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000
long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000
long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000
long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000
long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000
long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000
long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000
long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000
long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000
long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000
long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000
long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000
long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000
long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000
long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000
long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000
long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000
long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000
long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000
long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000
long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000
long 0x00000000,0x00000000,0x00000000,0x00000000
long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000
long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000
long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000
long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000
long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000
long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000
long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000
long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000
long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000
long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000
long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000
long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000
long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000
long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000
long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000
long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000
long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000
long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000
long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000
long 0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000
long 0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000
long 0x40040000,0x8A3AE64F,0x76F80584,0x21880000
long 0x40040000,0x90836524,0x88034B96,0xA0B00000
long 0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000
long 0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000
long 0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000
long 0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000
long 0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000
long 0x40040000,0xB6365E22,0xEE46F000,0xA1480000
long 0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000
long 0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000
long 0x40040000,0xC90FDAA2,0x2168C235,0xA1800000
set INARG,FP_SCR0
set TWOTO63,L_SCR1
set INT,L_SCR1
set ENDFLAG,L_SCR2
global stan
stan:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FD78000 # |X| >= 2**(-40)?
bge.b TANOK1
bra.w TANSM
TANOK1:
cmp.l %d1,&0x4004BC7E # |X| < 15 PI?
blt.b TANMAIN
bra.w REDUCEX
TANMAIN:
#--THIS IS THE USUAL CASE, |X| <= 15 PI.
#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
fmov.x %fp0,%fp1
fmul.d TWOBYPI(%pc),%fp1 # X*2/PI
lea.l PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32
fmov.l %fp1,%d1 # CONVERT TO INTEGER
asl.l &4,%d1
add.l %d1,%a1 # ADDRESS N*PIBY2 IN Y1, Y2
fsub.x (%a1)+,%fp0 # X-Y1
fsub.s (%a1),%fp0 # FP0 IS R = (X-Y1)-Y2
ror.l &5,%d1
and.l &0x80000000,%d1 # D0 WAS ODD IFF D0 < 0
TANCONT:
fmovm.x &0x0c,-(%sp) # save fp2,fp3
cmp.l %d1,&0
blt.w NODD
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # S = R*R
fmov.d TANQ4(%pc),%fp3
fmov.d TANP3(%pc),%fp2
fmul.x %fp1,%fp3 # SQ4
fmul.x %fp1,%fp2 # SP3
fadd.d TANQ3(%pc),%fp3 # Q3+SQ4
fadd.x TANP2(%pc),%fp2 # P2+SP3
fmul.x %fp1,%fp3 # S(Q3+SQ4)
fmul.x %fp1,%fp2 # S(P2+SP3)
fadd.x TANQ2(%pc),%fp3 # Q2+S(Q3+SQ4)
fadd.x TANP1(%pc),%fp2 # P1+S(P2+SP3)
fmul.x %fp1,%fp3 # S(Q2+S(Q3+SQ4))
fmul.x %fp1,%fp2 # S(P1+S(P2+SP3))
fadd.x TANQ1(%pc),%fp3 # Q1+S(Q2+S(Q3+SQ4))
fmul.x %fp0,%fp2 # RS(P1+S(P2+SP3))
fmul.x %fp3,%fp1 # S(Q1+S(Q2+S(Q3+SQ4)))
fadd.x %fp2,%fp0 # R+RS(P1+S(P2+SP3))
fadd.s &0x3F800000,%fp1 # 1+S(Q1+...)
fmovm.x (%sp)+,&0x30 # restore fp2,fp3
fmov.l %d0,%fpcr # restore users round mode,prec
fdiv.x %fp1,%fp0 # last inst - possible exception set
bra t_inx2
NODD:
fmov.x %fp0,%fp1
fmul.x %fp0,%fp0 # S = R*R
fmov.d TANQ4(%pc),%fp3
fmov.d TANP3(%pc),%fp2
fmul.x %fp0,%fp3 # SQ4
fmul.x %fp0,%fp2 # SP3
fadd.d TANQ3(%pc),%fp3 # Q3+SQ4
fadd.x TANP2(%pc),%fp2 # P2+SP3
fmul.x %fp0,%fp3 # S(Q3+SQ4)
fmul.x %fp0,%fp2 # S(P2+SP3)
fadd.x TANQ2(%pc),%fp3 # Q2+S(Q3+SQ4)
fadd.x TANP1(%pc),%fp2 # P1+S(P2+SP3)
fmul.x %fp0,%fp3 # S(Q2+S(Q3+SQ4))
fmul.x %fp0,%fp2 # S(P1+S(P2+SP3))
fadd.x TANQ1(%pc),%fp3 # Q1+S(Q2+S(Q3+SQ4))
fmul.x %fp1,%fp2 # RS(P1+S(P2+SP3))
fmul.x %fp3,%fp0 # S(Q1+S(Q2+S(Q3+SQ4)))
fadd.x %fp2,%fp1 # R+RS(P1+S(P2+SP3))
fadd.s &0x3F800000,%fp0 # 1+S(Q1+...)
fmovm.x (%sp)+,&0x30 # restore fp2,fp3
fmov.x %fp1,-(%sp)
eor.l &0x80000000,(%sp)
fmov.l %d0,%fpcr # restore users round mode,prec
fdiv.x (%sp)+,%fp0 # last inst - possible exception set
bra t_inx2
TANBORS:
#--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
#--IF |X| < 2**(-40), RETURN X OR 1.
cmp.l %d1,&0x3FFF8000
bgt.b REDUCEX
TANSM:
fmov.x %fp0,-(%sp)
fmov.l %d0,%fpcr # restore users round mode,prec
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x (%sp)+,%fp0 # last inst - posibble exception set
bra t_catch
global stand
#--TAN(X) = X FOR DENORMALIZED X
stand:
bra t_extdnrm
#--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
#--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
#--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
REDUCEX:
fmovm.x &0x3c,-(%sp) # save {fp2-fp5}
mov.l %d2,-(%sp) # save d2
fmov.s &0x00000000,%fp1 # fp1 = 0
#--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
#--there is a danger of unwanted overflow in first LOOP iteration. In this
#--case, reduce argument by one remainder step to make subsequent reduction
#--safe.
cmp.l %d1,&0x7ffeffff # is arg dangerously large?
bne.b LOOP # no
# yes; create 2**16383*PI/2
mov.w &0x7ffe,FP_SCR0_EX(%a6)
mov.l &0xc90fdaa2,FP_SCR0_HI(%a6)
clr.l FP_SCR0_LO(%a6)
# create low half of 2**16383*PI/2 at FP_SCR1
mov.w &0x7fdc,FP_SCR1_EX(%a6)
mov.l &0x85a308d3,FP_SCR1_HI(%a6)
clr.l FP_SCR1_LO(%a6)
ftest.x %fp0 # test sign of argument
fblt.w red_neg
or.b &0x80,FP_SCR0_EX(%a6) # positive arg
or.b &0x80,FP_SCR1_EX(%a6)
red_neg:
fadd.x FP_SCR0(%a6),%fp0 # high part of reduction is exact
fmov.x %fp0,%fp1 # save high result in fp1
fadd.x FP_SCR1(%a6),%fp0 # low part of reduction
fsub.x %fp0,%fp1 # determine low component of result
fadd.x FP_SCR1(%a6),%fp1 # fp0/fp1 are reduced argument.
#--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
#--integer quotient will be stored in N
#--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)
LOOP:
fmov.x %fp0,INARG(%a6) # +-2**K * F, 1 <= F < 2
mov.w INARG(%a6),%d1
mov.l %d1,%a1 # save a copy of D0
and.l &0x00007FFF,%d1
sub.l &0x00003FFF,%d1 # d0 = K
cmp.l %d1,&28
ble.b LASTLOOP
CONTLOOP:
sub.l &27,%d1 # d0 = L := K-27
mov.b &0,ENDFLAG(%a6)
bra.b WORK
LASTLOOP:
clr.l %d1 # d0 = L := 0
mov.b &1,ENDFLAG(%a6)
WORK:
#--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
#--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
#--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
#--2**L * (PIby2_1), 2**L * (PIby2_2)
mov.l &0x00003FFE,%d2 # BIASED EXP OF 2/PI
sub.l %d1,%d2 # BIASED EXP OF 2**(-L)*(2/PI)
mov.l &0xA2F9836E,FP_SCR0_HI(%a6)
mov.l &0x4E44152A,FP_SCR0_LO(%a6)
mov.w %d2,FP_SCR0_EX(%a6) # FP_SCR0 = 2**(-L)*(2/PI)
fmov.x %fp0,%fp2
fmul.x FP_SCR0(%a6),%fp2 # fp2 = X * 2**(-L)*(2/PI)
#--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
#--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
#--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
#--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
#--US THE DESIRED VALUE IN FLOATING POINT.
mov.l %a1,%d2
swap %d2
and.l &0x80000000,%d2
or.l &0x5F000000,%d2 # d2 = SIGN(INARG)*2**63 IN SGL
mov.l %d2,TWOTO63(%a6)
fadd.s TWOTO63(%a6),%fp2 # THE FRACTIONAL PART OF FP1 IS ROUNDED
fsub.s TWOTO63(%a6),%fp2 # fp2 = N
# fintrz.x %fp2,%fp2
#--CREATING 2**(L)*Piby2_1 and 2**(L)*Piby2_2
mov.l %d1,%d2 # d2 = L
add.l &0x00003FFF,%d2 # BIASED EXP OF 2**L * (PI/2)
mov.w %d2,FP_SCR0_EX(%a6)
mov.l &0xC90FDAA2,FP_SCR0_HI(%a6)
clr.l FP_SCR0_LO(%a6) # FP_SCR0 = 2**(L) * Piby2_1
add.l &0x00003FDD,%d1
mov.w %d1,FP_SCR1_EX(%a6)
mov.l &0x85A308D3,FP_SCR1_HI(%a6)
clr.l FP_SCR1_LO(%a6) # FP_SCR1 = 2**(L) * Piby2_2
mov.b ENDFLAG(%a6),%d1
#--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
#--P2 = 2**(L) * Piby2_2
fmov.x %fp2,%fp4 # fp4 = N
fmul.x FP_SCR0(%a6),%fp4 # fp4 = W = N*P1
fmov.x %fp2,%fp5 # fp5 = N
fmul.x FP_SCR1(%a6),%fp5 # fp5 = w = N*P2
fmov.x %fp4,%fp3 # fp3 = W = N*P1
#--we want P+p = W+w but |p| <= half ulp of P
#--Then, we need to compute A := R-P and a := r-p
fadd.x %fp5,%fp3 # fp3 = P
fsub.x %fp3,%fp4 # fp4 = W-P
fsub.x %fp3,%fp0 # fp0 = A := R - P
fadd.x %fp5,%fp4 # fp4 = p = (W-P)+w
fmov.x %fp0,%fp3 # fp3 = A
fsub.x %fp4,%fp1 # fp1 = a := r - p
#--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
#--|r| <= half ulp of R.
fadd.x %fp1,%fp0 # fp0 = R := A+a
#--No need to calculate r if this is the last loop
cmp.b %d1,&0
bgt.w RESTORE
#--Need to calculate r
fsub.x %fp0,%fp3 # fp3 = A-R
fadd.x %fp3,%fp1 # fp1 = r := (A-R)+a
bra.w LOOP
RESTORE:
fmov.l %fp2,INT(%a6)
mov.l (%sp)+,%d2 # restore d2
fmovm.x (%sp)+,&0x3c # restore {fp2-fp5}
mov.l INT(%a6),%d1
ror.l &1,%d1
bra.w TANCONT
#########################################################################
# satan(): computes the arctangent of a normalized number #
# satand(): computes the arctangent of a denormalized number #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = arctan(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 2 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5. #
# #
# Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. #
# Note that k = -4, -3,..., or 3. #
# Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 #
# significant bits of X with a bit-1 attached at the 6-th #
# bit position. Define u to be u = (X-F) / (1 + X*F). #
# #
# Step 3. Approximate arctan(u) by a polynomial poly. #
# #
# Step 4. Return arctan(F) + poly, arctan(F) is fetched from a #
# table of values calculated beforehand. Exit. #
# #
# Step 5. If |X| >= 16, go to Step 7. #
# #
# Step 6. Approximate arctan(X) by an odd polynomial in X. Exit. #
# #
# Step 7. Define X' = -1/X. Approximate arctan(X') by an odd #
# polynomial in X'. #
# Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit. #
# #
#########################################################################
ATANA3: long 0xBFF6687E,0x314987D8
ATANA2: long 0x4002AC69,0x34A26DB3
ATANA1: long 0xBFC2476F,0x4E1DA28E
ATANB6: long 0x3FB34444,0x7F876989
ATANB5: long 0xBFB744EE,0x7FAF45DB
ATANB4: long 0x3FBC71C6,0x46940220
ATANB3: long 0xBFC24924,0x921872F9
ATANB2: long 0x3FC99999,0x99998FA9
ATANB1: long 0xBFD55555,0x55555555
ATANC5: long 0xBFB70BF3,0x98539E6A
ATANC4: long 0x3FBC7187,0x962D1D7D
ATANC3: long 0xBFC24924,0x827107B8
ATANC2: long 0x3FC99999,0x9996263E
ATANC1: long 0xBFD55555,0x55555536
PPIBY2: long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
NPIBY2: long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
PTINY: long 0x00010000,0x80000000,0x00000000,0x00000000
NTINY: long 0x80010000,0x80000000,0x00000000,0x00000000
ATANTBL:
long 0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
long 0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
long 0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
long 0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
long 0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
long 0x3FFB0000,0xAB98E943,0x62765619,0x00000000
long 0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
long 0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
long 0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
long 0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
long 0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
long 0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
long 0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
long 0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
long 0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
long 0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
long 0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
long 0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
long 0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
long 0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
long 0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
long 0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
long 0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
long 0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
long 0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
long 0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
long 0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
long 0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
long 0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
long 0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
long 0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
long 0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
long 0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
long 0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
long 0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
long 0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
long 0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
long 0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
long 0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
long 0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
long 0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
long 0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
long 0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
long 0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
long 0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
long 0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
long 0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
long 0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
long 0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
long 0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
long 0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
long 0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
long 0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
long 0x3FFE0000,0x97731420,0x365E538C,0x00000000
long 0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
long 0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
long 0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
long 0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
long 0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
long 0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
long 0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
long 0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
long 0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
long 0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
long 0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
long 0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
long 0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
long 0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
long 0x3FFE0000,0xE8771129,0xC4353259,0x00000000
long 0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
long 0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
long 0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
long 0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
long 0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
long 0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
long 0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
long 0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
long 0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
long 0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
long 0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
long 0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
long 0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
long 0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
long 0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
long 0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
long 0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
long 0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
long 0x3FFF0000,0x9F100575,0x006CC571,0x00000000
long 0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
long 0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
long 0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
long 0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
long 0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
long 0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
long 0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
long 0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
long 0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
long 0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
long 0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
long 0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
long 0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
long 0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
long 0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
long 0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
long 0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
long 0x3FFF0000,0xB525529D,0x562246BD,0x00000000
long 0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
long 0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
long 0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
long 0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
long 0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
long 0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
long 0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
long 0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
long 0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
long 0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
long 0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
long 0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
long 0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
long 0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
long 0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
long 0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
long 0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
long 0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
long 0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
long 0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
long 0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
long 0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
set X,FP_SCR0
set XDCARE,X+2
set XFRAC,X+4
set XFRACLO,X+8
set ATANF,FP_SCR1
set ATANFHI,ATANF+4
set ATANFLO,ATANF+8
global satan
#--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
satan:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
fmov.x %fp0,X(%a6)
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FFB8000 # |X| >= 1/16?
bge.b ATANOK1
bra.w ATANSM
ATANOK1:
cmp.l %d1,&0x4002FFFF # |X| < 16 ?
ble.b ATANMAIN
bra.w ATANBIG
#--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
#--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
#--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
#--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
#--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
#--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
#--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
#--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
#--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
#--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
#--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
#--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
#--WILL INVOLVE A VERY LONG POLYNOMIAL.
#--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
#--WE CHOSE F TO BE +-2^K * 1.BBBB1
#--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
#--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
#--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
#-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
ATANMAIN:
and.l &0xF8000000,XFRAC(%a6) # FIRST 5 BITS
or.l &0x04000000,XFRAC(%a6) # SET 6-TH BIT TO 1
mov.l &0x00000000,XFRACLO(%a6) # LOCATION OF X IS NOW F
fmov.x %fp0,%fp1 # FP1 IS X
fmul.x X(%a6),%fp1 # FP1 IS X*F, NOTE THAT X*F > 0
fsub.x X(%a6),%fp0 # FP0 IS X-F
fadd.s &0x3F800000,%fp1 # FP1 IS 1 + X*F
fdiv.x %fp1,%fp0 # FP0 IS U = (X-F)/(1+X*F)
#--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
#--CREATE ATAN(F) AND STORE IT IN ATANF, AND
#--SAVE REGISTERS FP2.
mov.l %d2,-(%sp) # SAVE d2 TEMPORARILY
mov.l %d1,%d2 # THE EXP AND 16 BITS OF X
and.l &0x00007800,%d1 # 4 VARYING BITS OF F'S FRACTION
and.l &0x7FFF0000,%d2 # EXPONENT OF F
sub.l &0x3FFB0000,%d2 # K+4
asr.l &1,%d2
add.l %d2,%d1 # THE 7 BITS IDENTIFYING F
asr.l &7,%d1 # INDEX INTO TBL OF ATAN(|F|)
lea ATANTBL(%pc),%a1
add.l %d1,%a1 # ADDRESS OF ATAN(|F|)
mov.l (%a1)+,ATANF(%a6)
mov.l (%a1)+,ATANFHI(%a6)
mov.l (%a1)+,ATANFLO(%a6) # ATANF IS NOW ATAN(|F|)
mov.l X(%a6),%d1 # LOAD SIGN AND EXPO. AGAIN
and.l &0x80000000,%d1 # SIGN(F)
or.l %d1,ATANF(%a6) # ATANF IS NOW SIGN(F)*ATAN(|F|)
mov.l (%sp)+,%d2 # RESTORE d2
#--THAT'S ALL I HAVE TO DO FOR NOW,
#--BUT ALAS, THE DIVIDE IS STILL CRANKING!
#--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
#--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
#--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
#--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
#--WHAT WE HAVE HERE IS MERELY A1 = A3, A2 = A1/A3, A3 = A2/A3.
#--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
#--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
fmovm.x &0x04,-(%sp) # save fp2
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1
fmov.d ATANA3(%pc),%fp2
fadd.x %fp1,%fp2 # A3+V
fmul.x %fp1,%fp2 # V*(A3+V)
fmul.x %fp0,%fp1 # U*V
fadd.d ATANA2(%pc),%fp2 # A2+V*(A3+V)
fmul.d ATANA1(%pc),%fp1 # A1*U*V
fmul.x %fp2,%fp1 # A1*U*V*(A2+V*(A3+V))
fadd.x %fp1,%fp0 # ATAN(U), FP1 RELEASED
fmovm.x (%sp)+,&0x20 # restore fp2
fmov.l %d0,%fpcr # restore users rnd mode,prec
fadd.x ATANF(%a6),%fp0 # ATAN(X)
bra t_inx2
ATANBORS:
#--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
#--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
cmp.l %d1,&0x3FFF8000
bgt.w ATANBIG # I.E. |X| >= 16
ATANSM:
#--|X| <= 1/16
#--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
#--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
#--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
#--WHERE Y = X*X, AND Z = Y*Y.
cmp.l %d1,&0x3FD78000
blt.w ATANTINY
#--COMPUTE POLYNOMIAL
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmul.x %fp0,%fp0 # FPO IS Y = X*X
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS Z = Y*Y
fmov.d ATANB6(%pc),%fp2
fmov.d ATANB5(%pc),%fp3
fmul.x %fp1,%fp2 # Z*B6
fmul.x %fp1,%fp3 # Z*B5
fadd.d ATANB4(%pc),%fp2 # B4+Z*B6
fadd.d ATANB3(%pc),%fp3 # B3+Z*B5
fmul.x %fp1,%fp2 # Z*(B4+Z*B6)
fmul.x %fp3,%fp1 # Z*(B3+Z*B5)
fadd.d ATANB2(%pc),%fp2 # B2+Z*(B4+Z*B6)
fadd.d ATANB1(%pc),%fp1 # B1+Z*(B3+Z*B5)
fmul.x %fp0,%fp2 # Y*(B2+Z*(B4+Z*B6))
fmul.x X(%a6),%fp0 # X*Y
fadd.x %fp2,%fp1 # [B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
fmul.x %fp1,%fp0 # X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
fmovm.x (%sp)+,&0x30 # restore fp2/fp3
fmov.l %d0,%fpcr # restore users rnd mode,prec
fadd.x X(%a6),%fp0
bra t_inx2
ATANTINY:
#--|X| < 2^(-40), ATAN(X) = X
fmov.l %d0,%fpcr # restore users rnd mode,prec
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0 # last inst - possible exception set
bra t_catch
ATANBIG:
#--IF |X| > 2^(100), RETURN SIGN(X)*(PI/2 - TINY). OTHERWISE,
#--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
cmp.l %d1,&0x40638000
bgt.w ATANHUGE
#--APPROXIMATE ATAN(-1/X) BY
#--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
#--THIS CAN BE RE-WRITTEN AS
#--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmov.s &0xBF800000,%fp1 # LOAD -1
fdiv.x %fp0,%fp1 # FP1 IS -1/X
#--DIVIDE IS STILL CRANKING
fmov.x %fp1,%fp0 # FP0 IS X'
fmul.x %fp0,%fp0 # FP0 IS Y = X'*X'
fmov.x %fp1,X(%a6) # X IS REALLY X'
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS Z = Y*Y
fmov.d ATANC5(%pc),%fp3
fmov.d ATANC4(%pc),%fp2
fmul.x %fp1,%fp3 # Z*C5
fmul.x %fp1,%fp2 # Z*B4
fadd.d ATANC3(%pc),%fp3 # C3+Z*C5
fadd.d ATANC2(%pc),%fp2 # C2+Z*C4
fmul.x %fp3,%fp1 # Z*(C3+Z*C5), FP3 RELEASED
fmul.x %fp0,%fp2 # Y*(C2+Z*C4)
fadd.d ATANC1(%pc),%fp1 # C1+Z*(C3+Z*C5)
fmul.x X(%a6),%fp0 # X'*Y
fadd.x %fp2,%fp1 # [Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
fmul.x %fp1,%fp0 # X'*Y*([B1+Z*(B3+Z*B5)]
# ... +[Y*(B2+Z*(B4+Z*B6))])
fadd.x X(%a6),%fp0
fmovm.x (%sp)+,&0x30 # restore fp2/fp3
fmov.l %d0,%fpcr # restore users rnd mode,prec
tst.b (%a0)
bpl.b pos_big
neg_big:
fadd.x NPIBY2(%pc),%fp0
bra t_minx2
pos_big:
fadd.x PPIBY2(%pc),%fp0
bra t_pinx2
ATANHUGE:
#--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
tst.b (%a0)
bpl.b pos_huge
neg_huge:
fmov.x NPIBY2(%pc),%fp0
fmov.l %d0,%fpcr
fadd.x PTINY(%pc),%fp0
bra t_minx2
pos_huge:
fmov.x PPIBY2(%pc),%fp0
fmov.l %d0,%fpcr
fadd.x NTINY(%pc),%fp0
bra t_pinx2
global satand
#--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
satand:
bra t_extdnrm
#########################################################################
# sasin(): computes the inverse sine of a normalized input #
# sasind(): computes the inverse sine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = arcsin(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# ASIN #
# 1. If |X| >= 1, go to 3. #
# #
# 2. (|X| < 1) Calculate asin(X) by #
# z := sqrt( [1-X][1+X] ) #
# asin(X) = atan( x / z ). #
# Exit. #
# #
# 3. If |X| > 1, go to 5. #
# #
# 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.#
# #
# 5. (|X| > 1) Generate an invalid operation by 0 * infinity. #
# Exit. #
# #
#########################################################################
global sasin
sasin:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FFF8000
bge.b ASINBIG
# This catch is added here for the '060 QSP. Originally, the call to
# satan() would handle this case by causing the exception which would
# not be caught until gen_except(). Now, with the exceptions being
# detected inside of satan(), the exception would have been handled there
# instead of inside sasin() as expected.
cmp.l %d1,&0x3FD78000
blt.w ASINTINY
#--THIS IS THE USUAL CASE, |X| < 1
#--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
ASINMAIN:
fmov.s &0x3F800000,%fp1
fsub.x %fp0,%fp1 # 1-X
fmovm.x &0x4,-(%sp) # {fp2}
fmov.s &0x3F800000,%fp2
fadd.x %fp0,%fp2 # 1+X
fmul.x %fp2,%fp1 # (1+X)(1-X)
fmovm.x (%sp)+,&0x20 # {fp2}
fsqrt.x %fp1 # SQRT([1-X][1+X])
fdiv.x %fp1,%fp0 # X/SQRT([1-X][1+X])
fmovm.x &0x01,-(%sp) # save X/SQRT(...)
lea (%sp),%a0 # pass ptr to X/SQRT(...)
bsr satan
add.l &0xc,%sp # clear X/SQRT(...) from stack
bra t_inx2
ASINBIG:
fabs.x %fp0 # |X|
fcmp.s %fp0,&0x3F800000
fbgt t_operr # cause an operr exception
#--|X| = 1, ASIN(X) = +- PI/2.
ASINONE:
fmov.x PIBY2(%pc),%fp0
mov.l (%a0),%d1
and.l &0x80000000,%d1 # SIGN BIT OF X
or.l &0x3F800000,%d1 # +-1 IN SGL FORMAT
mov.l %d1,-(%sp) # push SIGN(X) IN SGL-FMT
fmov.l %d0,%fpcr
fmul.s (%sp)+,%fp0
bra t_inx2
#--|X| < 2^(-40), ATAN(X) = X
ASINTINY:
fmov.l %d0,%fpcr # restore users rnd mode,prec
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x (%a0),%fp0 # last inst - possible exception
bra t_catch
global sasind
#--ASIN(X) = X FOR DENORMALIZED X
sasind:
bra t_extdnrm
#########################################################################
# sacos(): computes the inverse cosine of a normalized input #
# sacosd(): computes the inverse cosine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = arccos(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# ACOS #
# 1. If |X| >= 1, go to 3. #
# #
# 2. (|X| < 1) Calculate acos(X) by #
# z := (1-X) / (1+X) #
# acos(X) = 2 * atan( sqrt(z) ). #
# Exit. #
# #
# 3. If |X| > 1, go to 5. #
# #
# 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit. #
# #
# 5. (|X| > 1) Generate an invalid operation by 0 * infinity. #
# Exit. #
# #
#########################################################################
global sacos
sacos:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l (%a0),%d1 # pack exp w/ upper 16 fraction
mov.w 4(%a0),%d1
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FFF8000
bge.b ACOSBIG
#--THIS IS THE USUAL CASE, |X| < 1
#--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
ACOSMAIN:
fmov.s &0x3F800000,%fp1
fadd.x %fp0,%fp1 # 1+X
fneg.x %fp0 # -X
fadd.s &0x3F800000,%fp0 # 1-X
fdiv.x %fp1,%fp0 # (1-X)/(1+X)
fsqrt.x %fp0 # SQRT((1-X)/(1+X))
mov.l %d0,-(%sp) # save original users fpcr
clr.l %d0
fmovm.x &0x01,-(%sp) # save SQRT(...) to stack
lea (%sp),%a0 # pass ptr to sqrt
bsr satan # ATAN(SQRT([1-X]/[1+X]))
add.l &0xc,%sp # clear SQRT(...) from stack
fmov.l (%sp)+,%fpcr # restore users round prec,mode
fadd.x %fp0,%fp0 # 2 * ATAN( STUFF )
bra t_pinx2
ACOSBIG:
fabs.x %fp0
fcmp.s %fp0,&0x3F800000
fbgt t_operr # cause an operr exception
#--|X| = 1, ACOS(X) = 0 OR PI
tst.b (%a0) # is X positive or negative?
bpl.b ACOSP1
#--X = -1
#Returns PI and inexact exception
ACOSM1:
fmov.x PI(%pc),%fp0 # load PI
fmov.l %d0,%fpcr # load round mode,prec
fadd.s &0x00800000,%fp0 # add a small value
bra t_pinx2
ACOSP1:
bra ld_pzero # answer is positive zero
global sacosd
#--ACOS(X) = PI/2 FOR DENORMALIZED X
sacosd:
fmov.l %d0,%fpcr # load user's rnd mode/prec
fmov.x PIBY2(%pc),%fp0
bra t_pinx2
#########################################################################
# setox(): computes the exponential for a normalized input #
# setoxd(): computes the exponential for a denormalized input #
# setoxm1(): computes the exponential minus 1 for a normalized input #
# setoxm1d(): computes the exponential minus 1 for a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = exp(X) or exp(X)-1 #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 0.85 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM and IMPLEMENTATION **************************************** #
# #
# setoxd #
# ------ #
# Step 1. Set ans := 1.0 #
# #
# Step 2. Return ans := ans + sign(X)*2^(-126). Exit. #
# Notes: This will always generate one exception -- inexact. #
# #
# #
# setox #
# ----- #
# #
# Step 1. Filter out extreme cases of input argument. #
# 1.1 If |X| >= 2^(-65), go to Step 1.3. #
# 1.2 Go to Step 7. #
# 1.3 If |X| < 16380 log(2), go to Step 2. #
# 1.4 Go to Step 8. #
# Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.#
# To avoid the use of floating-point comparisons, a #
# compact representation of |X| is used. This format is a #
# 32-bit integer, the upper (more significant) 16 bits #
# are the sign and biased exponent field of |X|; the #
# lower 16 bits are the 16 most significant fraction #
# (including the explicit bit) bits of |X|. Consequently, #
# the comparisons in Steps 1.1 and 1.3 can be performed #
# by integer comparison. Note also that the constant #
# 16380 log(2) used in Step 1.3 is also in the compact #
# form. Thus taking the branch to Step 2 guarantees #
# |X| < 16380 log(2). There is no harm to have a small #
# number of cases where |X| is less than, but close to, #
# 16380 log(2) and the branch to Step 9 is taken. #
# #
# Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). #
# 2.1 Set AdjFlag := 0 (indicates the branch 1.3 -> 2 #
# was taken) #
# 2.2 N := round-to-nearest-integer( X * 64/log2 ). #
# 2.3 Calculate J = N mod 64; so J = 0,1,2,..., #
# or 63. #
# 2.4 Calculate M = (N - J)/64; so N = 64M + J. #
# 2.5 Calculate the address of the stored value of #
# 2^(J/64). #
# 2.6 Create the value Scale = 2^M. #
# Notes: The calculation in 2.2 is really performed by #
# Z := X * constant #
# N := round-to-nearest-integer(Z) #
# where #
# constant := single-precision( 64/log 2 ). #
# #
# Using a single-precision constant avoids memory #
# access. Another effect of using a single-precision #
# "constant" is that the calculated value Z is #
# #
# Z = X*(64/log2)*(1+eps), |eps| <= 2^(-24). #
# #
# This error has to be considered later in Steps 3 and 4. #
# #
# Step 3. Calculate X - N*log2/64. #
# 3.1 R := X + N*L1, #
# where L1 := single-precision(-log2/64). #
# 3.2 R := R + N*L2, #
# L2 := extended-precision(-log2/64 - L1).#
# Notes: a) The way L1 and L2 are chosen ensures L1+L2 #
# approximate the value -log2/64 to 88 bits of accuracy. #
# b) N*L1 is exact because N is no longer than 22 bits #
# and L1 is no longer than 24 bits. #
# c) The calculation X+N*L1 is also exact due to #
# cancellation. Thus, R is practically X+N(L1+L2) to full #
# 64 bits. #
# d) It is important to estimate how large can |R| be #
# after Step 3.2. #
# #
# N = rnd-to-int( X*64/log2 (1+eps) ), |eps|<=2^(-24) #
# X*64/log2 (1+eps) = N + f, |f| <= 0.5 #
# X*64/log2 - N = f - eps*X 64/log2 #
# X - N*log2/64 = f*log2/64 - eps*X #
# #
# #
# Now |X| <= 16446 log2, thus #
# #
# |X - N*log2/64| <= (0.5 + 16446/2^(18))*log2/64 #
# <= 0.57 log2/64. #
# This bound will be used in Step 4. #
# #
# Step 4. Approximate exp(R)-1 by a polynomial #
# p = R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5)))) #
# Notes: a) In order to reduce memory access, the coefficients #
# are made as "short" as possible: A1 (which is 1/2), A4 #
# and A5 are single precision; A2 and A3 are double #
# precision. #
# b) Even with the restrictions above, #
# |p - (exp(R)-1)| < 2^(-68.8) for all |R| <= 0.0062. #
# Note that 0.0062 is slightly bigger than 0.57 log2/64. #
# c) To fully utilize the pipeline, p is separated into #
# two independent pieces of roughly equal complexities #
# p = [ R + R*S*(A2 + S*A4) ] + #
# [ S*(A1 + S*(A3 + S*A5)) ] #
# where S = R*R. #
# #
# Step 5. Compute 2^(J/64)*exp(R) = 2^(J/64)*(1+p) by #
# ans := T + ( T*p + t) #
# where T and t are the stored values for 2^(J/64). #
# Notes: 2^(J/64) is stored as T and t where T+t approximates #
# 2^(J/64) to roughly 85 bits; T is in extended precision #
# and t is in single precision. Note also that T is #
# rounded to 62 bits so that the last two bits of T are #
# zero. The reason for such a special form is that T-1, #
# T-2, and T-8 will all be exact --- a property that will #
# give much more accurate computation of the function #
# EXPM1. #
# #
# Step 6. Reconstruction of exp(X) #
# exp(X) = 2^M * 2^(J/64) * exp(R). #
# 6.1 If AdjFlag = 0, go to 6.3 #
# 6.2 ans := ans * AdjScale #
# 6.3 Restore the user FPCR #
# 6.4 Return ans := ans * Scale. Exit. #
# Notes: If AdjFlag = 0, we have X = Mlog2 + Jlog2/64 + R, #
# |M| <= 16380, and Scale = 2^M. Moreover, exp(X) will #
# neither overflow nor underflow. If AdjFlag = 1, that #
# means that #
# X = (M1+M)log2 + Jlog2/64 + R, |M1+M| >= 16380. #
# Hence, exp(X) may overflow or underflow or neither. #
# When that is the case, AdjScale = 2^(M1) where M1 is #
# approximately M. Thus 6.2 will never cause #
# over/underflow. Possible exception in 6.4 is overflow #
# or underflow. The inexact exception is not generated in #
# 6.4. Although one can argue that the inexact flag #
# should always be raised, to simulate that exception #
# cost to much than the flag is worth in practical uses. #
# #
# Step 7. Return 1 + X. #
# 7.1 ans := X #
# 7.2 Restore user FPCR. #
# 7.3 Return ans := 1 + ans. Exit #
# Notes: For non-zero X, the inexact exception will always be #
# raised by 7.3. That is the only exception raised by 7.3.#
# Note also that we use the FMOVEM instruction to move X #
# in Step 7.1 to avoid unnecessary trapping. (Although #
# the FMOVEM may not seem relevant since X is normalized, #
# the precaution will be useful in the library version of #
# this code where the separate entry for denormalized #
# inputs will be done away with.) #
# #
# Step 8. Handle exp(X) where |X| >= 16380log2. #
# 8.1 If |X| > 16480 log2, go to Step 9. #
# (mimic 2.2 - 2.6) #
# 8.2 N := round-to-integer( X * 64/log2 ) #
# 8.3 Calculate J = N mod 64, J = 0,1,...,63 #
# 8.4 K := (N-J)/64, M1 := truncate(K/2), M = K-M1, #
# AdjFlag := 1. #
# 8.5 Calculate the address of the stored value #
# 2^(J/64). #
# 8.6 Create the values Scale = 2^M, AdjScale = 2^M1. #
# 8.7 Go to Step 3. #
# Notes: Refer to notes for 2.2 - 2.6. #
# #
# Step 9. Handle exp(X), |X| > 16480 log2. #
# 9.1 If X < 0, go to 9.3 #
# 9.2 ans := Huge, go to 9.4 #
# 9.3 ans := Tiny. #
# 9.4 Restore user FPCR. #
# 9.5 Return ans := ans * ans. Exit. #
# Notes: Exp(X) will surely overflow or underflow, depending on #
# X's sign. "Huge" and "Tiny" are respectively large/tiny #
# extended-precision numbers whose square over/underflow #
# with an inexact result. Thus, 9.5 always raises the #
# inexact together with either overflow or underflow. #
# #
# setoxm1d #
# -------- #
# #
# Step 1. Set ans := 0 #
# #
# Step 2. Return ans := X + ans. Exit. #
# Notes: This will return X with the appropriate rounding #
# precision prescribed by the user FPCR. #
# #
# setoxm1 #
# ------- #
# #
# Step 1. Check |X| #
# 1.1 If |X| >= 1/4, go to Step 1.3. #
# 1.2 Go to Step 7. #
# 1.3 If |X| < 70 log(2), go to Step 2. #
# 1.4 Go to Step 10. #
# Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.#
# However, it is conceivable |X| can be small very often #
# because EXPM1 is intended to evaluate exp(X)-1 #
# accurately when |X| is small. For further details on #
# the comparisons, see the notes on Step 1 of setox. #
# #
# Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). #
# 2.1 N := round-to-nearest-integer( X * 64/log2 ). #
# 2.2 Calculate J = N mod 64; so J = 0,1,2,..., #
# or 63. #
# 2.3 Calculate M = (N - J)/64; so N = 64M + J. #
# 2.4 Calculate the address of the stored value of #
# 2^(J/64). #
# 2.5 Create the values Sc = 2^M and #
# OnebySc := -2^(-M). #
# Notes: See the notes on Step 2 of setox. #
# #
# Step 3. Calculate X - N*log2/64. #
# 3.1 R := X + N*L1, #
# where L1 := single-precision(-log2/64). #
# 3.2 R := R + N*L2, #
# L2 := extended-precision(-log2/64 - L1).#
# Notes: Applying the analysis of Step 3 of setox in this case #
# shows that |R| <= 0.0055 (note that |X| <= 70 log2 in #
# this case). #
# #
# Step 4. Approximate exp(R)-1 by a polynomial #
# p = R+R*R*(A1+R*(A2+R*(A3+R*(A4+R*(A5+R*A6))))) #
# Notes: a) In order to reduce memory access, the coefficients #
# are made as "short" as possible: A1 (which is 1/2), A5 #
# and A6 are single precision; A2, A3 and A4 are double #
# precision. #
# b) Even with the restriction above, #
# |p - (exp(R)-1)| < |R| * 2^(-72.7) #
# for all |R| <= 0.0055. #
# c) To fully utilize the pipeline, p is separated into #
# two independent pieces of roughly equal complexity #
# p = [ R*S*(A2 + S*(A4 + S*A6)) ] + #
# [ R + S*(A1 + S*(A3 + S*A5)) ] #
# where S = R*R. #
# #
# Step 5. Compute 2^(J/64)*p by #
# p := T*p #
# where T and t are the stored values for 2^(J/64). #
# Notes: 2^(J/64) is stored as T and t where T+t approximates #
# 2^(J/64) to roughly 85 bits; T is in extended precision #
# and t is in single precision. Note also that T is #
# rounded to 62 bits so that the last two bits of T are #
# zero. The reason for such a special form is that T-1, #
# T-2, and T-8 will all be exact --- a property that will #
# be exploited in Step 6 below. The total relative error #
# in p is no bigger than 2^(-67.7) compared to the final #
# result. #
# #
# Step 6. Reconstruction of exp(X)-1 #
# exp(X)-1 = 2^M * ( 2^(J/64) + p - 2^(-M) ). #
# 6.1 If M <= 63, go to Step 6.3. #
# 6.2 ans := T + (p + (t + OnebySc)). Go to 6.6 #
# 6.3 If M >= -3, go to 6.5. #
# 6.4 ans := (T + (p + t)) + OnebySc. Go to 6.6 #
# 6.5 ans := (T + OnebySc) + (p + t). #
# 6.6 Restore user FPCR. #
# 6.7 Return ans := Sc * ans. Exit. #
# Notes: The various arrangements of the expressions give #
# accurate evaluations. #
# #
# Step 7. exp(X)-1 for |X| < 1/4. #
# 7.1 If |X| >= 2^(-65), go to Step 9. #
# 7.2 Go to Step 8. #
# #
# Step 8. Calculate exp(X)-1, |X| < 2^(-65). #
# 8.1 If |X| < 2^(-16312), goto 8.3 #
# 8.2 Restore FPCR; return ans := X - 2^(-16382). #
# Exit. #
# 8.3 X := X * 2^(140). #
# 8.4 Restore FPCR; ans := ans - 2^(-16382). #
# Return ans := ans*2^(140). Exit #
# Notes: The idea is to return "X - tiny" under the user #
# precision and rounding modes. To avoid unnecessary #
# inefficiency, we stay away from denormalized numbers #
# the best we can. For |X| >= 2^(-16312), the #
# straightforward 8.2 generates the inexact exception as #
# the case warrants. #
# #
# Step 9. Calculate exp(X)-1, |X| < 1/4, by a polynomial #
# p = X + X*X*(B1 + X*(B2 + ... + X*B12)) #
# Notes: a) In order to reduce memory access, the coefficients #
# are made as "short" as possible: B1 (which is 1/2), B9 #
# to B12 are single precision; B3 to B8 are double #
# precision; and B2 is double extended. #
# b) Even with the restriction above, #
# |p - (exp(X)-1)| < |X| 2^(-70.6) #
# for all |X| <= 0.251. #
# Note that 0.251 is slightly bigger than 1/4. #
# c) To fully preserve accuracy, the polynomial is #
# computed as #
# X + ( S*B1 + Q ) where S = X*X and #
# Q = X*S*(B2 + X*(B3 + ... + X*B12)) #
# d) To fully utilize the pipeline, Q is separated into #
# two independent pieces of roughly equal complexity #
# Q = [ X*S*(B2 + S*(B4 + ... + S*B12)) ] + #
# [ S*S*(B3 + S*(B5 + ... + S*B11)) ] #
# #
# Step 10. Calculate exp(X)-1 for |X| >= 70 log 2. #
# 10.1 If X >= 70log2 , exp(X) - 1 = exp(X) for all #
# practical purposes. Therefore, go to Step 1 of setox. #
# 10.2 If X <= -70log2, exp(X) - 1 = -1 for all practical #
# purposes. #
# ans := -1 #
# Restore user FPCR #
# Return ans := ans + 2^(-126). Exit. #
# Notes: 10.2 will always create an inexact and return -1 + tiny #
# in the user rounding precision and mode. #
# #
#########################################################################
L2: long 0x3FDC0000,0x82E30865,0x4361C4C6,0x00000000
EEXPA3: long 0x3FA55555,0x55554CC1
EEXPA2: long 0x3FC55555,0x55554A54
EM1A4: long 0x3F811111,0x11174385
EM1A3: long 0x3FA55555,0x55554F5A
EM1A2: long 0x3FC55555,0x55555555,0x00000000,0x00000000
EM1B8: long 0x3EC71DE3,0xA5774682
EM1B7: long 0x3EFA01A0,0x19D7CB68
EM1B6: long 0x3F2A01A0,0x1A019DF3
EM1B5: long 0x3F56C16C,0x16C170E2
EM1B4: long 0x3F811111,0x11111111
EM1B3: long 0x3FA55555,0x55555555
EM1B2: long 0x3FFC0000,0xAAAAAAAA,0xAAAAAAAB
long 0x00000000
TWO140: long 0x48B00000,0x00000000
TWON140:
long 0x37300000,0x00000000
EEXPTBL:
long 0x3FFF0000,0x80000000,0x00000000,0x00000000
long 0x3FFF0000,0x8164D1F3,0xBC030774,0x9F841A9B
long 0x3FFF0000,0x82CD8698,0xAC2BA1D8,0x9FC1D5B9
long 0x3FFF0000,0x843A28C3,0xACDE4048,0xA0728369
long 0x3FFF0000,0x85AAC367,0xCC487B14,0x1FC5C95C
long 0x3FFF0000,0x871F6196,0x9E8D1010,0x1EE85C9F
long 0x3FFF0000,0x88980E80,0x92DA8528,0x9FA20729
long 0x3FFF0000,0x8A14D575,0x496EFD9C,0xA07BF9AF
long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E8,0xA0020DCF
long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E4,0x205A63DA
long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x1EB70051
long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x1F6EB029
long 0x3FFF0000,0x91C3D373,0xAB11C338,0xA0781494
long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0x9EB319B0
long 0x3FFF0000,0x94F4EFA8,0xFEF70960,0x2017457D
long 0x3FFF0000,0x96942D37,0x20185A00,0x1F11D537
long 0x3FFF0000,0x9837F051,0x8DB8A970,0x9FB952DD
long 0x3FFF0000,0x99E04593,0x20B7FA64,0x1FE43087
long 0x3FFF0000,0x9B8D39B9,0xD54E5538,0x1FA2A818
long 0x3FFF0000,0x9D3ED9A7,0x2CFFB750,0x1FDE494D
long 0x3FFF0000,0x9EF53260,0x91A111AC,0x20504890
long 0x3FFF0000,0xA0B0510F,0xB9714FC4,0xA073691C
long 0x3FFF0000,0xA2704303,0x0C496818,0x1F9B7A05
long 0x3FFF0000,0xA43515AE,0x09E680A0,0xA0797126
long 0x3FFF0000,0xA5FED6A9,0xB15138EC,0xA071A140
long 0x3FFF0000,0xA7CD93B4,0xE9653568,0x204F62DA
long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x1F283C4A
long 0x3FFF0000,0xAB7A39B5,0xA93ED338,0x9F9A7FDC
long 0x3FFF0000,0xAD583EEA,0x42A14AC8,0xA05B3FAC
long 0x3FFF0000,0xAF3B78AD,0x690A4374,0x1FDF2610
long 0x3FFF0000,0xB123F581,0xD2AC2590,0x9F705F90
long 0x3FFF0000,0xB311C412,0xA9112488,0x201F678A
long 0x3FFF0000,0xB504F333,0xF9DE6484,0x1F32FB13
long 0x3FFF0000,0xB6FD91E3,0x28D17790,0x20038B30
long 0x3FFF0000,0xB8FBAF47,0x62FB9EE8,0x200DC3CC
long 0x3FFF0000,0xBAFF5AB2,0x133E45FC,0x9F8B2AE6
long 0x3FFF0000,0xBD08A39F,0x580C36C0,0xA02BBF70
long 0x3FFF0000,0xBF1799B6,0x7A731084,0xA00BF518
long 0x3FFF0000,0xC12C4CCA,0x66709458,0xA041DD41
long 0x3FFF0000,0xC346CCDA,0x24976408,0x9FDF137B
long 0x3FFF0000,0xC5672A11,0x5506DADC,0x201F1568
long 0x3FFF0000,0xC78D74C8,0xABB9B15C,0x1FC13A2E
long 0x3FFF0000,0xC9B9BD86,0x6E2F27A4,0xA03F8F03
long 0x3FFF0000,0xCBEC14FE,0xF2727C5C,0x1FF4907D
long 0x3FFF0000,0xCE248C15,0x1F8480E4,0x9E6E53E4
long 0x3FFF0000,0xD06333DA,0xEF2B2594,0x1FD6D45C
long 0x3FFF0000,0xD2A81D91,0xF12AE45C,0xA076EDB9
long 0x3FFF0000,0xD4F35AAB,0xCFEDFA20,0x9FA6DE21
long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x1EE69A2F
long 0x3FFF0000,0xD99D15C2,0x78AFD7B4,0x207F439F
long 0x3FFF0000,0xDBFBB797,0xDAF23754,0x201EC207
long 0x3FFF0000,0xDE60F482,0x5E0E9124,0x9E8BE175
long 0x3FFF0000,0xE0CCDEEC,0x2A94E110,0x20032C4B
long 0x3FFF0000,0xE33F8972,0xBE8A5A50,0x2004DFF5
long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x1E72F47A
long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x1F722F22
long 0x3FFF0000,0xEAC0C6E7,0xDD243930,0xA017E945
long 0x3FFF0000,0xED4F301E,0xD9942B84,0x1F401A5B
long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CC,0x9FB9A9E3
long 0x3FFF0000,0xF281773C,0x59FFB138,0x20744C05
long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x1F773A19
long 0x3FFF0000,0xF7D0DF73,0x0AD13BB8,0x1FFE90D5
long 0x3FFF0000,0xFA83B2DB,0x722A033C,0xA041ED22
long 0x3FFF0000,0xFD3E0C0C,0xF486C174,0x1F853F3A
set ADJFLAG,L_SCR2
set SCALE,FP_SCR0
set ADJSCALE,FP_SCR1
set SC,FP_SCR0
set ONEBYSC,FP_SCR1
global setox
setox:
#--entry point for EXP(X), here X is finite, non-zero, and not NaN's
#--Step 1.
mov.l (%a0),%d1 # load part of input X
and.l &0x7FFF0000,%d1 # biased expo. of X
cmp.l %d1,&0x3FBE0000 # 2^(-65)
bge.b EXPC1 # normal case
bra EXPSM
EXPC1:
#--The case |X| >= 2^(-65)
mov.w 4(%a0),%d1 # expo. and partial sig. of |X|
cmp.l %d1,&0x400CB167 # 16380 log2 trunc. 16 bits
blt.b EXPMAIN # normal case
bra EEXPBIG
EXPMAIN:
#--Step 2.
#--This is the normal branch: 2^(-65) <= |X| < 16380 log2.
fmov.x (%a0),%fp0 # load input from (a0)
fmov.x %fp0,%fp1
fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
mov.l &0,ADJFLAG(%a6)
fmov.l %fp0,%d1 # N = int( X * 64/log2 )
lea EEXPTBL(%pc),%a1
fmov.l %d1,%fp0 # convert to floating-format
mov.l %d1,L_SCR1(%a6) # save N temporarily
and.l &0x3F,%d1 # D0 is J = N mod 64
lsl.l &4,%d1
add.l %d1,%a1 # address of 2^(J/64)
mov.l L_SCR1(%a6),%d1
asr.l &6,%d1 # D0 is M
add.w &0x3FFF,%d1 # biased expo. of 2^(M)
mov.w L2(%pc),L_SCR1(%a6) # prefetch L2, no need in CB
EXPCONT1:
#--Step 3.
#--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
#--a0 points to 2^(J/64), D0 is biased expo. of 2^(M)
fmov.x %fp0,%fp2
fmul.s &0xBC317218,%fp0 # N * L1, L1 = lead(-log2/64)
fmul.x L2(%pc),%fp2 # N * L2, L1+L2 = -log2/64
fadd.x %fp1,%fp0 # X + N*L1
fadd.x %fp2,%fp0 # fp0 is R, reduced arg.
#--Step 4.
#--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
#-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))
#--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
#--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))]
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # fp1 IS S = R*R
fmov.s &0x3AB60B70,%fp2 # fp2 IS A5
fmul.x %fp1,%fp2 # fp2 IS S*A5
fmov.x %fp1,%fp3
fmul.s &0x3C088895,%fp3 # fp3 IS S*A4
fadd.d EEXPA3(%pc),%fp2 # fp2 IS A3+S*A5
fadd.d EEXPA2(%pc),%fp3 # fp3 IS A2+S*A4
fmul.x %fp1,%fp2 # fp2 IS S*(A3+S*A5)
mov.w %d1,SCALE(%a6) # SCALE is 2^(M) in extended
mov.l &0x80000000,SCALE+4(%a6)
clr.l SCALE+8(%a6)
fmul.x %fp1,%fp3 # fp3 IS S*(A2+S*A4)
fadd.s &0x3F000000,%fp2 # fp2 IS A1+S*(A3+S*A5)
fmul.x %fp0,%fp3 # fp3 IS R*S*(A2+S*A4)
fmul.x %fp1,%fp2 # fp2 IS S*(A1+S*(A3+S*A5))
fadd.x %fp3,%fp0 # fp0 IS R+R*S*(A2+S*A4),
fmov.x (%a1)+,%fp1 # fp1 is lead. pt. of 2^(J/64)
fadd.x %fp2,%fp0 # fp0 is EXP(R) - 1
#--Step 5
#--final reconstruction process
#--EXP(X) = 2^M * ( 2^(J/64) + 2^(J/64)*(EXP(R)-1) )
fmul.x %fp1,%fp0 # 2^(J/64)*(Exp(R)-1)
fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3}
fadd.s (%a1),%fp0 # accurate 2^(J/64)
fadd.x %fp1,%fp0 # 2^(J/64) + 2^(J/64)*...
mov.l ADJFLAG(%a6),%d1
#--Step 6
tst.l %d1
beq.b NORMAL
ADJUST:
fmul.x ADJSCALE(%a6),%fp0
NORMAL:
fmov.l %d0,%fpcr # restore user FPCR
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x SCALE(%a6),%fp0 # multiply 2^(M)
bra t_catch
EXPSM:
#--Step 7
fmovm.x (%a0),&0x80 # load X
fmov.l %d0,%fpcr
fadd.s &0x3F800000,%fp0 # 1+X in user mode
bra t_pinx2
EEXPBIG:
#--Step 8
cmp.l %d1,&0x400CB27C # 16480 log2
bgt.b EXP2BIG
#--Steps 8.2 -- 8.6
fmov.x (%a0),%fp0 # load input from (a0)
fmov.x %fp0,%fp1
fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
mov.l &1,ADJFLAG(%a6)
fmov.l %fp0,%d1 # N = int( X * 64/log2 )
lea EEXPTBL(%pc),%a1
fmov.l %d1,%fp0 # convert to floating-format
mov.l %d1,L_SCR1(%a6) # save N temporarily
and.l &0x3F,%d1 # D0 is J = N mod 64
lsl.l &4,%d1
add.l %d1,%a1 # address of 2^(J/64)
mov.l L_SCR1(%a6),%d1
asr.l &6,%d1 # D0 is K
mov.l %d1,L_SCR1(%a6) # save K temporarily
asr.l &1,%d1 # D0 is M1
sub.l %d1,L_SCR1(%a6) # a1 is M
add.w &0x3FFF,%d1 # biased expo. of 2^(M1)
mov.w %d1,ADJSCALE(%a6) # ADJSCALE := 2^(M1)
mov.l &0x80000000,ADJSCALE+4(%a6)
clr.l ADJSCALE+8(%a6)
mov.l L_SCR1(%a6),%d1 # D0 is M
add.w &0x3FFF,%d1 # biased expo. of 2^(M)
bra.w EXPCONT1 # go back to Step 3
EXP2BIG:
#--Step 9
tst.b (%a0) # is X positive or negative?
bmi t_unfl2
bra t_ovfl2
global setoxd
setoxd:
#--entry point for EXP(X), X is denormalized
mov.l (%a0),-(%sp)
andi.l &0x80000000,(%sp)
ori.l &0x00800000,(%sp) # sign(X)*2^(-126)
fmov.s &0x3F800000,%fp0
fmov.l %d0,%fpcr
fadd.s (%sp)+,%fp0
bra t_pinx2
global setoxm1
setoxm1:
#--entry point for EXPM1(X), here X is finite, non-zero, non-NaN
#--Step 1.
#--Step 1.1
mov.l (%a0),%d1 # load part of input X
and.l &0x7FFF0000,%d1 # biased expo. of X
cmp.l %d1,&0x3FFD0000 # 1/4
bge.b EM1CON1 # |X| >= 1/4
bra EM1SM
EM1CON1:
#--Step 1.3
#--The case |X| >= 1/4
mov.w 4(%a0),%d1 # expo. and partial sig. of |X|
cmp.l %d1,&0x4004C215 # 70log2 rounded up to 16 bits
ble.b EM1MAIN # 1/4 <= |X| <= 70log2
bra EM1BIG
EM1MAIN:
#--Step 2.
#--This is the case: 1/4 <= |X| <= 70 log2.
fmov.x (%a0),%fp0 # load input from (a0)
fmov.x %fp0,%fp1
fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
fmov.l %fp0,%d1 # N = int( X * 64/log2 )
lea EEXPTBL(%pc),%a1
fmov.l %d1,%fp0 # convert to floating-format
mov.l %d1,L_SCR1(%a6) # save N temporarily
and.l &0x3F,%d1 # D0 is J = N mod 64
lsl.l &4,%d1
add.l %d1,%a1 # address of 2^(J/64)
mov.l L_SCR1(%a6),%d1
asr.l &6,%d1 # D0 is M
mov.l %d1,L_SCR1(%a6) # save a copy of M
#--Step 3.
#--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
#--a0 points to 2^(J/64), D0 and a1 both contain M
fmov.x %fp0,%fp2
fmul.s &0xBC317218,%fp0 # N * L1, L1 = lead(-log2/64)
fmul.x L2(%pc),%fp2 # N * L2, L1+L2 = -log2/64
fadd.x %fp1,%fp0 # X + N*L1
fadd.x %fp2,%fp0 # fp0 is R, reduced arg.
add.w &0x3FFF,%d1 # D0 is biased expo. of 2^M
#--Step 4.
#--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
#-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6)))))
#--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
#--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))]
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # fp1 IS S = R*R
fmov.s &0x3950097B,%fp2 # fp2 IS a6
fmul.x %fp1,%fp2 # fp2 IS S*A6
fmov.x %fp1,%fp3
fmul.s &0x3AB60B6A,%fp3 # fp3 IS S*A5
fadd.d EM1A4(%pc),%fp2 # fp2 IS A4+S*A6
fadd.d EM1A3(%pc),%fp3 # fp3 IS A3+S*A5
mov.w %d1,SC(%a6) # SC is 2^(M) in extended
mov.l &0x80000000,SC+4(%a6)
clr.l SC+8(%a6)
fmul.x %fp1,%fp2 # fp2 IS S*(A4+S*A6)
mov.l L_SCR1(%a6),%d1 # D0 is M
neg.w %d1 # D0 is -M
fmul.x %fp1,%fp3 # fp3 IS S*(A3+S*A5)
add.w &0x3FFF,%d1 # biased expo. of 2^(-M)
fadd.d EM1A2(%pc),%fp2 # fp2 IS A2+S*(A4+S*A6)
fadd.s &0x3F000000,%fp3 # fp3 IS A1+S*(A3+S*A5)
fmul.x %fp1,%fp2 # fp2 IS S*(A2+S*(A4+S*A6))
or.w &0x8000,%d1 # signed/expo. of -2^(-M)
mov.w %d1,ONEBYSC(%a6) # OnebySc is -2^(-M)
mov.l &0x80000000,ONEBYSC+4(%a6)
clr.l ONEBYSC+8(%a6)
fmul.x %fp3,%fp1 # fp1 IS S*(A1+S*(A3+S*A5))
fmul.x %fp0,%fp2 # fp2 IS R*S*(A2+S*(A4+S*A6))
fadd.x %fp1,%fp0 # fp0 IS R+S*(A1+S*(A3+S*A5))
fadd.x %fp2,%fp0 # fp0 IS EXP(R)-1
fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3}
#--Step 5
#--Compute 2^(J/64)*p
fmul.x (%a1),%fp0 # 2^(J/64)*(Exp(R)-1)
#--Step 6
#--Step 6.1
mov.l L_SCR1(%a6),%d1 # retrieve M
cmp.l %d1,&63
ble.b MLE63
#--Step 6.2 M >= 64
fmov.s 12(%a1),%fp1 # fp1 is t
fadd.x ONEBYSC(%a6),%fp1 # fp1 is t+OnebySc
fadd.x %fp1,%fp0 # p+(t+OnebySc), fp1 released
fadd.x (%a1),%fp0 # T+(p+(t+OnebySc))
bra EM1SCALE
MLE63:
#--Step 6.3 M <= 63
cmp.l %d1,&-3
bge.b MGEN3
MLTN3:
#--Step 6.4 M <= -4
fadd.s 12(%a1),%fp0 # p+t
fadd.x (%a1),%fp0 # T+(p+t)
fadd.x ONEBYSC(%a6),%fp0 # OnebySc + (T+(p+t))
bra EM1SCALE
MGEN3:
#--Step 6.5 -3 <= M <= 63
fmov.x (%a1)+,%fp1 # fp1 is T
fadd.s (%a1),%fp0 # fp0 is p+t
fadd.x ONEBYSC(%a6),%fp1 # fp1 is T+OnebySc
fadd.x %fp1,%fp0 # (T+OnebySc)+(p+t)
EM1SCALE:
#--Step 6.6
fmov.l %d0,%fpcr
fmul.x SC(%a6),%fp0
bra t_inx2
EM1SM:
#--Step 7 |X| < 1/4.
cmp.l %d1,&0x3FBE0000 # 2^(-65)
bge.b EM1POLY
EM1TINY:
#--Step 8 |X| < 2^(-65)
cmp.l %d1,&0x00330000 # 2^(-16312)
blt.b EM12TINY
#--Step 8.2
mov.l &0x80010000,SC(%a6) # SC is -2^(-16382)
mov.l &0x80000000,SC+4(%a6)
clr.l SC+8(%a6)
fmov.x (%a0),%fp0
fmov.l %d0,%fpcr
mov.b &FADD_OP,%d1 # last inst is ADD
fadd.x SC(%a6),%fp0
bra t_catch
EM12TINY:
#--Step 8.3
fmov.x (%a0),%fp0
fmul.d TWO140(%pc),%fp0
mov.l &0x80010000,SC(%a6)
mov.l &0x80000000,SC+4(%a6)
clr.l SC+8(%a6)
fadd.x SC(%a6),%fp0
fmov.l %d0,%fpcr
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.d TWON140(%pc),%fp0
bra t_catch
EM1POLY:
#--Step 9 exp(X)-1 by a simple polynomial
fmov.x (%a0),%fp0 # fp0 is X
fmul.x %fp0,%fp0 # fp0 is S := X*X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
fmov.s &0x2F30CAA8,%fp1 # fp1 is B12
fmul.x %fp0,%fp1 # fp1 is S*B12
fmov.s &0x310F8290,%fp2 # fp2 is B11
fadd.s &0x32D73220,%fp1 # fp1 is B10+S*B12
fmul.x %fp0,%fp2 # fp2 is S*B11
fmul.x %fp0,%fp1 # fp1 is S*(B10 + ...
fadd.s &0x3493F281,%fp2 # fp2 is B9+S*...
fadd.d EM1B8(%pc),%fp1 # fp1 is B8+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B9+...
fmul.x %fp0,%fp1 # fp1 is S*(B8+...
fadd.d EM1B7(%pc),%fp2 # fp2 is B7+S*...
fadd.d EM1B6(%pc),%fp1 # fp1 is B6+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B7+...
fmul.x %fp0,%fp1 # fp1 is S*(B6+...
fadd.d EM1B5(%pc),%fp2 # fp2 is B5+S*...
fadd.d EM1B4(%pc),%fp1 # fp1 is B4+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B5+...
fmul.x %fp0,%fp1 # fp1 is S*(B4+...
fadd.d EM1B3(%pc),%fp2 # fp2 is B3+S*...
fadd.x EM1B2(%pc),%fp1 # fp1 is B2+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B3+...
fmul.x %fp0,%fp1 # fp1 is S*(B2+...
fmul.x %fp0,%fp2 # fp2 is S*S*(B3+...)
fmul.x (%a0),%fp1 # fp1 is X*S*(B2...
fmul.s &0x3F000000,%fp0 # fp0 is S*B1
fadd.x %fp2,%fp1 # fp1 is Q
fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3}
fadd.x %fp1,%fp0 # fp0 is S*B1+Q
fmov.l %d0,%fpcr
fadd.x (%a0),%fp0
bra t_inx2
EM1BIG:
#--Step 10 |X| > 70 log2
mov.l (%a0),%d1
cmp.l %d1,&0
bgt.w EXPC1
#--Step 10.2
fmov.s &0xBF800000,%fp0 # fp0 is -1
fmov.l %d0,%fpcr
fadd.s &0x00800000,%fp0 # -1 + 2^(-126)
bra t_minx2
global setoxm1d
setoxm1d:
#--entry point for EXPM1(X), here X is denormalized
#--Step 0.
bra t_extdnrm
#########################################################################
# sgetexp(): returns the exponent portion of the input argument. #
# The exponent bias is removed and the exponent value is #
# returned as an extended precision number in fp0. #
# sgetexpd(): handles denormalized numbers. #
# #
# sgetman(): extracts the mantissa of the input argument. The #
# mantissa is converted to an extended precision number w/ #
# an exponent of $3fff and is returned in fp0. The range of #
# the result is [1.0 - 2.0). #
# sgetmand(): handles denormalized numbers. #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# #
# OUTPUT ************************************************************** #
# fp0 = exponent(X) or mantissa(X) #
# #
#########################################################################
global sgetexp
sgetexp:
mov.w SRC_EX(%a0),%d0 # get the exponent
bclr &0xf,%d0 # clear the sign bit
subi.w &0x3fff,%d0 # subtract off the bias
fmov.w %d0,%fp0 # return exp in fp0
blt.b sgetexpn # it's negative
rts
sgetexpn:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
global sgetexpd
sgetexpd:
bsr.l norm # normalize
neg.w %d0 # new exp = -(shft amt)
subi.w &0x3fff,%d0 # subtract off the bias
fmov.w %d0,%fp0 # return exp in fp0
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
global sgetman
sgetman:
mov.w SRC_EX(%a0),%d0 # get the exp
ori.w &0x7fff,%d0 # clear old exp
bclr &0xe,%d0 # make it the new exp +-3fff
# here, we build the result in a tmp location so as not to disturb the input
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6) # copy to tmp loc
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6) # copy to tmp loc
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmov.x FP_SCR0(%a6),%fp0 # put new value back in fp0
bmi.b sgetmann # it's negative
rts
sgetmann:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
#
# For denormalized numbers, shift the mantissa until the j-bit = 1,
# then load the exponent with +/1 $3fff.
#
global sgetmand
sgetmand:
bsr.l norm # normalize exponent
bra.b sgetman
#########################################################################
# scosh(): computes the hyperbolic cosine of a normalized input #
# scoshd(): computes the hyperbolic cosine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = cosh(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# COSH #
# 1. If |X| > 16380 log2, go to 3. #
# #
# 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae #
# y = |X|, z = exp(Y), and #
# cosh(X) = (1/2)*( z + 1/z ). #
# Exit. #
# #
# 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. #
# #
# 4. (16380 log2 < |X| <= 16480 log2) #
# cosh(X) = sign(X) * exp(|X|)/2. #
# However, invoking exp(|X|) may cause premature #
# overflow. Thus, we calculate sinh(X) as follows: #
# Y := |X| #
# Fact := 2**(16380) #
# Y' := Y - 16381 log2 #
# cosh(X) := Fact * exp(Y'). #
# Exit. #
# #
# 5. (|X| > 16480 log2) sinh(X) must overflow. Return #
# Huge*Huge to generate overflow and an infinity with #
# the appropriate sign. Huge is the largest finite number #
# in extended format. Exit. #
# #
#########################################################################
TWO16380:
long 0x7FFB0000,0x80000000,0x00000000,0x00000000
global scosh
scosh:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x400CB167
bgt.b COSHBIG
#--THIS IS THE USUAL CASE, |X| < 16380 LOG2
#--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )
fabs.x %fp0 # |X|
mov.l %d0,-(%sp)
clr.l %d0
fmovm.x &0x01,-(%sp) # save |X| to stack
lea (%sp),%a0 # pass ptr to |X|
bsr setox # FP0 IS EXP(|X|)
add.l &0xc,%sp # erase |X| from stack
fmul.s &0x3F000000,%fp0 # (1/2)EXP(|X|)
mov.l (%sp)+,%d0
fmov.s &0x3E800000,%fp1 # (1/4)
fdiv.x %fp0,%fp1 # 1/(2 EXP(|X|))
fmov.l %d0,%fpcr
mov.b &FADD_OP,%d1 # last inst is ADD
fadd.x %fp1,%fp0
bra t_catch
COSHBIG:
cmp.l %d1,&0x400CB2B3
bgt.b COSHHUGE
fabs.x %fp0
fsub.d T1(%pc),%fp0 # (|X|-16381LOG2_LEAD)
fsub.d T2(%pc),%fp0 # |X| - 16381 LOG2, ACCURATE
mov.l %d0,-(%sp)
clr.l %d0
fmovm.x &0x01,-(%sp) # save fp0 to stack
lea (%sp),%a0 # pass ptr to fp0
bsr setox
add.l &0xc,%sp # clear fp0 from stack
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x TWO16380(%pc),%fp0
bra t_catch
COSHHUGE:
bra t_ovfl2
global scoshd
#--COSH(X) = 1 FOR DENORMALIZED X
scoshd:
fmov.s &0x3F800000,%fp0
fmov.l %d0,%fpcr
fadd.s &0x00800000,%fp0
bra t_pinx2
#########################################################################
# ssinh(): computes the hyperbolic sine of a normalized input #
# ssinhd(): computes the hyperbolic sine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = sinh(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# SINH #
# 1. If |X| > 16380 log2, go to 3. #
# #
# 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formula #
# y = |X|, sgn = sign(X), and z = expm1(Y), #
# sinh(X) = sgn*(1/2)*( z + z/(1+z) ). #
# Exit. #
# #
# 3. If |X| > 16480 log2, go to 5. #
# #
# 4. (16380 log2 < |X| <= 16480 log2) #
# sinh(X) = sign(X) * exp(|X|)/2. #
# However, invoking exp(|X|) may cause premature overflow. #
# Thus, we calculate sinh(X) as follows: #
# Y := |X| #
# sgn := sign(X) #
# sgnFact := sgn * 2**(16380) #
# Y' := Y - 16381 log2 #
# sinh(X) := sgnFact * exp(Y'). #
# Exit. #
# #
# 5. (|X| > 16480 log2) sinh(X) must overflow. Return #
# sign(X)*Huge*Huge to generate overflow and an infinity with #
# the appropriate sign. Huge is the largest finite number in #
# extended format. Exit. #
# #
#########################################################################
global ssinh
ssinh:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
mov.l %d1,%a1 # save (compacted) operand
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x400CB167
bgt.b SINHBIG
#--THIS IS THE USUAL CASE, |X| < 16380 LOG2
#--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
fabs.x %fp0 # Y = |X|
movm.l &0x8040,-(%sp) # {a1/d0}
fmovm.x &0x01,-(%sp) # save Y on stack
lea (%sp),%a0 # pass ptr to Y
clr.l %d0
bsr setoxm1 # FP0 IS Z = EXPM1(Y)
add.l &0xc,%sp # clear Y from stack
fmov.l &0,%fpcr
movm.l (%sp)+,&0x0201 # {a1/d0}
fmov.x %fp0,%fp1
fadd.s &0x3F800000,%fp1 # 1+Z
fmov.x %fp0,-(%sp)
fdiv.x %fp1,%fp0 # Z/(1+Z)
mov.l %a1,%d1
and.l &0x80000000,%d1
or.l &0x3F000000,%d1
fadd.x (%sp)+,%fp0
mov.l %d1,-(%sp)
fmov.l %d0,%fpcr
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.s (%sp)+,%fp0 # last fp inst - possible exceptions set
bra t_catch
SINHBIG:
cmp.l %d1,&0x400CB2B3
bgt t_ovfl
fabs.x %fp0
fsub.d T1(%pc),%fp0 # (|X|-16381LOG2_LEAD)
mov.l &0,-(%sp)
mov.l &0x80000000,-(%sp)
mov.l %a1,%d1
and.l &0x80000000,%d1
or.l &0x7FFB0000,%d1
mov.l %d1,-(%sp) # EXTENDED FMT
fsub.d T2(%pc),%fp0 # |X| - 16381 LOG2, ACCURATE
mov.l %d0,-(%sp)
clr.l %d0
fmovm.x &0x01,-(%sp) # save fp0 on stack
lea (%sp),%a0 # pass ptr to fp0
bsr setox
add.l &0xc,%sp # clear fp0 from stack
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x (%sp)+,%fp0 # possible exception
bra t_catch
global ssinhd
#--SINH(X) = X FOR DENORMALIZED X
ssinhd:
bra t_extdnrm
#########################################################################
# stanh(): computes the hyperbolic tangent of a normalized input #
# stanhd(): computes the hyperbolic tangent of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = tanh(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# TANH #
# 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3. #
# #
# 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by #
# sgn := sign(X), y := 2|X|, z := expm1(Y), and #
# tanh(X) = sgn*( z/(2+z) ). #
# Exit. #
# #
# 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1, #
# go to 7. #
# #
# 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6. #
# #
# 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by #
# sgn := sign(X), y := 2|X|, z := exp(Y), #
# tanh(X) = sgn - [ sgn*2/(1+z) ]. #
# Exit. #
# #
# 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we #
# calculate Tanh(X) by #
# sgn := sign(X), Tiny := 2**(-126), #
# tanh(X) := sgn - sgn*Tiny. #
# Exit. #
# #
# 7. (|X| < 2**(-40)). Tanh(X) = X. Exit. #
# #
#########################################################################
set X,FP_SCR0
set XFRAC,X+4
set SGN,L_SCR3
set V,FP_SCR0
global stanh
stanh:
fmov.x (%a0),%fp0 # LOAD INPUT
fmov.x %fp0,X(%a6)
mov.l (%a0),%d1
mov.w 4(%a0),%d1
mov.l %d1,X(%a6)
and.l &0x7FFFFFFF,%d1
cmp.l %d1, &0x3fd78000 # is |X| < 2^(-40)?
blt.w TANHBORS # yes
cmp.l %d1, &0x3fffddce # is |X| > (5/2)LOG2?
bgt.w TANHBORS # yes
#--THIS IS THE USUAL CASE
#--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
mov.l X(%a6),%d1
mov.l %d1,SGN(%a6)
and.l &0x7FFF0000,%d1
add.l &0x00010000,%d1 # EXPONENT OF 2|X|
mov.l %d1,X(%a6)
and.l &0x80000000,SGN(%a6)
fmov.x X(%a6),%fp0 # FP0 IS Y = 2|X|
mov.l %d0,-(%sp)
clr.l %d0
fmovm.x &0x1,-(%sp) # save Y on stack
lea (%sp),%a0 # pass ptr to Y
bsr setoxm1 # FP0 IS Z = EXPM1(Y)
add.l &0xc,%sp # clear Y from stack
mov.l (%sp)+,%d0
fmov.x %fp0,%fp1
fadd.s &0x40000000,%fp1 # Z+2
mov.l SGN(%a6),%d1
fmov.x %fp1,V(%a6)
eor.l %d1,V(%a6)
fmov.l %d0,%fpcr # restore users round prec,mode
fdiv.x V(%a6),%fp0
bra t_inx2
TANHBORS:
cmp.l %d1,&0x3FFF8000
blt.w TANHSM
cmp.l %d1,&0x40048AA1
bgt.w TANHHUGE
#-- (5/2) LOG2 < |X| < 50 LOG2,
#--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
#--TANH(X) = SGN - SGN*2/[EXP(Y)+1].
mov.l X(%a6),%d1
mov.l %d1,SGN(%a6)
and.l &0x7FFF0000,%d1
add.l &0x00010000,%d1 # EXPO OF 2|X|
mov.l %d1,X(%a6) # Y = 2|X|
and.l &0x80000000,SGN(%a6)
mov.l SGN(%a6),%d1
fmov.x X(%a6),%fp0 # Y = 2|X|
mov.l %d0,-(%sp)
clr.l %d0
fmovm.x &0x01,-(%sp) # save Y on stack
lea (%sp),%a0 # pass ptr to Y
bsr setox # FP0 IS EXP(Y)
add.l &0xc,%sp # clear Y from stack
mov.l (%sp)+,%d0
mov.l SGN(%a6),%d1
fadd.s &0x3F800000,%fp0 # EXP(Y)+1
eor.l &0xC0000000,%d1 # -SIGN(X)*2
fmov.s %d1,%fp1 # -SIGN(X)*2 IN SGL FMT
fdiv.x %fp0,%fp1 # -SIGN(X)2 / [EXP(Y)+1 ]
mov.l SGN(%a6),%d1
or.l &0x3F800000,%d1 # SGN
fmov.s %d1,%fp0 # SGN IN SGL FMT
fmov.l %d0,%fpcr # restore users round prec,mode
mov.b &FADD_OP,%d1 # last inst is ADD
fadd.x %fp1,%fp0
bra t_inx2
TANHSM:
fmov.l %d0,%fpcr # restore users round prec,mode
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0 # last inst - possible exception set
bra t_catch
#---RETURN SGN(X) - SGN(X)EPS
TANHHUGE:
mov.l X(%a6),%d1
and.l &0x80000000,%d1
or.l &0x3F800000,%d1
fmov.s %d1,%fp0
and.l &0x80000000,%d1
eor.l &0x80800000,%d1 # -SIGN(X)*EPS
fmov.l %d0,%fpcr # restore users round prec,mode
fadd.s %d1,%fp0
bra t_inx2
global stanhd
#--TANH(X) = X FOR DENORMALIZED X
stanhd:
bra t_extdnrm
#########################################################################
# slogn(): computes the natural logarithm of a normalized input #
# slognd(): computes the natural logarithm of a denormalized input #
# slognp1(): computes the log(1+X) of a normalized input #
# slognp1d(): computes the log(1+X) of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = log(X) or log(1+X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 2 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# LOGN: #
# Step 1. If |X-1| < 1/16, approximate log(X) by an odd #
# polynomial in u, where u = 2(X-1)/(X+1). Otherwise, #
# move on to Step 2. #
# #
# Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first #
# seven significant bits of Y plus 2**(-7), i.e. #
# F = 1.xxxxxx1 in base 2 where the six "x" match those #
# of Y. Note that |Y-F| <= 2**(-7). #
# #
# Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a #
# polynomial in u, log(1+u) = poly. #
# #
# Step 4. Reconstruct #
# log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u) #
# by k*log(2) + (log(F) + poly). The values of log(F) are #
# calculated beforehand and stored in the program. #
# #
# lognp1: #
# Step 1: If |X| < 1/16, approximate log(1+X) by an odd #
# polynomial in u where u = 2X/(2+X). Otherwise, move on #
# to Step 2. #
# #
# Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done #
# in Step 2 of the algorithm for LOGN and compute #
# log(1+X) as k*log(2) + log(F) + poly where poly #
# approximates log(1+u), u = (Y-F)/F. #
# #
# Implementation Notes: #
# Note 1. There are 64 different possible values for F, thus 64 #
# log(F)'s need to be tabulated. Moreover, the values of #
# 1/F are also tabulated so that the division in (Y-F)/F #
# can be performed by a multiplication. #
# #
# Note 2. In Step 2 of lognp1, in order to preserved accuracy, #
# the value Y-F has to be calculated carefully when #
# 1/2 <= X < 3/2. #
# #
# Note 3. To fully exploit the pipeline, polynomials are usually #
# separated into two parts evaluated independently before #
# being added up. #
# #
#########################################################################
LOGOF2:
long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
one:
long 0x3F800000
zero:
long 0x00000000
infty:
long 0x7F800000
negone:
long 0xBF800000
LOGA6:
long 0x3FC2499A,0xB5E4040B
LOGA5:
long 0xBFC555B5,0x848CB7DB
LOGA4:
long 0x3FC99999,0x987D8730
LOGA3:
long 0xBFCFFFFF,0xFF6F7E97
LOGA2:
long 0x3FD55555,0x555555A4
LOGA1:
long 0xBFE00000,0x00000008
LOGB5:
long 0x3F175496,0xADD7DAD6
LOGB4:
long 0x3F3C71C2,0xFE80C7E0
LOGB3:
long 0x3F624924,0x928BCCFF
LOGB2:
long 0x3F899999,0x999995EC
LOGB1:
long 0x3FB55555,0x55555555
TWO:
long 0x40000000,0x00000000
LTHOLD:
long 0x3f990000,0x80000000,0x00000000,0x00000000
LOGTBL:
long 0x3FFE0000,0xFE03F80F,0xE03F80FE,0x00000000
long 0x3FF70000,0xFF015358,0x833C47E2,0x00000000
long 0x3FFE0000,0xFA232CF2,0x52138AC0,0x00000000
long 0x3FF90000,0xBDC8D83E,0xAD88D549,0x00000000
long 0x3FFE0000,0xF6603D98,0x0F6603DA,0x00000000
long 0x3FFA0000,0x9CF43DCF,0xF5EAFD48,0x00000000
long 0x3FFE0000,0xF2B9D648,0x0F2B9D65,0x00000000
long 0x3FFA0000,0xDA16EB88,0xCB8DF614,0x00000000
long 0x3FFE0000,0xEF2EB71F,0xC4345238,0x00000000
long 0x3FFB0000,0x8B29B775,0x1BD70743,0x00000000
long 0x3FFE0000,0xEBBDB2A5,0xC1619C8C,0x00000000
long 0x3FFB0000,0xA8D839F8,0x30C1FB49,0x00000000
long 0x3FFE0000,0xE865AC7B,0x7603A197,0x00000000
long 0x3FFB0000,0xC61A2EB1,0x8CD907AD,0x00000000
long 0x3FFE0000,0xE525982A,0xF70C880E,0x00000000
long 0x3FFB0000,0xE2F2A47A,0xDE3A18AF,0x00000000
long 0x3FFE0000,0xE1FC780E,0x1FC780E2,0x00000000
long 0x3FFB0000,0xFF64898E,0xDF55D551,0x00000000
long 0x3FFE0000,0xDEE95C4C,0xA037BA57,0x00000000
long 0x3FFC0000,0x8DB956A9,0x7B3D0148,0x00000000
long 0x3FFE0000,0xDBEB61EE,0xD19C5958,0x00000000
long 0x3FFC0000,0x9B8FE100,0xF47BA1DE,0x00000000
long 0x3FFE0000,0xD901B203,0x6406C80E,0x00000000
long 0x3FFC0000,0xA9372F1D,0x0DA1BD17,0x00000000
long 0x3FFE0000,0xD62B80D6,0x2B80D62C,0x00000000
long 0x3FFC0000,0xB6B07F38,0xCE90E46B,0x00000000
long 0x3FFE0000,0xD3680D36,0x80D3680D,0x00000000
long 0x3FFC0000,0xC3FD0329,0x06488481,0x00000000
long 0x3FFE0000,0xD0B69FCB,0xD2580D0B,0x00000000
long 0x3FFC0000,0xD11DE0FF,0x15AB18CA,0x00000000
long 0x3FFE0000,0xCE168A77,0x25080CE1,0x00000000
long 0x3FFC0000,0xDE1433A1,0x6C66B150,0x00000000
long 0x3FFE0000,0xCB8727C0,0x65C393E0,0x00000000
long 0x3FFC0000,0xEAE10B5A,0x7DDC8ADD,0x00000000
long 0x3FFE0000,0xC907DA4E,0x871146AD,0x00000000
long 0x3FFC0000,0xF7856E5E,0xE2C9B291,0x00000000
long 0x3FFE0000,0xC6980C69,0x80C6980C,0x00000000
long 0x3FFD0000,0x82012CA5,0xA68206D7,0x00000000
long 0x3FFE0000,0xC4372F85,0x5D824CA6,0x00000000
long 0x3FFD0000,0x882C5FCD,0x7256A8C5,0x00000000
long 0x3FFE0000,0xC1E4BBD5,0x95F6E947,0x00000000
long 0x3FFD0000,0x8E44C60B,0x4CCFD7DE,0x00000000
long 0x3FFE0000,0xBFA02FE8,0x0BFA02FF,0x00000000
long 0x3FFD0000,0x944AD09E,0xF4351AF6,0x00000000
long 0x3FFE0000,0xBD691047,0x07661AA3,0x00000000
long 0x3FFD0000,0x9A3EECD4,0xC3EAA6B2,0x00000000
long 0x3FFE0000,0xBB3EE721,0xA54D880C,0x00000000
long 0x3FFD0000,0xA0218434,0x353F1DE8,0x00000000
long 0x3FFE0000,0xB92143FA,0x36F5E02E,0x00000000
long 0x3FFD0000,0xA5F2FCAB,0xBBC506DA,0x00000000
long 0x3FFE0000,0xB70FBB5A,0x19BE3659,0x00000000
long 0x3FFD0000,0xABB3B8BA,0x2AD362A5,0x00000000
long 0x3FFE0000,0xB509E68A,0x9B94821F,0x00000000
long 0x3FFD0000,0xB1641795,0xCE3CA97B,0x00000000
long 0x3FFE0000,0xB30F6352,0x8917C80B,0x00000000
long 0x3FFD0000,0xB7047551,0x5D0F1C61,0x00000000
long 0x3FFE0000,0xB11FD3B8,0x0B11FD3C,0x00000000
long 0x3FFD0000,0xBC952AFE,0xEA3D13E1,0x00000000
long 0x3FFE0000,0xAF3ADDC6,0x80AF3ADE,0x00000000
long 0x3FFD0000,0xC2168ED0,0xF458BA4A,0x00000000
long 0x3FFE0000,0xAD602B58,0x0AD602B6,0x00000000
long 0x3FFD0000,0xC788F439,0xB3163BF1,0x00000000
long 0x3FFE0000,0xAB8F69E2,0x8359CD11,0x00000000
long 0x3FFD0000,0xCCECAC08,0xBF04565D,0x00000000
long 0x3FFE0000,0xA9C84A47,0xA07F5638,0x00000000
long 0x3FFD0000,0xD2420487,0x2DD85160,0x00000000
long 0x3FFE0000,0xA80A80A8,0x0A80A80B,0x00000000
long 0x3FFD0000,0xD7894992,0x3BC3588A,0x00000000
long 0x3FFE0000,0xA655C439,0x2D7B73A8,0x00000000
long 0x3FFD0000,0xDCC2C4B4,0x9887DACC,0x00000000
long 0x3FFE0000,0xA4A9CF1D,0x96833751,0x00000000
long 0x3FFD0000,0xE1EEBD3E,0x6D6A6B9E,0x00000000
long 0x3FFE0000,0xA3065E3F,0xAE7CD0E0,0x00000000
long 0x3FFD0000,0xE70D785C,0x2F9F5BDC,0x00000000
long 0x3FFE0000,0xA16B312E,0xA8FC377D,0x00000000
long 0x3FFD0000,0xEC1F392C,0x5179F283,0x00000000
long 0x3FFE0000,0x9FD809FD,0x809FD80A,0x00000000
long 0x3FFD0000,0xF12440D3,0xE36130E6,0x00000000
long 0x3FFE0000,0x9E4CAD23,0xDD5F3A20,0x00000000
long 0x3FFD0000,0xF61CCE92,0x346600BB,0x00000000
long 0x3FFE0000,0x9CC8E160,0xC3FB19B9,0x00000000
long 0x3FFD0000,0xFB091FD3,0x8145630A,0x00000000
long 0x3FFE0000,0x9B4C6F9E,0xF03A3CAA,0x00000000
long 0x3FFD0000,0xFFE97042,0xBFA4C2AD,0x00000000
long 0x3FFE0000,0x99D722DA,0xBDE58F06,0x00000000
long 0x3FFE0000,0x825EFCED,0x49369330,0x00000000
long 0x3FFE0000,0x9868C809,0x868C8098,0x00000000
long 0x3FFE0000,0x84C37A7A,0xB9A905C9,0x00000000
long 0x3FFE0000,0x97012E02,0x5C04B809,0x00000000
long 0x3FFE0000,0x87224C2E,0x8E645FB7,0x00000000
long 0x3FFE0000,0x95A02568,0x095A0257,0x00000000
long 0x3FFE0000,0x897B8CAC,0x9F7DE298,0x00000000
long 0x3FFE0000,0x94458094,0x45809446,0x00000000
long 0x3FFE0000,0x8BCF55DE,0xC4CD05FE,0x00000000
long 0x3FFE0000,0x92F11384,0x0497889C,0x00000000
long 0x3FFE0000,0x8E1DC0FB,0x89E125E5,0x00000000
long 0x3FFE0000,0x91A2B3C4,0xD5E6F809,0x00000000
long 0x3FFE0000,0x9066E68C,0x955B6C9B,0x00000000
long 0x3FFE0000,0x905A3863,0x3E06C43B,0x00000000
long 0x3FFE0000,0x92AADE74,0xC7BE59E0,0x00000000
long 0x3FFE0000,0x8F1779D9,0xFDC3A219,0x00000000
long 0x3FFE0000,0x94E9BFF6,0x15845643,0x00000000
long 0x3FFE0000,0x8DDA5202,0x37694809,0x00000000
long 0x3FFE0000,0x9723A1B7,0x20134203,0x00000000
long 0x3FFE0000,0x8CA29C04,0x6514E023,0x00000000
long 0x3FFE0000,0x995899C8,0x90EB8990,0x00000000
long 0x3FFE0000,0x8B70344A,0x139BC75A,0x00000000
long 0x3FFE0000,0x9B88BDAA,0x3A3DAE2F,0x00000000
long 0x3FFE0000,0x8A42F870,0x5669DB46,0x00000000
long 0x3FFE0000,0x9DB4224F,0xFFE1157C,0x00000000
long 0x3FFE0000,0x891AC73A,0xE9819B50,0x00000000
long 0x3FFE0000,0x9FDADC26,0x8B7A12DA,0x00000000
long 0x3FFE0000,0x87F78087,0xF78087F8,0x00000000
long 0x3FFE0000,0xA1FCFF17,0xCE733BD4,0x00000000
long 0x3FFE0000,0x86D90544,0x7A34ACC6,0x00000000
long 0x3FFE0000,0xA41A9E8F,0x5446FB9F,0x00000000
long 0x3FFE0000,0x85BF3761,0x2CEE3C9B,0x00000000
long 0x3FFE0000,0xA633CD7E,0x6771CD8B,0x00000000
long 0x3FFE0000,0x84A9F9C8,0x084A9F9D,0x00000000
long 0x3FFE0000,0xA8489E60,0x0B435A5E,0x00000000
long 0x3FFE0000,0x83993052,0x3FBE3368,0x00000000
long 0x3FFE0000,0xAA59233C,0xCCA4BD49,0x00000000
long 0x3FFE0000,0x828CBFBE,0xB9A020A3,0x00000000
long 0x3FFE0000,0xAC656DAE,0x6BCC4985,0x00000000
long 0x3FFE0000,0x81848DA8,0xFAF0D277,0x00000000
long 0x3FFE0000,0xAE6D8EE3,0x60BB2468,0x00000000
long 0x3FFE0000,0x80808080,0x80808081,0x00000000
long 0x3FFE0000,0xB07197A2,0x3C46C654,0x00000000
set ADJK,L_SCR1
set X,FP_SCR0
set XDCARE,X+2
set XFRAC,X+4
set F,FP_SCR1
set FFRAC,F+4
set KLOG2,FP_SCR0
set SAVEU,FP_SCR0
global slogn
#--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
slogn:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l &0x00000000,ADJK(%a6)
LOGBGN:
#--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
#--A FINITE, NON-ZERO, NORMALIZED NUMBER.
mov.l (%a0),%d1
mov.w 4(%a0),%d1
mov.l (%a0),X(%a6)
mov.l 4(%a0),X+4(%a6)
mov.l 8(%a0),X+8(%a6)
cmp.l %d1,&0 # CHECK IF X IS NEGATIVE
blt.w LOGNEG # LOG OF NEGATIVE ARGUMENT IS INVALID
# X IS POSITIVE, CHECK IF X IS NEAR 1
cmp.l %d1,&0x3ffef07d # IS X < 15/16?
blt.b LOGMAIN # YES
cmp.l %d1,&0x3fff8841 # IS X > 17/16?
ble.w LOGNEAR1 # NO
LOGMAIN:
#--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
#--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
#--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
#--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
#-- = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
#--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
#--LOG(1+U) CAN BE VERY EFFICIENT.
#--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
#--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
#--GET K, Y, F, AND ADDRESS OF 1/F.
asr.l &8,%d1
asr.l &8,%d1 # SHIFTED 16 BITS, BIASED EXPO. OF X
sub.l &0x3FFF,%d1 # THIS IS K
add.l ADJK(%a6),%d1 # ADJUST K, ORIGINAL INPUT MAY BE DENORM.
lea LOGTBL(%pc),%a0 # BASE ADDRESS OF 1/F AND LOG(F)
fmov.l %d1,%fp1 # CONVERT K TO FLOATING-POINT FORMAT
#--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
mov.l &0x3FFF0000,X(%a6) # X IS NOW Y, I.E. 2^(-K)*X
mov.l XFRAC(%a6),FFRAC(%a6)
and.l &0xFE000000,FFRAC(%a6) # FIRST 7 BITS OF Y
or.l &0x01000000,FFRAC(%a6) # GET F: ATTACH A 1 AT THE EIGHTH BIT
mov.l FFRAC(%a6),%d1 # READY TO GET ADDRESS OF 1/F
and.l &0x7E000000,%d1
asr.l &8,%d1
asr.l &8,%d1
asr.l &4,%d1 # SHIFTED 20, D0 IS THE DISPLACEMENT
add.l %d1,%a0 # A0 IS THE ADDRESS FOR 1/F
fmov.x X(%a6),%fp0
mov.l &0x3fff0000,F(%a6)
clr.l F+8(%a6)
fsub.x F(%a6),%fp0 # Y-F
fmovm.x &0xc,-(%sp) # SAVE FP2-3 WHILE FP0 IS NOT READY
#--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
#--REGISTERS SAVED: FPCR, FP1, FP2
LP1CONT1:
#--AN RE-ENTRY POINT FOR LOGNP1
fmul.x (%a0),%fp0 # FP0 IS U = (Y-F)/F
fmul.x LOGOF2(%pc),%fp1 # GET K*LOG2 WHILE FP0 IS NOT READY
fmov.x %fp0,%fp2
fmul.x %fp2,%fp2 # FP2 IS V=U*U
fmov.x %fp1,KLOG2(%a6) # PUT K*LOG2 IN MEMEORY, FREE FP1
#--LOG(1+U) IS APPROXIMATED BY
#--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
#--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4+V*A6))]
fmov.x %fp2,%fp3
fmov.x %fp2,%fp1
fmul.d LOGA6(%pc),%fp1 # V*A6
fmul.d LOGA5(%pc),%fp2 # V*A5
fadd.d LOGA4(%pc),%fp1 # A4+V*A6
fadd.d LOGA3(%pc),%fp2 # A3+V*A5
fmul.x %fp3,%fp1 # V*(A4+V*A6)
fmul.x %fp3,%fp2 # V*(A3+V*A5)
fadd.d LOGA2(%pc),%fp1 # A2+V*(A4+V*A6)
fadd.d LOGA1(%pc),%fp2 # A1+V*(A3+V*A5)
fmul.x %fp3,%fp1 # V*(A2+V*(A4+V*A6))
add.l &16,%a0 # ADDRESS OF LOG(F)
fmul.x %fp3,%fp2 # V*(A1+V*(A3+V*A5))
fmul.x %fp0,%fp1 # U*V*(A2+V*(A4+V*A6))
fadd.x %fp2,%fp0 # U+V*(A1+V*(A3+V*A5))
fadd.x (%a0),%fp1 # LOG(F)+U*V*(A2+V*(A4+V*A6))
fmovm.x (%sp)+,&0x30 # RESTORE FP2-3
fadd.x %fp1,%fp0 # FP0 IS LOG(F) + LOG(1+U)
fmov.l %d0,%fpcr
fadd.x KLOG2(%a6),%fp0 # FINAL ADD
bra t_inx2
LOGNEAR1:
# if the input is exactly equal to one, then exit through ld_pzero.
# if these 2 lines weren't here, the correct answer would be returned
# but the INEX2 bit would be set.
fcmp.b %fp0,&0x1 # is it equal to one?
fbeq.l ld_pzero # yes
#--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
fmov.x %fp0,%fp1
fsub.s one(%pc),%fp1 # FP1 IS X-1
fadd.s one(%pc),%fp0 # FP0 IS X+1
fadd.x %fp1,%fp1 # FP1 IS 2(X-1)
#--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
#--IN U, U = 2(X-1)/(X+1) = FP1/FP0
LP1CONT2:
#--THIS IS AN RE-ENTRY POINT FOR LOGNP1
fdiv.x %fp0,%fp1 # FP1 IS U
fmovm.x &0xc,-(%sp) # SAVE FP2-3
#--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
#--LET V=U*U, W=V*V, CALCULATE
#--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
#--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 + W*B4)] )
fmov.x %fp1,%fp0
fmul.x %fp0,%fp0 # FP0 IS V
fmov.x %fp1,SAVEU(%a6) # STORE U IN MEMORY, FREE FP1
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS W
fmov.d LOGB5(%pc),%fp3
fmov.d LOGB4(%pc),%fp2
fmul.x %fp1,%fp3 # W*B5
fmul.x %fp1,%fp2 # W*B4
fadd.d LOGB3(%pc),%fp3 # B3+W*B5
fadd.d LOGB2(%pc),%fp2 # B2+W*B4
fmul.x %fp3,%fp1 # W*(B3+W*B5), FP3 RELEASED
fmul.x %fp0,%fp2 # V*(B2+W*B4)
fadd.d LOGB1(%pc),%fp1 # B1+W*(B3+W*B5)
fmul.x SAVEU(%a6),%fp0 # FP0 IS U*V
fadd.x %fp2,%fp1 # B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED
fmovm.x (%sp)+,&0x30 # FP2-3 RESTORED
fmul.x %fp1,%fp0 # U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
fmov.l %d0,%fpcr
fadd.x SAVEU(%a6),%fp0
bra t_inx2
#--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
LOGNEG:
bra t_operr
global slognd
slognd:
#--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
mov.l &-100,ADJK(%a6) # INPUT = 2^(ADJK) * FP0
#----normalize the input value by left shifting k bits (k to be determined
#----below), adjusting exponent and storing -k to ADJK
#----the value TWOTO100 is no longer needed.
#----Note that this code assumes the denormalized input is NON-ZERO.
movm.l &0x3f00,-(%sp) # save some registers {d2-d7}
mov.l (%a0),%d3 # D3 is exponent of smallest norm. #
mov.l 4(%a0),%d4
mov.l 8(%a0),%d5 # (D4,D5) is (Hi_X,Lo_X)
clr.l %d2 # D2 used for holding K
tst.l %d4
bne.b Hi_not0
Hi_0:
mov.l %d5,%d4
clr.l %d5
mov.l &32,%d2
clr.l %d6
bfffo %d4{&0:&32},%d6
lsl.l %d6,%d4
add.l %d6,%d2 # (D3,D4,D5) is normalized
mov.l %d3,X(%a6)
mov.l %d4,XFRAC(%a6)
mov.l %d5,XFRAC+4(%a6)
neg.l %d2
mov.l %d2,ADJK(%a6)
fmov.x X(%a6),%fp0
movm.l (%sp)+,&0xfc # restore registers {d2-d7}
lea X(%a6),%a0
bra.w LOGBGN # begin regular log(X)
Hi_not0:
clr.l %d6
bfffo %d4{&0:&32},%d6 # find first 1
mov.l %d6,%d2 # get k
lsl.l %d6,%d4
mov.l %d5,%d7 # a copy of D5
lsl.l %d6,%d5
neg.l %d6
add.l &32,%d6
lsr.l %d6,%d7
or.l %d7,%d4 # (D3,D4,D5) normalized
mov.l %d3,X(%a6)
mov.l %d4,XFRAC(%a6)
mov.l %d5,XFRAC+4(%a6)
neg.l %d2
mov.l %d2,ADJK(%a6)
fmov.x X(%a6),%fp0
movm.l (%sp)+,&0xfc # restore registers {d2-d7}
lea X(%a6),%a0
bra.w LOGBGN # begin regular log(X)
global slognp1
#--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
slognp1:
fmov.x (%a0),%fp0 # LOAD INPUT
fabs.x %fp0 # test magnitude
fcmp.x %fp0,LTHOLD(%pc) # compare with min threshold
fbgt.w LP1REAL # if greater, continue
fmov.l %d0,%fpcr
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x (%a0),%fp0 # return signed argument
bra t_catch
LP1REAL:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l &0x00000000,ADJK(%a6)
fmov.x %fp0,%fp1 # FP1 IS INPUT Z
fadd.s one(%pc),%fp0 # X := ROUND(1+Z)
fmov.x %fp0,X(%a6)
mov.w XFRAC(%a6),XDCARE(%a6)
mov.l X(%a6),%d1
cmp.l %d1,&0
ble.w LP1NEG0 # LOG OF ZERO OR -VE
cmp.l %d1,&0x3ffe8000 # IS BOUNDS [1/2,3/2]?
blt.w LOGMAIN
cmp.l %d1,&0x3fffc000
bgt.w LOGMAIN
#--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
#--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
#--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
LP1NEAR1:
#--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
cmp.l %d1,&0x3ffef07d
blt.w LP1CARE
cmp.l %d1,&0x3fff8841
bgt.w LP1CARE
LP1ONE16:
#--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
#--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
fadd.x %fp1,%fp1 # FP1 IS 2Z
fadd.s one(%pc),%fp0 # FP0 IS 1+X
#--U = FP1/FP0
bra.w LP1CONT2
LP1CARE:
#--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
#--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
#--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
#--THERE ARE ONLY TWO CASES.
#--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
#--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F) + Z
#--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
#--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
mov.l XFRAC(%a6),FFRAC(%a6)
and.l &0xFE000000,FFRAC(%a6)
or.l &0x01000000,FFRAC(%a6) # F OBTAINED
cmp.l %d1,&0x3FFF8000 # SEE IF 1+Z > 1
bge.b KISZERO
KISNEG1:
fmov.s TWO(%pc),%fp0
mov.l &0x3fff0000,F(%a6)
clr.l F+8(%a6)
fsub.x F(%a6),%fp0 # 2-F
mov.l FFRAC(%a6),%d1
and.l &0x7E000000,%d1
asr.l &8,%d1
asr.l &8,%d1
asr.l &4,%d1 # D0 CONTAINS DISPLACEMENT FOR 1/F
fadd.x %fp1,%fp1 # GET 2Z
fmovm.x &0xc,-(%sp) # SAVE FP2 {%fp2/%fp3}
fadd.x %fp1,%fp0 # FP0 IS Y-F = (2-F)+2Z
lea LOGTBL(%pc),%a0 # A0 IS ADDRESS OF 1/F
add.l %d1,%a0
fmov.s negone(%pc),%fp1 # FP1 IS K = -1
bra.w LP1CONT1
KISZERO:
fmov.s one(%pc),%fp0
mov.l &0x3fff0000,F(%a6)
clr.l F+8(%a6)
fsub.x F(%a6),%fp0 # 1-F
mov.l FFRAC(%a6),%d1
and.l &0x7E000000,%d1
asr.l &8,%d1
asr.l &8,%d1
asr.l &4,%d1
fadd.x %fp1,%fp0 # FP0 IS Y-F
fmovm.x &0xc,-(%sp) # FP2 SAVED {%fp2/%fp3}
lea LOGTBL(%pc),%a0
add.l %d1,%a0 # A0 IS ADDRESS OF 1/F
fmov.s zero(%pc),%fp1 # FP1 IS K = 0
bra.w LP1CONT1
LP1NEG0:
#--FPCR SAVED. D0 IS X IN COMPACT FORM.
cmp.l %d1,&0
blt.b LP1NEG
LP1ZERO:
fmov.s negone(%pc),%fp0
fmov.l %d0,%fpcr
bra t_dz
LP1NEG:
fmov.s zero(%pc),%fp0
fmov.l %d0,%fpcr
bra t_operr
global slognp1d
#--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT
# Simply return the denorm
slognp1d:
bra t_extdnrm
#########################################################################
# satanh(): computes the inverse hyperbolic tangent of a norm input #
# satanhd(): computes the inverse hyperbolic tangent of a denorm input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = arctanh(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# ATANH #
# 1. If |X| >= 1, go to 3. #
# #
# 2. (|X| < 1) Calculate atanh(X) by #
# sgn := sign(X) #
# y := |X| #
# z := 2y/(1-y) #
# atanh(X) := sgn * (1/2) * logp1(z) #
# Exit. #
# #
# 3. If |X| > 1, go to 5. #
# #
# 4. (|X| = 1) Generate infinity with an appropriate sign and #
# divide-by-zero by #
# sgn := sign(X) #
# atan(X) := sgn / (+0). #
# Exit. #
# #
# 5. (|X| > 1) Generate an invalid operation by 0 * infinity. #
# Exit. #
# #
#########################################################################
global satanh
satanh:
mov.l (%a0),%d1
mov.w 4(%a0),%d1
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FFF8000
bge.b ATANHBIG
#--THIS IS THE USUAL CASE, |X| < 1
#--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
fabs.x (%a0),%fp0 # Y = |X|
fmov.x %fp0,%fp1
fneg.x %fp1 # -Y
fadd.x %fp0,%fp0 # 2Y
fadd.s &0x3F800000,%fp1 # 1-Y
fdiv.x %fp1,%fp0 # 2Y/(1-Y)
mov.l (%a0),%d1
and.l &0x80000000,%d1
or.l &0x3F000000,%d1 # SIGN(X)*HALF
mov.l %d1,-(%sp)
mov.l %d0,-(%sp) # save rnd prec,mode
clr.l %d0 # pass ext prec,RN
fmovm.x &0x01,-(%sp) # save Z on stack
lea (%sp),%a0 # pass ptr to Z
bsr slognp1 # LOG1P(Z)
add.l &0xc,%sp # clear Z from stack
mov.l (%sp)+,%d0 # fetch old prec,mode
fmov.l %d0,%fpcr # load it
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.s (%sp)+,%fp0
bra t_catch
ATANHBIG:
fabs.x (%a0),%fp0 # |X|
fcmp.s %fp0,&0x3F800000
fbgt t_operr
bra t_dz
global satanhd
#--ATANH(X) = X FOR DENORMALIZED X
satanhd:
bra t_extdnrm
#########################################################################
# slog10(): computes the base-10 logarithm of a normalized input #
# slog10d(): computes the base-10 logarithm of a denormalized input #
# slog2(): computes the base-2 logarithm of a normalized input #
# slog2d(): computes the base-2 logarithm of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = log_10(X) or log_2(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 1.7 ulps in 64 significant bit, #
# i.e. within 0.5003 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# slog10d: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. Call slognd to obtain Y = log(X), the natural log of X. #
# Notes: Even if X is denormalized, log(X) is always normalized. #
# #
# Step 2. Compute log_10(X) = log(X) * (1/log(10)). #
# 2.1 Restore the user FPCR #
# 2.2 Return ans := Y * INV_L10. #
# #
# slog10: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. Call sLogN to obtain Y = log(X), the natural log of X. #
# #
# Step 2. Compute log_10(X) = log(X) * (1/log(10)). #
# 2.1 Restore the user FPCR #
# 2.2 Return ans := Y * INV_L10. #
# #
# sLog2d: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. Call slognd to obtain Y = log(X), the natural log of X. #
# Notes: Even if X is denormalized, log(X) is always normalized. #
# #
# Step 2. Compute log_10(X) = log(X) * (1/log(2)). #
# 2.1 Restore the user FPCR #
# 2.2 Return ans := Y * INV_L2. #
# #
# sLog2: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. If X is not an integer power of two, i.e., X != 2^k, #
# go to Step 3. #
# #
# Step 2. Return k. #
# 2.1 Get integer k, X = 2^k. #
# 2.2 Restore the user FPCR. #
# 2.3 Return ans := convert-to-double-extended(k). #
# #
# Step 3. Call sLogN to obtain Y = log(X), the natural log of X. #
# #
# Step 4. Compute log_2(X) = log(X) * (1/log(2)). #
# 4.1 Restore the user FPCR #
# 4.2 Return ans := Y * INV_L2. #
# #
#########################################################################
INV_L10:
long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
INV_L2:
long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
global slog10
#--entry point for Log10(X), X is normalized
slog10:
fmov.b &0x1,%fp0
fcmp.x %fp0,(%a0) # if operand == 1,
fbeq.l ld_pzero # return an EXACT zero
mov.l (%a0),%d1
blt.w invalid
mov.l %d0,-(%sp)
clr.l %d0
bsr slogn # log(X), X normal.
fmov.l (%sp)+,%fpcr
fmul.x INV_L10(%pc),%fp0
bra t_inx2
global slog10d
#--entry point for Log10(X), X is denormalized
slog10d:
mov.l (%a0),%d1
blt.w invalid
mov.l %d0,-(%sp)
clr.l %d0
bsr slognd # log(X), X denorm.
fmov.l (%sp)+,%fpcr
fmul.x INV_L10(%pc),%fp0
bra t_minx2
global slog2
#--entry point for Log2(X), X is normalized
slog2:
mov.l (%a0),%d1
blt.w invalid
mov.l 8(%a0),%d1
bne.b continue # X is not 2^k
mov.l 4(%a0),%d1
and.l &0x7FFFFFFF,%d1
bne.b continue
#--X = 2^k.
mov.w (%a0),%d1
and.l &0x00007FFF,%d1
sub.l &0x3FFF,%d1
beq.l ld_pzero
fmov.l %d0,%fpcr
fmov.l %d1,%fp0
bra t_inx2
continue:
mov.l %d0,-(%sp)
clr.l %d0
bsr slogn # log(X), X normal.
fmov.l (%sp)+,%fpcr
fmul.x INV_L2(%pc),%fp0
bra t_inx2
invalid:
bra t_operr
global slog2d
#--entry point for Log2(X), X is denormalized
slog2d:
mov.l (%a0),%d1
blt.w invalid
mov.l %d0,-(%sp)
clr.l %d0
bsr slognd # log(X), X denorm.
fmov.l (%sp)+,%fpcr
fmul.x INV_L2(%pc),%fp0
bra t_minx2
#########################################################################
# stwotox(): computes 2**X for a normalized input #
# stwotoxd(): computes 2**X for a denormalized input #
# stentox(): computes 10**X for a normalized input #
# stentoxd(): computes 10**X for a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = 2**X or 10**X #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 2 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# twotox #
# 1. If |X| > 16480, go to ExpBig. #
# #
# 2. If |X| < 2**(-70), go to ExpSm. #
# #
# 3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore #
# decompose N as #
# N = 64(M + M') + j, j = 0,1,2,...,63. #
# #
# 4. Overwrite r := r * log2. Then #
# 2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r). #
# Go to expr to compute that expression. #
# #
# tentox #
# 1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig. #
# #
# 2. If |X| < 2**(-70), go to ExpSm. #
# #
# 3. Set y := X*log_2(10)*64 (base 2 log of 10). Set #
# N := round-to-int(y). Decompose N as #
# N = 64(M + M') + j, j = 0,1,2,...,63. #
# #
# 4. Define r as #
# r := ((X - N*L1)-N*L2) * L10 #
# where L1, L2 are the leading and trailing parts of #
# log_10(2)/64 and L10 is the natural log of 10. Then #
# 10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r). #
# Go to expr to compute that expression. #
# #
# expr #
# 1. Fetch 2**(j/64) from table as Fact1 and Fact2. #
# #
# 2. Overwrite Fact1 and Fact2 by #
# Fact1 := 2**(M) * Fact1 #
# Fact2 := 2**(M) * Fact2 #
# Thus Fact1 + Fact2 = 2**(M) * 2**(j/64). #
# #
# 3. Calculate P where 1 + P approximates exp(r): #
# P = r + r*r*(A1+r*(A2+...+r*A5)). #
# #
# 4. Let AdjFact := 2**(M'). Return #
# AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ). #
# Exit. #
# #
# ExpBig #
# 1. Generate overflow by Huge * Huge if X > 0; otherwise, #
# generate underflow by Tiny * Tiny. #
# #
# ExpSm #
# 1. Return 1 + X. #
# #
#########################################################################
L2TEN64:
long 0x406A934F,0x0979A371 # 64LOG10/LOG2
L10TWO1:
long 0x3F734413,0x509F8000 # LOG2/64LOG10
L10TWO2:
long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000
LOG10: long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000
LOG2: long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
EXPA5: long 0x3F56C16D,0x6F7BD0B2
EXPA4: long 0x3F811112,0x302C712C
EXPA3: long 0x3FA55555,0x55554CC1
EXPA2: long 0x3FC55555,0x55554A54
EXPA1: long 0x3FE00000,0x00000000,0x00000000,0x00000000
TEXPTBL:
long 0x3FFF0000,0x80000000,0x00000000,0x3F738000
long 0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA
long 0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9
long 0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9
long 0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA
long 0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C
long 0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1
long 0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA
long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373
long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670
long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700
long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0
long 0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D
long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319
long 0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B
long 0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5
long 0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A
long 0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B
long 0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF
long 0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA
long 0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD
long 0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E
long 0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B
long 0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB
long 0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB
long 0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274
long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C
long 0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00
long 0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301
long 0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367
long 0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F
long 0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C
long 0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB
long 0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB
long 0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C
long 0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA
long 0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD
long 0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51
long 0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A
long 0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2
long 0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB
long 0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17
long 0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C
long 0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8
long 0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53
long 0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE
long 0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124
long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243
long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A
long 0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61
long 0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610
long 0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1
long 0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12
long 0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE
long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4
long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F
long 0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A
long 0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A
long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC
long 0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F
long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A
long 0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795
long 0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B
long 0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581
set INT,L_SCR1
set X,FP_SCR0
set XDCARE,X+2
set XFRAC,X+4
set ADJFACT,FP_SCR0
set FACT1,FP_SCR0
set FACT1HI,FACT1+4
set FACT1LOW,FACT1+8
set FACT2,FP_SCR1
set FACT2HI,FACT2+4
set FACT2LOW,FACT2+8
global stwotox
#--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
stwotox:
fmovm.x (%a0),&0x80 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
fmov.x %fp0,X(%a6)
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FB98000 # |X| >= 2**(-70)?
bge.b TWOOK1
bra.w EXPBORS
TWOOK1:
cmp.l %d1,&0x400D80C0 # |X| > 16480?
ble.b TWOMAIN
bra.w EXPBORS
TWOMAIN:
#--USUAL CASE, 2^(-70) <= |X| <= 16480
fmov.x %fp0,%fp1
fmul.s &0x42800000,%fp1 # 64 * X
fmov.l %fp1,INT(%a6) # N = ROUND-TO-INT(64 X)
mov.l %d2,-(%sp)
lea TEXPTBL(%pc),%a1 # LOAD ADDRESS OF TABLE OF 2^(J/64)
fmov.l INT(%a6),%fp1 # N --> FLOATING FMT
mov.l INT(%a6),%d1
mov.l %d1,%d2
and.l &0x3F,%d1 # D0 IS J
asl.l &4,%d1 # DISPLACEMENT FOR 2^(J/64)
add.l %d1,%a1 # ADDRESS FOR 2^(J/64)
asr.l &6,%d2 # d2 IS L, N = 64L + J
mov.l %d2,%d1
asr.l &1,%d1 # D0 IS M
sub.l %d1,%d2 # d2 IS M', N = 64(M+M') + J
add.l &0x3FFF,%d2
#--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
#--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
#--ADJFACT = 2^(M').
#--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmul.s &0x3C800000,%fp1 # (1/64)*N
mov.l (%a1)+,FACT1(%a6)
mov.l (%a1)+,FACT1HI(%a6)
mov.l (%a1)+,FACT1LOW(%a6)
mov.w (%a1)+,FACT2(%a6)
fsub.x %fp1,%fp0 # X - (1/64)*INT(64 X)
mov.w (%a1)+,FACT2HI(%a6)
clr.w FACT2HI+2(%a6)
clr.l FACT2LOW(%a6)
add.w %d1,FACT1(%a6)
fmul.x LOG2(%pc),%fp0 # FP0 IS R
add.w %d1,FACT2(%a6)
bra.w expr
EXPBORS:
#--FPCR, D0 SAVED
cmp.l %d1,&0x3FFF8000
bgt.b TEXPBIG
#--|X| IS SMALL, RETURN 1 + X
fmov.l %d0,%fpcr # restore users round prec,mode
fadd.s &0x3F800000,%fp0 # RETURN 1 + X
bra t_pinx2
TEXPBIG:
#--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW
#--REGISTERS SAVE SO FAR ARE FPCR AND D0
mov.l X(%a6),%d1
cmp.l %d1,&0
blt.b EXPNEG
bra t_ovfl2 # t_ovfl expects positive value
EXPNEG:
bra t_unfl2 # t_unfl expects positive value
global stwotoxd
stwotoxd:
#--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
fmov.l %d0,%fpcr # set user's rounding mode/precision
fmov.s &0x3F800000,%fp0 # RETURN 1 + X
mov.l (%a0),%d1
or.l &0x00800001,%d1
fadd.s %d1,%fp0
bra t_pinx2
global stentox
#--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
stentox:
fmovm.x (%a0),&0x80 # LOAD INPUT
mov.l (%a0),%d1
mov.w 4(%a0),%d1
fmov.x %fp0,X(%a6)
and.l &0x7FFFFFFF,%d1
cmp.l %d1,&0x3FB98000 # |X| >= 2**(-70)?
bge.b TENOK1
bra.w EXPBORS
TENOK1:
cmp.l %d1,&0x400B9B07 # |X| <= 16480*log2/log10 ?
ble.b TENMAIN
bra.w EXPBORS
TENMAIN:
#--USUAL CASE, 2^(-70) <= |X| <= 16480 LOG 2 / LOG 10
fmov.x %fp0,%fp1
fmul.d L2TEN64(%pc),%fp1 # X*64*LOG10/LOG2
fmov.l %fp1,INT(%a6) # N=INT(X*64*LOG10/LOG2)
mov.l %d2,-(%sp)
lea TEXPTBL(%pc),%a1 # LOAD ADDRESS OF TABLE OF 2^(J/64)
fmov.l INT(%a6),%fp1 # N --> FLOATING FMT
mov.l INT(%a6),%d1
mov.l %d1,%d2
and.l &0x3F,%d1 # D0 IS J
asl.l &4,%d1 # DISPLACEMENT FOR 2^(J/64)
add.l %d1,%a1 # ADDRESS FOR 2^(J/64)
asr.l &6,%d2 # d2 IS L, N = 64L + J
mov.l %d2,%d1
asr.l &1,%d1 # D0 IS M
sub.l %d1,%d2 # d2 IS M', N = 64(M+M') + J
add.l &0x3FFF,%d2
#--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
#--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
#--ADJFACT = 2^(M').
#--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmov.x %fp1,%fp2
fmul.d L10TWO1(%pc),%fp1 # N*(LOG2/64LOG10)_LEAD
mov.l (%a1)+,FACT1(%a6)
fmul.x L10TWO2(%pc),%fp2 # N*(LOG2/64LOG10)_TRAIL
mov.l (%a1)+,FACT1HI(%a6)
mov.l (%a1)+,FACT1LOW(%a6)
fsub.x %fp1,%fp0 # X - N L_LEAD
mov.w (%a1)+,FACT2(%a6)
fsub.x %fp2,%fp0 # X - N L_TRAIL
mov.w (%a1)+,FACT2HI(%a6)
clr.w FACT2HI+2(%a6)
clr.l FACT2LOW(%a6)
fmul.x LOG10(%pc),%fp0 # FP0 IS R
add.w %d1,FACT1(%a6)
add.w %d1,FACT2(%a6)
expr:
#--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
#--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64).
#--FP0 IS R. THE FOLLOWING CODE COMPUTES
#-- 2**(M'+M) * 2**(J/64) * EXP(R)
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS S = R*R
fmov.d EXPA5(%pc),%fp2 # FP2 IS A5
fmov.d EXPA4(%pc),%fp3 # FP3 IS A4
fmul.x %fp1,%fp2 # FP2 IS S*A5
fmul.x %fp1,%fp3 # FP3 IS S*A4
fadd.d EXPA3(%pc),%fp2 # FP2 IS A3+S*A5
fadd.d EXPA2(%pc),%fp3 # FP3 IS A2+S*A4
fmul.x %fp1,%fp2 # FP2 IS S*(A3+S*A5)
fmul.x %fp1,%fp3 # FP3 IS S*(A2+S*A4)
fadd.d EXPA1(%pc),%fp2 # FP2 IS A1+S*(A3+S*A5)
fmul.x %fp0,%fp3 # FP3 IS R*S*(A2+S*A4)
fmul.x %fp1,%fp2 # FP2 IS S*(A1+S*(A3+S*A5))
fadd.x %fp3,%fp0 # FP0 IS R+R*S*(A2+S*A4)
fadd.x %fp2,%fp0 # FP0 IS EXP(R) - 1
fmovm.x (%sp)+,&0x30 # restore fp2/fp3
#--FINAL RECONSTRUCTION PROCESS
#--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1) - (1 OR 0)
fmul.x FACT1(%a6),%fp0
fadd.x FACT2(%a6),%fp0
fadd.x FACT1(%a6),%fp0
fmov.l %d0,%fpcr # restore users round prec,mode
mov.w %d2,ADJFACT(%a6) # INSERT EXPONENT
mov.l (%sp)+,%d2
mov.l &0x80000000,ADJFACT+4(%a6)
clr.l ADJFACT+8(%a6)
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x ADJFACT(%a6),%fp0 # FINAL ADJUSTMENT
bra t_catch
global stentoxd
stentoxd:
#--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
fmov.l %d0,%fpcr # set user's rounding mode/precision
fmov.s &0x3F800000,%fp0 # RETURN 1 + X
mov.l (%a0),%d1
or.l &0x00800001,%d1
fadd.s %d1,%fp0
bra t_pinx2
#########################################################################
# smovcr(): returns the ROM constant at the offset specified in d1 #
# rounded to the mode and precision specified in d0. #
# #
# INPUT *************************************************************** #
# d0 = rnd prec,mode #
# d1 = ROM offset #
# #
# OUTPUT ************************************************************** #
# fp0 = the ROM constant rounded to the user's rounding mode,prec #
# #
#########################################################################
global smovcr
smovcr:
mov.l %d1,-(%sp) # save rom offset for a sec
lsr.b &0x4,%d0 # shift ctrl bits to lo
mov.l %d0,%d1 # make a copy
andi.w &0x3,%d1 # extract rnd mode
andi.w &0xc,%d0 # extract rnd prec
swap %d0 # put rnd prec in hi
mov.w %d1,%d0 # put rnd mode in lo
mov.l (%sp)+,%d1 # get rom offset
#
# check range of offset
#
tst.b %d1 # if zero, offset is to pi
beq.b pi_tbl # it is pi
cmpi.b %d1,&0x0a # check range $01 - $0a
ble.b z_val # if in this range, return zero
cmpi.b %d1,&0x0e # check range $0b - $0e
ble.b sm_tbl # valid constants in this range
cmpi.b %d1,&0x2f # check range $10 - $2f
ble.b z_val # if in this range, return zero
cmpi.b %d1,&0x3f # check range $30 - $3f
ble.b bg_tbl # valid constants in this range
z_val:
bra.l ld_pzero # return a zero
#
# the answer is PI rounded to the proper precision.
#
# fetch a pointer to the answer table relating to the proper rounding
# precision.
#
pi_tbl:
tst.b %d0 # is rmode RN?
bne.b pi_not_rn # no
pi_rn:
lea.l PIRN(%pc),%a0 # yes; load PI RN table addr
bra.w set_finx
pi_not_rn:
cmpi.b %d0,&rp_mode # is rmode RP?
beq.b pi_rp # yes
pi_rzrm:
lea.l PIRZRM(%pc),%a0 # no; load PI RZ,RM table addr
bra.b set_finx
pi_rp:
lea.l PIRP(%pc),%a0 # load PI RP table addr
bra.b set_finx
#
# the answer is one of:
# $0B log10(2) (inexact)
# $0C e (inexact)
# $0D log2(e) (inexact)
# $0E log10(e) (exact)
#
# fetch a pointer to the answer table relating to the proper rounding
# precision.
#
sm_tbl:
subi.b &0xb,%d1 # make offset in 0-4 range
tst.b %d0 # is rmode RN?
bne.b sm_not_rn # no
sm_rn:
lea.l SMALRN(%pc),%a0 # yes; load RN table addr
sm_tbl_cont:
cmpi.b %d1,&0x2 # is result log10(e)?
ble.b set_finx # no; answer is inexact
bra.b no_finx # yes; answer is exact
sm_not_rn:
cmpi.b %d0,&rp_mode # is rmode RP?
beq.b sm_rp # yes
sm_rzrm:
lea.l SMALRZRM(%pc),%a0 # no; load RZ,RM table addr
bra.b sm_tbl_cont
sm_rp:
lea.l SMALRP(%pc),%a0 # load RP table addr
bra.b sm_tbl_cont
#
# the answer is one of:
# $30 ln(2) (inexact)
# $31 ln(10) (inexact)
# $32 10^0 (exact)
# $33 10^1 (exact)
# $34 10^2 (exact)
# $35 10^4 (exact)
# $36 10^8 (exact)
# $37 10^16 (exact)
# $38 10^32 (inexact)
# $39 10^64 (inexact)
# $3A 10^128 (inexact)
# $3B 10^256 (inexact)
# $3C 10^512 (inexact)
# $3D 10^1024 (inexact)
# $3E 10^2048 (inexact)
# $3F 10^4096 (inexact)
#
# fetch a pointer to the answer table relating to the proper rounding
# precision.
#
bg_tbl:
subi.b &0x30,%d1 # make offset in 0-f range
tst.b %d0 # is rmode RN?
bne.b bg_not_rn # no
bg_rn:
lea.l BIGRN(%pc),%a0 # yes; load RN table addr
bg_tbl_cont:
cmpi.b %d1,&0x1 # is offset <= $31?
ble.b set_finx # yes; answer is inexact
cmpi.b %d1,&0x7 # is $32 <= offset <= $37?
ble.b no_finx # yes; answer is exact
bra.b set_finx # no; answer is inexact
bg_not_rn:
cmpi.b %d0,&rp_mode # is rmode RP?
beq.b bg_rp # yes
bg_rzrm:
lea.l BIGRZRM(%pc),%a0 # no; load RZ,RM table addr
bra.b bg_tbl_cont
bg_rp:
lea.l BIGRP(%pc),%a0 # load RP table addr
bra.b bg_tbl_cont
# answer is inexact, so set INEX2 and AINEX in the user's FPSR.
set_finx:
ori.l &inx2a_mask,USER_FPSR(%a6) # set INEX2/AINEX
no_finx:
mulu.w &0xc,%d1 # offset points into tables
swap %d0 # put rnd prec in lo word
tst.b %d0 # is precision extended?
bne.b not_ext # if xprec, do not call round
# Precision is extended
fmovm.x (%a0,%d1.w),&0x80 # return result in fp0
rts
# Precision is single or double
not_ext:
swap %d0 # rnd prec in upper word
# call round() to round the answer to the proper precision.
# exponents out of range for single or double DO NOT cause underflow
# or overflow.
mov.w 0x0(%a0,%d1.w),FP_SCR1_EX(%a6) # load first word
mov.l 0x4(%a0,%d1.w),FP_SCR1_HI(%a6) # load second word
mov.l 0x8(%a0,%d1.w),FP_SCR1_LO(%a6) # load third word
mov.l %d0,%d1
clr.l %d0 # clear g,r,s
lea FP_SCR1(%a6),%a0 # pass ptr to answer
clr.w LOCAL_SGN(%a0) # sign always positive
bsr.l _round # round the mantissa
fmovm.x (%a0),&0x80 # return rounded result in fp0
rts
align 0x4
PIRN: long 0x40000000,0xc90fdaa2,0x2168c235 # pi
PIRZRM: long 0x40000000,0xc90fdaa2,0x2168c234 # pi
PIRP: long 0x40000000,0xc90fdaa2,0x2168c235 # pi
SMALRN: long 0x3ffd0000,0x9a209a84,0xfbcff798 # log10(2)
long 0x40000000,0xadf85458,0xa2bb4a9a # e
long 0x3fff0000,0xb8aa3b29,0x5c17f0bc # log2(e)
long 0x3ffd0000,0xde5bd8a9,0x37287195 # log10(e)
long 0x00000000,0x00000000,0x00000000 # 0.0
SMALRZRM:
long 0x3ffd0000,0x9a209a84,0xfbcff798 # log10(2)
long 0x40000000,0xadf85458,0xa2bb4a9a # e
long 0x3fff0000,0xb8aa3b29,0x5c17f0bb # log2(e)
long 0x3ffd0000,0xde5bd8a9,0x37287195 # log10(e)
long 0x00000000,0x00000000,0x00000000 # 0.0
SMALRP: long 0x3ffd0000,0x9a209a84,0xfbcff799 # log10(2)
long 0x40000000,0xadf85458,0xa2bb4a9b # e
long 0x3fff0000,0xb8aa3b29,0x5c17f0bc # log2(e)
long 0x3ffd0000,0xde5bd8a9,0x37287195 # log10(e)
long 0x00000000,0x00000000,0x00000000 # 0.0
BIGRN: long 0x3ffe0000,0xb17217f7,0xd1cf79ac # ln(2)
long 0x40000000,0x935d8ddd,0xaaa8ac17 # ln(10)
long 0x3fff0000,0x80000000,0x00000000 # 10 ^ 0
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59E # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D5 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CE0 # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8E # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C7 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C17 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE5 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979B # 10 ^ 4096
BIGRZRM:
long 0x3ffe0000,0xb17217f7,0xd1cf79ab # ln(2)
long 0x40000000,0x935d8ddd,0xaaa8ac16 # ln(10)
long 0x3fff0000,0x80000000,0x00000000 # 10 ^ 0
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59D # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D5 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CDF # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8D # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C6 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C17 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE4 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979A # 10 ^ 4096
BIGRP:
long 0x3ffe0000,0xb17217f7,0xd1cf79ac # ln(2)
long 0x40000000,0x935d8ddd,0xaaa8ac17 # ln(10)
long 0x3fff0000,0x80000000,0x00000000 # 10 ^ 0
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59E # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D6 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CE0 # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8E # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C7 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C18 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE5 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979B # 10 ^ 4096
#########################################################################
# sscale(): computes the destination operand scaled by the source #
# operand. If the absoulute value of the source operand is #
# >= 2^14, an overflow or underflow is returned. #
# #
# INPUT *************************************************************** #
# a0 = pointer to double-extended source operand X #
# a1 = pointer to double-extended destination operand Y #
# #
# OUTPUT ************************************************************** #
# fp0 = scale(X,Y) #
# #
#########################################################################
set SIGN, L_SCR1
global sscale
sscale:
mov.l %d0,-(%sp) # store off ctrl bits for now
mov.w DST_EX(%a1),%d1 # get dst exponent
smi.b SIGN(%a6) # use SIGN to hold dst sign
andi.l &0x00007fff,%d1 # strip sign from dst exp
mov.w SRC_EX(%a0),%d0 # check src bounds
andi.w &0x7fff,%d0 # clr src sign bit
cmpi.w %d0,&0x3fff # is src ~ ZERO?
blt.w src_small # yes
cmpi.w %d0,&0x400c # no; is src too big?
bgt.w src_out # yes
#
# Source is within 2^14 range.
#
src_ok:
fintrz.x SRC(%a0),%fp0 # calc int of src
fmov.l %fp0,%d0 # int src to d0
# don't want any accrued bits from the fintrz showing up later since
# we may need to read the fpsr for the last fp op in t_catch2().
fmov.l &0x0,%fpsr
tst.b DST_HI(%a1) # is dst denormalized?
bmi.b sok_norm
# the dst is a DENORM. normalize the DENORM and add the adjustment to
# the src value. then, jump to the norm part of the routine.
sok_dnrm:
mov.l %d0,-(%sp) # save src for now
mov.w DST_EX(%a1),FP_SCR0_EX(%a6) # make a copy
mov.l DST_HI(%a1),FP_SCR0_HI(%a6)
mov.l DST_LO(%a1),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0 # pass ptr to DENORM
bsr.l norm # normalize the DENORM
neg.l %d0
add.l (%sp)+,%d0 # add adjustment to src
fmovm.x FP_SCR0(%a6),&0x80 # load normalized DENORM
cmpi.w %d0,&-0x3fff # is the shft amt really low?
bge.b sok_norm2 # thank goodness no
# the multiply factor that we're trying to create should be a denorm
# for the multiply to work. therefore, we're going to actually do a
# multiply with a denorm which will cause an unimplemented data type
# exception to be put into the machine which will be caught and corrected
# later. we don't do this with the DENORMs above because this method
# is slower. but, don't fret, I don't see it being used much either.
fmov.l (%sp)+,%fpcr # restore user fpcr
mov.l &0x80000000,%d1 # load normalized mantissa
subi.l &-0x3fff,%d0 # how many should we shift?
neg.l %d0 # make it positive
cmpi.b %d0,&0x20 # is it > 32?
bge.b sok_dnrm_32 # yes
lsr.l %d0,%d1 # no; bit stays in upper lw
clr.l -(%sp) # insert zero low mantissa
mov.l %d1,-(%sp) # insert new high mantissa
clr.l -(%sp) # make zero exponent
bra.b sok_norm_cont
sok_dnrm_32:
subi.b &0x20,%d0 # get shift count
lsr.l %d0,%d1 # make low mantissa longword
mov.l %d1,-(%sp) # insert new low mantissa
clr.l -(%sp) # insert zero high mantissa
clr.l -(%sp) # make zero exponent
bra.b sok_norm_cont
# the src will force the dst to a DENORM value or worse. so, let's
# create an fp multiply that will create the result.
sok_norm:
fmovm.x DST(%a1),&0x80 # load fp0 with normalized src
sok_norm2:
fmov.l (%sp)+,%fpcr # restore user fpcr
addi.w &0x3fff,%d0 # turn src amt into exp value
swap %d0 # put exponent in high word
clr.l -(%sp) # insert new exponent
mov.l &0x80000000,-(%sp) # insert new high mantissa
mov.l %d0,-(%sp) # insert new lo mantissa
sok_norm_cont:
fmov.l %fpcr,%d0 # d0 needs fpcr for t_catch2
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x (%sp)+,%fp0 # do the multiply
bra t_catch2 # catch any exceptions
#
# Source is outside of 2^14 range. Test the sign and branch
# to the appropriate exception handler.
#
src_out:
mov.l (%sp)+,%d0 # restore ctrl bits
exg %a0,%a1 # swap src,dst ptrs
tst.b SRC_EX(%a1) # is src negative?
bmi t_unfl # yes; underflow
bra t_ovfl_sc # no; overflow
#
# The source input is below 1, so we check for denormalized numbers
# and set unfl.
#
src_small:
tst.b DST_HI(%a1) # is dst denormalized?
bpl.b ssmall_done # yes
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr # no; load control bits
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x DST(%a1),%fp0 # simply return dest
bra t_catch2
ssmall_done:
mov.l (%sp)+,%d0 # load control bits into d1
mov.l %a1,%a0 # pass ptr to dst
bra t_resdnrm
#########################################################################
# smod(): computes the fp MOD of the input values X,Y. #
# srem(): computes the fp (IEEE) REM of the input values X,Y. #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input X #
# a1 = pointer to extended precision input Y #
# d0 = round precision,mode #
# #
# The input operands X and Y can be either normalized or #
# denormalized. #
# #
# OUTPUT ************************************************************** #
# fp0 = FREM(X,Y) or FMOD(X,Y) #
# #
# ALGORITHM *********************************************************** #
# #
# Step 1. Save and strip signs of X and Y: signX := sign(X), #
# signY := sign(Y), X := |X|, Y := |Y|, #
# signQ := signX EOR signY. Record whether MOD or REM #
# is requested. #
# #
# Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0. #
# If (L < 0) then #
# R := X, go to Step 4. #
# else #
# R := 2^(-L)X, j := L. #
# endif #
# #
# Step 3. Perform MOD(X,Y) #
# 3.1 If R = Y, go to Step 9. #
# 3.2 If R > Y, then { R := R - Y, Q := Q + 1} #
# 3.3 If j = 0, go to Step 4. #
# 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to #
# Step 3.1. #
# #
# Step 4. At this point, R = X - QY = MOD(X,Y). Set #
# Last_Subtract := false (used in Step 7 below). If #
# MOD is requested, go to Step 6. #
# #
# Step 5. R = MOD(X,Y), but REM(X,Y) is requested. #
# 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to #
# Step 6. #
# 5.2 If R > Y/2, then { set Last_Subtract := true, #
# Q := Q + 1, Y := signY*Y }. Go to Step 6. #
# 5.3 This is the tricky case of R = Y/2. If Q is odd, #
# then { Q := Q + 1, signX := -signX }. #
# #
# Step 6. R := signX*R. #
# #
# Step 7. If Last_Subtract = true, R := R - Y. #
# #
# Step 8. Return signQ, last 7 bits of Q, and R as required. #
# #
# Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus, #
# X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1), #
# R := 0. Return signQ, last 7 bits of Q, and R. #
# #
#########################################################################
set Mod_Flag,L_SCR3
set Sc_Flag,L_SCR3+1
set SignY,L_SCR2
set SignX,L_SCR2+2
set SignQ,L_SCR3+2
set Y,FP_SCR0
set Y_Hi,Y+4
set Y_Lo,Y+8
set R,FP_SCR1
set R_Hi,R+4
set R_Lo,R+8
Scale:
long 0x00010000,0x80000000,0x00000000,0x00000000
global smod
smod:
clr.b FPSR_QBYTE(%a6)
mov.l %d0,-(%sp) # save ctrl bits
clr.b Mod_Flag(%a6)
bra.b Mod_Rem
global srem
srem:
clr.b FPSR_QBYTE(%a6)
mov.l %d0,-(%sp) # save ctrl bits
mov.b &0x1,Mod_Flag(%a6)
Mod_Rem:
#..Save sign of X and Y
movm.l &0x3f00,-(%sp) # save data registers
mov.w SRC_EX(%a0),%d3
mov.w %d3,SignY(%a6)
and.l &0x00007FFF,%d3 # Y := |Y|
#
mov.l SRC_HI(%a0),%d4
mov.l SRC_LO(%a0),%d5 # (D3,D4,D5) is |Y|
tst.l %d3
bne.b Y_Normal
mov.l &0x00003FFE,%d3 # $3FFD + 1
tst.l %d4
bne.b HiY_not0
HiY_0:
mov.l %d5,%d4
clr.l %d5
sub.l &32,%d3
clr.l %d6
bfffo %d4{&0:&32},%d6
lsl.l %d6,%d4
sub.l %d6,%d3 # (D3,D4,D5) is normalized
# ...with bias $7FFD
bra.b Chk_X
HiY_not0:
clr.l %d6
bfffo %d4{&0:&32},%d6
sub.l %d6,%d3
lsl.l %d6,%d4
mov.l %d5,%d7 # a copy of D5
lsl.l %d6,%d5
neg.l %d6
add.l &32,%d6
lsr.l %d6,%d7
or.l %d7,%d4 # (D3,D4,D5) normalized
# ...with bias $7FFD
bra.b Chk_X
Y_Normal:
add.l &0x00003FFE,%d3 # (D3,D4,D5) normalized
# ...with bias $7FFD
Chk_X:
mov.w DST_EX(%a1),%d0
mov.w %d0,SignX(%a6)
mov.w SignY(%a6),%d1
eor.l %d0,%d1
and.l &0x00008000,%d1
mov.w %d1,SignQ(%a6) # sign(Q) obtained
and.l &0x00007FFF,%d0
mov.l DST_HI(%a1),%d1
mov.l DST_LO(%a1),%d2 # (D0,D1,D2) is |X|
tst.l %d0
bne.b X_Normal
mov.l &0x00003FFE,%d0
tst.l %d1
bne.b HiX_not0
HiX_0:
mov.l %d2,%d1
clr.l %d2
sub.l &32,%d0
clr.l %d6
bfffo %d1{&0:&32},%d6
lsl.l %d6,%d1
sub.l %d6,%d0 # (D0,D1,D2) is normalized
# ...with bias $7FFD
bra.b Init
HiX_not0:
clr.l %d6
bfffo %d1{&0:&32},%d6
sub.l %d6,%d0
lsl.l %d6,%d1
mov.l %d2,%d7 # a copy of D2
lsl.l %d6,%d2
neg.l %d6
add.l &32,%d6
lsr.l %d6,%d7
or.l %d7,%d1 # (D0,D1,D2) normalized
# ...with bias $7FFD
bra.b Init
X_Normal:
add.l &0x00003FFE,%d0 # (D0,D1,D2) normalized
# ...with bias $7FFD
Init:
#
mov.l %d3,L_SCR1(%a6) # save biased exp(Y)
mov.l %d0,-(%sp) # save biased exp(X)
sub.l %d3,%d0 # L := expo(X)-expo(Y)
clr.l %d6 # D6 := carry <- 0
clr.l %d3 # D3 is Q
mov.l &0,%a1 # A1 is k; j+k=L, Q=0
#..(Carry,D1,D2) is R
tst.l %d0
bge.b Mod_Loop_pre
#..expo(X) < expo(Y). Thus X = mod(X,Y)
#
mov.l (%sp)+,%d0 # restore d0
bra.w Get_Mod
Mod_Loop_pre:
addq.l &0x4,%sp # erase exp(X)
#..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
Mod_Loop:
tst.l %d6 # test carry bit
bgt.b R_GT_Y
#..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
cmp.l %d1,%d4 # compare hi(R) and hi(Y)
bne.b R_NE_Y
cmp.l %d2,%d5 # compare lo(R) and lo(Y)
bne.b R_NE_Y
#..At this point, R = Y
bra.w Rem_is_0
R_NE_Y:
#..use the borrow of the previous compare
bcs.b R_LT_Y # borrow is set iff R < Y
R_GT_Y:
#..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
#..and Y < (D1,D2) < 2Y. Either way, perform R - Y
sub.l %d5,%d2 # lo(R) - lo(Y)
subx.l %d4,%d1 # hi(R) - hi(Y)
clr.l %d6 # clear carry
addq.l &1,%d3 # Q := Q + 1
R_LT_Y:
#..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
tst.l %d0 # see if j = 0.
beq.b PostLoop
add.l %d3,%d3 # Q := 2Q
add.l %d2,%d2 # lo(R) = 2lo(R)
roxl.l &1,%d1 # hi(R) = 2hi(R) + carry
scs %d6 # set Carry if 2(R) overflows
addq.l &1,%a1 # k := k+1
subq.l &1,%d0 # j := j - 1
#..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
bra.b Mod_Loop
PostLoop:
#..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
#..normalize R.
mov.l L_SCR1(%a6),%d0 # new biased expo of R
tst.l %d1
bne.b HiR_not0
HiR_0:
mov.l %d2,%d1
clr.l %d2
sub.l &32,%d0
clr.l %d6
bfffo %d1{&0:&32},%d6
lsl.l %d6,%d1
sub.l %d6,%d0 # (D0,D1,D2) is normalized
# ...with bias $7FFD
bra.b Get_Mod
HiR_not0:
clr.l %d6
bfffo %d1{&0:&32},%d6
bmi.b Get_Mod # already normalized
sub.l %d6,%d0
lsl.l %d6,%d1
mov.l %d2,%d7 # a copy of D2
lsl.l %d6,%d2
neg.l %d6
add.l &32,%d6
lsr.l %d6,%d7
or.l %d7,%d1 # (D0,D1,D2) normalized
#
Get_Mod:
cmp.l %d0,&0x000041FE
bge.b No_Scale
Do_Scale:
mov.w %d0,R(%a6)
mov.l %d1,R_Hi(%a6)
mov.l %d2,R_Lo(%a6)
mov.l L_SCR1(%a6),%d6
mov.w %d6,Y(%a6)
mov.l %d4,Y_Hi(%a6)
mov.l %d5,Y_Lo(%a6)
fmov.x R(%a6),%fp0 # no exception
mov.b &1,Sc_Flag(%a6)
bra.b ModOrRem
No_Scale:
mov.l %d1,R_Hi(%a6)
mov.l %d2,R_Lo(%a6)
sub.l &0x3FFE,%d0
mov.w %d0,R(%a6)
mov.l L_SCR1(%a6),%d6
sub.l &0x3FFE,%d6
mov.l %d6,L_SCR1(%a6)
fmov.x R(%a6),%fp0
mov.w %d6,Y(%a6)
mov.l %d4,Y_Hi(%a6)
mov.l %d5,Y_Lo(%a6)
clr.b Sc_Flag(%a6)
#
ModOrRem:
tst.b Mod_Flag(%a6)
beq.b Fix_Sign
mov.l L_SCR1(%a6),%d6 # new biased expo(Y)
subq.l &1,%d6 # biased expo(Y/2)
cmp.l %d0,%d6
blt.b Fix_Sign
bgt.b Last_Sub
cmp.l %d1,%d4
bne.b Not_EQ
cmp.l %d2,%d5
bne.b Not_EQ
bra.w Tie_Case
Not_EQ:
bcs.b Fix_Sign
Last_Sub:
#
fsub.x Y(%a6),%fp0 # no exceptions
addq.l &1,%d3 # Q := Q + 1
#
Fix_Sign:
#..Get sign of X
mov.w SignX(%a6),%d6
bge.b Get_Q
fneg.x %fp0
#..Get Q
#
Get_Q:
clr.l %d6
mov.w SignQ(%a6),%d6 # D6 is sign(Q)
mov.l &8,%d7
lsr.l %d7,%d6
and.l &0x0000007F,%d3 # 7 bits of Q
or.l %d6,%d3 # sign and bits of Q
# swap %d3
# fmov.l %fpsr,%d6
# and.l &0xFF00FFFF,%d6
# or.l %d3,%d6
# fmov.l %d6,%fpsr # put Q in fpsr
mov.b %d3,FPSR_QBYTE(%a6) # put Q in fpsr
#
Restore:
movm.l (%sp)+,&0xfc # {%d2-%d7}
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr
tst.b Sc_Flag(%a6)
beq.b Finish
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x Scale(%pc),%fp0 # may cause underflow
bra t_catch2
# the '040 package did this apparently to see if the dst operand for the
# preceding fmul was a denorm. but, it better not have been since the
# algorithm just got done playing with fp0 and expected no exceptions
# as a result. trust me...
# bra t_avoid_unsupp # check for denorm as a
# ;result of the scaling
Finish:
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x %fp0,%fp0 # capture exceptions & round
bra t_catch2
Rem_is_0:
#..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
addq.l &1,%d3
cmp.l %d0,&8 # D0 is j
bge.b Q_Big
lsl.l %d0,%d3
bra.b Set_R_0
Q_Big:
clr.l %d3
Set_R_0:
fmov.s &0x00000000,%fp0
clr.b Sc_Flag(%a6)
bra.w Fix_Sign
Tie_Case:
#..Check parity of Q
mov.l %d3,%d6
and.l &0x00000001,%d6
tst.l %d6
beq.w Fix_Sign # Q is even
#..Q is odd, Q := Q + 1, signX := -signX
addq.l &1,%d3
mov.w SignX(%a6),%d6
eor.l &0x00008000,%d6
mov.w %d6,SignX(%a6)
bra.w Fix_Sign
qnan: long 0x7fff0000, 0xffffffff, 0xffffffff
#########################################################################
# XDEF **************************************************************** #
# t_dz(): Handle DZ exception during transcendental emulation. #
# Sets N bit according to sign of source operand. #
# t_dz2(): Handle DZ exception during transcendental emulation. #
# Sets N bit always. #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = pointer to source operand #
# #
# OUTPUT ************************************************************** #
# fp0 = default result #
# #
# ALGORITHM *********************************************************** #
# - Store properly signed INF into fp0. #
# - Set FPSR exception status dz bit, ccode inf bit, and #
# accrued dz bit. #
# #
#########################################################################
global t_dz
t_dz:
tst.b SRC_EX(%a0) # no; is src negative?
bmi.b t_dz2 # yes
dz_pinf:
fmov.s &0x7f800000,%fp0 # return +INF in fp0
ori.l &dzinf_mask,USER_FPSR(%a6) # set I/DZ/ADZ
rts
global t_dz2
t_dz2:
fmov.s &0xff800000,%fp0 # return -INF in fp0
ori.l &dzinf_mask+neg_mask,USER_FPSR(%a6) # set N/I/DZ/ADZ
rts
#################################################################
# OPERR exception: #
# - set FPSR exception status operr bit, condition code #
# nan bit; Store default NAN into fp0 #
#################################################################
global t_operr
t_operr:
ori.l &opnan_mask,USER_FPSR(%a6) # set NaN/OPERR/AIOP
fmovm.x qnan(%pc),&0x80 # return default NAN in fp0
rts
#################################################################
# Extended DENORM: #
# - For all functions that have a denormalized input and #
# that f(x)=x, this is the entry point. #
# - we only return the EXOP here if either underflow or #
# inexact is enabled. #
#################################################################
# Entry point for scale w/ extended denorm. The function does
# NOT set INEX2/AUNFL/AINEX.
global t_resdnrm
t_resdnrm:
ori.l &unfl_mask,USER_FPSR(%a6) # set UNFL
bra.b xdnrm_con
global t_extdnrm
t_extdnrm:
ori.l &unfinx_mask,USER_FPSR(%a6) # set UNFL/INEX2/AUNFL/AINEX
xdnrm_con:
mov.l %a0,%a1 # make copy of src ptr
mov.l %d0,%d1 # make copy of rnd prec,mode
andi.b &0xc0,%d1 # extended precision?
bne.b xdnrm_sd # no
# result precision is extended.
tst.b LOCAL_EX(%a0) # is denorm negative?
bpl.b xdnrm_exit # no
bset &neg_bit,FPSR_CC(%a6) # yes; set 'N' ccode bit
bra.b xdnrm_exit
# result precision is single or double
xdnrm_sd:
mov.l %a1,-(%sp)
tst.b LOCAL_EX(%a0) # is denorm pos or neg?
smi.b %d1 # set d0 accodingly
bsr.l unf_sub
mov.l (%sp)+,%a1
xdnrm_exit:
fmovm.x (%a0),&0x80 # return default result in fp0
mov.b FPCR_ENABLE(%a6),%d0
andi.b &0x0a,%d0 # is UNFL or INEX enabled?
bne.b xdnrm_ena # yes
rts
################
# unfl enabled #
################
# we have a DENORM that needs to be converted into an EXOP.
# so, normalize the mantissa, add 0x6000 to the new exponent,
# and return the result in fp1.
xdnrm_ena:
mov.w LOCAL_EX(%a1),FP_SCR0_EX(%a6)
mov.l LOCAL_HI(%a1),FP_SCR0_HI(%a6)
mov.l LOCAL_LO(%a1),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0
bsr.l norm # normalize mantissa
addi.l &0x6000,%d0 # add extra bias
andi.w &0x8000,FP_SCR0_EX(%a6) # keep old sign
or.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#################################################################
# UNFL exception: #
# - This routine is for cases where even an EXOP isn't #
# large enough to hold the range of this result. #
# In such a case, the EXOP equals zero. #
# - Return the default result to the proper precision #
# with the sign of this result being the same as that #
# of the src operand. #
# - t_unfl2() is provided to force the result sign to #
# positive which is the desired result for fetox(). #
#################################################################
global t_unfl
t_unfl:
ori.l &unfinx_mask,USER_FPSR(%a6) # set UNFL/INEX2/AUNFL/AINEX
tst.b (%a0) # is result pos or neg?
smi.b %d1 # set d1 accordingly
bsr.l unf_sub # calc default unfl result
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x00000000,%fp1 # return EXOP in fp1
rts
# t_unfl2 ALWAYS tells unf_sub to create a positive result
global t_unfl2
t_unfl2:
ori.l &unfinx_mask,USER_FPSR(%a6) # set UNFL/INEX2/AUNFL/AINEX
sf.b %d1 # set d0 to represent positive
bsr.l unf_sub # calc default unfl result
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x0000000,%fp1 # return EXOP in fp1
rts
#################################################################
# OVFL exception: #
# - This routine is for cases where even an EXOP isn't #
# large enough to hold the range of this result. #
# - Return the default result to the proper precision #
# with the sign of this result being the same as that #
# of the src operand. #
# - t_ovfl2() is provided to force the result sign to #
# positive which is the desired result for fcosh(). #
# - t_ovfl_sc() is provided for scale() which only sets #
# the inexact bits if the number is inexact for the #
# precision indicated. #
#################################################################
global t_ovfl_sc
t_ovfl_sc:
ori.l &ovfl_inx_mask,USER_FPSR(%a6) # set OVFL/AOVFL/AINEX
mov.b %d0,%d1 # fetch rnd mode/prec
andi.b &0xc0,%d1 # extract rnd prec
beq.b ovfl_work # prec is extended
tst.b LOCAL_HI(%a0) # is dst a DENORM?
bmi.b ovfl_sc_norm # no
# dst op is a DENORM. we have to normalize the mantissa to see if the
# result would be inexact for the given precision. make a copy of the
# dst so we don't screw up the version passed to us.
mov.w LOCAL_EX(%a0),FP_SCR0_EX(%a6)
mov.l LOCAL_HI(%a0),FP_SCR0_HI(%a6)
mov.l LOCAL_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0 # pass ptr to FP_SCR0
movm.l &0xc080,-(%sp) # save d0-d1/a0
bsr.l norm # normalize mantissa
movm.l (%sp)+,&0x0103 # restore d0-d1/a0
ovfl_sc_norm:
cmpi.b %d1,&0x40 # is prec dbl?
bne.b ovfl_sc_dbl # no; sgl
ovfl_sc_sgl:
tst.l LOCAL_LO(%a0) # is lo lw of sgl set?
bne.b ovfl_sc_inx # yes
tst.b 3+LOCAL_HI(%a0) # is lo byte of hi lw set?
bne.b ovfl_sc_inx # yes
bra.b ovfl_work # don't set INEX2
ovfl_sc_dbl:
mov.l LOCAL_LO(%a0),%d1 # are any of lo 11 bits of
andi.l &0x7ff,%d1 # dbl mantissa set?
beq.b ovfl_work # no; don't set INEX2
ovfl_sc_inx:
ori.l &inex2_mask,USER_FPSR(%a6) # set INEX2
bra.b ovfl_work # continue
global t_ovfl
t_ovfl:
ori.l &ovfinx_mask,USER_FPSR(%a6) # set OVFL/INEX2/AOVFL/AINEX
ovfl_work:
tst.b LOCAL_EX(%a0) # what is the sign?
smi.b %d1 # set d1 accordingly
bsr.l ovf_res # calc default ovfl result
mov.b %d0,FPSR_CC(%a6) # insert new ccodes
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x00000000,%fp1 # return EXOP in fp1
rts
# t_ovfl2 ALWAYS tells ovf_res to create a positive result
global t_ovfl2
t_ovfl2:
ori.l &ovfinx_mask,USER_FPSR(%a6) # set OVFL/INEX2/AOVFL/AINEX
sf.b %d1 # clear sign flag for positive
bsr.l ovf_res # calc default ovfl result
mov.b %d0,FPSR_CC(%a6) # insert new ccodes
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x00000000,%fp1 # return EXOP in fp1
rts
#################################################################
# t_catch(): #
# - the last operation of a transcendental emulation #
# routine may have caused an underflow or overflow. #
# we find out if this occurred by doing an fsave and #
# checking the exception bit. if one did occur, then we #
# jump to fgen_except() which creates the default #
# result and EXOP for us. #
#################################################################
global t_catch
t_catch:
fsave -(%sp)
tst.b 0x2(%sp)
bmi.b catch
add.l &0xc,%sp
#################################################################
# INEX2 exception: #
# - The inex2 and ainex bits are set. #
#################################################################
global t_inx2
t_inx2:
fblt.w t_minx2
fbeq.w inx2_zero
global t_pinx2
t_pinx2:
ori.w &inx2a_mask,2+USER_FPSR(%a6) # set INEX2/AINEX
rts
global t_minx2
t_minx2:
ori.l &inx2a_mask+neg_mask,USER_FPSR(%a6) # set N/INEX2/AINEX
rts
inx2_zero:
mov.b &z_bmask,FPSR_CC(%a6)
ori.w &inx2a_mask,2+USER_FPSR(%a6) # set INEX2/AINEX
rts
# an underflow or overflow exception occurred.
# we must set INEX/AINEX since the fmul/fdiv/fmov emulation may not!
catch:
ori.w &inx2a_mask,FPSR_EXCEPT(%a6)
catch2:
bsr.l fgen_except
add.l &0xc,%sp
rts
global t_catch2
t_catch2:
fsave -(%sp)
tst.b 0x2(%sp)
bmi.b catch2
add.l &0xc,%sp
fmov.l %fpsr,%d0
or.l %d0,USER_FPSR(%a6)
rts
#########################################################################
#########################################################################
# unf_res(): underflow default result calculation for transcendentals #
# #
# INPUT: #
# d0 : rnd mode,precision #
# d1.b : sign bit of result ('11111111 = (-) ; '00000000 = (+)) #
# OUTPUT: #
# a0 : points to result (in instruction memory) #
#########################################################################
unf_sub:
ori.l &unfinx_mask,USER_FPSR(%a6)
andi.w &0x10,%d1 # keep sign bit in 4th spot
lsr.b &0x4,%d0 # shift rnd prec,mode to lo bits
andi.b &0xf,%d0 # strip hi rnd mode bit
or.b %d1,%d0 # concat {sgn,mode,prec}
mov.l %d0,%d1 # make a copy
lsl.b &0x1,%d1 # mult index 2 by 2
mov.b (tbl_unf_cc.b,%pc,%d0.w*1),FPSR_CC(%a6) # insert ccode bits
lea (tbl_unf_result.b,%pc,%d1.w*8),%a0 # grab result ptr
rts
tbl_unf_cc:
byte 0x4, 0x4, 0x4, 0x0
byte 0x4, 0x4, 0x4, 0x0
byte 0x4, 0x4, 0x4, 0x0
byte 0x0, 0x0, 0x0, 0x0
byte 0x8+0x4, 0x8+0x4, 0x8, 0x8+0x4
byte 0x8+0x4, 0x8+0x4, 0x8, 0x8+0x4
byte 0x8+0x4, 0x8+0x4, 0x8, 0x8+0x4
tbl_unf_result:
long 0x00000000, 0x00000000, 0x00000000, 0x0 # ZERO;ext
long 0x00000000, 0x00000000, 0x00000000, 0x0 # ZERO;ext
long 0x00000000, 0x00000000, 0x00000000, 0x0 # ZERO;ext
long 0x00000000, 0x00000000, 0x00000001, 0x0 # MIN; ext
long 0x3f810000, 0x00000000, 0x00000000, 0x0 # ZERO;sgl
long 0x3f810000, 0x00000000, 0x00000000, 0x0 # ZERO;sgl
long 0x3f810000, 0x00000000, 0x00000000, 0x0 # ZERO;sgl
long 0x3f810000, 0x00000100, 0x00000000, 0x0 # MIN; sgl
long 0x3c010000, 0x00000000, 0x00000000, 0x0 # ZERO;dbl
long 0x3c010000, 0x00000000, 0x00000000, 0x0 # ZER0;dbl
long 0x3c010000, 0x00000000, 0x00000000, 0x0 # ZERO;dbl
long 0x3c010000, 0x00000000, 0x00000800, 0x0 # MIN; dbl
long 0x0,0x0,0x0,0x0
long 0x0,0x0,0x0,0x0
long 0x0,0x0,0x0,0x0
long 0x0,0x0,0x0,0x0
long 0x80000000, 0x00000000, 0x00000000, 0x0 # ZERO;ext
long 0x80000000, 0x00000000, 0x00000000, 0x0 # ZERO;ext
long 0x80000000, 0x00000000, 0x00000001, 0x0 # MIN; ext
long 0x80000000, 0x00000000, 0x00000000, 0x0 # ZERO;ext
long 0xbf810000, 0x00000000, 0x00000000, 0x0 # ZERO;sgl
long 0xbf810000, 0x00000000, 0x00000000, 0x0 # ZERO;sgl
long 0xbf810000, 0x00000100, 0x00000000, 0x0 # MIN; sgl
long 0xbf810000, 0x00000000, 0x00000000, 0x0 # ZERO;sgl
long 0xbc010000, 0x00000000, 0x00000000, 0x0 # ZERO;dbl
long 0xbc010000, 0x00000000, 0x00000000, 0x0 # ZERO;dbl
long 0xbc010000, 0x00000000, 0x00000800, 0x0 # MIN; dbl
long 0xbc010000, 0x00000000, 0x00000000, 0x0 # ZERO;dbl
############################################################
#########################################################################
# src_zero(): Return signed zero according to sign of src operand. #
#########################################################################
global src_zero
src_zero:
tst.b SRC_EX(%a0) # get sign of src operand
bmi.b ld_mzero # if neg, load neg zero
#
# ld_pzero(): return a positive zero.
#
global ld_pzero
ld_pzero:
fmov.s &0x00000000,%fp0 # load +0
mov.b &z_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
# ld_mzero(): return a negative zero.
global ld_mzero
ld_mzero:
fmov.s &0x80000000,%fp0 # load -0
mov.b &neg_bmask+z_bmask,FPSR_CC(%a6) # set 'N','Z' ccode bits
rts
#########################################################################
# dst_zero(): Return signed zero according to sign of dst operand. #
#########################################################################
global dst_zero
dst_zero:
tst.b DST_EX(%a1) # get sign of dst operand
bmi.b ld_mzero # if neg, load neg zero
bra.b ld_pzero # load positive zero
#########################################################################
# src_inf(): Return signed inf according to sign of src operand. #
#########################################################################
global src_inf
src_inf:
tst.b SRC_EX(%a0) # get sign of src operand
bmi.b ld_minf # if negative branch
#
# ld_pinf(): return a positive infinity.
#
global ld_pinf
ld_pinf:
fmov.s &0x7f800000,%fp0 # load +INF
mov.b &inf_bmask,FPSR_CC(%a6) # set 'INF' ccode bit
rts
#
# ld_minf():return a negative infinity.
#
global ld_minf
ld_minf:
fmov.s &0xff800000,%fp0 # load -INF
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set 'N','I' ccode bits
rts
#########################################################################
# dst_inf(): Return signed inf according to sign of dst operand. #
#########################################################################
global dst_inf
dst_inf:
tst.b DST_EX(%a1) # get sign of dst operand
bmi.b ld_minf # if negative branch
bra.b ld_pinf
global szr_inf
#################################################################
# szr_inf(): Return +ZERO for a negative src operand or #
# +INF for a positive src operand. #
# Routine used for fetox, ftwotox, and ftentox. #
#################################################################
szr_inf:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_pzero
bra.b ld_pinf
#########################################################################
# sopr_inf(): Return +INF for a positive src operand or #
# jump to operand error routine for a negative src operand. #
# Routine used for flogn, flognp1, flog10, and flog2. #
#########################################################################
global sopr_inf
sopr_inf:
tst.b SRC_EX(%a0) # check sign of source
bmi.w t_operr
bra.b ld_pinf
#################################################################
# setoxm1i(): Return minus one for a negative src operand or #
# positive infinity for a positive src operand. #
# Routine used for fetoxm1. #
#################################################################
global setoxm1i
setoxm1i:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_mone
bra.b ld_pinf
#########################################################################
# src_one(): Return signed one according to sign of src operand. #
#########################################################################
global src_one
src_one:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_mone
#
# ld_pone(): return positive one.
#
global ld_pone
ld_pone:
fmov.s &0x3f800000,%fp0 # load +1
clr.b FPSR_CC(%a6)
rts
#
# ld_mone(): return negative one.
#
global ld_mone
ld_mone:
fmov.s &0xbf800000,%fp0 # load -1
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
ppiby2: long 0x3fff0000, 0xc90fdaa2, 0x2168c235
mpiby2: long 0xbfff0000, 0xc90fdaa2, 0x2168c235
#################################################################
# spi_2(): Return signed PI/2 according to sign of src operand. #
#################################################################
global spi_2
spi_2:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_mpi2
#
# ld_ppi2(): return positive PI/2.
#
global ld_ppi2
ld_ppi2:
fmov.l %d0,%fpcr
fmov.x ppiby2(%pc),%fp0 # load +pi/2
bra.w t_pinx2 # set INEX2
#
# ld_mpi2(): return negative PI/2.
#
global ld_mpi2
ld_mpi2:
fmov.l %d0,%fpcr
fmov.x mpiby2(%pc),%fp0 # load -pi/2
bra.w t_minx2 # set INEX2
####################################################
# The following routines give support for fsincos. #
####################################################
#
# ssincosz(): When the src operand is ZERO, store a one in the
# cosine register and return a ZERO in fp0 w/ the same sign
# as the src operand.
#
global ssincosz
ssincosz:
fmov.s &0x3f800000,%fp1
tst.b SRC_EX(%a0) # test sign
bpl.b sincoszp
fmov.s &0x80000000,%fp0 # return sin result in fp0
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6)
bra.b sto_cos # store cosine result
sincoszp:
fmov.s &0x00000000,%fp0 # return sin result in fp0
mov.b &z_bmask,FPSR_CC(%a6)
bra.b sto_cos # store cosine result
#
# ssincosi(): When the src operand is INF, store a QNAN in the cosine
# register and jump to the operand error routine for negative
# src operands.
#
global ssincosi
ssincosi:
fmov.x qnan(%pc),%fp1 # load NAN
bsr.l sto_cos # store cosine result
bra.w t_operr
#
# ssincosqnan(): When the src operand is a QNAN, store the QNAN in the cosine
# register and branch to the src QNAN routine.
#
global ssincosqnan
ssincosqnan:
fmov.x LOCAL_EX(%a0),%fp1
bsr.l sto_cos
bra.w src_qnan
#
# ssincossnan(): When the src operand is an SNAN, store the SNAN w/ the SNAN bit set
# in the cosine register and branch to the src SNAN routine.
#
global ssincossnan
ssincossnan:
fmov.x LOCAL_EX(%a0),%fp1
bsr.l sto_cos
bra.w src_snan
########################################################################
#########################################################################
# sto_cos(): store fp1 to the fpreg designated by the CMDREG dst field. #
# fp1 holds the result of the cosine portion of ssincos(). #
# the value in fp1 will not take any exceptions when moved. #
# INPUT: #
# fp1 : fp value to store #
# MODIFIED: #
# d0 #
#########################################################################
global sto_cos
sto_cos:
mov.b 1+EXC_CMDREG(%a6),%d0
andi.w &0x7,%d0
mov.w (tbl_sto_cos.b,%pc,%d0.w*2),%d0
jmp (tbl_sto_cos.b,%pc,%d0.w*1)
tbl_sto_cos:
short sto_cos_0 - tbl_sto_cos
short sto_cos_1 - tbl_sto_cos
short sto_cos_2 - tbl_sto_cos
short sto_cos_3 - tbl_sto_cos
short sto_cos_4 - tbl_sto_cos
short sto_cos_5 - tbl_sto_cos
short sto_cos_6 - tbl_sto_cos
short sto_cos_7 - tbl_sto_cos
sto_cos_0:
fmovm.x &0x40,EXC_FP0(%a6)
rts
sto_cos_1:
fmovm.x &0x40,EXC_FP1(%a6)
rts
sto_cos_2:
fmov.x %fp1,%fp2
rts
sto_cos_3:
fmov.x %fp1,%fp3
rts
sto_cos_4:
fmov.x %fp1,%fp4
rts
sto_cos_5:
fmov.x %fp1,%fp5
rts
sto_cos_6:
fmov.x %fp1,%fp6
rts
sto_cos_7:
fmov.x %fp1,%fp7
rts
##################################################################
global smod_sdnrm
global smod_snorm
smod_sdnrm:
smod_snorm:
mov.b DTAG(%a6),%d1
beq.l smod
cmpi.b %d1,&ZERO
beq.w smod_zro
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l smod
cmpi.b %d1,&SNAN
beq.l dst_snan
bra.l dst_qnan
global smod_szero
smod_szero:
mov.b DTAG(%a6),%d1
beq.l t_operr
cmpi.b %d1,&ZERO
beq.l t_operr
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l t_operr
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
global smod_sinf
smod_sinf:
mov.b DTAG(%a6),%d1
beq.l smod_fpn
cmpi.b %d1,&ZERO
beq.l smod_zro
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l smod_fpn
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
smod_zro:
srem_zro:
mov.b SRC_EX(%a0),%d1 # get src sign
mov.b DST_EX(%a1),%d0 # get dst sign
eor.b %d0,%d1 # get qbyte sign
andi.b &0x80,%d1
mov.b %d1,FPSR_QBYTE(%a6)
tst.b %d0
bpl.w ld_pzero
bra.w ld_mzero
smod_fpn:
srem_fpn:
clr.b FPSR_QBYTE(%a6)
mov.l %d0,-(%sp)
mov.b SRC_EX(%a0),%d1 # get src sign
mov.b DST_EX(%a1),%d0 # get dst sign
eor.b %d0,%d1 # get qbyte sign
andi.b &0x80,%d1
mov.b %d1,FPSR_QBYTE(%a6)
cmpi.b DTAG(%a6),&DENORM
bne.b smod_nrm
lea DST(%a1),%a0
mov.l (%sp)+,%d0
bra t_resdnrm
smod_nrm:
fmov.l (%sp)+,%fpcr
fmov.x DST(%a1),%fp0
tst.b DST_EX(%a1)
bmi.b smod_nrm_neg
rts
smod_nrm_neg:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode
rts
#########################################################################
global srem_snorm
global srem_sdnrm
srem_sdnrm:
srem_snorm:
mov.b DTAG(%a6),%d1
beq.l srem
cmpi.b %d1,&ZERO
beq.w srem_zro
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l srem
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
global srem_szero
srem_szero:
mov.b DTAG(%a6),%d1
beq.l t_operr
cmpi.b %d1,&ZERO
beq.l t_operr
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l t_operr
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
global srem_sinf
srem_sinf:
mov.b DTAG(%a6),%d1
beq.w srem_fpn
cmpi.b %d1,&ZERO
beq.w srem_zro
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l srem_fpn
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
#########################################################################
global sscale_snorm
global sscale_sdnrm
sscale_snorm:
sscale_sdnrm:
mov.b DTAG(%a6),%d1
beq.l sscale
cmpi.b %d1,&ZERO
beq.l dst_zero
cmpi.b %d1,&INF
beq.l dst_inf
cmpi.b %d1,&DENORM
beq.l sscale
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
global sscale_szero
sscale_szero:
mov.b DTAG(%a6),%d1
beq.l sscale
cmpi.b %d1,&ZERO
beq.l dst_zero
cmpi.b %d1,&INF
beq.l dst_inf
cmpi.b %d1,&DENORM
beq.l sscale
cmpi.b %d1,&QNAN
beq.l dst_qnan
bra.l dst_snan
global sscale_sinf
sscale_sinf:
mov.b DTAG(%a6),%d1
beq.l t_operr
cmpi.b %d1,&QNAN
beq.l dst_qnan
cmpi.b %d1,&SNAN
beq.l dst_snan
bra.l t_operr
########################################################################
#
# sop_sqnan(): The src op for frem/fmod/fscale was a QNAN.
#
global sop_sqnan
sop_sqnan:
mov.b DTAG(%a6),%d1
cmpi.b %d1,&QNAN
beq.b dst_qnan
cmpi.b %d1,&SNAN
beq.b dst_snan
bra.b src_qnan
#
# sop_ssnan(): The src op for frem/fmod/fscale was an SNAN.
#
global sop_ssnan
sop_ssnan:
mov.b DTAG(%a6),%d1
cmpi.b %d1,&QNAN
beq.b dst_qnan_src_snan
cmpi.b %d1,&SNAN
beq.b dst_snan
bra.b src_snan
dst_qnan_src_snan:
ori.l &snaniop_mask,USER_FPSR(%a6) # set NAN/SNAN/AIOP
bra.b dst_qnan
#
# dst_qnan(): Return the dst SNAN w/ the SNAN bit set.
#
global dst_snan
dst_snan:
fmov.x DST(%a1),%fp0 # the fmove sets the SNAN bit
fmov.l %fpsr,%d0 # catch resulting status
or.l %d0,USER_FPSR(%a6) # store status
rts
#
# dst_qnan(): Return the dst QNAN.
#
global dst_qnan
dst_qnan:
fmov.x DST(%a1),%fp0 # return the non-signalling nan
tst.b DST_EX(%a1) # set ccodes according to QNAN sign
bmi.b dst_qnan_m
dst_qnan_p:
mov.b &nan_bmask,FPSR_CC(%a6)
rts
dst_qnan_m:
mov.b &neg_bmask+nan_bmask,FPSR_CC(%a6)
rts
#
# src_snan(): Return the src SNAN w/ the SNAN bit set.
#
global src_snan
src_snan:
fmov.x SRC(%a0),%fp0 # the fmove sets the SNAN bit
fmov.l %fpsr,%d0 # catch resulting status
or.l %d0,USER_FPSR(%a6) # store status
rts
#
# src_qnan(): Return the src QNAN.
#
global src_qnan
src_qnan:
fmov.x SRC(%a0),%fp0 # return the non-signalling nan
tst.b SRC_EX(%a0) # set ccodes according to QNAN sign
bmi.b dst_qnan_m
src_qnan_p:
mov.b &nan_bmask,FPSR_CC(%a6)
rts
src_qnan_m:
mov.b &neg_bmask+nan_bmask,FPSR_CC(%a6)
rts
#
# fkern2.s:
# These entry points are used by the exception handler
# routines where an instruction is selected by an index into
# a large jump table corresponding to a given instruction which
# has been decoded. Flow continues here where we now decode
# further accoding to the source operand type.
#
global fsinh
fsinh:
mov.b STAG(%a6),%d1
beq.l ssinh
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l src_inf
cmpi.b %d1,&DENORM
beq.l ssinhd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global flognp1
flognp1:
mov.b STAG(%a6),%d1
beq.l slognp1
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l sopr_inf
cmpi.b %d1,&DENORM
beq.l slognp1d
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fetoxm1
fetoxm1:
mov.b STAG(%a6),%d1
beq.l setoxm1
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l setoxm1i
cmpi.b %d1,&DENORM
beq.l setoxm1d
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global ftanh
ftanh:
mov.b STAG(%a6),%d1
beq.l stanh
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l src_one
cmpi.b %d1,&DENORM
beq.l stanhd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fatan
fatan:
mov.b STAG(%a6),%d1
beq.l satan
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l spi_2
cmpi.b %d1,&DENORM
beq.l satand
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fasin
fasin:
mov.b STAG(%a6),%d1
beq.l sasin
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l sasind
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fatanh
fatanh:
mov.b STAG(%a6),%d1
beq.l satanh
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l satanhd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fsine
fsine:
mov.b STAG(%a6),%d1
beq.l ssin
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l ssind
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global ftan
ftan:
mov.b STAG(%a6),%d1
beq.l stan
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l stand
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fetox
fetox:
mov.b STAG(%a6),%d1
beq.l setox
cmpi.b %d1,&ZERO
beq.l ld_pone
cmpi.b %d1,&INF
beq.l szr_inf
cmpi.b %d1,&DENORM
beq.l setoxd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global ftwotox
ftwotox:
mov.b STAG(%a6),%d1
beq.l stwotox
cmpi.b %d1,&ZERO
beq.l ld_pone
cmpi.b %d1,&INF
beq.l szr_inf
cmpi.b %d1,&DENORM
beq.l stwotoxd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global ftentox
ftentox:
mov.b STAG(%a6),%d1
beq.l stentox
cmpi.b %d1,&ZERO
beq.l ld_pone
cmpi.b %d1,&INF
beq.l szr_inf
cmpi.b %d1,&DENORM
beq.l stentoxd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global flogn
flogn:
mov.b STAG(%a6),%d1
beq.l slogn
cmpi.b %d1,&ZERO
beq.l t_dz2
cmpi.b %d1,&INF
beq.l sopr_inf
cmpi.b %d1,&DENORM
beq.l slognd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global flog10
flog10:
mov.b STAG(%a6),%d1
beq.l slog10
cmpi.b %d1,&ZERO
beq.l t_dz2
cmpi.b %d1,&INF
beq.l sopr_inf
cmpi.b %d1,&DENORM
beq.l slog10d
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global flog2
flog2:
mov.b STAG(%a6),%d1
beq.l slog2
cmpi.b %d1,&ZERO
beq.l t_dz2
cmpi.b %d1,&INF
beq.l sopr_inf
cmpi.b %d1,&DENORM
beq.l slog2d
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fcosh
fcosh:
mov.b STAG(%a6),%d1
beq.l scosh
cmpi.b %d1,&ZERO
beq.l ld_pone
cmpi.b %d1,&INF
beq.l ld_pinf
cmpi.b %d1,&DENORM
beq.l scoshd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global facos
facos:
mov.b STAG(%a6),%d1
beq.l sacos
cmpi.b %d1,&ZERO
beq.l ld_ppi2
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l sacosd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fcos
fcos:
mov.b STAG(%a6),%d1
beq.l scos
cmpi.b %d1,&ZERO
beq.l ld_pone
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l scosd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fgetexp
fgetexp:
mov.b STAG(%a6),%d1
beq.l sgetexp
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l sgetexpd
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fgetman
fgetman:
mov.b STAG(%a6),%d1
beq.l sgetman
cmpi.b %d1,&ZERO
beq.l src_zero
cmpi.b %d1,&INF
beq.l t_operr
cmpi.b %d1,&DENORM
beq.l sgetmand
cmpi.b %d1,&QNAN
beq.l src_qnan
bra.l src_snan
global fsincos
fsincos:
mov.b STAG(%a6),%d1
beq.l ssincos
cmpi.b %d1,&ZERO
beq.l ssincosz
cmpi.b %d1,&INF
beq.l ssincosi
cmpi.b %d1,&DENORM
beq.l ssincosd
cmpi.b %d1,&QNAN
beq.l ssincosqnan
bra.l ssincossnan
global fmod
fmod:
mov.b STAG(%a6),%d1
beq.l smod_snorm
cmpi.b %d1,&ZERO
beq.l smod_szero
cmpi.b %d1,&INF
beq.l smod_sinf
cmpi.b %d1,&DENORM
beq.l smod_sdnrm
cmpi.b %d1,&QNAN
beq.l sop_sqnan
bra.l sop_ssnan
global frem
frem:
mov.b STAG(%a6),%d1
beq.l srem_snorm
cmpi.b %d1,&ZERO
beq.l srem_szero
cmpi.b %d1,&INF
beq.l srem_sinf
cmpi.b %d1,&DENORM
beq.l srem_sdnrm
cmpi.b %d1,&QNAN
beq.l sop_sqnan
bra.l sop_ssnan
global fscale
fscale:
mov.b STAG(%a6),%d1
beq.l sscale_snorm
cmpi.b %d1,&ZERO
beq.l sscale_szero
cmpi.b %d1,&INF
beq.l sscale_sinf
cmpi.b %d1,&DENORM
beq.l sscale_sdnrm
cmpi.b %d1,&QNAN
beq.l sop_sqnan
bra.l sop_ssnan
#########################################################################
# XDEF **************************************************************** #
# fgen_except(): catch an exception during transcendental #
# emulation #
# #
# XREF **************************************************************** #
# fmul() - emulate a multiply instruction #
# fadd() - emulate an add instruction #
# fin() - emulate an fmove instruction #
# #
# INPUT *************************************************************** #
# fp0 = destination operand #
# d0 = type of instruction that took exception #
# fsave frame = source operand #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP #
# #
# ALGORITHM *********************************************************** #
# An exception occurred on the last instruction of the #
# transcendental emulation. hopefully, this won't be happening much #
# because it will be VERY slow. #
# The only exceptions capable of passing through here are #
# Overflow, Underflow, and Unsupported Data Type. #
# #
#########################################################################
global fgen_except
fgen_except:
cmpi.b 0x3(%sp),&0x7 # is exception UNSUPP?
beq.b fge_unsupp # yes
mov.b &NORM,STAG(%a6)
fge_cont:
mov.b &NORM,DTAG(%a6)
# ok, I have a problem with putting the dst op at FP_DST. the emulation
# routines aren't supposed to alter the operands but we've just squashed
# FP_DST here...
# 8/17/93 - this turns out to be more of a "cleanliness" standpoint
# then a potential bug. to begin with, only the dyadic functions
# frem,fmod, and fscale would get the dst trashed here. But, for
# the 060SP, the FP_DST is never used again anyways.
fmovm.x &0x80,FP_DST(%a6) # dst op is in fp0
lea 0x4(%sp),%a0 # pass: ptr to src op
lea FP_DST(%a6),%a1 # pass: ptr to dst op
cmpi.b %d1,&FMOV_OP
beq.b fge_fin # it was an "fmov"
cmpi.b %d1,&FADD_OP
beq.b fge_fadd # it was an "fadd"
fge_fmul:
bsr.l fmul
rts
fge_fadd:
bsr.l fadd
rts
fge_fin:
bsr.l fin
rts
fge_unsupp:
mov.b &DENORM,STAG(%a6)
bra.b fge_cont
#
# This table holds the offsets of the emulation routines for each individual
# math operation relative to the address of this table. Included are
# routines like fadd/fmul/fabs as well as the transcendentals.
# The location within the table is determined by the extension bits of the
# operation longword.
#
swbeg &109
tbl_unsupp:
long fin - tbl_unsupp # 00: fmove
long fint - tbl_unsupp # 01: fint
long fsinh - tbl_unsupp # 02: fsinh
long fintrz - tbl_unsupp # 03: fintrz
long fsqrt - tbl_unsupp # 04: fsqrt
long tbl_unsupp - tbl_unsupp
long flognp1 - tbl_unsupp # 06: flognp1
long tbl_unsupp - tbl_unsupp
long fetoxm1 - tbl_unsupp # 08: fetoxm1
long ftanh - tbl_unsupp # 09: ftanh
long fatan - tbl_unsupp # 0a: fatan
long tbl_unsupp - tbl_unsupp
long fasin - tbl_unsupp # 0c: fasin
long fatanh - tbl_unsupp # 0d: fatanh
long fsine - tbl_unsupp # 0e: fsin
long ftan - tbl_unsupp # 0f: ftan
long fetox - tbl_unsupp # 10: fetox
long ftwotox - tbl_unsupp # 11: ftwotox
long ftentox - tbl_unsupp # 12: ftentox
long tbl_unsupp - tbl_unsupp
long flogn - tbl_unsupp # 14: flogn
long flog10 - tbl_unsupp # 15: flog10
long flog2 - tbl_unsupp # 16: flog2
long tbl_unsupp - tbl_unsupp
long fabs - tbl_unsupp # 18: fabs
long fcosh - tbl_unsupp # 19: fcosh
long fneg - tbl_unsupp # 1a: fneg
long tbl_unsupp - tbl_unsupp
long facos - tbl_unsupp # 1c: facos
long fcos - tbl_unsupp # 1d: fcos
long fgetexp - tbl_unsupp # 1e: fgetexp
long fgetman - tbl_unsupp # 1f: fgetman
long fdiv - tbl_unsupp # 20: fdiv
long fmod - tbl_unsupp # 21: fmod
long fadd - tbl_unsupp # 22: fadd
long fmul - tbl_unsupp # 23: fmul
long fsgldiv - tbl_unsupp # 24: fsgldiv
long frem - tbl_unsupp # 25: frem
long fscale - tbl_unsupp # 26: fscale
long fsglmul - tbl_unsupp # 27: fsglmul
long fsub - tbl_unsupp # 28: fsub
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fsincos - tbl_unsupp # 30: fsincos
long fsincos - tbl_unsupp # 31: fsincos
long fsincos - tbl_unsupp # 32: fsincos
long fsincos - tbl_unsupp # 33: fsincos
long fsincos - tbl_unsupp # 34: fsincos
long fsincos - tbl_unsupp # 35: fsincos
long fsincos - tbl_unsupp # 36: fsincos
long fsincos - tbl_unsupp # 37: fsincos
long fcmp - tbl_unsupp # 38: fcmp
long tbl_unsupp - tbl_unsupp
long ftst - tbl_unsupp # 3a: ftst
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fsin - tbl_unsupp # 40: fsmove
long fssqrt - tbl_unsupp # 41: fssqrt
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fdin - tbl_unsupp # 44: fdmove
long fdsqrt - tbl_unsupp # 45: fdsqrt
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fsabs - tbl_unsupp # 58: fsabs
long tbl_unsupp - tbl_unsupp
long fsneg - tbl_unsupp # 5a: fsneg
long tbl_unsupp - tbl_unsupp
long fdabs - tbl_unsupp # 5c: fdabs
long tbl_unsupp - tbl_unsupp
long fdneg - tbl_unsupp # 5e: fdneg
long tbl_unsupp - tbl_unsupp
long fsdiv - tbl_unsupp # 60: fsdiv
long tbl_unsupp - tbl_unsupp
long fsadd - tbl_unsupp # 62: fsadd
long fsmul - tbl_unsupp # 63: fsmul
long fddiv - tbl_unsupp # 64: fddiv
long tbl_unsupp - tbl_unsupp
long fdadd - tbl_unsupp # 66: fdadd
long fdmul - tbl_unsupp # 67: fdmul
long fssub - tbl_unsupp # 68: fssub
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fdsub - tbl_unsupp # 6c: fdsub
#########################################################################
# XDEF **************************************************************** #
# fmul(): emulates the fmul instruction #
# fsmul(): emulates the fsmul instruction #
# fdmul(): emulates the fdmul instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res() - return default underflow result #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a multiply #
# instruction won't cause an exception. Use the regular fmul to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
align 0x10
tbl_fmul_ovfl:
long 0x3fff - 0x7ffe # ext_max
long 0x3fff - 0x407e # sgl_max
long 0x3fff - 0x43fe # dbl_max
tbl_fmul_unfl:
long 0x3fff + 0x0001 # ext_unfl
long 0x3fff - 0x3f80 # sgl_unfl
long 0x3fff - 0x3c00 # dbl_unfl
global fsmul
fsmul:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl prec
bra.b fmul
global fdmul
fdmul:
andi.b &0x30,%d0
ori.b &d_mode*0x10,%d0 # insert dbl prec
global fmul
fmul:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1 # combine src tags
bne.w fmul_not_norm # optimize on non-norm input
fmul_norm:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale src exponent
mov.l %d0,-(%sp) # save scale factor 1
bsr.l scale_to_zero_dst # scale dst exponent
add.l %d0,(%sp) # SCALE_FACTOR = scale1 + scale2
mov.w 2+L_SCR3(%a6),%d1 # fetch precision
lsr.b &0x6,%d1 # shift to lo bits
mov.l (%sp)+,%d0 # load S.F.
cmp.l %d0,(tbl_fmul_ovfl.w,%pc,%d1.w*4) # would result ovfl?
beq.w fmul_may_ovfl # result may rnd to overflow
blt.w fmul_ovfl # result will overflow
cmp.l %d0,(tbl_fmul_unfl.w,%pc,%d1.w*4) # would result unfl?
beq.w fmul_may_unfl # result may rnd to no unfl
bgt.w fmul_unfl # result will underflow
#
# NORMAL:
# - the result of the multiply operation will neither overflow nor underflow.
# - do the multiply to the proper precision and rounding mode.
# - scale the result exponent using the scale factor. if both operands were
# normalized then we really don't need to go through this scaling. but for now,
# this will do.
#
fmul_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fmul_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# OVERFLOW:
# - the result of the multiply operation is an overflow.
# - do the multiply to the proper precision and rounding mode in order to
# set the inexact bits.
# - calculate the default result and return it in fp0.
# - if overflow or inexact is enabled, we need a multiply result rounded to
# extended precision. if the original operation was extended, then we have this
# result. if the original operation was single or double, we have to do another
# multiply using extended precision and the correct rounding mode. the result
# of this operation then has its exponent scaled by -0x6000 to create the
# exceptional operand.
#
fmul_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
# save setting this until now because this is where fmul_may_ovfl may jump in
fmul_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fmul_ovfl_ena # yes
# calculate the default result
fmul_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass rnd prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled; Create EXOP:
# - if precision is extended, then we have the EXOP. simply bias the exponent
# with an extra -0x6000. if the precision is single or double, we need to
# calculate a result rounded to extended precision.
#
fmul_ovfl_ena:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # test the rnd prec
bne.b fmul_ovfl_ena_sd # it's sgl or dbl
fmul_ovfl_ena_cont:
fmovm.x &0x80,FP_SCR0(%a6) # move result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1 # clear sign bit
andi.w &0x8000,%d2 # keep old sign
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fmul_ovfl_dis
fmul_ovfl_ena_sd:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # keep rnd mode only
fmov.l %d1,%fpcr # set FPCR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l &0x0,%fpcr # clear FPCR
bra.b fmul_ovfl_ena_cont
#
# may OVERFLOW:
# - the result of the multiply operation MAY overflow.
# - do the multiply to the proper precision and rounding mode in order to
# set the inexact bits.
# - calculate the default result and return it in fp0.
#
fmul_may_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fmul_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fmul_normal_exit
#
# UNDERFLOW:
# - the result of the multiply operation is an underflow.
# - do the multiply to the proper precision and rounding mode in order to
# set the inexact bits.
# - calculate the default result and return it in fp0.
# - if overflow or inexact is enabled, we need a multiply result rounded to
# extended precision. if the original operation was extended, then we have this
# result. if the original operation was single or double, we have to do another
# multiply using extended precision and the correct rounding mode. the result
# of this operation then has its exponent scaled by -0x6000 to create the
# exceptional operand.
#
fmul_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
# for fun, let's use only extended precision, round to zero. then, let
# the unf_res() routine figure out all the rest.
# will we get the correct answer.
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fmul_unfl_ena # yes
fmul_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # unf_res2 may have set 'Z'
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fmul_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fmul_unfl_ena_sd # no, sgl or dbl
# if the rnd mode is anything but RZ, then we have to re-do the above
# multiplication becuase we used RZ for all.
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmul_unfl_ena_cont:
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp1 # execute multiply
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fmul_unfl_dis
fmul_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # use only rnd mode
fmov.l %d1,%fpcr # set FPCR
bra.b fmul_unfl_ena_cont
# MAY UNDERFLOW:
# -use the correct rounding mode and precision. this code favors operations
# that do not underflow.
fmul_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| > 2.b?
fbgt.w fmul_normal_exit # no; no underflow occurred
fblt.w fmul_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 2. but,
# we don't know if the result was an underflow that rounded up to a 2 or
# a normalized number that rounded down to a 2. so, redo the entire operation
# using RZ as the rounding mode to see what the pre-rounded result is.
# this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst operand
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # keep rnd prec
ori.b &rz_mode*0x10,%d1 # insert RZ
fmov.l %d1,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp1 # execute multiply
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp1 # make absolute value
fcmp.b %fp1,&0x2 # is |result| < 2.b?
fbge.w fmul_normal_exit # no; no underflow occurred
bra.w fmul_unfl # yes, underflow occurred
################################################################################
#
# Multiply: inputs are not both normalized; what are they?
#
fmul_not_norm:
mov.w (tbl_fmul_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fmul_op.b,%pc,%d1.w)
swbeg &48
tbl_fmul_op:
short fmul_norm - tbl_fmul_op # NORM x NORM
short fmul_zero - tbl_fmul_op # NORM x ZERO
short fmul_inf_src - tbl_fmul_op # NORM x INF
short fmul_res_qnan - tbl_fmul_op # NORM x QNAN
short fmul_norm - tbl_fmul_op # NORM x DENORM
short fmul_res_snan - tbl_fmul_op # NORM x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_zero - tbl_fmul_op # ZERO x NORM
short fmul_zero - tbl_fmul_op # ZERO x ZERO
short fmul_res_operr - tbl_fmul_op # ZERO x INF
short fmul_res_qnan - tbl_fmul_op # ZERO x QNAN
short fmul_zero - tbl_fmul_op # ZERO x DENORM
short fmul_res_snan - tbl_fmul_op # ZERO x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_inf_dst - tbl_fmul_op # INF x NORM
short fmul_res_operr - tbl_fmul_op # INF x ZERO
short fmul_inf_dst - tbl_fmul_op # INF x INF
short fmul_res_qnan - tbl_fmul_op # INF x QNAN
short fmul_inf_dst - tbl_fmul_op # INF x DENORM
short fmul_res_snan - tbl_fmul_op # INF x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_res_qnan - tbl_fmul_op # QNAN x NORM
short fmul_res_qnan - tbl_fmul_op # QNAN x ZERO
short fmul_res_qnan - tbl_fmul_op # QNAN x INF
short fmul_res_qnan - tbl_fmul_op # QNAN x QNAN
short fmul_res_qnan - tbl_fmul_op # QNAN x DENORM
short fmul_res_snan - tbl_fmul_op # QNAN x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_norm - tbl_fmul_op # NORM x NORM
short fmul_zero - tbl_fmul_op # NORM x ZERO
short fmul_inf_src - tbl_fmul_op # NORM x INF
short fmul_res_qnan - tbl_fmul_op # NORM x QNAN
short fmul_norm - tbl_fmul_op # NORM x DENORM
short fmul_res_snan - tbl_fmul_op # NORM x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_res_snan - tbl_fmul_op # SNAN x NORM
short fmul_res_snan - tbl_fmul_op # SNAN x ZERO
short fmul_res_snan - tbl_fmul_op # SNAN x INF
short fmul_res_snan - tbl_fmul_op # SNAN x QNAN
short fmul_res_snan - tbl_fmul_op # SNAN x DENORM
short fmul_res_snan - tbl_fmul_op # SNAN x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
fmul_res_operr:
bra.l res_operr
fmul_res_snan:
bra.l res_snan
fmul_res_qnan:
bra.l res_qnan
#
# Multiply: (Zero x Zero) || (Zero x norm) || (Zero x denorm)
#
global fmul_zero # global for fsglmul
fmul_zero:
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fmul_zero_p # result ZERO is pos.
fmul_zero_n:
fmov.s &0x80000000,%fp0 # load -ZERO
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set Z/N
rts
fmul_zero_p:
fmov.s &0x00000000,%fp0 # load +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# Multiply: (inf x inf) || (inf x norm) || (inf x denorm)
#
# Note: The j-bit for an infinity is a don't-care. However, to be
# strictly compatible w/ the 68881/882, we make sure to return an
# INF w/ the j-bit set if the input INF j-bit was set. Destination
# INFs take priority.
#
global fmul_inf_dst # global for fsglmul
fmul_inf_dst:
fmovm.x DST(%a1),&0x80 # return INF result in fp0
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fmul_inf_dst_p # result INF is pos.
fmul_inf_dst_n:
fabs.x %fp0 # clear result sign
fneg.x %fp0 # set result sign
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set INF/N
rts
fmul_inf_dst_p:
fabs.x %fp0 # clear result sign
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
global fmul_inf_src # global for fsglmul
fmul_inf_src:
fmovm.x SRC(%a0),&0x80 # return INF result in fp0
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fmul_inf_dst_p # result INF is pos.
bra.b fmul_inf_dst_n
#########################################################################
# XDEF **************************************************************** #
# fin(): emulates the fmove instruction #
# fsin(): emulates the fsmove instruction #
# fdin(): emulates the fdmove instruction #
# #
# XREF **************************************************************** #
# norm() - normalize mantissa for EXOP on denorm #
# scale_to_zero_src() - scale src exponent to zero #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan_1op() - return QNAN result #
# res_snan_1op() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round prec/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Norms can be emulated w/ a regular fmove instruction. For #
# sgl/dbl, must scale exponent and perform an "fmove". Check to see #
# if the result would have overflowed/underflowed. If so, use unf_res() #
# or ovf_res() to return the default result. Also return EXOP if #
# exception is enabled. If no exception, return the default result. #
# Unnorms don't pass through here. #
# #
#########################################################################
global fsin
fsin:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl precision
bra.b fin
global fdin
fdin:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl precision
global fin
fin:
mov.l %d0,L_SCR3(%a6) # store rnd info
mov.b STAG(%a6),%d1 # fetch src optype tag
bne.w fin_not_norm # optimize on non-norm input
#
# FP MOVE IN: NORMs and DENORMs ONLY!
#
fin_norm:
andi.b &0xc0,%d0 # is precision extended?
bne.w fin_not_ext # no, so go handle dbl or sgl
#
# precision selected is extended. so...we cannot get an underflow
# or overflow because of rounding to the correct precision. so...
# skip the scaling and unscaling...
#
tst.b SRC_EX(%a0) # is the operand negative?
bpl.b fin_norm_done # no
bset &neg_bit,FPSR_CC(%a6) # yes, so set 'N' ccode bit
fin_norm_done:
fmovm.x SRC(%a0),&0x80 # return result in fp0
rts
#
# for an extended precision DENORM, the UNFL exception bit is set
# the accrued bit is NOT set in this instance(no inexactness!)
#
fin_denorm:
andi.b &0xc0,%d0 # is precision extended?
bne.w fin_not_ext # no, so go handle dbl or sgl
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
tst.b SRC_EX(%a0) # is the operand negative?
bpl.b fin_denorm_done # no
bset &neg_bit,FPSR_CC(%a6) # yes, so set 'N' ccode bit
fin_denorm_done:
fmovm.x SRC(%a0),&0x80 # return result in fp0
btst &unfl_bit,FPCR_ENABLE(%a6) # is UNFL enabled?
bne.b fin_denorm_unfl_ena # yes
rts
#
# the input is an extended DENORM and underflow is enabled in the FPCR.
# normalize the mantissa and add the bias of 0x6000 to the resulting negative
# exponent and insert back into the operand.
#
fin_denorm_unfl_ena:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
bsr.l norm # normalize result
neg.w %d0 # new exponent = -(shft val)
addi.w &0x6000,%d0 # add new bias to exponent
mov.w FP_SCR0_EX(%a6),%d1 # fetch old sign,exp
andi.w &0x8000,%d1 # keep old sign
andi.w &0x7fff,%d0 # clear sign position
or.w %d1,%d0 # concat new exo,old sign
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#
# operand is to be rounded to single or double precision
#
fin_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.b fin_dbl
#
# operand is to be rounded to single precision
#
fin_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f80 # will move in underflow?
bge.w fin_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407e # will move in overflow?
beq.w fin_sd_may_ovfl # maybe; go check
blt.w fin_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved into the fp reg file
#
fin_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # perform move
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fin_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exponent
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fin_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c00 # will move in underflow?
bge.w fin_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43fe # will move in overflow?
beq.w fin_sd_may_ovfl # maybe; go check
blt.w fin_sd_ovfl # yes; go handle overflow
bra.w fin_sd_normal # no; ho handle normalized op
#
# operand WILL underflow when moved in to the fp register file
#
fin_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
tst.b FP_SCR0_EX(%a6) # is operand negative?
bpl.b fin_sd_unfl_tst
bset &neg_bit,FPSR_CC(%a6) # set 'N' ccode bit
# if underflow or inexact is enabled, then go calculate the EXOP first.
fin_sd_unfl_tst:
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fin_sd_unfl_ena # yes
fin_sd_unfl_dis:
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # unf_res may have set 'Z'
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow or inexact is enabled.
# therefore, we must return the result rounded to extended precision.
#
fin_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # subtract scale factor
andi.w &0x8000,%d2 # extract old sign
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR1_EX(%a6) # insert new exponent
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fin_sd_unfl_dis
#
# operand WILL overflow.
#
fin_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # perform move
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fin_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fin_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fin_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fin_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
sub.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fin_sd_ovfl_dis
#
# the move in MAY overflow. so...
#
fin_sd_may_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # perform the move
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fin_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fin_sd_normal_exit
##########################################################################
#
# operand is not a NORM: check its optype and branch accordingly
#
fin_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fin_denorm
cmpi.b %d1,&SNAN # weed out SNANs
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNANs
beq.l res_qnan_1op
#
# do the fmove in; at this point, only possible ops are ZERO and INF.
# use fmov to determine ccodes.
# prec:mode should be zero at this point but it won't affect answer anyways.
#
fmov.x SRC(%a0),%fp0 # do fmove in
fmov.l %fpsr,%d0 # no exceptions possible
rol.l &0x8,%d0 # put ccodes in lo byte
mov.b %d0,FPSR_CC(%a6) # insert correct ccodes
rts
#########################################################################
# XDEF **************************************************************** #
# fdiv(): emulates the fdiv instruction #
# fsdiv(): emulates the fsdiv instruction #
# fddiv(): emulates the fddiv instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res() - return default underflow result #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a divide #
# instruction won't cause an exception. Use the regular fdiv to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
align 0x10
tbl_fdiv_unfl:
long 0x3fff - 0x0000 # ext_unfl
long 0x3fff - 0x3f81 # sgl_unfl
long 0x3fff - 0x3c01 # dbl_unfl
tbl_fdiv_ovfl:
long 0x3fff - 0x7ffe # ext overflow exponent
long 0x3fff - 0x407e # sgl overflow exponent
long 0x3fff - 0x43fe # dbl overflow exponent
global fsdiv
fsdiv:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl prec
bra.b fdiv
global fddiv
fddiv:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl prec
global fdiv
fdiv:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1 # combine src tags
bne.w fdiv_not_norm # optimize on non-norm input
#
# DIVIDE: NORMs and DENORMs ONLY!
#
fdiv_norm:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale src exponent
mov.l %d0,-(%sp) # save scale factor 1
bsr.l scale_to_zero_dst # scale dst exponent
neg.l (%sp) # SCALE FACTOR = scale1 - scale2
add.l %d0,(%sp)
mov.w 2+L_SCR3(%a6),%d1 # fetch precision
lsr.b &0x6,%d1 # shift to lo bits
mov.l (%sp)+,%d0 # load S.F.
cmp.l %d0,(tbl_fdiv_ovfl.b,%pc,%d1.w*4) # will result overflow?
ble.w fdiv_may_ovfl # result will overflow
cmp.l %d0,(tbl_fdiv_unfl.w,%pc,%d1.w*4) # will result underflow?
beq.w fdiv_may_unfl # maybe
bgt.w fdiv_unfl # yes; go handle underflow
fdiv_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # save FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp0 # perform divide
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fdiv_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store result on stack
mov.l %d2,-(%sp) # store d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
tbl_fdiv_ovfl2:
long 0x7fff
long 0x407f
long 0x43ff
fdiv_no_ovfl:
mov.l (%sp)+,%d0 # restore scale factor
bra.b fdiv_normal_exit
fdiv_may_ovfl:
mov.l %d0,-(%sp) # save scale factor
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # set FPSR
fdiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d0
fmov.l &0x0,%fpcr
or.l %d0,USER_FPSR(%a6) # save INEX,N
fmovm.x &0x01,-(%sp) # save result to stack
mov.w (%sp),%d0 # fetch new exponent
add.l &0xc,%sp # clear result from stack
andi.l &0x7fff,%d0 # strip sign
sub.l (%sp),%d0 # add scale factor
cmp.l %d0,(tbl_fdiv_ovfl2.b,%pc,%d1.w*4)
blt.b fdiv_no_ovfl
mov.l (%sp)+,%d0
fdiv_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fdiv_ovfl_ena # yes
fdiv_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass prec:rnd
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
fdiv_ovfl_ena:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fdiv_ovfl_ena_sd # no, do sgl or dbl
fdiv_ovfl_ena_cont:
fmovm.x &0x80,FP_SCR0(%a6) # move result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1 # clear sign bit
andi.w &0x8000,%d2 # keep old sign
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fdiv_ovfl_dis
fdiv_ovfl_ena_sd:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # keep rnd mode
fmov.l %d1,%fpcr # set FPCR
fdiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l &0x0,%fpcr # clear FPCR
bra.b fdiv_ovfl_ena_cont
fdiv_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fdiv_unfl_ena # yes
fdiv_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fdiv_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fdiv_unfl_ena_sd # no, sgl or dbl
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fdiv_unfl_ena_cont:
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp1 # execute divide
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factoer
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exp
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fdiv_unfl_dis
fdiv_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # use only rnd mode
fmov.l %d1,%fpcr # set FPCR
bra.b fdiv_unfl_ena_cont
#
# the divide operation MAY underflow:
#
fdiv_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x1 # is |result| > 1.b?
fbgt.w fdiv_normal_exit # no; no underflow occurred
fblt.w fdiv_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 1. but,
# we don't know if the result was an underflow that rounded up to a 1
# or a normalized number that rounded down to a 1. so, redo the entire
# operation using RZ as the rounding mode to see what the pre-rounded
# result is. this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # keep rnd prec
ori.b &rz_mode*0x10,%d1 # insert RZ
fmov.l %d1,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp1 # execute divide
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp1 # make absolute value
fcmp.b %fp1,&0x1 # is |result| < 1.b?
fbge.w fdiv_normal_exit # no; no underflow occurred
bra.w fdiv_unfl # yes; underflow occurred
############################################################################
#
# Divide: inputs are not both normalized; what are they?
#
fdiv_not_norm:
mov.w (tbl_fdiv_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fdiv_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fdiv_op:
short fdiv_norm - tbl_fdiv_op # NORM / NORM
short fdiv_inf_load - tbl_fdiv_op # NORM / ZERO
short fdiv_zero_load - tbl_fdiv_op # NORM / INF
short fdiv_res_qnan - tbl_fdiv_op # NORM / QNAN
short fdiv_norm - tbl_fdiv_op # NORM / DENORM
short fdiv_res_snan - tbl_fdiv_op # NORM / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_zero_load - tbl_fdiv_op # ZERO / NORM
short fdiv_res_operr - tbl_fdiv_op # ZERO / ZERO
short fdiv_zero_load - tbl_fdiv_op # ZERO / INF
short fdiv_res_qnan - tbl_fdiv_op # ZERO / QNAN
short fdiv_zero_load - tbl_fdiv_op # ZERO / DENORM
short fdiv_res_snan - tbl_fdiv_op # ZERO / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_inf_dst - tbl_fdiv_op # INF / NORM
short fdiv_inf_dst - tbl_fdiv_op # INF / ZERO
short fdiv_res_operr - tbl_fdiv_op # INF / INF
short fdiv_res_qnan - tbl_fdiv_op # INF / QNAN
short fdiv_inf_dst - tbl_fdiv_op # INF / DENORM
short fdiv_res_snan - tbl_fdiv_op # INF / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_res_qnan - tbl_fdiv_op # QNAN / NORM
short fdiv_res_qnan - tbl_fdiv_op # QNAN / ZERO
short fdiv_res_qnan - tbl_fdiv_op # QNAN / INF
short fdiv_res_qnan - tbl_fdiv_op # QNAN / QNAN
short fdiv_res_qnan - tbl_fdiv_op # QNAN / DENORM
short fdiv_res_snan - tbl_fdiv_op # QNAN / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_norm - tbl_fdiv_op # DENORM / NORM
short fdiv_inf_load - tbl_fdiv_op # DENORM / ZERO
short fdiv_zero_load - tbl_fdiv_op # DENORM / INF
short fdiv_res_qnan - tbl_fdiv_op # DENORM / QNAN
short fdiv_norm - tbl_fdiv_op # DENORM / DENORM
short fdiv_res_snan - tbl_fdiv_op # DENORM / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_res_snan - tbl_fdiv_op # SNAN / NORM
short fdiv_res_snan - tbl_fdiv_op # SNAN / ZERO
short fdiv_res_snan - tbl_fdiv_op # SNAN / INF
short fdiv_res_snan - tbl_fdiv_op # SNAN / QNAN
short fdiv_res_snan - tbl_fdiv_op # SNAN / DENORM
short fdiv_res_snan - tbl_fdiv_op # SNAN / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
fdiv_res_qnan:
bra.l res_qnan
fdiv_res_snan:
bra.l res_snan
fdiv_res_operr:
bra.l res_operr
global fdiv_zero_load # global for fsgldiv
fdiv_zero_load:
mov.b SRC_EX(%a0),%d0 # result sign is exclusive
mov.b DST_EX(%a1),%d1 # or of input signs.
eor.b %d0,%d1
bpl.b fdiv_zero_load_p # result is positive
fmov.s &0x80000000,%fp0 # load a -ZERO
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set Z/N
rts
fdiv_zero_load_p:
fmov.s &0x00000000,%fp0 # load a +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# The destination was In Range and the source was a ZERO. The result,
# therefore, is an INF w/ the proper sign.
# So, determine the sign and return a new INF (w/ the j-bit cleared).
#
global fdiv_inf_load # global for fsgldiv
fdiv_inf_load:
ori.w &dz_mask+adz_mask,2+USER_FPSR(%a6) # no; set DZ/ADZ
mov.b SRC_EX(%a0),%d0 # load both signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fdiv_inf_load_p # result is positive
fmov.s &0xff800000,%fp0 # make result -INF
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set INF/N
rts
fdiv_inf_load_p:
fmov.s &0x7f800000,%fp0 # make result +INF
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#
# The destination was an INF w/ an In Range or ZERO source, the result is
# an INF w/ the proper sign.
# The 68881/882 returns the destination INF w/ the new sign(if the j-bit of the
# dst INF is set, then then j-bit of the result INF is also set).
#
global fdiv_inf_dst # global for fsgldiv
fdiv_inf_dst:
mov.b DST_EX(%a1),%d0 # load both signs
mov.b SRC_EX(%a0),%d1
eor.b %d0,%d1
bpl.b fdiv_inf_dst_p # result is positive
fmovm.x DST(%a1),&0x80 # return result in fp0
fabs.x %fp0 # clear sign bit
fneg.x %fp0 # set sign bit
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fdiv_inf_dst_p:
fmovm.x DST(%a1),&0x80 # return result in fp0
fabs.x %fp0 # return positive INF
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#########################################################################
# XDEF **************************************************************** #
# fneg(): emulates the fneg instruction #
# fsneg(): emulates the fsneg instruction #
# fdneg(): emulates the fdneg instruction #
# #
# XREF **************************************************************** #
# norm() - normalize a denorm to provide EXOP #
# scale_to_zero_src() - scale sgl/dbl source exponent #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan_1op() - return QNAN result #
# res_snan_1op() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, zeroes, and infinities as special cases. Separate #
# norms/denorms into ext/sgl/dbl precisions. Extended precision can be #
# emulated by simply setting sign bit. Sgl/dbl operands must be scaled #
# and an actual fneg performed to see if overflow/underflow would have #
# occurred. If so, return default underflow/overflow result. Else, #
# scale the result exponent and return result. FPSR gets set based on #
# the result value. #
# #
#########################################################################
global fsneg
fsneg:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl precision
bra.b fneg
global fdneg
fdneg:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl prec
global fneg
fneg:
mov.l %d0,L_SCR3(%a6) # store rnd info
mov.b STAG(%a6),%d1
bne.w fneg_not_norm # optimize on non-norm input
#
# NEGATE SIGN : norms and denorms ONLY!
#
fneg_norm:
andi.b &0xc0,%d0 # is precision extended?
bne.w fneg_not_ext # no; go handle sgl or dbl
#
# precision selected is extended. so...we can not get an underflow
# or overflow because of rounding to the correct precision. so...
# skip the scaling and unscaling...
#
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d0
eori.w &0x8000,%d0 # negate sign
bpl.b fneg_norm_load # sign is positive
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
fneg_norm_load:
mov.w %d0,FP_SCR0_EX(%a6)
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# for an extended precision DENORM, the UNFL exception bit is set
# the accrued bit is NOT set in this instance(no inexactness!)
#
fneg_denorm:
andi.b &0xc0,%d0 # is precision extended?
bne.b fneg_not_ext # no; go handle sgl or dbl
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d0
eori.w &0x8000,%d0 # negate sign
bpl.b fneg_denorm_done # no
mov.b &neg_bmask,FPSR_CC(%a6) # yes, set 'N' ccode bit
fneg_denorm_done:
mov.w %d0,FP_SCR0_EX(%a6)
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
btst &unfl_bit,FPCR_ENABLE(%a6) # is UNFL enabled?
bne.b fneg_ext_unfl_ena # yes
rts
#
# the input is an extended DENORM and underflow is enabled in the FPCR.
# normalize the mantissa and add the bias of 0x6000 to the resulting negative
# exponent and insert back into the operand.
#
fneg_ext_unfl_ena:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
bsr.l norm # normalize result
neg.w %d0 # new exponent = -(shft val)
addi.w &0x6000,%d0 # add new bias to exponent
mov.w FP_SCR0_EX(%a6),%d1 # fetch old sign,exp
andi.w &0x8000,%d1 # keep old sign
andi.w &0x7fff,%d0 # clear sign position
or.w %d1,%d0 # concat old sign, new exponent
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#
# operand is either single or double
#
fneg_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.b fneg_dbl
#
# operand is to be rounded to single precision
#
fneg_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f80 # will move in underflow?
bge.w fneg_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407e # will move in overflow?
beq.w fneg_sd_may_ovfl # maybe; go check
blt.w fneg_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved in to the fp reg file
#
fneg_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fneg.x FP_SCR0(%a6),%fp0 # perform negation
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fneg_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load sgn,exp
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fneg_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c00 # will move in underflow?
bge.b fneg_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43fe # will move in overflow?
beq.w fneg_sd_may_ovfl # maybe; go check
blt.w fneg_sd_ovfl # yes; go handle overflow
bra.w fneg_sd_normal # no; ho handle normalized op
#
# operand WILL underflow when moved in to the fp register file
#
fneg_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
eori.b &0x80,FP_SCR0_EX(%a6) # negate sign
bpl.b fneg_sd_unfl_tst
bset &neg_bit,FPSR_CC(%a6) # set 'N' ccode bit
# if underflow or inexact is enabled, go calculate EXOP first.
fneg_sd_unfl_tst:
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fneg_sd_unfl_ena # yes
fneg_sd_unfl_dis:
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # unf_res may have set 'Z'
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow is enabled.
# therefore, we must return the result rounded to extended precision.
#
fneg_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # subtract scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat new sign,new exp
mov.w %d1,FP_SCR1_EX(%a6) # insert new exp
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fneg_sd_unfl_dis
#
# operand WILL overflow.
#
fneg_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fneg.x FP_SCR0(%a6),%fp0 # perform negation
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fneg_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fneg_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fneg_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fneg_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat sign,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fneg_sd_ovfl_dis
#
# the move in MAY underflow. so...
#
fneg_sd_may_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fneg.x FP_SCR0(%a6),%fp0 # perform negation
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fneg_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fneg_sd_normal_exit
##########################################################################
#
# input is not normalized; what is it?
#
fneg_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fneg_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNAN
beq.l res_qnan_1op
#
# do the fneg; at this point, only possible ops are ZERO and INF.
# use fneg to determine ccodes.
# prec:mode should be zero at this point but it won't affect answer anyways.
#
fneg.x SRC_EX(%a0),%fp0 # do fneg
fmov.l %fpsr,%d0
rol.l &0x8,%d0 # put ccodes in lo byte
mov.b %d0,FPSR_CC(%a6) # insert correct ccodes
rts
#########################################################################
# XDEF **************************************************************** #
# ftst(): emulates the ftest instruction #
# #
# XREF **************************************************************** #
# res{s,q}nan_1op() - set NAN result for monadic instruction #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# #
# OUTPUT ************************************************************** #
# none #
# #
# ALGORITHM *********************************************************** #
# Check the source operand tag (STAG) and set the FPCR according #
# to the operand type and sign. #
# #
#########################################################################
global ftst
ftst:
mov.b STAG(%a6),%d1
bne.b ftst_not_norm # optimize on non-norm input
#
# Norm:
#
ftst_norm:
tst.b SRC_EX(%a0) # is operand negative?
bmi.b ftst_norm_m # yes
rts
ftst_norm_m:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
#
# input is not normalized; what is it?
#
ftst_not_norm:
cmpi.b %d1,&ZERO # weed out ZERO
beq.b ftst_zero
cmpi.b %d1,&INF # weed out INF
beq.b ftst_inf
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNAN
beq.l res_qnan_1op
#
# Denorm:
#
ftst_denorm:
tst.b SRC_EX(%a0) # is operand negative?
bmi.b ftst_denorm_m # yes
rts
ftst_denorm_m:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
#
# Infinity:
#
ftst_inf:
tst.b SRC_EX(%a0) # is operand negative?
bmi.b ftst_inf_m # yes
ftst_inf_p:
mov.b &inf_bmask,FPSR_CC(%a6) # set 'I' ccode bit
rts
ftst_inf_m:
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set 'I','N' ccode bits
rts
#
# Zero:
#
ftst_zero:
tst.b SRC_EX(%a0) # is operand negative?
bmi.b ftst_zero_m # yes
ftst_zero_p:
mov.b &z_bmask,FPSR_CC(%a6) # set 'N' ccode bit
rts
ftst_zero_m:
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set 'Z','N' ccode bits
rts
#########################################################################
# XDEF **************************************************************** #
# fint(): emulates the fint instruction #
# #
# XREF **************************************************************** #
# res_{s,q}nan_1op() - set NAN result for monadic operation #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round precision/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# #
# ALGORITHM *********************************************************** #
# Separate according to operand type. Unnorms don't pass through #
# here. For norms, load the rounding mode/prec, execute a "fint", then #
# store the resulting FPSR bits. #
# For denorms, force the j-bit to a one and do the same as for #
# norms. Denorms are so low that the answer will either be a zero or a #
# one. #
# For zeroes/infs/NANs, return the same while setting the FPSR #
# as appropriate. #
# #
#########################################################################
global fint
fint:
mov.b STAG(%a6),%d1
bne.b fint_not_norm # optimize on non-norm input
#
# Norm:
#
fint_norm:
andi.b &0x30,%d0 # set prec = ext
fmov.l %d0,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fint.x SRC(%a0),%fp0 # execute fint
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d0 # save FPSR
or.l %d0,USER_FPSR(%a6) # set exception bits
rts
#
# input is not normalized; what is it?
#
fint_not_norm:
cmpi.b %d1,&ZERO # weed out ZERO
beq.b fint_zero
cmpi.b %d1,&INF # weed out INF
beq.b fint_inf
cmpi.b %d1,&DENORM # weed out DENORM
beq.b fint_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
bra.l res_qnan_1op # weed out QNAN
#
# Denorm:
#
# for DENORMs, the result will be either (+/-)ZERO or (+/-)1.
# also, the INEX2 and AINEX exception bits will be set.
# so, we could either set these manually or force the DENORM
# to a very small NORM and ship it to the NORM routine.
# I do the latter.
#
fint_denorm:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6) # copy sign, zero exp
mov.b &0x80,FP_SCR0_HI(%a6) # force DENORM ==> small NORM
lea FP_SCR0(%a6),%a0
bra.b fint_norm
#
# Zero:
#
fint_zero:
tst.b SRC_EX(%a0) # is ZERO negative?
bmi.b fint_zero_m # yes
fint_zero_p:
fmov.s &0x00000000,%fp0 # return +ZERO in fp0
mov.b &z_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
fint_zero_m:
fmov.s &0x80000000,%fp0 # return -ZERO in fp0
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set 'Z','N' ccode bits
rts
#
# Infinity:
#
fint_inf:
fmovm.x SRC(%a0),&0x80 # return result in fp0
tst.b SRC_EX(%a0) # is INF negative?
bmi.b fint_inf_m # yes
fint_inf_p:
mov.b &inf_bmask,FPSR_CC(%a6) # set 'I' ccode bit
rts
fint_inf_m:
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set 'N','I' ccode bits
rts
#########################################################################
# XDEF **************************************************************** #
# fintrz(): emulates the fintrz instruction #
# #
# XREF **************************************************************** #
# res_{s,q}nan_1op() - set NAN result for monadic operation #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round precision/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# #
# ALGORITHM *********************************************************** #
# Separate according to operand type. Unnorms don't pass through #
# here. For norms, load the rounding mode/prec, execute a "fintrz", #
# then store the resulting FPSR bits. #
# For denorms, force the j-bit to a one and do the same as for #
# norms. Denorms are so low that the answer will either be a zero or a #
# one. #
# For zeroes/infs/NANs, return the same while setting the FPSR #
# as appropriate. #
# #
#########################################################################
global fintrz
fintrz:
mov.b STAG(%a6),%d1
bne.b fintrz_not_norm # optimize on non-norm input
#
# Norm:
#
fintrz_norm:
fmov.l &0x0,%fpsr # clear FPSR
fintrz.x SRC(%a0),%fp0 # execute fintrz
fmov.l %fpsr,%d0 # save FPSR
or.l %d0,USER_FPSR(%a6) # set exception bits
rts
#
# input is not normalized; what is it?
#
fintrz_not_norm:
cmpi.b %d1,&ZERO # weed out ZERO
beq.b fintrz_zero
cmpi.b %d1,&INF # weed out INF
beq.b fintrz_inf
cmpi.b %d1,&DENORM # weed out DENORM
beq.b fintrz_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
bra.l res_qnan_1op # weed out QNAN
#
# Denorm:
#
# for DENORMs, the result will be (+/-)ZERO.
# also, the INEX2 and AINEX exception bits will be set.
# so, we could either set these manually or force the DENORM
# to a very small NORM and ship it to the NORM routine.
# I do the latter.
#
fintrz_denorm:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6) # copy sign, zero exp
mov.b &0x80,FP_SCR0_HI(%a6) # force DENORM ==> small NORM
lea FP_SCR0(%a6),%a0
bra.b fintrz_norm
#
# Zero:
#
fintrz_zero:
tst.b SRC_EX(%a0) # is ZERO negative?
bmi.b fintrz_zero_m # yes
fintrz_zero_p:
fmov.s &0x00000000,%fp0 # return +ZERO in fp0
mov.b &z_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
fintrz_zero_m:
fmov.s &0x80000000,%fp0 # return -ZERO in fp0
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set 'Z','N' ccode bits
rts
#
# Infinity:
#
fintrz_inf:
fmovm.x SRC(%a0),&0x80 # return result in fp0
tst.b SRC_EX(%a0) # is INF negative?
bmi.b fintrz_inf_m # yes
fintrz_inf_p:
mov.b &inf_bmask,FPSR_CC(%a6) # set 'I' ccode bit
rts
fintrz_inf_m:
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set 'N','I' ccode bits
rts
#########################################################################
# XDEF **************************************************************** #
# fabs(): emulates the fabs instruction #
# fsabs(): emulates the fsabs instruction #
# fdabs(): emulates the fdabs instruction #
# #
# XREF **************************************************************** #
# norm() - normalize denorm mantissa to provide EXOP #
# scale_to_zero_src() - make exponent. = 0; get scale factor #
# unf_res() - calculate underflow result #
# ovf_res() - calculate overflow result #
# res_{s,q}nan_1op() - set NAN result for monadic operation #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = rnd precision/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Simply clear sign for extended precision norm. Ext prec denorm #
# gets an EXOP created for it since it's an underflow. #
# Double and single precision can overflow and underflow. First, #
# scale the operand such that the exponent is zero. Perform an "fabs" #
# using the correct rnd mode/prec. Check to see if the original #
# exponent would take an exception. If so, use unf_res() or ovf_res() #
# to calculate the default result. Also, create the EXOP for the #
# exceptional case. If no exception should occur, insert the correct #
# result exponent and return. #
# Unnorms don't pass through here. #
# #
#########################################################################
global fsabs
fsabs:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl precision
bra.b fabs
global fdabs
fdabs:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl precision
global fabs
fabs:
mov.l %d0,L_SCR3(%a6) # store rnd info
mov.b STAG(%a6),%d1
bne.w fabs_not_norm # optimize on non-norm input
#
# ABSOLUTE VALUE: norms and denorms ONLY!
#
fabs_norm:
andi.b &0xc0,%d0 # is precision extended?
bne.b fabs_not_ext # no; go handle sgl or dbl
#
# precision selected is extended. so...we can not get an underflow
# or overflow because of rounding to the correct precision. so...
# skip the scaling and unscaling...
#
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d1
bclr &15,%d1 # force absolute value
mov.w %d1,FP_SCR0_EX(%a6) # insert exponent
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# for an extended precision DENORM, the UNFL exception bit is set
# the accrued bit is NOT set in this instance(no inexactness!)
#
fabs_denorm:
andi.b &0xc0,%d0 # is precision extended?
bne.b fabs_not_ext # no
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d0
bclr &15,%d0 # clear sign
mov.w %d0,FP_SCR0_EX(%a6) # insert exponent
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
btst &unfl_bit,FPCR_ENABLE(%a6) # is UNFL enabled?
bne.b fabs_ext_unfl_ena
rts
#
# the input is an extended DENORM and underflow is enabled in the FPCR.
# normalize the mantissa and add the bias of 0x6000 to the resulting negative
# exponent and insert back into the operand.
#
fabs_ext_unfl_ena:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
bsr.l norm # normalize result
neg.w %d0 # new exponent = -(shft val)
addi.w &0x6000,%d0 # add new bias to exponent
mov.w FP_SCR0_EX(%a6),%d1 # fetch old sign,exp
andi.w &0x8000,%d1 # keep old sign
andi.w &0x7fff,%d0 # clear sign position
or.w %d1,%d0 # concat old sign, new exponent
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#
# operand is either single or double
#
fabs_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.b fabs_dbl
#
# operand is to be rounded to single precision
#
fabs_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f80 # will move in underflow?
bge.w fabs_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407e # will move in overflow?
beq.w fabs_sd_may_ovfl # maybe; go check
blt.w fabs_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved in to the fp reg file
#
fabs_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fabs.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load sgn,exp
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fabs_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c00 # will move in underflow?
bge.b fabs_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43fe # will move in overflow?
beq.w fabs_sd_may_ovfl # maybe; go check
blt.w fabs_sd_ovfl # yes; go handle overflow
bra.w fabs_sd_normal # no; ho handle normalized op
#
# operand WILL underflow when moved in to the fp register file
#
fabs_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
bclr &0x7,FP_SCR0_EX(%a6) # force absolute value
# if underflow or inexact is enabled, go calculate EXOP first.
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fabs_sd_unfl_ena # yes
fabs_sd_unfl_dis:
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set possible 'Z' ccode
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow is enabled.
# therefore, we must return the result rounded to extended precision.
#
fabs_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # subtract scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat new sign,new exp
mov.w %d1,FP_SCR1_EX(%a6) # insert new exp
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fabs_sd_unfl_dis
#
# operand WILL overflow.
#
fabs_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fabs.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fabs_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fabs_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fabs_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat sign,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fabs_sd_ovfl_dis
#
# the move in MAY underflow. so...
#
fabs_sd_may_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fabs.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fabs_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fabs_sd_normal_exit
##########################################################################
#
# input is not normalized; what is it?
#
fabs_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fabs_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNAN
beq.l res_qnan_1op
fabs.x SRC(%a0),%fp0 # force absolute value
cmpi.b %d1,&INF # weed out INF
beq.b fabs_inf
fabs_zero:
mov.b &z_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
fabs_inf:
mov.b &inf_bmask,FPSR_CC(%a6) # set 'I' ccode bit
rts
#########################################################################
# XDEF **************************************************************** #
# fcmp(): fp compare op routine #
# #
# XREF **************************************************************** #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 = round prec/mode #
# #
# OUTPUT ************************************************************** #
# None #
# #
# ALGORITHM *********************************************************** #
# Handle NANs and denorms as special cases. For everything else, #
# just use the actual fcmp instruction to produce the correct condition #
# codes. #
# #
#########################################################################
global fcmp
fcmp:
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1
bne.b fcmp_not_norm # optimize on non-norm input
#
# COMPARE FP OPs : NORMs, ZEROs, INFs, and "corrected" DENORMs
#
fcmp_norm:
fmovm.x DST(%a1),&0x80 # load dst op
fcmp.x %fp0,SRC(%a0) # do compare
fmov.l %fpsr,%d0 # save FPSR
rol.l &0x8,%d0 # extract ccode bits
mov.b %d0,FPSR_CC(%a6) # set ccode bits(no exc bits are set)
rts
#
# fcmp: inputs are not both normalized; what are they?
#
fcmp_not_norm:
mov.w (tbl_fcmp_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fcmp_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fcmp_op:
short fcmp_norm - tbl_fcmp_op # NORM - NORM
short fcmp_norm - tbl_fcmp_op # NORM - ZERO
short fcmp_norm - tbl_fcmp_op # NORM - INF
short fcmp_res_qnan - tbl_fcmp_op # NORM - QNAN
short fcmp_nrm_dnrm - tbl_fcmp_op # NORM - DENORM
short fcmp_res_snan - tbl_fcmp_op # NORM - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_norm - tbl_fcmp_op # ZERO - NORM
short fcmp_norm - tbl_fcmp_op # ZERO - ZERO
short fcmp_norm - tbl_fcmp_op # ZERO - INF
short fcmp_res_qnan - tbl_fcmp_op # ZERO - QNAN
short fcmp_dnrm_s - tbl_fcmp_op # ZERO - DENORM
short fcmp_res_snan - tbl_fcmp_op # ZERO - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_norm - tbl_fcmp_op # INF - NORM
short fcmp_norm - tbl_fcmp_op # INF - ZERO
short fcmp_norm - tbl_fcmp_op # INF - INF
short fcmp_res_qnan - tbl_fcmp_op # INF - QNAN
short fcmp_dnrm_s - tbl_fcmp_op # INF - DENORM
short fcmp_res_snan - tbl_fcmp_op # INF - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_res_qnan - tbl_fcmp_op # QNAN - NORM
short fcmp_res_qnan - tbl_fcmp_op # QNAN - ZERO
short fcmp_res_qnan - tbl_fcmp_op # QNAN - INF
short fcmp_res_qnan - tbl_fcmp_op # QNAN - QNAN
short fcmp_res_qnan - tbl_fcmp_op # QNAN - DENORM
short fcmp_res_snan - tbl_fcmp_op # QNAN - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_dnrm_nrm - tbl_fcmp_op # DENORM - NORM
short fcmp_dnrm_d - tbl_fcmp_op # DENORM - ZERO
short fcmp_dnrm_d - tbl_fcmp_op # DENORM - INF
short fcmp_res_qnan - tbl_fcmp_op # DENORM - QNAN
short fcmp_dnrm_sd - tbl_fcmp_op # DENORM - DENORM
short fcmp_res_snan - tbl_fcmp_op # DENORM - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_res_snan - tbl_fcmp_op # SNAN - NORM
short fcmp_res_snan - tbl_fcmp_op # SNAN - ZERO
short fcmp_res_snan - tbl_fcmp_op # SNAN - INF
short fcmp_res_snan - tbl_fcmp_op # SNAN - QNAN
short fcmp_res_snan - tbl_fcmp_op # SNAN - DENORM
short fcmp_res_snan - tbl_fcmp_op # SNAN - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
# unlike all other functions for QNAN and SNAN, fcmp does NOT set the
# 'N' bit for a negative QNAN or SNAN input so we must squelch it here.
fcmp_res_qnan:
bsr.l res_qnan
andi.b &0xf7,FPSR_CC(%a6)
rts
fcmp_res_snan:
bsr.l res_snan
andi.b &0xf7,FPSR_CC(%a6)
rts
#
# DENORMs are a little more difficult.
# If you have a 2 DENORMs, then you can just force the j-bit to a one
# and use the fcmp_norm routine.
# If you have a DENORM and an INF or ZERO, just force the DENORM's j-bit to a one
# and use the fcmp_norm routine.
# If you have a DENORM and a NORM with opposite signs, then use fcmp_norm, also.
# But with a DENORM and a NORM of the same sign, the neg bit is set if the
# (1) signs are (+) and the DENORM is the dst or
# (2) signs are (-) and the DENORM is the src
#
fcmp_dnrm_s:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),%d0
bset &31,%d0 # DENORM src; make into small norm
mov.l %d0,FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0
bra.w fcmp_norm
fcmp_dnrm_d:
mov.l DST_EX(%a1),FP_SCR0_EX(%a6)
mov.l DST_HI(%a1),%d0
bset &31,%d0 # DENORM src; make into small norm
mov.l %d0,FP_SCR0_HI(%a6)
mov.l DST_LO(%a1),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a1
bra.w fcmp_norm
fcmp_dnrm_sd:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l DST_HI(%a1),%d0
bset &31,%d0 # DENORM dst; make into small norm
mov.l %d0,FP_SCR1_HI(%a6)
mov.l SRC_HI(%a0),%d0
bset &31,%d0 # DENORM dst; make into small norm
mov.l %d0,FP_SCR0_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR1(%a6),%a1
lea FP_SCR0(%a6),%a0
bra.w fcmp_norm
fcmp_nrm_dnrm:
mov.b SRC_EX(%a0),%d0 # determine if like signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bmi.w fcmp_dnrm_s
# signs are the same, so must determine the answer ourselves.
tst.b %d0 # is src op negative?
bmi.b fcmp_nrm_dnrm_m # yes
rts
fcmp_nrm_dnrm_m:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
fcmp_dnrm_nrm:
mov.b SRC_EX(%a0),%d0 # determine if like signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bmi.w fcmp_dnrm_d
# signs are the same, so must determine the answer ourselves.
tst.b %d0 # is src op negative?
bpl.b fcmp_dnrm_nrm_m # no
rts
fcmp_dnrm_nrm_m:
mov.b &neg_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
#########################################################################
# XDEF **************************************************************** #
# fsglmul(): emulates the fsglmul instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res4() - return default underflow result for sglop #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a multiply #
# instruction won't cause an exception. Use the regular fsglmul to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
global fsglmul
fsglmul:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1
bne.w fsglmul_not_norm # optimize on non-norm input
fsglmul_norm:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale exponent
mov.l %d0,-(%sp) # save scale factor 1
bsr.l scale_to_zero_dst # scale dst exponent
add.l (%sp)+,%d0 # SCALE_FACTOR = scale1 + scale2
cmpi.l %d0,&0x3fff-0x7ffe # would result ovfl?
beq.w fsglmul_may_ovfl # result may rnd to overflow
blt.w fsglmul_ovfl # result will overflow
cmpi.l %d0,&0x3fff+0x0001 # would result unfl?
beq.w fsglmul_may_unfl # result may rnd to no unfl
bgt.w fsglmul_unfl # result will underflow
fsglmul_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp0 # execute sgl multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsglmul_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
fsglmul_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp0 # execute sgl multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsglmul_ovfl_tst:
# save setting this until now because this is where fsglmul_may_ovfl may jump in
or.l &ovfl_inx_mask, USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fsglmul_ovfl_ena # yes
fsglmul_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass prec:rnd
andi.b &0x30,%d0 # force prec = ext
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
fsglmul_ovfl_ena:
fmovm.x &0x80,FP_SCR0(%a6) # move result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
andi.w &0x8000,%d2 # keep old sign
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fsglmul_ovfl_dis
fsglmul_may_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp0 # execute sgl multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fsglmul_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fsglmul_normal_exit
fsglmul_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp0 # execute sgl multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsglmul_unfl_ena # yes
fsglmul_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res4 # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' bit may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fsglmul_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp1 # execute sgl multiply
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fsglmul_unfl_dis
fsglmul_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp0 # execute sgl multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| > 2.b?
fbgt.w fsglmul_normal_exit # no; no underflow occurred
fblt.w fsglmul_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 2. but,
# we don't know if the result was an underflow that rounded up to a 2 or
# a normalized number that rounded down to a 2. so, redo the entire operation
# using RZ as the rounding mode to see what the pre-rounded result is.
# this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # keep rnd prec
ori.b &rz_mode*0x10,%d1 # insert RZ
fmov.l %d1,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsglmul.x FP_SCR0(%a6),%fp1 # execute sgl multiply
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp1 # make absolute value
fcmp.b %fp1,&0x2 # is |result| < 2.b?
fbge.w fsglmul_normal_exit # no; no underflow occurred
bra.w fsglmul_unfl # yes, underflow occurred
##############################################################################
#
# Single Precision Multiply: inputs are not both normalized; what are they?
#
fsglmul_not_norm:
mov.w (tbl_fsglmul_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fsglmul_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fsglmul_op:
short fsglmul_norm - tbl_fsglmul_op # NORM x NORM
short fsglmul_zero - tbl_fsglmul_op # NORM x ZERO
short fsglmul_inf_src - tbl_fsglmul_op # NORM x INF
short fsglmul_res_qnan - tbl_fsglmul_op # NORM x QNAN
short fsglmul_norm - tbl_fsglmul_op # NORM x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # NORM x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_zero - tbl_fsglmul_op # ZERO x NORM
short fsglmul_zero - tbl_fsglmul_op # ZERO x ZERO
short fsglmul_res_operr - tbl_fsglmul_op # ZERO x INF
short fsglmul_res_qnan - tbl_fsglmul_op # ZERO x QNAN
short fsglmul_zero - tbl_fsglmul_op # ZERO x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # ZERO x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_inf_dst - tbl_fsglmul_op # INF x NORM
short fsglmul_res_operr - tbl_fsglmul_op # INF x ZERO
short fsglmul_inf_dst - tbl_fsglmul_op # INF x INF
short fsglmul_res_qnan - tbl_fsglmul_op # INF x QNAN
short fsglmul_inf_dst - tbl_fsglmul_op # INF x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # INF x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x NORM
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x ZERO
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x INF
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x QNAN
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # QNAN x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_norm - tbl_fsglmul_op # NORM x NORM
short fsglmul_zero - tbl_fsglmul_op # NORM x ZERO
short fsglmul_inf_src - tbl_fsglmul_op # NORM x INF
short fsglmul_res_qnan - tbl_fsglmul_op # NORM x QNAN
short fsglmul_norm - tbl_fsglmul_op # NORM x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # NORM x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x NORM
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x ZERO
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x INF
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x QNAN
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
fsglmul_res_operr:
bra.l res_operr
fsglmul_res_snan:
bra.l res_snan
fsglmul_res_qnan:
bra.l res_qnan
fsglmul_zero:
bra.l fmul_zero
fsglmul_inf_src:
bra.l fmul_inf_src
fsglmul_inf_dst:
bra.l fmul_inf_dst
#########################################################################
# XDEF **************************************************************** #
# fsgldiv(): emulates the fsgldiv instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res4() - return default underflow result for sglop #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a divide #
# instruction won't cause an exception. Use the regular fsgldiv to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
global fsgldiv
fsgldiv:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1 # combine src tags
bne.w fsgldiv_not_norm # optimize on non-norm input
#
# DIVIDE: NORMs and DENORMs ONLY!
#
fsgldiv_norm:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor 1
mov.l %d0,-(%sp) # save scale factor 1
bsr.l scale_to_zero_dst # calculate scale factor 2
neg.l (%sp) # S.F. = scale1 - scale2
add.l %d0,(%sp)
mov.w 2+L_SCR3(%a6),%d1 # fetch precision,mode
lsr.b &0x6,%d1
mov.l (%sp)+,%d0
cmpi.l %d0,&0x3fff-0x7ffe
ble.w fsgldiv_may_ovfl
cmpi.l %d0,&0x3fff-0x0000 # will result underflow?
beq.w fsgldiv_may_unfl # maybe
bgt.w fsgldiv_unfl # yes; go handle underflow
fsgldiv_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # save FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # perform sgl divide
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsgldiv_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store result on stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
fsgldiv_may_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # set FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d1
fmov.l &0x0,%fpcr
or.l %d1,USER_FPSR(%a6) # save INEX,N
fmovm.x &0x01,-(%sp) # save result to stack
mov.w (%sp),%d1 # fetch new exponent
add.l &0xc,%sp # clear result
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
cmp.l %d1,&0x7fff # did divide overflow?
blt.b fsgldiv_normal_exit
fsgldiv_ovfl_tst:
or.w &ovfl_inx_mask,2+USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fsgldiv_ovfl_ena # yes
fsgldiv_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass prec:rnd
andi.b &0x30,%d0 # kill precision
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
fsgldiv_ovfl_ena:
fmovm.x &0x80,FP_SCR0(%a6) # move result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract new bias
andi.w &0x7fff,%d1 # clear ms bit
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fsgldiv_ovfl_dis
fsgldiv_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # execute sgl divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsgldiv_unfl_ena # yes
fsgldiv_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res4 # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' bit may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fsgldiv_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp1 # execute sgl divide
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1 # clear top bit
or.w %d2,%d1 # concat old sign, new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fsgldiv_unfl_dis
#
# the divide operation MAY underflow:
#
fsgldiv_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # execute sgl divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x1 # is |result| > 1.b?
fbgt.w fsgldiv_normal_exit # no; no underflow occurred
fblt.w fsgldiv_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 1. but,
# we don't know if the result was an underflow that rounded up to a 1
# or a normalized number that rounded down to a 1. so, redo the entire
# operation using RZ as the rounding mode to see what the pre-rounded
# result is. this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into %fp1
clr.l %d1 # clear scratch register
ori.b &rz_mode*0x10,%d1 # force RZ rnd mode
fmov.l %d1,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp1 # execute sgl divide
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp1 # make absolute value
fcmp.b %fp1,&0x1 # is |result| < 1.b?
fbge.w fsgldiv_normal_exit # no; no underflow occurred
bra.w fsgldiv_unfl # yes; underflow occurred
############################################################################
#
# Divide: inputs are not both normalized; what are they?
#
fsgldiv_not_norm:
mov.w (tbl_fsgldiv_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fsgldiv_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fsgldiv_op:
short fsgldiv_norm - tbl_fsgldiv_op # NORM / NORM
short fsgldiv_inf_load - tbl_fsgldiv_op # NORM / ZERO
short fsgldiv_zero_load - tbl_fsgldiv_op # NORM / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # NORM / QNAN
short fsgldiv_norm - tbl_fsgldiv_op # NORM / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # NORM / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_zero_load - tbl_fsgldiv_op # ZERO / NORM
short fsgldiv_res_operr - tbl_fsgldiv_op # ZERO / ZERO
short fsgldiv_zero_load - tbl_fsgldiv_op # ZERO / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # ZERO / QNAN
short fsgldiv_zero_load - tbl_fsgldiv_op # ZERO / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # ZERO / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_inf_dst - tbl_fsgldiv_op # INF / NORM
short fsgldiv_inf_dst - tbl_fsgldiv_op # INF / ZERO
short fsgldiv_res_operr - tbl_fsgldiv_op # INF / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # INF / QNAN
short fsgldiv_inf_dst - tbl_fsgldiv_op # INF / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # INF / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / NORM
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / ZERO
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / QNAN
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # QNAN / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_norm - tbl_fsgldiv_op # DENORM / NORM
short fsgldiv_inf_load - tbl_fsgldiv_op # DENORM / ZERO
short fsgldiv_zero_load - tbl_fsgldiv_op # DENORM / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # DENORM / QNAN
short fsgldiv_norm - tbl_fsgldiv_op # DENORM / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # DENORM / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / NORM
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / ZERO
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / INF
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / QNAN
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
fsgldiv_res_qnan:
bra.l res_qnan
fsgldiv_res_snan:
bra.l res_snan
fsgldiv_res_operr:
bra.l res_operr
fsgldiv_inf_load:
bra.l fdiv_inf_load
fsgldiv_zero_load:
bra.l fdiv_zero_load
fsgldiv_inf_dst:
bra.l fdiv_inf_dst
#########################################################################
# XDEF **************************************************************** #
# fadd(): emulates the fadd instruction #
# fsadd(): emulates the fadd instruction #
# fdadd(): emulates the fdadd instruction #
# #
# XREF **************************************************************** #
# addsub_scaler2() - scale the operands so they won't take exc #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan() - set QNAN result #
# res_snan() - set SNAN result #
# res_operr() - set OPERR result #
# scale_to_zero_src() - set src operand exponent equal to zero #
# scale_to_zero_dst() - set dst operand exponent equal to zero #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Do addition after scaling exponents such that exception won't #
# occur. Then, check result exponent to see if exception would have #
# occurred. If so, return default result and maybe EXOP. Else, insert #
# the correct result exponent and return. Set FPSR bits as appropriate. #
# #
#########################################################################
global fsadd
fsadd:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl prec
bra.b fadd
global fdadd
fdadd:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl prec
global fadd
fadd:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1 # combine src tags
bne.w fadd_not_norm # optimize on non-norm input
#
# ADD: norms and denorms
#
fadd_norm:
bsr.l addsub_scaler2 # scale exponents
fadd_zero_entry:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fadd.x FP_SCR0(%a6),%fp0 # execute add
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # fetch INEX2,N,Z
or.l %d1,USER_FPSR(%a6) # save exc and ccode bits
fbeq.w fadd_zero_exit # if result is zero, end now
mov.l %d2,-(%sp) # save d2
fmovm.x &0x01,-(%sp) # save result to stack
mov.w 2+L_SCR3(%a6),%d1
lsr.b &0x6,%d1
mov.w (%sp),%d2 # fetch new sign, exp
andi.l &0x7fff,%d2 # strip sign
sub.l %d0,%d2 # add scale factor
cmp.l %d2,(tbl_fadd_ovfl.b,%pc,%d1.w*4) # is it an overflow?
bge.b fadd_ovfl # yes
cmp.l %d2,(tbl_fadd_unfl.b,%pc,%d1.w*4) # is it an underflow?
blt.w fadd_unfl # yes
beq.w fadd_may_unfl # maybe; go find out
fadd_normal:
mov.w (%sp),%d1
andi.w &0x8000,%d1 # keep sign
or.w %d2,%d1 # concat sign,new exp
mov.w %d1,(%sp) # insert new exponent
fmovm.x (%sp)+,&0x80 # return result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fadd_zero_exit:
# fmov.s &0x00000000,%fp0 # return zero in fp0
rts
tbl_fadd_ovfl:
long 0x7fff # ext ovfl
long 0x407f # sgl ovfl
long 0x43ff # dbl ovfl
tbl_fadd_unfl:
long 0x0000 # ext unfl
long 0x3f81 # sgl unfl
long 0x3c01 # dbl unfl
fadd_ovfl:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fadd_ovfl_ena # yes
add.l &0xc,%sp
fadd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass prec:rnd
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fadd_ovfl_ena:
mov.b L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fadd_ovfl_ena_sd # no; prec = sgl or dbl
fadd_ovfl_ena_cont:
mov.w (%sp),%d1
andi.w &0x8000,%d1 # keep sign
subi.l &0x6000,%d2 # add extra bias
andi.w &0x7fff,%d2
or.w %d2,%d1 # concat sign,new exp
mov.w %d1,(%sp) # insert new exponent
fmovm.x (%sp)+,&0x40 # return EXOP in fp1
bra.b fadd_ovfl_dis
fadd_ovfl_ena_sd:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # keep rnd mode
fmov.l %d1,%fpcr # set FPCR
fadd.x FP_SCR0(%a6),%fp0 # execute add
fmov.l &0x0,%fpcr # clear FPCR
add.l &0xc,%sp
fmovm.x &0x01,-(%sp)
bra.b fadd_ovfl_ena_cont
fadd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
add.l &0xc,%sp
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fadd.x FP_SCR0(%a6),%fp0 # execute add
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save status
or.l %d1,USER_FPSR(%a6) # save INEX,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fadd_unfl_ena # yes
fadd_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' bit may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fadd_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fadd_unfl_ena_sd # no; sgl or dbl
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fadd_unfl_ena_cont:
fmov.l &0x0,%fpsr # clear FPSR
fadd.x FP_SCR0(%a6),%fp1 # execute multiply
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1 # clear top bit
or.w %d2,%d1 # concat sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fadd_unfl_dis
fadd_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # use only rnd mode
fmov.l %d1,%fpcr # set FPCR
bra.b fadd_unfl_ena_cont
#
# result is equal to the smallest normalized number in the selected precision
# if the precision is extended, this result could not have come from an
# underflow that rounded up.
#
fadd_may_unfl:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1
beq.w fadd_normal # yes; no underflow occurred
mov.l 0x4(%sp),%d1 # extract hi(man)
cmpi.l %d1,&0x80000000 # is hi(man) = 0x80000000?
bne.w fadd_normal # no; no underflow occurred
tst.l 0x8(%sp) # is lo(man) = 0x0?
bne.w fadd_normal # no; no underflow occurred
btst &inex2_bit,FPSR_EXCEPT(%a6) # is INEX2 set?
beq.w fadd_normal # no; no underflow occurred
#
# ok, so now the result has a exponent equal to the smallest normalized
# exponent for the selected precision. also, the mantissa is equal to
# 0x8000000000000000 and this mantissa is the result of rounding non-zero
# g,r,s.
# now, we must determine whether the pre-rounded result was an underflow
# rounded "up" or a normalized number rounded "down".
# so, we do this be re-executing the add using RZ as the rounding mode and
# seeing if the new result is smaller or equal to the current result.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # keep rnd prec
ori.b &rz_mode*0x10,%d1 # insert rnd mode
fmov.l %d1,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fadd.x FP_SCR0(%a6),%fp1 # execute add
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp0 # compare absolute values
fabs.x %fp1
fcmp.x %fp0,%fp1 # is first result > second?
fbgt.w fadd_unfl # yes; it's an underflow
bra.w fadd_normal # no; it's not an underflow
##########################################################################
#
# Add: inputs are not both normalized; what are they?
#
fadd_not_norm:
mov.w (tbl_fadd_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fadd_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fadd_op:
short fadd_norm - tbl_fadd_op # NORM + NORM
short fadd_zero_src - tbl_fadd_op # NORM + ZERO
short fadd_inf_src - tbl_fadd_op # NORM + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_norm - tbl_fadd_op # NORM + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_zero_dst - tbl_fadd_op # ZERO + NORM
short fadd_zero_2 - tbl_fadd_op # ZERO + ZERO
short fadd_inf_src - tbl_fadd_op # ZERO + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_zero_dst - tbl_fadd_op # ZERO + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_inf_dst - tbl_fadd_op # INF + NORM
short fadd_inf_dst - tbl_fadd_op # INF + ZERO
short fadd_inf_2 - tbl_fadd_op # INF + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_inf_dst - tbl_fadd_op # INF + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_res_qnan - tbl_fadd_op # QNAN + NORM
short fadd_res_qnan - tbl_fadd_op # QNAN + ZERO
short fadd_res_qnan - tbl_fadd_op # QNAN + INF
short fadd_res_qnan - tbl_fadd_op # QNAN + QNAN
short fadd_res_qnan - tbl_fadd_op # QNAN + DENORM
short fadd_res_snan - tbl_fadd_op # QNAN + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_norm - tbl_fadd_op # DENORM + NORM
short fadd_zero_src - tbl_fadd_op # DENORM + ZERO
short fadd_inf_src - tbl_fadd_op # DENORM + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_norm - tbl_fadd_op # DENORM + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_res_snan - tbl_fadd_op # SNAN + NORM
short fadd_res_snan - tbl_fadd_op # SNAN + ZERO
short fadd_res_snan - tbl_fadd_op # SNAN + INF
short fadd_res_snan - tbl_fadd_op # SNAN + QNAN
short fadd_res_snan - tbl_fadd_op # SNAN + DENORM
short fadd_res_snan - tbl_fadd_op # SNAN + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
fadd_res_qnan:
bra.l res_qnan
fadd_res_snan:
bra.l res_snan
#
# both operands are ZEROes
#
fadd_zero_2:
mov.b SRC_EX(%a0),%d0 # are the signs opposite
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bmi.w fadd_zero_2_chk_rm # weed out (-ZERO)+(+ZERO)
# the signs are the same. so determine whether they are positive or negative
# and return the appropriately signed zero.
tst.b %d0 # are ZEROes positive or negative?
bmi.b fadd_zero_rm # negative
fmov.s &0x00000000,%fp0 # return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# the ZEROes have opposite signs:
# - therefore, we return +ZERO if the rounding modes are RN,RZ, or RP.
# - -ZERO is returned in the case of RM.
#
fadd_zero_2_chk_rm:
mov.b 3+L_SCR3(%a6),%d1
andi.b &0x30,%d1 # extract rnd mode
cmpi.b %d1,&rm_mode*0x10 # is rnd mode == RM?
beq.b fadd_zero_rm # yes
fmov.s &0x00000000,%fp0 # return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
fadd_zero_rm:
fmov.s &0x80000000,%fp0 # return -ZERO
mov.b &neg_bmask+z_bmask,FPSR_CC(%a6) # set NEG/Z
rts
#
# one operand is a ZERO and the other is a DENORM or NORM. scale
# the DENORM or NORM and jump to the regular fadd routine.
#
fadd_zero_dst:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale the operand
clr.w FP_SCR1_EX(%a6)
clr.l FP_SCR1_HI(%a6)
clr.l FP_SCR1_LO(%a6)
bra.w fadd_zero_entry # go execute fadd
fadd_zero_src:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
bsr.l scale_to_zero_dst # scale the operand
clr.w FP_SCR0_EX(%a6)
clr.l FP_SCR0_HI(%a6)
clr.l FP_SCR0_LO(%a6)
bra.w fadd_zero_entry # go execute fadd
#
# both operands are INFs. an OPERR will result if the INFs have
# different signs. else, an INF of the same sign is returned
#
fadd_inf_2:
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d1,%d0
bmi.l res_operr # weed out (-INF)+(+INF)
# ok, so it's not an OPERR. but, we do have to remember to return the
# src INF since that's where the 881/882 gets the j-bit from...
#
# operands are INF and one of {ZERO, INF, DENORM, NORM}
#
fadd_inf_src:
fmovm.x SRC(%a0),&0x80 # return src INF
tst.b SRC_EX(%a0) # is INF positive?
bpl.b fadd_inf_done # yes; we're done
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
#
# operands are INF and one of {ZERO, INF, DENORM, NORM}
#
fadd_inf_dst:
fmovm.x DST(%a1),&0x80 # return dst INF
tst.b DST_EX(%a1) # is INF positive?
bpl.b fadd_inf_done # yes; we're done
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fadd_inf_done:
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#########################################################################
# XDEF **************************************************************** #
# fsub(): emulates the fsub instruction #
# fssub(): emulates the fssub instruction #
# fdsub(): emulates the fdsub instruction #
# #
# XREF **************************************************************** #
# addsub_scaler2() - scale the operands so they won't take exc #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan() - set QNAN result #
# res_snan() - set SNAN result #
# res_operr() - set OPERR result #
# scale_to_zero_src() - set src operand exponent equal to zero #
# scale_to_zero_dst() - set dst operand exponent equal to zero #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Do subtraction after scaling exponents such that exception won't#
# occur. Then, check result exponent to see if exception would have #
# occurred. If so, return default result and maybe EXOP. Else, insert #
# the correct result exponent and return. Set FPSR bits as appropriate. #
# #
#########################################################################
global fssub
fssub:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl prec
bra.b fsub
global fdsub
fdsub:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl prec
global fsub
fsub:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1 # combine src tags
bne.w fsub_not_norm # optimize on non-norm input
#
# SUB: norms and denorms
#
fsub_norm:
bsr.l addsub_scaler2 # scale exponents
fsub_zero_entry:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsub.x FP_SCR0(%a6),%fp0 # execute subtract
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # fetch INEX2, N, Z
or.l %d1,USER_FPSR(%a6) # save exc and ccode bits
fbeq.w fsub_zero_exit # if result zero, end now
mov.l %d2,-(%sp) # save d2
fmovm.x &0x01,-(%sp) # save result to stack
mov.w 2+L_SCR3(%a6),%d1
lsr.b &0x6,%d1
mov.w (%sp),%d2 # fetch new exponent
andi.l &0x7fff,%d2 # strip sign
sub.l %d0,%d2 # add scale factor
cmp.l %d2,(tbl_fsub_ovfl.b,%pc,%d1.w*4) # is it an overflow?
bge.b fsub_ovfl # yes
cmp.l %d2,(tbl_fsub_unfl.b,%pc,%d1.w*4) # is it an underflow?
blt.w fsub_unfl # yes
beq.w fsub_may_unfl # maybe; go find out
fsub_normal:
mov.w (%sp),%d1
andi.w &0x8000,%d1 # keep sign
or.w %d2,%d1 # insert new exponent
mov.w %d1,(%sp) # insert new exponent
fmovm.x (%sp)+,&0x80 # return result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fsub_zero_exit:
# fmov.s &0x00000000,%fp0 # return zero in fp0
rts
tbl_fsub_ovfl:
long 0x7fff # ext ovfl
long 0x407f # sgl ovfl
long 0x43ff # dbl ovfl
tbl_fsub_unfl:
long 0x0000 # ext unfl
long 0x3f81 # sgl unfl
long 0x3c01 # dbl unfl
fsub_ovfl:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fsub_ovfl_ena # yes
add.l &0xc,%sp
fsub_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass prec:rnd
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fsub_ovfl_ena:
mov.b L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fsub_ovfl_ena_sd # no
fsub_ovfl_ena_cont:
mov.w (%sp),%d1 # fetch {sgn,exp}
andi.w &0x8000,%d1 # keep sign
subi.l &0x6000,%d2 # subtract new bias
andi.w &0x7fff,%d2 # clear top bit
or.w %d2,%d1 # concat sign,exp
mov.w %d1,(%sp) # insert new exponent
fmovm.x (%sp)+,&0x40 # return EXOP in fp1
bra.b fsub_ovfl_dis
fsub_ovfl_ena_sd:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # clear rnd prec
fmov.l %d1,%fpcr # set FPCR
fsub.x FP_SCR0(%a6),%fp0 # execute subtract
fmov.l &0x0,%fpcr # clear FPCR
add.l &0xc,%sp
fmovm.x &0x01,-(%sp)
bra.b fsub_ovfl_ena_cont
fsub_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
add.l &0xc,%sp
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsub.x FP_SCR0(%a6),%fp0 # execute subtract
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save status
or.l %d1,USER_FPSR(%a6)
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsub_unfl_ena # yes
fsub_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fsub_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fsub_unfl_ena_sd # no
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsub_unfl_ena_cont:
fmov.l &0x0,%fpsr # clear FPSR
fsub.x FP_SCR0(%a6),%fp1 # execute subtract
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # store result to stack
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # subtract new bias
andi.w &0x7fff,%d1 # clear top bit
or.w %d2,%d1 # concat sgn,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fsub_unfl_dis
fsub_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # clear rnd prec
fmov.l %d1,%fpcr # set FPCR
bra.b fsub_unfl_ena_cont
#
# result is equal to the smallest normalized number in the selected precision
# if the precision is extended, this result could not have come from an
# underflow that rounded up.
#
fsub_may_unfl:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # fetch rnd prec
beq.w fsub_normal # yes; no underflow occurred
mov.l 0x4(%sp),%d1
cmpi.l %d1,&0x80000000 # is hi(man) = 0x80000000?
bne.w fsub_normal # no; no underflow occurred
tst.l 0x8(%sp) # is lo(man) = 0x0?
bne.w fsub_normal # no; no underflow occurred
btst &inex2_bit,FPSR_EXCEPT(%a6) # is INEX2 set?
beq.w fsub_normal # no; no underflow occurred
#
# ok, so now the result has a exponent equal to the smallest normalized
# exponent for the selected precision. also, the mantissa is equal to
# 0x8000000000000000 and this mantissa is the result of rounding non-zero
# g,r,s.
# now, we must determine whether the pre-rounded result was an underflow
# rounded "up" or a normalized number rounded "down".
# so, we do this be re-executing the add using RZ as the rounding mode and
# seeing if the new result is smaller or equal to the current result.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # keep rnd prec
ori.b &rz_mode*0x10,%d1 # insert rnd mode
fmov.l %d1,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsub.x FP_SCR0(%a6),%fp1 # execute subtract
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp0 # compare absolute values
fabs.x %fp1
fcmp.x %fp0,%fp1 # is first result > second?
fbgt.w fsub_unfl # yes; it's an underflow
bra.w fsub_normal # no; it's not an underflow
##########################################################################
#
# Sub: inputs are not both normalized; what are they?
#
fsub_not_norm:
mov.w (tbl_fsub_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fsub_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fsub_op:
short fsub_norm - tbl_fsub_op # NORM - NORM
short fsub_zero_src - tbl_fsub_op # NORM - ZERO
short fsub_inf_src - tbl_fsub_op # NORM - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_norm - tbl_fsub_op # NORM - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_zero_dst - tbl_fsub_op # ZERO - NORM
short fsub_zero_2 - tbl_fsub_op # ZERO - ZERO
short fsub_inf_src - tbl_fsub_op # ZERO - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_zero_dst - tbl_fsub_op # ZERO - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_inf_dst - tbl_fsub_op # INF - NORM
short fsub_inf_dst - tbl_fsub_op # INF - ZERO
short fsub_inf_2 - tbl_fsub_op # INF - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_inf_dst - tbl_fsub_op # INF - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_res_qnan - tbl_fsub_op # QNAN - NORM
short fsub_res_qnan - tbl_fsub_op # QNAN - ZERO
short fsub_res_qnan - tbl_fsub_op # QNAN - INF
short fsub_res_qnan - tbl_fsub_op # QNAN - QNAN
short fsub_res_qnan - tbl_fsub_op # QNAN - DENORM
short fsub_res_snan - tbl_fsub_op # QNAN - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_norm - tbl_fsub_op # DENORM - NORM
short fsub_zero_src - tbl_fsub_op # DENORM - ZERO
short fsub_inf_src - tbl_fsub_op # DENORM - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_norm - tbl_fsub_op # DENORM - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_res_snan - tbl_fsub_op # SNAN - NORM
short fsub_res_snan - tbl_fsub_op # SNAN - ZERO
short fsub_res_snan - tbl_fsub_op # SNAN - INF
short fsub_res_snan - tbl_fsub_op # SNAN - QNAN
short fsub_res_snan - tbl_fsub_op # SNAN - DENORM
short fsub_res_snan - tbl_fsub_op # SNAN - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
fsub_res_qnan:
bra.l res_qnan
fsub_res_snan:
bra.l res_snan
#
# both operands are ZEROes
#
fsub_zero_2:
mov.b SRC_EX(%a0),%d0
mov.b DST_EX(%a1),%d1
eor.b %d1,%d0
bpl.b fsub_zero_2_chk_rm
# the signs are opposite, so, return a ZERO w/ the sign of the dst ZERO
tst.b %d0 # is dst negative?
bmi.b fsub_zero_2_rm # yes
fmov.s &0x00000000,%fp0 # no; return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# the ZEROes have the same signs:
# - therefore, we return +ZERO if the rounding mode is RN,RZ, or RP
# - -ZERO is returned in the case of RM.
#
fsub_zero_2_chk_rm:
mov.b 3+L_SCR3(%a6),%d1
andi.b &0x30,%d1 # extract rnd mode
cmpi.b %d1,&rm_mode*0x10 # is rnd mode = RM?
beq.b fsub_zero_2_rm # yes
fmov.s &0x00000000,%fp0 # no; return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
fsub_zero_2_rm:
fmov.s &0x80000000,%fp0 # return -ZERO
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set Z/NEG
rts
#
# one operand is a ZERO and the other is a DENORM or a NORM.
# scale the DENORM or NORM and jump to the regular fsub routine.
#
fsub_zero_dst:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale the operand
clr.w FP_SCR1_EX(%a6)
clr.l FP_SCR1_HI(%a6)
clr.l FP_SCR1_LO(%a6)
bra.w fsub_zero_entry # go execute fsub
fsub_zero_src:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
bsr.l scale_to_zero_dst # scale the operand
clr.w FP_SCR0_EX(%a6)
clr.l FP_SCR0_HI(%a6)
clr.l FP_SCR0_LO(%a6)
bra.w fsub_zero_entry # go execute fsub
#
# both operands are INFs. an OPERR will result if the INFs have the
# same signs. else,
#
fsub_inf_2:
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d1,%d0
bpl.l res_operr # weed out (-INF)+(+INF)
# ok, so it's not an OPERR. but we do have to remember to return
# the src INF since that's where the 881/882 gets the j-bit.
fsub_inf_src:
fmovm.x SRC(%a0),&0x80 # return src INF
fneg.x %fp0 # invert sign
fbge.w fsub_inf_done # sign is now positive
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fsub_inf_dst:
fmovm.x DST(%a1),&0x80 # return dst INF
tst.b DST_EX(%a1) # is INF negative?
bpl.b fsub_inf_done # no
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fsub_inf_done:
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#########################################################################
# XDEF **************************************************************** #
# fsqrt(): emulates the fsqrt instruction #
# fssqrt(): emulates the fssqrt instruction #
# fdsqrt(): emulates the fdsqrt instruction #
# #
# XREF **************************************************************** #
# scale_sqrt() - scale the source operand #
# unf_res() - return default underflow result #
# ovf_res() - return default overflow result #
# res_qnan_1op() - return QNAN result #
# res_snan_1op() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a sqrt #
# instruction won't cause an exception. Use the regular fsqrt to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
global fssqrt
fssqrt:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl precision
bra.b fsqrt
global fdsqrt
fdsqrt:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl precision
global fsqrt
fsqrt:
mov.l %d0,L_SCR3(%a6) # store rnd info
clr.w %d1
mov.b STAG(%a6),%d1
bne.w fsqrt_not_norm # optimize on non-norm input
#
# SQUARE ROOT: norms and denorms ONLY!
#
fsqrt_norm:
tst.b SRC_EX(%a0) # is operand negative?
bmi.l res_operr # yes
andi.b &0xc0,%d0 # is precision extended?
bne.b fsqrt_not_ext # no; go handle sgl or dbl
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsqrt.x (%a0),%fp0 # execute square root
fmov.l %fpsr,%d1
or.l %d1,USER_FPSR(%a6) # set N,INEX
rts
fsqrt_denorm:
tst.b SRC_EX(%a0) # is operand negative?
bmi.l res_operr # yes
andi.b &0xc0,%d0 # is precision extended?
bne.b fsqrt_not_ext # no; go handle sgl or dbl
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_sqrt # calculate scale factor
bra.w fsqrt_sd_normal
#
# operand is either single or double
#
fsqrt_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.w fsqrt_dbl
#
# operand is to be rounded to single precision
#
fsqrt_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_sqrt # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f81 # will move in underflow?
beq.w fsqrt_sd_may_unfl
bgt.w fsqrt_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407f # will move in overflow?
beq.w fsqrt_sd_may_ovfl # maybe; go check
blt.w fsqrt_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved in to the fp reg file
#
fsqrt_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsqrt.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsqrt_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load sgn,exp
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fsqrt_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_sqrt # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c01 # will move in underflow?
beq.w fsqrt_sd_may_unfl
bgt.b fsqrt_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43ff # will move in overflow?
beq.w fsqrt_sd_may_ovfl # maybe; go check
blt.w fsqrt_sd_ovfl # yes; go handle overflow
bra.w fsqrt_sd_normal # no; ho handle normalized op
# we're on the line here and the distinguising characteristic is whether
# the exponent is 3fff or 3ffe. if it's 3ffe, then it's a safe number
# elsewise fall through to underflow.
fsqrt_sd_may_unfl:
btst &0x0,1+FP_SCR0_EX(%a6) # is exponent 0x3fff?
bne.w fsqrt_sd_normal # yes, so no underflow
#
# operand WILL underflow when moved in to the fp register file
#
fsqrt_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsqrt.x FP_SCR0(%a6),%fp0 # execute square root
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
# if underflow or inexact is enabled, go calculate EXOP first.
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsqrt_sd_unfl_ena # yes
fsqrt_sd_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set possible 'Z' ccode
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow is enabled.
# therefore, we must return the result rounded to extended precision.
#
fsqrt_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # subtract scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat new sign,new exp
mov.w %d1,FP_SCR1_EX(%a6) # insert new exp
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fsqrt_sd_unfl_dis
#
# operand WILL overflow.
#
fsqrt_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsqrt.x FP_SCR0(%a6),%fp0 # perform square root
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsqrt_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fsqrt_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fsqrt_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fsqrt_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign
sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat sign,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fsqrt_sd_ovfl_dis
#
# the move in MAY underflow. so...
#
fsqrt_sd_may_ovfl:
btst &0x0,1+FP_SCR0_EX(%a6) # is exponent 0x3fff?
bne.w fsqrt_sd_ovfl # yes, so overflow
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsqrt.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fmov.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x1 # is |result| >= 1.b?
fbge.w fsqrt_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fsqrt_sd_normal_exit
##########################################################################
#
# input is not normalized; what is it?
#
fsqrt_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fsqrt_denorm
cmpi.b %d1,&ZERO # weed out ZERO
beq.b fsqrt_zero
cmpi.b %d1,&INF # weed out INF
beq.b fsqrt_inf
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
bra.l res_qnan_1op
#
# fsqrt(+0) = +0
# fsqrt(-0) = -0
# fsqrt(+INF) = +INF
# fsqrt(-INF) = OPERR
#
fsqrt_zero:
tst.b SRC_EX(%a0) # is ZERO positive or negative?
bmi.b fsqrt_zero_m # negative
fsqrt_zero_p:
fmov.s &0x00000000,%fp0 # return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set 'Z' ccode bit
rts
fsqrt_zero_m:
fmov.s &0x80000000,%fp0 # return -ZERO
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set 'Z','N' ccode bits
rts
fsqrt_inf:
tst.b SRC_EX(%a0) # is INF positive or negative?
bmi.l res_operr # negative
fsqrt_inf_p:
fmovm.x SRC(%a0),&0x80 # return +INF in fp0
mov.b &inf_bmask,FPSR_CC(%a6) # set 'I' ccode bit
rts
##########################################################################
#########################################################################
# XDEF **************************************************************** #
# addsub_scaler2(): scale inputs to fadd/fsub such that no #
# OVFL/UNFL exceptions will result #
# #
# XREF **************************************************************** #
# norm() - normalize mantissa after adjusting exponent #
# #
# INPUT *************************************************************** #
# FP_SRC(a6) = fp op1(src) #
# FP_DST(a6) = fp op2(dst) #
# #
# OUTPUT ************************************************************** #
# FP_SRC(a6) = fp op1 scaled(src) #
# FP_DST(a6) = fp op2 scaled(dst) #
# d0 = scale amount #
# #
# ALGORITHM *********************************************************** #
# If the DST exponent is > the SRC exponent, set the DST exponent #
# equal to 0x3fff and scale the SRC exponent by the value that the #
# DST exponent was scaled by. If the SRC exponent is greater or equal, #
# do the opposite. Return this scale factor in d0. #
# If the two exponents differ by > the number of mantissa bits #
# plus two, then set the smallest exponent to a very small value as a #
# quick shortcut. #
# #
#########################################################################
global addsub_scaler2
addsub_scaler2:
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l DST_HI(%a1),FP_SCR1_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.w SRC_EX(%a0),%d0
mov.w DST_EX(%a1),%d1
mov.w %d0,FP_SCR0_EX(%a6)
mov.w %d1,FP_SCR1_EX(%a6)
andi.w &0x7fff,%d0
andi.w &0x7fff,%d1
mov.w %d0,L_SCR1(%a6) # store src exponent
mov.w %d1,2+L_SCR1(%a6) # store dst exponent
cmp.w %d0, %d1 # is src exp >= dst exp?
bge.l src_exp_ge2
# dst exp is > src exp; scale dst to exp = 0x3fff
dst_exp_gt2:
bsr.l scale_to_zero_dst
mov.l %d0,-(%sp) # save scale factor
cmpi.b STAG(%a6),&DENORM # is dst denormalized?
bne.b cmpexp12
lea FP_SCR0(%a6),%a0
bsr.l norm # normalize the denorm; result is new exp
neg.w %d0 # new exp = -(shft val)
mov.w %d0,L_SCR1(%a6) # inset new exp
cmpexp12:
mov.w 2+L_SCR1(%a6),%d0
subi.w &mantissalen+2,%d0 # subtract mantissalen+2 from larger exp
cmp.w %d0,L_SCR1(%a6) # is difference >= len(mantissa)+2?
bge.b quick_scale12
mov.w L_SCR1(%a6),%d0
add.w 0x2(%sp),%d0 # scale src exponent by scale factor
mov.w FP_SCR0_EX(%a6),%d1
and.w &0x8000,%d1
or.w %d1,%d0 # concat {sgn,new exp}
mov.w %d0,FP_SCR0_EX(%a6) # insert new dst exponent
mov.l (%sp)+,%d0 # return SCALE factor
rts
quick_scale12:
andi.w &0x8000,FP_SCR0_EX(%a6) # zero src exponent
bset &0x0,1+FP_SCR0_EX(%a6) # set exp = 1
mov.l (%sp)+,%d0 # return SCALE factor
rts
# src exp is >= dst exp; scale src to exp = 0x3fff
src_exp_ge2:
bsr.l scale_to_zero_src
mov.l %d0,-(%sp) # save scale factor
cmpi.b DTAG(%a6),&DENORM # is dst denormalized?
bne.b cmpexp22
lea FP_SCR1(%a6),%a0
bsr.l norm # normalize the denorm; result is new exp
neg.w %d0 # new exp = -(shft val)
mov.w %d0,2+L_SCR1(%a6) # inset new exp
cmpexp22:
mov.w L_SCR1(%a6),%d0
subi.w &mantissalen+2,%d0 # subtract mantissalen+2 from larger exp
cmp.w %d0,2+L_SCR1(%a6) # is difference >= len(mantissa)+2?
bge.b quick_scale22
mov.w 2+L_SCR1(%a6),%d0
add.w 0x2(%sp),%d0 # scale dst exponent by scale factor
mov.w FP_SCR1_EX(%a6),%d1
andi.w &0x8000,%d1
or.w %d1,%d0 # concat {sgn,new exp}
mov.w %d0,FP_SCR1_EX(%a6) # insert new dst exponent
mov.l (%sp)+,%d0 # return SCALE factor
rts
quick_scale22:
andi.w &0x8000,FP_SCR1_EX(%a6) # zero dst exponent
bset &0x0,1+FP_SCR1_EX(%a6) # set exp = 1
mov.l (%sp)+,%d0 # return SCALE factor
rts
##########################################################################
#########################################################################
# XDEF **************************************************************** #
# scale_to_zero_src(): scale the exponent of extended precision #
# value at FP_SCR0(a6). #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa if the operand was a DENORM #
# #
# INPUT *************************************************************** #
# FP_SCR0(a6) = extended precision operand to be scaled #
# #
# OUTPUT ************************************************************** #
# FP_SCR0(a6) = scaled extended precision operand #
# d0 = scale value #
# #
# ALGORITHM *********************************************************** #
# Set the exponent of the input operand to 0x3fff. Save the value #
# of the difference between the original and new exponent. Then, #
# normalize the operand if it was a DENORM. Add this normalization #
# value to the previous value. Return the result. #
# #
#########################################################################
global scale_to_zero_src
scale_to_zero_src:
mov.w FP_SCR0_EX(%a6),%d1 # extract operand's {sgn,exp}
mov.w %d1,%d0 # make a copy
andi.l &0x7fff,%d1 # extract operand's exponent
andi.w &0x8000,%d0 # extract operand's sgn
or.w &0x3fff,%d0 # insert new operand's exponent(=0)
mov.w %d0,FP_SCR0_EX(%a6) # insert biased exponent
cmpi.b STAG(%a6),&DENORM # is operand normalized?
beq.b stzs_denorm # normalize the DENORM
stzs_norm:
mov.l &0x3fff,%d0
sub.l %d1,%d0 # scale = BIAS + (-exp)
rts
stzs_denorm:
lea FP_SCR0(%a6),%a0 # pass ptr to src op
bsr.l norm # normalize denorm
neg.l %d0 # new exponent = -(shft val)
mov.l %d0,%d1 # prepare for op_norm call
bra.b stzs_norm # finish scaling
###
#########################################################################
# XDEF **************************************************************** #
# scale_sqrt(): scale the input operand exponent so a subsequent #
# fsqrt operation won't take an exception. #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa if the operand was a DENORM #
# #
# INPUT *************************************************************** #
# FP_SCR0(a6) = extended precision operand to be scaled #
# #
# OUTPUT ************************************************************** #
# FP_SCR0(a6) = scaled extended precision operand #
# d0 = scale value #
# #
# ALGORITHM *********************************************************** #
# If the input operand is a DENORM, normalize it. #
# If the exponent of the input operand is even, set the exponent #
# to 0x3ffe and return a scale factor of "(exp-0x3ffe)/2". If the #
# exponent of the input operand is off, set the exponent to ox3fff and #
# return a scale factor of "(exp-0x3fff)/2". #
# #
#########################################################################
global scale_sqrt
scale_sqrt:
cmpi.b STAG(%a6),&DENORM # is operand normalized?
beq.b ss_denorm # normalize the DENORM
mov.w FP_SCR0_EX(%a6),%d1 # extract operand's {sgn,exp}
andi.l &0x7fff,%d1 # extract operand's exponent
andi.w &0x8000,FP_SCR0_EX(%a6) # extract operand's sgn
btst &0x0,%d1 # is exp even or odd?
beq.b ss_norm_even
ori.w &0x3fff,FP_SCR0_EX(%a6) # insert new operand's exponent(=0)
mov.l &0x3fff,%d0
sub.l %d1,%d0 # scale = BIAS + (-exp)
asr.l &0x1,%d0 # divide scale factor by 2
rts
ss_norm_even:
ori.w &0x3ffe,FP_SCR0_EX(%a6) # insert new operand's exponent(=0)
mov.l &0x3ffe,%d0
sub.l %d1,%d0 # scale = BIAS + (-exp)
asr.l &0x1,%d0 # divide scale factor by 2
rts
ss_denorm:
lea FP_SCR0(%a6),%a0 # pass ptr to src op
bsr.l norm # normalize denorm
btst &0x0,%d0 # is exp even or odd?
beq.b ss_denorm_even
ori.w &0x3fff,FP_SCR0_EX(%a6) # insert new operand's exponent(=0)
add.l &0x3fff,%d0
asr.l &0x1,%d0 # divide scale factor by 2
rts
ss_denorm_even:
ori.w &0x3ffe,FP_SCR0_EX(%a6) # insert new operand's exponent(=0)
add.l &0x3ffe,%d0
asr.l &0x1,%d0 # divide scale factor by 2
rts
###
#########################################################################
# XDEF **************************************************************** #
# scale_to_zero_dst(): scale the exponent of extended precision #
# value at FP_SCR1(a6). #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa if the operand was a DENORM #
# #
# INPUT *************************************************************** #
# FP_SCR1(a6) = extended precision operand to be scaled #
# #
# OUTPUT ************************************************************** #
# FP_SCR1(a6) = scaled extended precision operand #
# d0 = scale value #
# #
# ALGORITHM *********************************************************** #
# Set the exponent of the input operand to 0x3fff. Save the value #
# of the difference between the original and new exponent. Then, #
# normalize the operand if it was a DENORM. Add this normalization #
# value to the previous value. Return the result. #
# #
#########################################################################
global scale_to_zero_dst
scale_to_zero_dst:
mov.w FP_SCR1_EX(%a6),%d1 # extract operand's {sgn,exp}
mov.w %d1,%d0 # make a copy
andi.l &0x7fff,%d1 # extract operand's exponent
andi.w &0x8000,%d0 # extract operand's sgn
or.w &0x3fff,%d0 # insert new operand's exponent(=0)
mov.w %d0,FP_SCR1_EX(%a6) # insert biased exponent
cmpi.b DTAG(%a6),&DENORM # is operand normalized?
beq.b stzd_denorm # normalize the DENORM
stzd_norm:
mov.l &0x3fff,%d0
sub.l %d1,%d0 # scale = BIAS + (-exp)
rts
stzd_denorm:
lea FP_SCR1(%a6),%a0 # pass ptr to dst op
bsr.l norm # normalize denorm
neg.l %d0 # new exponent = -(shft val)
mov.l %d0,%d1 # prepare for op_norm call
bra.b stzd_norm # finish scaling
##########################################################################
#########################################################################
# XDEF **************************************************************** #
# res_qnan(): return default result w/ QNAN operand for dyadic #
# res_snan(): return default result w/ SNAN operand for dyadic #
# res_qnan_1op(): return dflt result w/ QNAN operand for monadic #
# res_snan_1op(): return dflt result w/ SNAN operand for monadic #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# FP_SRC(a6) = pointer to extended precision src operand #
# FP_DST(a6) = pointer to extended precision dst operand #
# #
# OUTPUT ************************************************************** #
# fp0 = default result #
# #
# ALGORITHM *********************************************************** #
# If either operand (but not both operands) of an operation is a #
# nonsignalling NAN, then that NAN is returned as the result. If both #
# operands are nonsignalling NANs, then the destination operand #
# nonsignalling NAN is returned as the result. #
# If either operand to an operation is a signalling NAN (SNAN), #
# then, the SNAN bit is set in the FPSR EXC byte. If the SNAN trap #
# enable bit is set in the FPCR, then the trap is taken and the #
# destination is not modified. If the SNAN trap enable bit is not set, #
# then the SNAN is converted to a nonsignalling NAN (by setting the #
# SNAN bit in the operand to one), and the operation continues as #
# described in the preceding paragraph, for nonsignalling NANs. #
# Make sure the appropriate FPSR bits are set before exiting. #
# #
#########################################################################
global res_qnan
global res_snan
res_qnan:
res_snan:
cmp.b DTAG(%a6), &SNAN # is the dst an SNAN?
beq.b dst_snan2
cmp.b DTAG(%a6), &QNAN # is the dst a QNAN?
beq.b dst_qnan2
src_nan:
cmp.b STAG(%a6), &QNAN
beq.b src_qnan2
global res_snan_1op
res_snan_1op:
src_snan2:
bset &0x6, FP_SRC_HI(%a6) # set SNAN bit
or.l &nan_mask+aiop_mask+snan_mask, USER_FPSR(%a6)
lea FP_SRC(%a6), %a0
bra.b nan_comp
global res_qnan_1op
res_qnan_1op:
src_qnan2:
or.l &nan_mask, USER_FPSR(%a6)
lea FP_SRC(%a6), %a0
bra.b nan_comp
dst_snan2:
or.l &nan_mask+aiop_mask+snan_mask, USER_FPSR(%a6)
bset &0x6, FP_DST_HI(%a6) # set SNAN bit
lea FP_DST(%a6), %a0
bra.b nan_comp
dst_qnan2:
lea FP_DST(%a6), %a0
cmp.b STAG(%a6), &SNAN
bne nan_done
or.l &aiop_mask+snan_mask, USER_FPSR(%a6)
nan_done:
or.l &nan_mask, USER_FPSR(%a6)
nan_comp:
btst &0x7, FTEMP_EX(%a0) # is NAN neg?
beq.b nan_not_neg
or.l &neg_mask, USER_FPSR(%a6)
nan_not_neg:
fmovm.x (%a0), &0x80
rts
#########################################################################
# XDEF **************************************************************** #
# res_operr(): return default result during operand error #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# fp0 = default operand error result #
# #
# ALGORITHM *********************************************************** #
# An nonsignalling NAN is returned as the default result when #
# an operand error occurs for the following cases: #
# #
# Multiply: (Infinity x Zero) #
# Divide : (Zero / Zero) || (Infinity / Infinity) #
# #
#########################################################################
global res_operr
res_operr:
or.l &nan_mask+operr_mask+aiop_mask, USER_FPSR(%a6)
fmovm.x nan_return(%pc), &0x80
rts
nan_return:
long 0x7fff0000, 0xffffffff, 0xffffffff
#########################################################################
# fdbcc(): routine to emulate the fdbcc instruction #
# #
# XDEF **************************************************************** #
# _fdbcc() #
# #
# XREF **************************************************************** #
# fetch_dreg() - fetch Dn value #
# store_dreg_l() - store updated Dn value #
# #
# INPUT *************************************************************** #
# d0 = displacement #
# #
# OUTPUT ************************************************************** #
# none #
# #
# ALGORITHM *********************************************************** #
# This routine checks which conditional predicate is specified by #
# the stacked fdbcc instruction opcode and then branches to a routine #
# for that predicate. The corresponding fbcc instruction is then used #
# to see whether the condition (specified by the stacked FPSR) is true #
# or false. #
# If a BSUN exception should be indicated, the BSUN and ABSUN #
# bits are set in the stacked FPSR. If the BSUN exception is enabled, #
# the fbsun_flg is set in the SPCOND_FLG location on the stack. If an #
# enabled BSUN should not be flagged and the predicate is true, then #
# Dn is fetched and decremented by one. If Dn is not equal to -1, add #
# the displacement value to the stacked PC so that when an "rte" is #
# finally executed, the branch occurs. #
# #
#########################################################################
global _fdbcc
_fdbcc:
mov.l %d0,L_SCR1(%a6) # save displacement
mov.w EXC_CMDREG(%a6),%d0 # fetch predicate
clr.l %d1 # clear scratch reg
mov.b FPSR_CC(%a6),%d1 # fetch fp ccodes
ror.l &0x8,%d1 # rotate to top byte
fmov.l %d1,%fpsr # insert into FPSR
mov.w (tbl_fdbcc.b,%pc,%d0.w*2),%d1 # load table
jmp (tbl_fdbcc.b,%pc,%d1.w) # jump to fdbcc routine
tbl_fdbcc:
short fdbcc_f - tbl_fdbcc # 00
short fdbcc_eq - tbl_fdbcc # 01
short fdbcc_ogt - tbl_fdbcc # 02
short fdbcc_oge - tbl_fdbcc # 03
short fdbcc_olt - tbl_fdbcc # 04
short fdbcc_ole - tbl_fdbcc # 05
short fdbcc_ogl - tbl_fdbcc # 06
short fdbcc_or - tbl_fdbcc # 07
short fdbcc_un - tbl_fdbcc # 08
short fdbcc_ueq - tbl_fdbcc # 09
short fdbcc_ugt - tbl_fdbcc # 10
short fdbcc_uge - tbl_fdbcc # 11
short fdbcc_ult - tbl_fdbcc # 12
short fdbcc_ule - tbl_fdbcc # 13
short fdbcc_neq - tbl_fdbcc # 14
short fdbcc_t - tbl_fdbcc # 15
short fdbcc_sf - tbl_fdbcc # 16
short fdbcc_seq - tbl_fdbcc # 17
short fdbcc_gt - tbl_fdbcc # 18
short fdbcc_ge - tbl_fdbcc # 19
short fdbcc_lt - tbl_fdbcc # 20
short fdbcc_le - tbl_fdbcc # 21
short fdbcc_gl - tbl_fdbcc # 22
short fdbcc_gle - tbl_fdbcc # 23
short fdbcc_ngle - tbl_fdbcc # 24
short fdbcc_ngl - tbl_fdbcc # 25
short fdbcc_nle - tbl_fdbcc # 26
short fdbcc_nlt - tbl_fdbcc # 27
short fdbcc_nge - tbl_fdbcc # 28
short fdbcc_ngt - tbl_fdbcc # 29
short fdbcc_sneq - tbl_fdbcc # 30
short fdbcc_st - tbl_fdbcc # 31
#########################################################################
# #
# IEEE Nonaware tests #
# #
# For the IEEE nonaware tests, only the false branch changes the #
# counter. However, the true branch may set bsun so we check to see #
# if the NAN bit is set, in which case BSUN and AIOP will be set. #
# #
# The cases EQ and NE are shared by the Aware and Nonaware groups #
# and are incapable of setting the BSUN exception bit. #
# #
# Typically, only one of the two possible branch directions could #
# have the NAN bit set. #
# (This is assuming the mutual exclusiveness of FPSR cc bit groupings #
# is preserved.) #
# #
#########################################################################
#
# equal:
#
# Z
#
fdbcc_eq:
fbeq.w fdbcc_eq_yes # equal?
fdbcc_eq_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_eq_yes:
rts
#
# not equal:
# _
# Z
#
fdbcc_neq:
fbneq.w fdbcc_neq_yes # not equal?
fdbcc_neq_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_neq_yes:
rts
#
# greater than:
# _______
# NANvZvN
#
fdbcc_gt:
fbgt.w fdbcc_gt_yes # greater than?
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_gt_yes:
rts # do nothing
#
# not greater than:
#
# NANvZvN
#
fdbcc_ngt:
fbngt.w fdbcc_ngt_yes # not greater than?
fdbcc_ngt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ngt_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_ngt_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_ngt_done:
rts # no; do nothing
#
# greater than or equal:
# _____
# Zv(NANvN)
#
fdbcc_ge:
fbge.w fdbcc_ge_yes # greater than or equal?
fdbcc_ge_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_ge_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_ge_yes_done # no;go do nothing
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_ge_yes_done:
rts # do nothing
#
# not (greater than or equal):
# _
# NANv(N^Z)
#
fdbcc_nge:
fbnge.w fdbcc_nge_yes # not (greater than or equal)?
fdbcc_nge_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_nge_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_nge_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_nge_done:
rts # no; do nothing
#
# less than:
# _____
# N^(NANvZ)
#
fdbcc_lt:
fblt.w fdbcc_lt_yes # less than?
fdbcc_lt_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no; go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_lt_yes:
rts # do nothing
#
# not less than:
# _
# NANv(ZvN)
#
fdbcc_nlt:
fbnlt.w fdbcc_nlt_yes # not less than?
fdbcc_nlt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_nlt_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_nlt_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_nlt_done:
rts # no; do nothing
#
# less than or equal:
# ___
# Zv(N^NAN)
#
fdbcc_le:
fble.w fdbcc_le_yes # less than or equal?
fdbcc_le_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no; go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_le_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_le_yes_done # no; go do nothing
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_le_yes_done:
rts # do nothing
#
# not (less than or equal):
# ___
# NANv(NvZ)
#
fdbcc_nle:
fbnle.w fdbcc_nle_yes # not (less than or equal)?
fdbcc_nle_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_nle_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_nle_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_nle_done:
rts # no; do nothing
#
# greater or less than:
# _____
# NANvZ
#
fdbcc_gl:
fbgl.w fdbcc_gl_yes # greater or less than?
fdbcc_gl_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no; handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_gl_yes:
rts # do nothing
#
# not (greater or less than):
#
# NANvZ
#
fdbcc_ngl:
fbngl.w fdbcc_ngl_yes # not (greater or less than)?
fdbcc_ngl_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ngl_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_ngl_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_ngl_done:
rts # no; do nothing
#
# greater, less, or equal:
# ___
# NAN
#
fdbcc_gle:
fbgle.w fdbcc_gle_yes # greater, less, or equal?
fdbcc_gle_no:
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_gle_yes:
rts # do nothing
#
# not (greater, less, or equal):
#
# NAN
#
fdbcc_ngle:
fbngle.w fdbcc_ngle_yes # not (greater, less, or equal)?
fdbcc_ngle_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ngle_yes:
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
rts # no; do nothing
#########################################################################
# #
# Miscellaneous tests #
# #
# For the IEEE miscellaneous tests, all but fdbf and fdbt can set bsun. #
# #
#########################################################################
#
# false:
#
# False
#
fdbcc_f: # no bsun possible
bra.w fdbcc_false # go handle counter
#
# true:
#
# True
#
fdbcc_t: # no bsun possible
rts # do nothing
#
# signalling false:
#
# False
#
fdbcc_sf:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # go handle counter
#
# signalling true:
#
# True
#
fdbcc_st:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.b fdbcc_st_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_st_done:
rts
#
# signalling equal:
#
# Z
#
fdbcc_seq:
fbseq.w fdbcc_seq_yes # signalling equal?
fdbcc_seq_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # go handle counter
fdbcc_seq_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.b fdbcc_seq_yes_done # no;go do nothing
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_seq_yes_done:
rts # yes; do nothing
#
# signalling not equal:
# _
# Z
#
fdbcc_sneq:
fbsneq.w fdbcc_sneq_yes # signalling not equal?
fdbcc_sneq_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # go handle counter
fdbcc_sneq_yes:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fdbcc_sneq_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_sneq_done:
rts
#########################################################################
# #
# IEEE Aware tests #
# #
# For the IEEE aware tests, action is only taken if the result is false.#
# Therefore, the opposite branch type is used to jump to the decrement #
# routine. #
# The BSUN exception will not be set for any of these tests. #
# #
#########################################################################
#
# ordered greater than:
# _______
# NANvZvN
#
fdbcc_ogt:
fbogt.w fdbcc_ogt_yes # ordered greater than?
fdbcc_ogt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ogt_yes:
rts # yes; do nothing
#
# unordered or less or equal:
# _______
# NANvZvN
#
fdbcc_ule:
fbule.w fdbcc_ule_yes # unordered or less or equal?
fdbcc_ule_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ule_yes:
rts # yes; do nothing
#
# ordered greater than or equal:
# _____
# Zv(NANvN)
#
fdbcc_oge:
fboge.w fdbcc_oge_yes # ordered greater than or equal?
fdbcc_oge_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_oge_yes:
rts # yes; do nothing
#
# unordered or less than:
# _
# NANv(N^Z)
#
fdbcc_ult:
fbult.w fdbcc_ult_yes # unordered or less than?
fdbcc_ult_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ult_yes:
rts # yes; do nothing
#
# ordered less than:
# _____
# N^(NANvZ)
#
fdbcc_olt:
fbolt.w fdbcc_olt_yes # ordered less than?
fdbcc_olt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_olt_yes:
rts # yes; do nothing
#
# unordered or greater or equal:
#
# NANvZvN
#
fdbcc_uge:
fbuge.w fdbcc_uge_yes # unordered or greater than?
fdbcc_uge_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_uge_yes:
rts # yes; do nothing
#
# ordered less than or equal:
# ___
# Zv(N^NAN)
#
fdbcc_ole:
fbole.w fdbcc_ole_yes # ordered greater or less than?
fdbcc_ole_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ole_yes:
rts # yes; do nothing
#
# unordered or greater than:
# ___
# NANv(NvZ)
#
fdbcc_ugt:
fbugt.w fdbcc_ugt_yes # unordered or greater than?
fdbcc_ugt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ugt_yes:
rts # yes; do nothing
#
# ordered greater or less than:
# _____
# NANvZ
#
fdbcc_ogl:
fbogl.w fdbcc_ogl_yes # ordered greater or less than?
fdbcc_ogl_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ogl_yes:
rts # yes; do nothing
#
# unordered or equal:
#
# NANvZ
#
fdbcc_ueq:
fbueq.w fdbcc_ueq_yes # unordered or equal?
fdbcc_ueq_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ueq_yes:
rts # yes; do nothing
#
# ordered:
# ___
# NAN
#
fdbcc_or:
fbor.w fdbcc_or_yes # ordered?
fdbcc_or_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_or_yes:
rts # yes; do nothing
#
# unordered:
#
# NAN
#
fdbcc_un:
fbun.w fdbcc_un_yes # unordered?
fdbcc_un_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_un_yes:
rts # yes; do nothing
#######################################################################
#
# the bsun exception bit was not set.
#
# (1) subtract 1 from the count register
# (2) if (cr == -1) then
# pc = pc of next instruction
# else
# pc += sign_ext(16-bit displacement)
#
fdbcc_false:
mov.b 1+EXC_OPWORD(%a6), %d1 # fetch lo opword
andi.w &0x7, %d1 # extract count register
bsr.l fetch_dreg # fetch count value
# make sure that d0 isn't corrupted between calls...
subq.w &0x1, %d0 # Dn - 1 -> Dn
bsr.l store_dreg_l # store new count value
cmpi.w %d0, &-0x1 # is (Dn == -1)?
bne.b fdbcc_false_cont # no;
rts
fdbcc_false_cont:
mov.l L_SCR1(%a6),%d0 # fetch displacement
add.l USER_FPIAR(%a6),%d0 # add instruction PC
addq.l &0x4,%d0 # add instruction length
mov.l %d0,EXC_PC(%a6) # set new PC
rts
# the emulation routine set bsun and BSUN was enabled. have to
# fix stack and jump to the bsun handler.
# let the caller of this routine shift the stack frame up to
# eliminate the effective address field.
fdbcc_bsun:
mov.b &fbsun_flg,SPCOND_FLG(%a6)
rts
#########################################################################
# ftrapcc(): routine to emulate the ftrapcc instruction #
# #
# XDEF **************************************************************** #
# _ftrapcc() #
# #
# XREF **************************************************************** #
# none #
# #
# INPUT *************************************************************** #
# none #
# #
# OUTPUT ************************************************************** #
# none #
# #
# ALGORITHM *********************************************************** #
# This routine checks which conditional predicate is specified by #
# the stacked ftrapcc instruction opcode and then branches to a routine #
# for that predicate. The corresponding fbcc instruction is then used #
# to see whether the condition (specified by the stacked FPSR) is true #
# or false. #
# If a BSUN exception should be indicated, the BSUN and ABSUN #
# bits are set in the stacked FPSR. If the BSUN exception is enabled, #
# the fbsun_flg is set in the SPCOND_FLG location on the stack. If an #
# enabled BSUN should not be flagged and the predicate is true, then #
# the ftrapcc_flg is set in the SPCOND_FLG location. These special #
# flags indicate to the calling routine to emulate the exceptional #
# condition. #
# #
#########################################################################
global _ftrapcc
_ftrapcc:
mov.w EXC_CMDREG(%a6),%d0 # fetch predicate
clr.l %d1 # clear scratch reg
mov.b FPSR_CC(%a6),%d1 # fetch fp ccodes
ror.l &0x8,%d1 # rotate to top byte
fmov.l %d1,%fpsr # insert into FPSR
mov.w (tbl_ftrapcc.b,%pc,%d0.w*2), %d1 # load table
jmp (tbl_ftrapcc.b,%pc,%d1.w) # jump to ftrapcc routine
tbl_ftrapcc:
short ftrapcc_f - tbl_ftrapcc # 00
short ftrapcc_eq - tbl_ftrapcc # 01
short ftrapcc_ogt - tbl_ftrapcc # 02
short ftrapcc_oge - tbl_ftrapcc # 03
short ftrapcc_olt - tbl_ftrapcc # 04
short ftrapcc_ole - tbl_ftrapcc # 05
short ftrapcc_ogl - tbl_ftrapcc # 06
short ftrapcc_or - tbl_ftrapcc # 07
short ftrapcc_un - tbl_ftrapcc # 08
short ftrapcc_ueq - tbl_ftrapcc # 09
short ftrapcc_ugt - tbl_ftrapcc # 10
short ftrapcc_uge - tbl_ftrapcc # 11
short ftrapcc_ult - tbl_ftrapcc # 12
short ftrapcc_ule - tbl_ftrapcc # 13
short ftrapcc_neq - tbl_ftrapcc # 14
short ftrapcc_t - tbl_ftrapcc # 15
short ftrapcc_sf - tbl_ftrapcc # 16
short ftrapcc_seq - tbl_ftrapcc # 17
short ftrapcc_gt - tbl_ftrapcc # 18
short ftrapcc_ge - tbl_ftrapcc # 19
short ftrapcc_lt - tbl_ftrapcc # 20
short ftrapcc_le - tbl_ftrapcc # 21
short ftrapcc_gl - tbl_ftrapcc # 22
short ftrapcc_gle - tbl_ftrapcc # 23
short ftrapcc_ngle - tbl_ftrapcc # 24
short ftrapcc_ngl - tbl_ftrapcc # 25
short ftrapcc_nle - tbl_ftrapcc # 26
short ftrapcc_nlt - tbl_ftrapcc # 27
short ftrapcc_nge - tbl_ftrapcc # 28
short ftrapcc_ngt - tbl_ftrapcc # 29
short ftrapcc_sneq - tbl_ftrapcc # 30
short ftrapcc_st - tbl_ftrapcc # 31
#########################################################################
# #
# IEEE Nonaware tests #
# #
# For the IEEE nonaware tests, we set the result based on the #
# floating point condition codes. In addition, we check to see #
# if the NAN bit is set, in which case BSUN and AIOP will be set. #
# #
# The cases EQ and NE are shared by the Aware and Nonaware groups #
# and are incapable of setting the BSUN exception bit. #
# #
# Typically, only one of the two possible branch directions could #
# have the NAN bit set. #
# #
#########################################################################
#
# equal:
#
# Z
#
ftrapcc_eq:
fbeq.w ftrapcc_trap # equal?
ftrapcc_eq_no:
rts # do nothing
#
# not equal:
# _
# Z
#
ftrapcc_neq:
fbneq.w ftrapcc_trap # not equal?
ftrapcc_neq_no:
rts # do nothing
#
# greater than:
# _______
# NANvZvN
#
ftrapcc_gt:
fbgt.w ftrapcc_trap # greater than?
ftrapcc_gt_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b ftrapcc_gt_done # no
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_gt_done:
rts # no; do nothing
#
# not greater than:
#
# NANvZvN
#
ftrapcc_ngt:
fbngt.w ftrapcc_ngt_yes # not greater than?
ftrapcc_ngt_no:
rts # do nothing
ftrapcc_ngt_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# greater than or equal:
# _____
# Zv(NANvN)
#
ftrapcc_ge:
fbge.w ftrapcc_ge_yes # greater than or equal?
ftrapcc_ge_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b ftrapcc_ge_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_ge_done:
rts # no; do nothing
ftrapcc_ge_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# not (greater than or equal):
# _
# NANv(N^Z)
#
ftrapcc_nge:
fbnge.w ftrapcc_nge_yes # not (greater than or equal)?
ftrapcc_nge_no:
rts # do nothing
ftrapcc_nge_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# less than:
# _____
# N^(NANvZ)
#
ftrapcc_lt:
fblt.w ftrapcc_trap # less than?
ftrapcc_lt_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b ftrapcc_lt_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_lt_done:
rts # no; do nothing
#
# not less than:
# _
# NANv(ZvN)
#
ftrapcc_nlt:
fbnlt.w ftrapcc_nlt_yes # not less than?
ftrapcc_nlt_no:
rts # do nothing
ftrapcc_nlt_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# less than or equal:
# ___
# Zv(N^NAN)
#
ftrapcc_le:
fble.w ftrapcc_le_yes # less than or equal?
ftrapcc_le_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b ftrapcc_le_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_le_done:
rts # no; do nothing
ftrapcc_le_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# not (less than or equal):
# ___
# NANv(NvZ)
#
ftrapcc_nle:
fbnle.w ftrapcc_nle_yes # not (less than or equal)?
ftrapcc_nle_no:
rts # do nothing
ftrapcc_nle_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# greater or less than:
# _____
# NANvZ
#
ftrapcc_gl:
fbgl.w ftrapcc_trap # greater or less than?
ftrapcc_gl_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b ftrapcc_gl_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_gl_done:
rts # no; do nothing
#
# not (greater or less than):
#
# NANvZ
#
ftrapcc_ngl:
fbngl.w ftrapcc_ngl_yes # not (greater or less than)?
ftrapcc_ngl_no:
rts # do nothing
ftrapcc_ngl_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# greater, less, or equal:
# ___
# NAN
#
ftrapcc_gle:
fbgle.w ftrapcc_trap # greater, less, or equal?
ftrapcc_gle_no:
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
rts # no; do nothing
#
# not (greater, less, or equal):
#
# NAN
#
ftrapcc_ngle:
fbngle.w ftrapcc_ngle_yes # not (greater, less, or equal)?
ftrapcc_ngle_no:
rts # do nothing
ftrapcc_ngle_yes:
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#########################################################################
# #
# Miscellaneous tests #
# #
# For the IEEE aware tests, we only have to set the result based on the #
# floating point condition codes. The BSUN exception will not be #
# set for any of these tests. #
# #
#########################################################################
#
# false:
#
# False
#
ftrapcc_f:
rts # do nothing
#
# true:
#
# True
#
ftrapcc_t:
bra.w ftrapcc_trap # go take trap
#
# signalling false:
#
# False
#
ftrapcc_sf:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.b ftrapcc_sf_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_sf_done:
rts # no; do nothing
#
# signalling true:
#
# True
#
ftrapcc_st:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# signalling equal:
#
# Z
#
ftrapcc_seq:
fbseq.w ftrapcc_seq_yes # signalling equal?
ftrapcc_seq_no:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w ftrapcc_seq_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_seq_done:
rts # no; do nothing
ftrapcc_seq_yes:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#
# signalling not equal:
# _
# Z
#
ftrapcc_sneq:
fbsneq.w ftrapcc_sneq_yes # signalling equal?
ftrapcc_sneq_no:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w ftrapcc_sneq_no_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
ftrapcc_sneq_no_done:
rts # do nothing
ftrapcc_sneq_yes:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w ftrapcc_trap # no; go take trap
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # was BSUN set?
bne.w ftrapcc_bsun # yes
bra.w ftrapcc_trap # no; go take trap
#########################################################################
# #
# IEEE Aware tests #
# #
# For the IEEE aware tests, we only have to set the result based on the #
# floating point condition codes. The BSUN exception will not be #
# set for any of these tests. #
# #
#########################################################################
#
# ordered greater than:
# _______
# NANvZvN
#
ftrapcc_ogt:
fbogt.w ftrapcc_trap # ordered greater than?
ftrapcc_ogt_no:
rts # do nothing
#
# unordered or less or equal:
# _______
# NANvZvN
#
ftrapcc_ule:
fbule.w ftrapcc_trap # unordered or less or equal?
ftrapcc_ule_no:
rts # do nothing
#
# ordered greater than or equal:
# _____
# Zv(NANvN)
#
ftrapcc_oge:
fboge.w ftrapcc_trap # ordered greater than or equal?
ftrapcc_oge_no:
rts # do nothing
#
# unordered or less than:
# _
# NANv(N^Z)
#
ftrapcc_ult:
fbult.w ftrapcc_trap # unordered or less than?
ftrapcc_ult_no:
rts # do nothing
#
# ordered less than:
# _____
# N^(NANvZ)
#
ftrapcc_olt:
fbolt.w ftrapcc_trap # ordered less than?
ftrapcc_olt_no:
rts # do nothing
#
# unordered or greater or equal:
#
# NANvZvN
#
ftrapcc_uge:
fbuge.w ftrapcc_trap # unordered or greater than?
ftrapcc_uge_no:
rts # do nothing
#
# ordered less than or equal:
# ___
# Zv(N^NAN)
#
ftrapcc_ole:
fbole.w ftrapcc_trap # ordered greater or less than?
ftrapcc_ole_no:
rts # do nothing
#
# unordered or greater than:
# ___
# NANv(NvZ)
#
ftrapcc_ugt:
fbugt.w ftrapcc_trap # unordered or greater than?
ftrapcc_ugt_no:
rts # do nothing
#
# ordered greater or less than:
# _____
# NANvZ
#
ftrapcc_ogl:
fbogl.w ftrapcc_trap # ordered greater or less than?
ftrapcc_ogl_no:
rts # do nothing
#
# unordered or equal:
#
# NANvZ
#
ftrapcc_ueq:
fbueq.w ftrapcc_trap # unordered or equal?
ftrapcc_ueq_no:
rts # do nothing
#
# ordered:
# ___
# NAN
#
ftrapcc_or:
fbor.w ftrapcc_trap # ordered?
ftrapcc_or_no:
rts # do nothing
#
# unordered:
#
# NAN
#
ftrapcc_un:
fbun.w ftrapcc_trap # unordered?
ftrapcc_un_no:
rts # do nothing
#######################################################################
# the bsun exception bit was not set.
# we will need to jump to the ftrapcc vector. the stack frame
# is the same size as that of the fp unimp instruction. the
# only difference is that the <ea> field should hold the PC
# of the ftrapcc instruction and the vector offset field
# should denote the ftrapcc trap.
ftrapcc_trap:
mov.b &ftrapcc_flg,SPCOND_FLG(%a6)
rts
# the emulation routine set bsun and BSUN was enabled. have to
# fix stack and jump to the bsun handler.
# let the caller of this routine shift the stack frame up to
# eliminate the effective address field.
ftrapcc_bsun:
mov.b &fbsun_flg,SPCOND_FLG(%a6)
rts
#########################################################################
# fscc(): routine to emulate the fscc instruction #
# #
# XDEF **************************************************************** #
# _fscc() #
# #
# XREF **************************************************************** #
# store_dreg_b() - store result to data register file #
# dec_areg() - decrement an areg for -(an) mode #
# inc_areg() - increment an areg for (an)+ mode #
# _dmem_write_byte() - store result to memory #
# #
# INPUT *************************************************************** #
# none #
# #
# OUTPUT ************************************************************** #
# none #
# #
# ALGORITHM *********************************************************** #
# This routine checks which conditional predicate is specified by #
# the stacked fscc instruction opcode and then branches to a routine #
# for that predicate. The corresponding fbcc instruction is then used #
# to see whether the condition (specified by the stacked FPSR) is true #
# or false. #
# If a BSUN exception should be indicated, the BSUN and ABSUN #
# bits are set in the stacked FPSR. If the BSUN exception is enabled, #
# the fbsun_flg is set in the SPCOND_FLG location on the stack. If an #
# enabled BSUN should not be flagged and the predicate is true, then #
# the result is stored to the data register file or memory #
# #
#########################################################################
global _fscc
_fscc:
mov.w EXC_CMDREG(%a6),%d0 # fetch predicate
clr.l %d1 # clear scratch reg
mov.b FPSR_CC(%a6),%d1 # fetch fp ccodes
ror.l &0x8,%d1 # rotate to top byte
fmov.l %d1,%fpsr # insert into FPSR
mov.w (tbl_fscc.b,%pc,%d0.w*2),%d1 # load table
jmp (tbl_fscc.b,%pc,%d1.w) # jump to fscc routine
tbl_fscc:
short fscc_f - tbl_fscc # 00
short fscc_eq - tbl_fscc # 01
short fscc_ogt - tbl_fscc # 02
short fscc_oge - tbl_fscc # 03
short fscc_olt - tbl_fscc # 04
short fscc_ole - tbl_fscc # 05
short fscc_ogl - tbl_fscc # 06
short fscc_or - tbl_fscc # 07
short fscc_un - tbl_fscc # 08
short fscc_ueq - tbl_fscc # 09
short fscc_ugt - tbl_fscc # 10
short fscc_uge - tbl_fscc # 11
short fscc_ult - tbl_fscc # 12
short fscc_ule - tbl_fscc # 13
short fscc_neq - tbl_fscc # 14
short fscc_t - tbl_fscc # 15
short fscc_sf - tbl_fscc # 16
short fscc_seq - tbl_fscc # 17
short fscc_gt - tbl_fscc # 18
short fscc_ge - tbl_fscc # 19
short fscc_lt - tbl_fscc # 20
short fscc_le - tbl_fscc # 21
short fscc_gl - tbl_fscc # 22
short fscc_gle - tbl_fscc # 23
short fscc_ngle - tbl_fscc # 24
short fscc_ngl - tbl_fscc # 25
short fscc_nle - tbl_fscc # 26
short fscc_nlt - tbl_fscc # 27
short fscc_nge - tbl_fscc # 28
short fscc_ngt - tbl_fscc # 29
short fscc_sneq - tbl_fscc # 30
short fscc_st - tbl_fscc # 31
#########################################################################
# #
# IEEE Nonaware tests #
# #
# For the IEEE nonaware tests, we set the result based on the #
# floating point condition codes. In addition, we check to see #
# if the NAN bit is set, in which case BSUN and AIOP will be set. #
# #
# The cases EQ and NE are shared by the Aware and Nonaware groups #
# and are incapable of setting the BSUN exception bit. #
# #
# Typically, only one of the two possible branch directions could #
# have the NAN bit set. #
# #
#########################################################################
#
# equal:
#
# Z
#
fscc_eq:
fbeq.w fscc_eq_yes # equal?
fscc_eq_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_eq_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# not equal:
# _
# Z
#
fscc_neq:
fbneq.w fscc_neq_yes # not equal?
fscc_neq_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_neq_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# greater than:
# _______
# NANvZvN
#
fscc_gt:
fbgt.w fscc_gt_yes # greater than?
fscc_gt_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_gt_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# not greater than:
#
# NANvZvN
#
fscc_ngt:
fbngt.w fscc_ngt_yes # not greater than?
fscc_ngt_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ngt_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# greater than or equal:
# _____
# Zv(NANvN)
#
fscc_ge:
fbge.w fscc_ge_yes # greater than or equal?
fscc_ge_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_ge_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# not (greater than or equal):
# _
# NANv(N^Z)
#
fscc_nge:
fbnge.w fscc_nge_yes # not (greater than or equal)?
fscc_nge_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_nge_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# less than:
# _____
# N^(NANvZ)
#
fscc_lt:
fblt.w fscc_lt_yes # less than?
fscc_lt_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_lt_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# not less than:
# _
# NANv(ZvN)
#
fscc_nlt:
fbnlt.w fscc_nlt_yes # not less than?
fscc_nlt_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_nlt_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# less than or equal:
# ___
# Zv(N^NAN)
#
fscc_le:
fble.w fscc_le_yes # less than or equal?
fscc_le_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_le_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# not (less than or equal):
# ___
# NANv(NvZ)
#
fscc_nle:
fbnle.w fscc_nle_yes # not (less than or equal)?
fscc_nle_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_nle_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# greater or less than:
# _____
# NANvZ
#
fscc_gl:
fbgl.w fscc_gl_yes # greater or less than?
fscc_gl_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_gl_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# not (greater or less than):
#
# NANvZ
#
fscc_ngl:
fbngl.w fscc_ngl_yes # not (greater or less than)?
fscc_ngl_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ngl_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# greater, less, or equal:
# ___
# NAN
#
fscc_gle:
fbgle.w fscc_gle_yes # greater, less, or equal?
fscc_gle_no:
clr.b %d0 # set false
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_gle_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# not (greater, less, or equal):
#
# NAN
#
fscc_ngle:
fbngle.w fscc_ngle_yes # not (greater, less, or equal)?
fscc_ngle_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ngle_yes:
st %d0 # set true
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#########################################################################
# #
# Miscellaneous tests #
# #
# For the IEEE aware tests, we only have to set the result based on the #
# floating point condition codes. The BSUN exception will not be #
# set for any of these tests. #
# #
#########################################################################
#
# false:
#
# False
#
fscc_f:
clr.b %d0 # set false
bra.w fscc_done # go finish
#
# true:
#
# True
#
fscc_t:
st %d0 # set true
bra.w fscc_done # go finish
#
# signalling false:
#
# False
#
fscc_sf:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# signalling true:
#
# True
#
fscc_st:
st %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# signalling equal:
#
# Z
#
fscc_seq:
fbseq.w fscc_seq_yes # signalling equal?
fscc_seq_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_seq_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#
# signalling not equal:
# _
# Z
#
fscc_sneq:
fbsneq.w fscc_sneq_yes # signalling equal?
fscc_sneq_no:
clr.b %d0 # set false
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
fscc_sneq_yes:
st %d0 # set true
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fscc_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
bra.w fscc_chk_bsun # go finish
#########################################################################
# #
# IEEE Aware tests #
# #
# For the IEEE aware tests, we only have to set the result based on the #
# floating point condition codes. The BSUN exception will not be #
# set for any of these tests. #
# #
#########################################################################
#
# ordered greater than:
# _______
# NANvZvN
#
fscc_ogt:
fbogt.w fscc_ogt_yes # ordered greater than?
fscc_ogt_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ogt_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# unordered or less or equal:
# _______
# NANvZvN
#
fscc_ule:
fbule.w fscc_ule_yes # unordered or less or equal?
fscc_ule_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ule_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# ordered greater than or equal:
# _____
# Zv(NANvN)
#
fscc_oge:
fboge.w fscc_oge_yes # ordered greater than or equal?
fscc_oge_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_oge_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# unordered or less than:
# _
# NANv(N^Z)
#
fscc_ult:
fbult.w fscc_ult_yes # unordered or less than?
fscc_ult_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ult_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# ordered less than:
# _____
# N^(NANvZ)
#
fscc_olt:
fbolt.w fscc_olt_yes # ordered less than?
fscc_olt_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_olt_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# unordered or greater or equal:
#
# NANvZvN
#
fscc_uge:
fbuge.w fscc_uge_yes # unordered or greater than?
fscc_uge_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_uge_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# ordered less than or equal:
# ___
# Zv(N^NAN)
#
fscc_ole:
fbole.w fscc_ole_yes # ordered greater or less than?
fscc_ole_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ole_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# unordered or greater than:
# ___
# NANv(NvZ)
#
fscc_ugt:
fbugt.w fscc_ugt_yes # unordered or greater than?
fscc_ugt_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ugt_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# ordered greater or less than:
# _____
# NANvZ
#
fscc_ogl:
fbogl.w fscc_ogl_yes # ordered greater or less than?
fscc_ogl_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ogl_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# unordered or equal:
#
# NANvZ
#
fscc_ueq:
fbueq.w fscc_ueq_yes # unordered or equal?
fscc_ueq_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_ueq_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# ordered:
# ___
# NAN
#
fscc_or:
fbor.w fscc_or_yes # ordered?
fscc_or_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_or_yes:
st %d0 # set true
bra.w fscc_done # go finish
#
# unordered:
#
# NAN
#
fscc_un:
fbun.w fscc_un_yes # unordered?
fscc_un_no:
clr.b %d0 # set false
bra.w fscc_done # go finish
fscc_un_yes:
st %d0 # set true
bra.w fscc_done # go finish
#######################################################################
#
# the bsun exception bit was set. now, check to see is BSUN
# is enabled. if so, don't store result and correct stack frame
# for a bsun exception.
#
fscc_chk_bsun:
btst &bsun_bit,FPCR_ENABLE(%a6) # was BSUN set?
bne.w fscc_bsun
#
# the bsun exception bit was not set.
# the result has been selected.
# now, check to see if the result is to be stored in the data register
# file or in memory.
#
fscc_done:
mov.l %d0,%a0 # save result for a moment
mov.b 1+EXC_OPWORD(%a6),%d1 # fetch lo opword
mov.l %d1,%d0 # make a copy
andi.b &0x38,%d1 # extract src mode
bne.b fscc_mem_op # it's a memory operation
mov.l %d0,%d1
andi.w &0x7,%d1 # pass index in d1
mov.l %a0,%d0 # pass result in d0
bsr.l store_dreg_b # save result in regfile
rts
#
# the stacked <ea> is correct with the exception of:
# -> Dn : <ea> is garbage
#
# if the addressing mode is post-increment or pre-decrement,
# then the address registers have not been updated.
#
fscc_mem_op:
cmpi.b %d1,&0x18 # is <ea> (An)+ ?
beq.b fscc_mem_inc # yes
cmpi.b %d1,&0x20 # is <ea> -(An) ?
beq.b fscc_mem_dec # yes
mov.l %a0,%d0 # pass result in d0
mov.l EXC_EA(%a6),%a0 # fetch <ea>
bsr.l _dmem_write_byte # write result byte
tst.l %d1 # did dstore fail?
bne.w fscc_err # yes
rts
# addresing mode is post-increment. write the result byte. if the write
# fails then don't update the address register. if write passes then
# call inc_areg() to update the address register.
fscc_mem_inc:
mov.l %a0,%d0 # pass result in d0
mov.l EXC_EA(%a6),%a0 # fetch <ea>
bsr.l _dmem_write_byte # write result byte
tst.l %d1 # did dstore fail?
bne.w fscc_err # yes
mov.b 0x1+EXC_OPWORD(%a6),%d1 # fetch opword
andi.w &0x7,%d1 # pass index in d1
movq.l &0x1,%d0 # pass amt to inc by
bsr.l inc_areg # increment address register
rts
# addressing mode is pre-decrement. write the result byte. if the write
# fails then don't update the address register. if the write passes then
# call dec_areg() to update the address register.
fscc_mem_dec:
mov.l %a0,%d0 # pass result in d0
mov.l EXC_EA(%a6),%a0 # fetch <ea>
bsr.l _dmem_write_byte # write result byte
tst.l %d1 # did dstore fail?
bne.w fscc_err # yes
mov.b 0x1+EXC_OPWORD(%a6),%d1 # fetch opword
andi.w &0x7,%d1 # pass index in d1
movq.l &0x1,%d0 # pass amt to dec by
bsr.l dec_areg # decrement address register
rts
# the emulation routine set bsun and BSUN was enabled. have to
# fix stack and jump to the bsun handler.
# let the caller of this routine shift the stack frame up to
# eliminate the effective address field.
fscc_bsun:
mov.b &fbsun_flg,SPCOND_FLG(%a6)
rts
# the byte write to memory has failed. pass the failing effective address
# and a FSLW to funimp_dacc().
fscc_err:
mov.w &0x00a1,EXC_VOFF(%a6)
bra.l facc_finish
#########################################################################
# XDEF **************************************************************** #
# fmovm_dynamic(): emulate "fmovm" dynamic instruction #
# #
# XREF **************************************************************** #
# fetch_dreg() - fetch data register #
# {i,d,}mem_read() - fetch data from memory #
# _mem_write() - write data to memory #
# iea_iacc() - instruction memory access error occurred #
# iea_dacc() - data memory access error occurred #
# restore() - restore An index regs if access error occurred #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# If instr is "fmovm Dn,-(A7)" from supervisor mode, #
# d0 = size of dump #
# d1 = Dn #
# Else if instruction access error, #
# d0 = FSLW #
# Else if data access error, #
# d0 = FSLW #
# a0 = address of fault #
# Else #
# none. #
# #
# ALGORITHM *********************************************************** #
# The effective address must be calculated since this is entered #
# from an "Unimplemented Effective Address" exception handler. So, we #
# have our own fcalc_ea() routine here. If an access error is flagged #
# by a _{i,d,}mem_read() call, we must exit through the special #
# handler. #
# The data register is determined and its value loaded to get the #
# string of FP registers affected. This value is used as an index into #
# a lookup table such that we can determine the number of bytes #
# involved. #
# If the instruction is "fmovm.x <ea>,Dn", a _mem_read() is used #
# to read in all FP values. Again, _mem_read() may fail and require a #
# special exit. #
# If the instruction is "fmovm.x DN,<ea>", a _mem_write() is used #
# to write all FP values. _mem_write() may also fail. #
# If the instruction is "fmovm.x DN,-(a7)" from supervisor mode, #
# then we return the size of the dump and the string to the caller #
# so that the move can occur outside of this routine. This special #
# case is required so that moves to the system stack are handled #
# correctly. #
# #
# DYNAMIC: #
# fmovm.x dn, <ea> #
# fmovm.x <ea>, dn #
# #
# <WORD 1> <WORD2> #
# 1111 0010 00 |<ea>| 11@& 1000 0$$$ 0000 #
# #
# & = (0): predecrement addressing mode #
# (1): postincrement or control addressing mode #
# @ = (0): move listed regs from memory to the FPU #
# (1): move listed regs from the FPU to memory #
# $$$ : index of data register holding reg select mask #
# #
# NOTES: #
# If the data register holds a zero, then the #
# instruction is a nop. #
# #
#########################################################################
global fmovm_dynamic
fmovm_dynamic:
# extract the data register in which the bit string resides...
mov.b 1+EXC_EXTWORD(%a6),%d1 # fetch extword
andi.w &0x70,%d1 # extract reg bits
lsr.b &0x4,%d1 # shift into lo bits
# fetch the bit string into d0...
bsr.l fetch_dreg # fetch reg string
andi.l &0x000000ff,%d0 # keep only lo byte
mov.l %d0,-(%sp) # save strg
mov.b (tbl_fmovm_size.w,%pc,%d0),%d0
mov.l %d0,-(%sp) # save size
bsr.l fmovm_calc_ea # calculate <ea>
mov.l (%sp)+,%d0 # restore size
mov.l (%sp)+,%d1 # restore strg
# if the bit string is a zero, then the operation is a no-op
# but, make sure that we've calculated ea and advanced the opword pointer
beq.w fmovm_data_done
# separate move ins from move outs...
btst &0x5,EXC_EXTWORD(%a6) # is it a move in or out?
beq.w fmovm_data_in # it's a move out
#############
# MOVE OUT: #
#############
fmovm_data_out:
btst &0x4,EXC_EXTWORD(%a6) # control or predecrement?
bne.w fmovm_out_ctrl # control
############################
fmovm_out_predec:
# for predecrement mode, the bit string is the opposite of both control
# operations and postincrement mode. (bit7 = FP7 ... bit0 = FP0)
# here, we convert it to be just like the others...
mov.b (tbl_fmovm_convert.w,%pc,%d1.w*1),%d1
btst &0x5,EXC_SR(%a6) # user or supervisor mode?
beq.b fmovm_out_ctrl # user
fmovm_out_predec_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg # is <ea> mode -(a7)?
bne.b fmovm_out_ctrl
# the operation was unfortunately an: fmovm.x dn,-(sp)
# called from supervisor mode.
# we're also passing "size" and "strg" back to the calling routine
rts
############################
fmovm_out_ctrl:
mov.l %a0,%a1 # move <ea> to a1
sub.l %d0,%sp # subtract size of dump
lea (%sp),%a0
tst.b %d1 # should FP0 be moved?
bpl.b fmovm_out_ctrl_fp1 # no
mov.l 0x0+EXC_FP0(%a6),(%a0)+ # yes
mov.l 0x4+EXC_FP0(%a6),(%a0)+
mov.l 0x8+EXC_FP0(%a6),(%a0)+
fmovm_out_ctrl_fp1:
lsl.b &0x1,%d1 # should FP1 be moved?
bpl.b fmovm_out_ctrl_fp2 # no
mov.l 0x0+EXC_FP1(%a6),(%a0)+ # yes
mov.l 0x4+EXC_FP1(%a6),(%a0)+
mov.l 0x8+EXC_FP1(%a6),(%a0)+
fmovm_out_ctrl_fp2:
lsl.b &0x1,%d1 # should FP2 be moved?
bpl.b fmovm_out_ctrl_fp3 # no
fmovm.x &0x20,(%a0) # yes
add.l &0xc,%a0
fmovm_out_ctrl_fp3:
lsl.b &0x1,%d1 # should FP3 be moved?
bpl.b fmovm_out_ctrl_fp4 # no
fmovm.x &0x10,(%a0) # yes
add.l &0xc,%a0
fmovm_out_ctrl_fp4:
lsl.b &0x1,%d1 # should FP4 be moved?
bpl.b fmovm_out_ctrl_fp5 # no
fmovm.x &0x08,(%a0) # yes
add.l &0xc,%a0
fmovm_out_ctrl_fp5:
lsl.b &0x1,%d1 # should FP5 be moved?
bpl.b fmovm_out_ctrl_fp6 # no
fmovm.x &0x04,(%a0) # yes
add.l &0xc,%a0
fmovm_out_ctrl_fp6:
lsl.b &0x1,%d1 # should FP6 be moved?
bpl.b fmovm_out_ctrl_fp7 # no
fmovm.x &0x02,(%a0) # yes
add.l &0xc,%a0
fmovm_out_ctrl_fp7:
lsl.b &0x1,%d1 # should FP7 be moved?
bpl.b fmovm_out_ctrl_done # no
fmovm.x &0x01,(%a0) # yes
add.l &0xc,%a0
fmovm_out_ctrl_done:
mov.l %a1,L_SCR1(%a6)
lea (%sp),%a0 # pass: supervisor src
mov.l %d0,-(%sp) # save size
bsr.l _dmem_write # copy data to user mem
mov.l (%sp)+,%d0
add.l %d0,%sp # clear fpreg data from stack
tst.l %d1 # did dstore err?
bne.w fmovm_out_err # yes
rts
############
# MOVE IN: #
############
fmovm_data_in:
mov.l %a0,L_SCR1(%a6)
sub.l %d0,%sp # make room for fpregs
lea (%sp),%a1
mov.l %d1,-(%sp) # save bit string for later
mov.l %d0,-(%sp) # save # of bytes
bsr.l _dmem_read # copy data from user mem
mov.l (%sp)+,%d0 # retrieve # of bytes
tst.l %d1 # did dfetch fail?
bne.w fmovm_in_err # yes
mov.l (%sp)+,%d1 # load bit string
lea (%sp),%a0 # addr of stack
tst.b %d1 # should FP0 be moved?
bpl.b fmovm_data_in_fp1 # no
mov.l (%a0)+,0x0+EXC_FP0(%a6) # yes
mov.l (%a0)+,0x4+EXC_FP0(%a6)
mov.l (%a0)+,0x8+EXC_FP0(%a6)
fmovm_data_in_fp1:
lsl.b &0x1,%d1 # should FP1 be moved?
bpl.b fmovm_data_in_fp2 # no
mov.l (%a0)+,0x0+EXC_FP1(%a6) # yes
mov.l (%a0)+,0x4+EXC_FP1(%a6)
mov.l (%a0)+,0x8+EXC_FP1(%a6)
fmovm_data_in_fp2:
lsl.b &0x1,%d1 # should FP2 be moved?
bpl.b fmovm_data_in_fp3 # no
fmovm.x (%a0)+,&0x20 # yes
fmovm_data_in_fp3:
lsl.b &0x1,%d1 # should FP3 be moved?
bpl.b fmovm_data_in_fp4 # no
fmovm.x (%a0)+,&0x10 # yes
fmovm_data_in_fp4:
lsl.b &0x1,%d1 # should FP4 be moved?
bpl.b fmovm_data_in_fp5 # no
fmovm.x (%a0)+,&0x08 # yes
fmovm_data_in_fp5:
lsl.b &0x1,%d1 # should FP5 be moved?
bpl.b fmovm_data_in_fp6 # no
fmovm.x (%a0)+,&0x04 # yes
fmovm_data_in_fp6:
lsl.b &0x1,%d1 # should FP6 be moved?
bpl.b fmovm_data_in_fp7 # no
fmovm.x (%a0)+,&0x02 # yes
fmovm_data_in_fp7:
lsl.b &0x1,%d1 # should FP7 be moved?
bpl.b fmovm_data_in_done # no
fmovm.x (%a0)+,&0x01 # yes
fmovm_data_in_done:
add.l %d0,%sp # remove fpregs from stack
rts
#####################################
fmovm_data_done:
rts
##############################################################################
#
# table indexed by the operation's bit string that gives the number
# of bytes that will be moved.
#
# number of bytes = (# of 1's in bit string) * 12(bytes/fpreg)
#
tbl_fmovm_size:
byte 0x00,0x0c,0x0c,0x18,0x0c,0x18,0x18,0x24
byte 0x0c,0x18,0x18,0x24,0x18,0x24,0x24,0x30
byte 0x0c,0x18,0x18,0x24,0x18,0x24,0x24,0x30
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x0c,0x18,0x18,0x24,0x18,0x24,0x24,0x30
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x0c,0x18,0x18,0x24,0x18,0x24,0x24,0x30
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x30,0x3c,0x3c,0x48,0x3c,0x48,0x48,0x54
byte 0x0c,0x18,0x18,0x24,0x18,0x24,0x24,0x30
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x30,0x3c,0x3c,0x48,0x3c,0x48,0x48,0x54
byte 0x18,0x24,0x24,0x30,0x24,0x30,0x30,0x3c
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x30,0x3c,0x3c,0x48,0x3c,0x48,0x48,0x54
byte 0x24,0x30,0x30,0x3c,0x30,0x3c,0x3c,0x48
byte 0x30,0x3c,0x3c,0x48,0x3c,0x48,0x48,0x54
byte 0x30,0x3c,0x3c,0x48,0x3c,0x48,0x48,0x54
byte 0x3c,0x48,0x48,0x54,0x48,0x54,0x54,0x60
#
# table to convert a pre-decrement bit string into a post-increment
# or control bit string.
# ex: 0x00 ==> 0x00
# 0x01 ==> 0x80
# 0x02 ==> 0x40
# .
# .
# 0xfd ==> 0xbf
# 0xfe ==> 0x7f
# 0xff ==> 0xff
#
tbl_fmovm_convert:
byte 0x00,0x80,0x40,0xc0,0x20,0xa0,0x60,0xe0
byte 0x10,0x90,0x50,0xd0,0x30,0xb0,0x70,0xf0
byte 0x08,0x88,0x48,0xc8,0x28,0xa8,0x68,0xe8
byte 0x18,0x98,0x58,0xd8,0x38,0xb8,0x78,0xf8
byte 0x04,0x84,0x44,0xc4,0x24,0xa4,0x64,0xe4
byte 0x14,0x94,0x54,0xd4,0x34,0xb4,0x74,0xf4
byte 0x0c,0x8c,0x4c,0xcc,0x2c,0xac,0x6c,0xec
byte 0x1c,0x9c,0x5c,0xdc,0x3c,0xbc,0x7c,0xfc
byte 0x02,0x82,0x42,0xc2,0x22,0xa2,0x62,0xe2
byte 0x12,0x92,0x52,0xd2,0x32,0xb2,0x72,0xf2
byte 0x0a,0x8a,0x4a,0xca,0x2a,0xaa,0x6a,0xea
byte 0x1a,0x9a,0x5a,0xda,0x3a,0xba,0x7a,0xfa
byte 0x06,0x86,0x46,0xc6,0x26,0xa6,0x66,0xe6
byte 0x16,0x96,0x56,0xd6,0x36,0xb6,0x76,0xf6
byte 0x0e,0x8e,0x4e,0xce,0x2e,0xae,0x6e,0xee
byte 0x1e,0x9e,0x5e,0xde,0x3e,0xbe,0x7e,0xfe
byte 0x01,0x81,0x41,0xc1,0x21,0xa1,0x61,0xe1
byte 0x11,0x91,0x51,0xd1,0x31,0xb1,0x71,0xf1
byte 0x09,0x89,0x49,0xc9,0x29,0xa9,0x69,0xe9
byte 0x19,0x99,0x59,0xd9,0x39,0xb9,0x79,0xf9
byte 0x05,0x85,0x45,0xc5,0x25,0xa5,0x65,0xe5
byte 0x15,0x95,0x55,0xd5,0x35,0xb5,0x75,0xf5
byte 0x0d,0x8d,0x4d,0xcd,0x2d,0xad,0x6d,0xed
byte 0x1d,0x9d,0x5d,0xdd,0x3d,0xbd,0x7d,0xfd
byte 0x03,0x83,0x43,0xc3,0x23,0xa3,0x63,0xe3
byte 0x13,0x93,0x53,0xd3,0x33,0xb3,0x73,0xf3
byte 0x0b,0x8b,0x4b,0xcb,0x2b,0xab,0x6b,0xeb
byte 0x1b,0x9b,0x5b,0xdb,0x3b,0xbb,0x7b,0xfb
byte 0x07,0x87,0x47,0xc7,0x27,0xa7,0x67,0xe7
byte 0x17,0x97,0x57,0xd7,0x37,0xb7,0x77,0xf7
byte 0x0f,0x8f,0x4f,0xcf,0x2f,0xaf,0x6f,0xef
byte 0x1f,0x9f,0x5f,0xdf,0x3f,0xbf,0x7f,0xff
global fmovm_calc_ea
###############################################
# _fmovm_calc_ea: calculate effective address #
###############################################
fmovm_calc_ea:
mov.l %d0,%a0 # move # bytes to a0
# currently, MODE and REG are taken from the EXC_OPWORD. this could be
# easily changed if they were inputs passed in registers.
mov.w EXC_OPWORD(%a6),%d0 # fetch opcode word
mov.w %d0,%d1 # make a copy
andi.w &0x3f,%d0 # extract mode field
andi.l &0x7,%d1 # extract reg field
# jump to the corresponding function for each {MODE,REG} pair.
mov.w (tbl_fea_mode.b,%pc,%d0.w*2),%d0 # fetch jmp distance
jmp (tbl_fea_mode.b,%pc,%d0.w*1) # jmp to correct ea mode
swbeg &64
tbl_fea_mode:
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short faddr_ind_a0 - tbl_fea_mode
short faddr_ind_a1 - tbl_fea_mode
short faddr_ind_a2 - tbl_fea_mode
short faddr_ind_a3 - tbl_fea_mode
short faddr_ind_a4 - tbl_fea_mode
short faddr_ind_a5 - tbl_fea_mode
short faddr_ind_a6 - tbl_fea_mode
short faddr_ind_a7 - tbl_fea_mode
short faddr_ind_p_a0 - tbl_fea_mode
short faddr_ind_p_a1 - tbl_fea_mode
short faddr_ind_p_a2 - tbl_fea_mode
short faddr_ind_p_a3 - tbl_fea_mode
short faddr_ind_p_a4 - tbl_fea_mode
short faddr_ind_p_a5 - tbl_fea_mode
short faddr_ind_p_a6 - tbl_fea_mode
short faddr_ind_p_a7 - tbl_fea_mode
short faddr_ind_m_a0 - tbl_fea_mode
short faddr_ind_m_a1 - tbl_fea_mode
short faddr_ind_m_a2 - tbl_fea_mode
short faddr_ind_m_a3 - tbl_fea_mode
short faddr_ind_m_a4 - tbl_fea_mode
short faddr_ind_m_a5 - tbl_fea_mode
short faddr_ind_m_a6 - tbl_fea_mode
short faddr_ind_m_a7 - tbl_fea_mode
short faddr_ind_disp_a0 - tbl_fea_mode
short faddr_ind_disp_a1 - tbl_fea_mode
short faddr_ind_disp_a2 - tbl_fea_mode
short faddr_ind_disp_a3 - tbl_fea_mode
short faddr_ind_disp_a4 - tbl_fea_mode
short faddr_ind_disp_a5 - tbl_fea_mode
short faddr_ind_disp_a6 - tbl_fea_mode
short faddr_ind_disp_a7 - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short faddr_ind_ext - tbl_fea_mode
short fabs_short - tbl_fea_mode
short fabs_long - tbl_fea_mode
short fpc_ind - tbl_fea_mode
short fpc_ind_ext - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
short tbl_fea_mode - tbl_fea_mode
###################################
# Address register indirect: (An) #
###################################
faddr_ind_a0:
mov.l EXC_DREGS+0x8(%a6),%a0 # Get current a0
rts
faddr_ind_a1:
mov.l EXC_DREGS+0xc(%a6),%a0 # Get current a1
rts
faddr_ind_a2:
mov.l %a2,%a0 # Get current a2
rts
faddr_ind_a3:
mov.l %a3,%a0 # Get current a3
rts
faddr_ind_a4:
mov.l %a4,%a0 # Get current a4
rts
faddr_ind_a5:
mov.l %a5,%a0 # Get current a5
rts
faddr_ind_a6:
mov.l (%a6),%a0 # Get current a6
rts
faddr_ind_a7:
mov.l EXC_A7(%a6),%a0 # Get current a7
rts
#####################################################
# Address register indirect w/ postincrement: (An)+ #
#####################################################
faddr_ind_p_a0:
mov.l EXC_DREGS+0x8(%a6),%d0 # Get current a0
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,EXC_DREGS+0x8(%a6) # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a1:
mov.l EXC_DREGS+0xc(%a6),%d0 # Get current a1
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,EXC_DREGS+0xc(%a6) # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a2:
mov.l %a2,%d0 # Get current a2
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,%a2 # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a3:
mov.l %a3,%d0 # Get current a3
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,%a3 # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a4:
mov.l %a4,%d0 # Get current a4
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,%a4 # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a5:
mov.l %a5,%d0 # Get current a5
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,%a5 # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a6:
mov.l (%a6),%d0 # Get current a6
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,(%a6) # Save incr value
mov.l %d0,%a0
rts
faddr_ind_p_a7:
mov.b &mia7_flg,SPCOND_FLG(%a6) # set "special case" flag
mov.l EXC_A7(%a6),%d0 # Get current a7
mov.l %d0,%d1
add.l %a0,%d1 # Increment
mov.l %d1,EXC_A7(%a6) # Save incr value
mov.l %d0,%a0
rts
####################################################
# Address register indirect w/ predecrement: -(An) #
####################################################
faddr_ind_m_a0:
mov.l EXC_DREGS+0x8(%a6),%d0 # Get current a0
sub.l %a0,%d0 # Decrement
mov.l %d0,EXC_DREGS+0x8(%a6) # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a1:
mov.l EXC_DREGS+0xc(%a6),%d0 # Get current a1
sub.l %a0,%d0 # Decrement
mov.l %d0,EXC_DREGS+0xc(%a6) # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a2:
mov.l %a2,%d0 # Get current a2
sub.l %a0,%d0 # Decrement
mov.l %d0,%a2 # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a3:
mov.l %a3,%d0 # Get current a3
sub.l %a0,%d0 # Decrement
mov.l %d0,%a3 # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a4:
mov.l %a4,%d0 # Get current a4
sub.l %a0,%d0 # Decrement
mov.l %d0,%a4 # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a5:
mov.l %a5,%d0 # Get current a5
sub.l %a0,%d0 # Decrement
mov.l %d0,%a5 # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a6:
mov.l (%a6),%d0 # Get current a6
sub.l %a0,%d0 # Decrement
mov.l %d0,(%a6) # Save decr value
mov.l %d0,%a0
rts
faddr_ind_m_a7:
mov.b &mda7_flg,SPCOND_FLG(%a6) # set "special case" flag
mov.l EXC_A7(%a6),%d0 # Get current a7
sub.l %a0,%d0 # Decrement
mov.l %d0,EXC_A7(%a6) # Save decr value
mov.l %d0,%a0
rts
########################################################
# Address register indirect w/ displacement: (d16, An) #
########################################################
faddr_ind_disp_a0:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l EXC_DREGS+0x8(%a6),%a0 # a0 + d16
rts
faddr_ind_disp_a1:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l EXC_DREGS+0xc(%a6),%a0 # a1 + d16
rts
faddr_ind_disp_a2:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l %a2,%a0 # a2 + d16
rts
faddr_ind_disp_a3:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l %a3,%a0 # a3 + d16
rts
faddr_ind_disp_a4:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l %a4,%a0 # a4 + d16
rts
faddr_ind_disp_a5:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l %a5,%a0 # a5 + d16
rts
faddr_ind_disp_a6:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l (%a6),%a0 # a6 + d16
rts
faddr_ind_disp_a7:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l EXC_A7(%a6),%a0 # a7 + d16
rts
########################################################################
# Address register indirect w/ index(8-bit displacement): (d8, An, Xn) #
# " " " w/ " (base displacement): (bd, An, Xn) #
# Memory indirect postindexed: ([bd, An], Xn, od) #
# Memory indirect preindexed: ([bd, An, Xn], od) #
########################################################################
faddr_ind_ext:
addq.l &0x8,%d1
bsr.l fetch_dreg # fetch base areg
mov.l %d0,-(%sp)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word # fetch extword in d0
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l (%sp)+,%a0
btst &0x8,%d0
bne.w fcalc_mem_ind
mov.l %d0,L_SCR1(%a6) # hold opword
mov.l %d0,%d1
rol.w &0x4,%d1
andi.w &0xf,%d1 # extract index regno
# count on fetch_dreg() not to alter a0...
bsr.l fetch_dreg # fetch index
mov.l %d2,-(%sp) # save d2
mov.l L_SCR1(%a6),%d2 # fetch opword
btst &0xb,%d2 # is it word or long?
bne.b faii8_long
ext.l %d0 # sign extend word index
faii8_long:
mov.l %d2,%d1
rol.w &0x7,%d1
andi.l &0x3,%d1 # extract scale value
lsl.l %d1,%d0 # shift index by scale
extb.l %d2 # sign extend displacement
add.l %d2,%d0 # index + disp
add.l %d0,%a0 # An + (index + disp)
mov.l (%sp)+,%d2 # restore old d2
rts
###########################
# Absolute short: (XXX).W #
###########################
fabs_short:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word # fetch short address
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # return <ea> in a0
rts
##########################
# Absolute long: (XXX).L #
##########################
fabs_long:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch long address
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,%a0 # return <ea> in a0
rts
#######################################################
# Program counter indirect w/ displacement: (d16, PC) #
#######################################################
fpc_ind:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word # fetch word displacement
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.w %d0,%a0 # sign extend displacement
add.l EXC_EXTWPTR(%a6),%a0 # pc + d16
# _imem_read_word() increased the extwptr by 2. need to adjust here.
subq.l &0x2,%a0 # adjust <ea>
rts
##########################################################
# PC indirect w/ index(8-bit displacement): (d8, PC, An) #
# " " w/ " (base displacement): (bd, PC, An) #
# PC memory indirect postindexed: ([bd, PC], Xn, od) #
# PC memory indirect preindexed: ([bd, PC, Xn], od) #
##########################################################
fpc_ind_ext:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word # fetch ext word
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l EXC_EXTWPTR(%a6),%a0 # put base in a0
subq.l &0x2,%a0 # adjust base
btst &0x8,%d0 # is disp only 8 bits?
bne.w fcalc_mem_ind # calc memory indirect
mov.l %d0,L_SCR1(%a6) # store opword
mov.l %d0,%d1 # make extword copy
rol.w &0x4,%d1 # rotate reg num into place
andi.w &0xf,%d1 # extract register number
# count on fetch_dreg() not to alter a0...
bsr.l fetch_dreg # fetch index
mov.l %d2,-(%sp) # save d2
mov.l L_SCR1(%a6),%d2 # fetch opword
btst &0xb,%d2 # is index word or long?
bne.b fpii8_long # long
ext.l %d0 # sign extend word index
fpii8_long:
mov.l %d2,%d1
rol.w &0x7,%d1 # rotate scale value into place
andi.l &0x3,%d1 # extract scale value
lsl.l %d1,%d0 # shift index by scale
extb.l %d2 # sign extend displacement
add.l %d2,%d0 # disp + index
add.l %d0,%a0 # An + (index + disp)
mov.l (%sp)+,%d2 # restore temp register
rts
# d2 = index
# d3 = base
# d4 = od
# d5 = extword
fcalc_mem_ind:
btst &0x6,%d0 # is the index suppressed?
beq.b fcalc_index
movm.l &0x3c00,-(%sp) # save d2-d5
mov.l %d0,%d5 # put extword in d5
mov.l %a0,%d3 # put base in d3
clr.l %d2 # yes, so index = 0
bra.b fbase_supp_ck
# index:
fcalc_index:
mov.l %d0,L_SCR1(%a6) # save d0 (opword)
bfextu %d0{&16:&4},%d1 # fetch dreg index
bsr.l fetch_dreg
movm.l &0x3c00,-(%sp) # save d2-d5
mov.l %d0,%d2 # put index in d2
mov.l L_SCR1(%a6),%d5
mov.l %a0,%d3
btst &0xb,%d5 # is index word or long?
bne.b fno_ext
ext.l %d2
fno_ext:
bfextu %d5{&21:&2},%d0
lsl.l %d0,%d2
# base address (passed as parameter in d3):
# we clear the value here if it should actually be suppressed.
fbase_supp_ck:
btst &0x7,%d5 # is the bd suppressed?
beq.b fno_base_sup
clr.l %d3
# base displacement:
fno_base_sup:
bfextu %d5{&26:&2},%d0 # get bd size
# beq.l fmovm_error # if (size == 0) it's reserved
cmpi.b %d0,&0x2
blt.b fno_bd
beq.b fget_word_bd
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long
tst.l %d1 # did ifetch fail?
bne.l fcea_iacc # yes
bra.b fchk_ind
fget_word_bd:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l fcea_iacc # yes
ext.l %d0 # sign extend bd
fchk_ind:
add.l %d0,%d3 # base += bd
# outer displacement:
fno_bd:
bfextu %d5{&30:&2},%d0 # is od suppressed?
beq.w faii_bd
cmpi.b %d0,&0x2
blt.b fnull_od
beq.b fword_od
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long
tst.l %d1 # did ifetch fail?
bne.l fcea_iacc # yes
bra.b fadd_them
fword_od:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x2,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_word
tst.l %d1 # did ifetch fail?
bne.l fcea_iacc # yes
ext.l %d0 # sign extend od
bra.b fadd_them
fnull_od:
clr.l %d0
fadd_them:
mov.l %d0,%d4
btst &0x2,%d5 # pre or post indexing?
beq.b fpre_indexed
mov.l %d3,%a0
bsr.l _dmem_read_long
tst.l %d1 # did dfetch fail?
bne.w fcea_err # yes
add.l %d2,%d0 # <ea> += index
add.l %d4,%d0 # <ea> += od
bra.b fdone_ea
fpre_indexed:
add.l %d2,%d3 # preindexing
mov.l %d3,%a0
bsr.l _dmem_read_long
tst.l %d1 # did dfetch fail?
bne.w fcea_err # yes
add.l %d4,%d0 # ea += od
bra.b fdone_ea
faii_bd:
add.l %d2,%d3 # ea = (base + bd) + index
mov.l %d3,%d0
fdone_ea:
mov.l %d0,%a0
movm.l (%sp)+,&0x003c # restore d2-d5
rts
#########################################################
fcea_err:
mov.l %d3,%a0
movm.l (%sp)+,&0x003c # restore d2-d5
mov.w &0x0101,%d0
bra.l iea_dacc
fcea_iacc:
movm.l (%sp)+,&0x003c # restore d2-d5
bra.l iea_iacc
fmovm_out_err:
bsr.l restore
mov.w &0x00e1,%d0
bra.b fmovm_err
fmovm_in_err:
bsr.l restore
mov.w &0x0161,%d0
fmovm_err:
mov.l L_SCR1(%a6),%a0
bra.l iea_dacc
#########################################################################
# XDEF **************************************************************** #
# fmovm_ctrl(): emulate fmovm.l of control registers instr #
# #
# XREF **************************************************************** #
# _imem_read_long() - read longword from memory #
# iea_iacc() - _imem_read_long() failed; error recovery #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# If _imem_read_long() doesn't fail: #
# USER_FPCR(a6) = new FPCR value #
# USER_FPSR(a6) = new FPSR value #
# USER_FPIAR(a6) = new FPIAR value #
# #
# ALGORITHM *********************************************************** #
# Decode the instruction type by looking at the extension word #
# in order to see how many control registers to fetch from memory. #
# Fetch them using _imem_read_long(). If this fetch fails, exit through #
# the special access error exit handler iea_iacc(). #
# #
# Instruction word decoding: #
# #
# fmovem.l #<data>, {FPIAR&|FPCR&|FPSR} #
# #
# WORD1 WORD2 #
# 1111 0010 00 111100 100$ $$00 0000 0000 #
# #
# $$$ (100): FPCR #
# (010): FPSR #
# (001): FPIAR #
# (000): FPIAR #
# #
#########################################################################
global fmovm_ctrl
fmovm_ctrl:
mov.b EXC_EXTWORD(%a6),%d0 # fetch reg select bits
cmpi.b %d0,&0x9c # fpcr & fpsr & fpiar ?
beq.w fctrl_in_7 # yes
cmpi.b %d0,&0x98 # fpcr & fpsr ?
beq.w fctrl_in_6 # yes
cmpi.b %d0,&0x94 # fpcr & fpiar ?
beq.b fctrl_in_5 # yes
# fmovem.l #<data>, fpsr/fpiar
fctrl_in_3:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPSR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPSR(%a6) # store new FPSR to stack
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPIAR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPIAR(%a6) # store new FPIAR to stack
rts
# fmovem.l #<data>, fpcr/fpiar
fctrl_in_5:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPCR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPCR(%a6) # store new FPCR to stack
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPIAR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPIAR(%a6) # store new FPIAR to stack
rts
# fmovem.l #<data>, fpcr/fpsr
fctrl_in_6:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPCR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPCR(%a6) # store new FPCR to mem
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPSR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPSR(%a6) # store new FPSR to mem
rts
# fmovem.l #<data>, fpcr/fpsr/fpiar
fctrl_in_7:
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPCR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPCR(%a6) # store new FPCR to mem
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPSR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPSR(%a6) # store new FPSR to mem
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch FPIAR from mem
tst.l %d1 # did ifetch fail?
bne.l iea_iacc # yes
mov.l %d0,USER_FPIAR(%a6) # store new FPIAR to mem
rts
#########################################################################
# XDEF **************************************************************** #
# _dcalc_ea(): calc correct <ea> from <ea> stacked on exception #
# #
# XREF **************************************************************** #
# inc_areg() - increment an address register #
# dec_areg() - decrement an address register #
# #
# INPUT *************************************************************** #
# d0 = number of bytes to adjust <ea> by #
# #
# OUTPUT ************************************************************** #
# None #
# #
# ALGORITHM *********************************************************** #
# "Dummy" CALCulate Effective Address: #
# The stacked <ea> for FP unimplemented instructions and opclass #
# two packed instructions is correct with the exception of... #
# #
# 1) -(An) : The register is not updated regardless of size. #
# Also, for extended precision and packed, the #
# stacked <ea> value is 8 bytes too big #
# 2) (An)+ : The register is not updated. #
# 3) #<data> : The upper longword of the immediate operand is #
# stacked b,w,l and s sizes are completely stacked. #
# d,x, and p are not. #
# #
#########################################################################
global _dcalc_ea
_dcalc_ea:
mov.l %d0, %a0 # move # bytes to %a0
mov.b 1+EXC_OPWORD(%a6), %d0 # fetch opcode word
mov.l %d0, %d1 # make a copy
andi.w &0x38, %d0 # extract mode field
andi.l &0x7, %d1 # extract reg field
cmpi.b %d0,&0x18 # is mode (An)+ ?
beq.b dcea_pi # yes
cmpi.b %d0,&0x20 # is mode -(An) ?
beq.b dcea_pd # yes
or.w %d1,%d0 # concat mode,reg
cmpi.b %d0,&0x3c # is mode #<data>?
beq.b dcea_imm # yes
mov.l EXC_EA(%a6),%a0 # return <ea>
rts
# need to set immediate data flag here since we'll need to do
# an imem_read to fetch this later.
dcea_imm:
mov.b &immed_flg,SPCOND_FLG(%a6)
lea ([USER_FPIAR,%a6],0x4),%a0 # no; return <ea>
rts
# here, the <ea> is stacked correctly. however, we must update the
# address register...
dcea_pi:
mov.l %a0,%d0 # pass amt to inc by
bsr.l inc_areg # inc addr register
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
rts
# the <ea> is stacked correctly for all but extended and packed which
# the <ea>s are 8 bytes too large.
# it would make no sense to have a pre-decrement to a7 in supervisor
# mode so we don't even worry about this tricky case here : )
dcea_pd:
mov.l %a0,%d0 # pass amt to dec by
bsr.l dec_areg # dec addr register
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
cmpi.b %d0,&0xc # is opsize ext or packed?
beq.b dcea_pd2 # yes
rts
dcea_pd2:
sub.l &0x8,%a0 # correct <ea>
mov.l %a0,EXC_EA(%a6) # put correct <ea> on stack
rts
#########################################################################
# XDEF **************************************************************** #
# _calc_ea_fout(): calculate correct stacked <ea> for extended #
# and packed data opclass 3 operations. #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# a0 = return correct effective address #
# #
# ALGORITHM *********************************************************** #
# For opclass 3 extended and packed data operations, the <ea> #
# stacked for the exception is incorrect for -(an) and (an)+ addressing #
# modes. Also, while we're at it, the index register itself must get #
# updated. #
# So, for -(an), we must subtract 8 off of the stacked <ea> value #
# and return that value as the correct <ea> and store that value in An. #
# For (an)+, the stacked <ea> is correct but we must adjust An by +12. #
# #
#########################################################################
# This calc_ea is currently used to retrieve the correct <ea>
# for fmove outs of type extended and packed.
global _calc_ea_fout
_calc_ea_fout:
mov.b 1+EXC_OPWORD(%a6),%d0 # fetch opcode word
mov.l %d0,%d1 # make a copy
andi.w &0x38,%d0 # extract mode field
andi.l &0x7,%d1 # extract reg field
cmpi.b %d0,&0x18 # is mode (An)+ ?
beq.b ceaf_pi # yes
cmpi.b %d0,&0x20 # is mode -(An) ?
beq.w ceaf_pd # yes
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
rts
# (An)+ : extended and packed fmove out
# : stacked <ea> is correct
# : "An" not updated
ceaf_pi:
mov.w (tbl_ceaf_pi.b,%pc,%d1.w*2),%d1
mov.l EXC_EA(%a6),%a0
jmp (tbl_ceaf_pi.b,%pc,%d1.w*1)
swbeg &0x8
tbl_ceaf_pi:
short ceaf_pi0 - tbl_ceaf_pi
short ceaf_pi1 - tbl_ceaf_pi
short ceaf_pi2 - tbl_ceaf_pi
short ceaf_pi3 - tbl_ceaf_pi
short ceaf_pi4 - tbl_ceaf_pi
short ceaf_pi5 - tbl_ceaf_pi
short ceaf_pi6 - tbl_ceaf_pi
short ceaf_pi7 - tbl_ceaf_pi
ceaf_pi0:
addi.l &0xc,EXC_DREGS+0x8(%a6)
rts
ceaf_pi1:
addi.l &0xc,EXC_DREGS+0xc(%a6)
rts
ceaf_pi2:
add.l &0xc,%a2
rts
ceaf_pi3:
add.l &0xc,%a3
rts
ceaf_pi4:
add.l &0xc,%a4
rts
ceaf_pi5:
add.l &0xc,%a5
rts
ceaf_pi6:
addi.l &0xc,EXC_A6(%a6)
rts
ceaf_pi7:
mov.b &mia7_flg,SPCOND_FLG(%a6)
addi.l &0xc,EXC_A7(%a6)
rts
# -(An) : extended and packed fmove out
# : stacked <ea> = actual <ea> + 8
# : "An" not updated
ceaf_pd:
mov.w (tbl_ceaf_pd.b,%pc,%d1.w*2),%d1
mov.l EXC_EA(%a6),%a0
sub.l &0x8,%a0
sub.l &0x8,EXC_EA(%a6)
jmp (tbl_ceaf_pd.b,%pc,%d1.w*1)
swbeg &0x8
tbl_ceaf_pd:
short ceaf_pd0 - tbl_ceaf_pd
short ceaf_pd1 - tbl_ceaf_pd
short ceaf_pd2 - tbl_ceaf_pd
short ceaf_pd3 - tbl_ceaf_pd
short ceaf_pd4 - tbl_ceaf_pd
short ceaf_pd5 - tbl_ceaf_pd
short ceaf_pd6 - tbl_ceaf_pd
short ceaf_pd7 - tbl_ceaf_pd
ceaf_pd0:
mov.l %a0,EXC_DREGS+0x8(%a6)
rts
ceaf_pd1:
mov.l %a0,EXC_DREGS+0xc(%a6)
rts
ceaf_pd2:
mov.l %a0,%a2
rts
ceaf_pd3:
mov.l %a0,%a3
rts
ceaf_pd4:
mov.l %a0,%a4
rts
ceaf_pd5:
mov.l %a0,%a5
rts
ceaf_pd6:
mov.l %a0,EXC_A6(%a6)
rts
ceaf_pd7:
mov.l %a0,EXC_A7(%a6)
mov.b &mda7_flg,SPCOND_FLG(%a6)
rts
#########################################################################
# XDEF **************************************************************** #
# _load_fop(): load operand for unimplemented FP exception #
# #
# XREF **************************************************************** #
# set_tag_x() - determine ext prec optype tag #
# set_tag_s() - determine sgl prec optype tag #
# set_tag_d() - determine dbl prec optype tag #
# unnorm_fix() - convert normalized number to denorm or zero #
# norm() - normalize a denormalized number #
# get_packed() - fetch a packed operand from memory #
# _dcalc_ea() - calculate <ea>, fixing An in process #
# #
# _imem_read_{word,long}() - read from instruction memory #
# _dmem_read() - read from data memory #
# _dmem_read_{byte,word,long}() - read from data memory #
# #
# facc_in_{b,w,l,d,x}() - mem read failed; special exit point #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# If memory access doesn't fail: #
# FP_SRC(a6) = source operand in extended precision #
# FP_DST(a6) = destination operand in extended precision #
# #
# ALGORITHM *********************************************************** #
# This is called from the Unimplemented FP exception handler in #
# order to load the source and maybe destination operand into #
# FP_SRC(a6) and FP_DST(a6). If the instruction was opclass zero, load #
# the source and destination from the FP register file. Set the optype #
# tags for both if dyadic, one for monadic. If a number is an UNNORM, #
# convert it to a DENORM or a ZERO. #
# If the instruction is opclass two (memory->reg), then fetch #
# the destination from the register file and the source operand from #
# memory. Tag and fix both as above w/ opclass zero instructions. #
# If the source operand is byte,word,long, or single, it may be #
# in the data register file. If it's actually out in memory, use one of #
# the mem_read() routines to fetch it. If the mem_read() access returns #
# a failing value, exit through the special facc_in() routine which #
# will create an acess error exception frame from the current exception #
# frame. #
# Immediate data and regular data accesses are separated because #
# if an immediate data access fails, the resulting fault status #
# longword stacked for the access error exception must have the #
# instruction bit set. #
# #
#########################################################################
global _load_fop
_load_fop:
# 15 13 12 10 9 7 6 0
# / \ / \ / \ / \
# ---------------------------------
# | opclass | RX | RY | EXTENSION | (2nd word of general FP instruction)
# ---------------------------------
#
# bfextu EXC_CMDREG(%a6){&0:&3}, %d0 # extract opclass
# cmpi.b %d0, &0x2 # which class is it? ('000,'010,'011)
# beq.w op010 # handle <ea> -> fpn
# bgt.w op011 # handle fpn -> <ea>
# we're not using op011 for now...
btst &0x6,EXC_CMDREG(%a6)
bne.b op010
############################
# OPCLASS '000: reg -> reg #
############################
op000:
mov.b 1+EXC_CMDREG(%a6),%d0 # fetch extension word lo
btst &0x5,%d0 # testing extension bits
beq.b op000_src # (bit 5 == 0) => monadic
btst &0x4,%d0 # (bit 5 == 1)
beq.b op000_dst # (bit 4 == 0) => dyadic
and.w &0x007f,%d0 # extract extension bits {6:0}
cmpi.w %d0,&0x0038 # is it an fcmp (dyadic) ?
bne.b op000_src # it's an fcmp
op000_dst:
bfextu EXC_CMDREG(%a6){&6:&3}, %d0 # extract dst field
bsr.l load_fpn2 # fetch dst fpreg into FP_DST
bsr.l set_tag_x # get dst optype tag
cmpi.b %d0, &UNNORM # is dst fpreg an UNNORM?
beq.b op000_dst_unnorm # yes
op000_dst_cont:
mov.b %d0, DTAG(%a6) # store the dst optype tag
op000_src:
bfextu EXC_CMDREG(%a6){&3:&3}, %d0 # extract src field
bsr.l load_fpn1 # fetch src fpreg into FP_SRC
bsr.l set_tag_x # get src optype tag
cmpi.b %d0, &UNNORM # is src fpreg an UNNORM?
beq.b op000_src_unnorm # yes
op000_src_cont:
mov.b %d0, STAG(%a6) # store the src optype tag
rts
op000_dst_unnorm:
bsr.l unnorm_fix # fix the dst UNNORM
bra.b op000_dst_cont
op000_src_unnorm:
bsr.l unnorm_fix # fix the src UNNORM
bra.b op000_src_cont
#############################
# OPCLASS '010: <ea> -> reg #
#############################
op010:
mov.w EXC_CMDREG(%a6),%d0 # fetch extension word
btst &0x5,%d0 # testing extension bits
beq.b op010_src # (bit 5 == 0) => monadic
btst &0x4,%d0 # (bit 5 == 1)
beq.b op010_dst # (bit 4 == 0) => dyadic
and.w &0x007f,%d0 # extract extension bits {6:0}
cmpi.w %d0,&0x0038 # is it an fcmp (dyadic) ?
bne.b op010_src # it's an fcmp
op010_dst:
bfextu EXC_CMDREG(%a6){&6:&3}, %d0 # extract dst field
bsr.l load_fpn2 # fetch dst fpreg ptr
bsr.l set_tag_x # get dst type tag
cmpi.b %d0, &UNNORM # is dst fpreg an UNNORM?
beq.b op010_dst_unnorm # yes
op010_dst_cont:
mov.b %d0, DTAG(%a6) # store the dst optype tag
op010_src:
bfextu EXC_CMDREG(%a6){&3:&3}, %d0 # extract src type field
bfextu EXC_OPWORD(%a6){&10:&3}, %d1 # extract <ea> mode field
bne.w fetch_from_mem # src op is in memory
op010_dreg:
clr.b STAG(%a6) # either NORM or ZERO
bfextu EXC_OPWORD(%a6){&13:&3}, %d1 # extract src reg field
mov.w (tbl_op010_dreg.b,%pc,%d0.w*2), %d0 # jmp based on optype
jmp (tbl_op010_dreg.b,%pc,%d0.w*1) # fetch src from dreg
op010_dst_unnorm:
bsr.l unnorm_fix # fix the dst UNNORM
bra.b op010_dst_cont
swbeg &0x8
tbl_op010_dreg:
short opd_long - tbl_op010_dreg
short opd_sgl - tbl_op010_dreg
short tbl_op010_dreg - tbl_op010_dreg
short tbl_op010_dreg - tbl_op010_dreg
short opd_word - tbl_op010_dreg
short tbl_op010_dreg - tbl_op010_dreg
short opd_byte - tbl_op010_dreg
short tbl_op010_dreg - tbl_op010_dreg
#
# LONG: can be either NORM or ZERO...
#
opd_long:
bsr.l fetch_dreg # fetch long in d0
fmov.l %d0, %fp0 # load a long
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
fbeq.w opd_long_zero # long is a ZERO
rts
opd_long_zero:
mov.b &ZERO, STAG(%a6) # set ZERO optype flag
rts
#
# WORD: can be either NORM or ZERO...
#
opd_word:
bsr.l fetch_dreg # fetch word in d0
fmov.w %d0, %fp0 # load a word
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
fbeq.w opd_word_zero # WORD is a ZERO
rts
opd_word_zero:
mov.b &ZERO, STAG(%a6) # set ZERO optype flag
rts
#
# BYTE: can be either NORM or ZERO...
#
opd_byte:
bsr.l fetch_dreg # fetch word in d0
fmov.b %d0, %fp0 # load a byte
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
fbeq.w opd_byte_zero # byte is a ZERO
rts
opd_byte_zero:
mov.b &ZERO, STAG(%a6) # set ZERO optype flag
rts
#
# SGL: can be either NORM, DENORM, ZERO, INF, QNAN or SNAN but not UNNORM
#
# separate SNANs and DENORMs so they can be loaded w/ special care.
# all others can simply be moved "in" using fmove.
#
opd_sgl:
bsr.l fetch_dreg # fetch sgl in d0
mov.l %d0,L_SCR1(%a6)
lea L_SCR1(%a6), %a0 # pass: ptr to the sgl
bsr.l set_tag_s # determine sgl type
mov.b %d0, STAG(%a6) # save the src tag
cmpi.b %d0, &SNAN # is it an SNAN?
beq.w get_sgl_snan # yes
cmpi.b %d0, &DENORM # is it a DENORM?
beq.w get_sgl_denorm # yes
fmov.s (%a0), %fp0 # no, so can load it regular
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
rts
##############################################################################
#########################################################################
# fetch_from_mem(): #
# - src is out in memory. must: #
# (1) calc ea - must read AFTER you know the src type since #
# if the ea is -() or ()+, need to know # of bytes. #
# (2) read it in from either user or supervisor space #
# (3) if (b || w || l) then simply read in #
# if (s || d || x) then check for SNAN,UNNORM,DENORM #
# if (packed) then punt for now #
# INPUT: #
# %d0 : src type field #
#########################################################################
fetch_from_mem:
clr.b STAG(%a6) # either NORM or ZERO
mov.w (tbl_fp_type.b,%pc,%d0.w*2), %d0 # index by src type field
jmp (tbl_fp_type.b,%pc,%d0.w*1)
swbeg &0x8
tbl_fp_type:
short load_long - tbl_fp_type
short load_sgl - tbl_fp_type
short load_ext - tbl_fp_type
short load_packed - tbl_fp_type
short load_word - tbl_fp_type
short load_dbl - tbl_fp_type
short load_byte - tbl_fp_type
short tbl_fp_type - tbl_fp_type
#########################################
# load a LONG into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 4 bytes into L_SCR1 #
# (3) fmov.l into %fp0 #
#########################################
load_long:
movq.l &0x4, %d0 # pass: 4 (bytes)
bsr.l _dcalc_ea # calc <ea>; <ea> in %a0
cmpi.b SPCOND_FLG(%a6),&immed_flg
beq.b load_long_immed
bsr.l _dmem_read_long # fetch src operand from memory
tst.l %d1 # did dfetch fail?
bne.l facc_in_l # yes
load_long_cont:
fmov.l %d0, %fp0 # read into %fp0;convert to xprec
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
fbeq.w load_long_zero # src op is a ZERO
rts
load_long_zero:
mov.b &ZERO, STAG(%a6) # set optype tag to ZERO
rts
load_long_immed:
bsr.l _imem_read_long # fetch src operand immed data
tst.l %d1 # did ifetch fail?
bne.l funimp_iacc # yes
bra.b load_long_cont
#########################################
# load a WORD into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 2 bytes into L_SCR1 #
# (3) fmov.w into %fp0 #
#########################################
load_word:
movq.l &0x2, %d0 # pass: 2 (bytes)
bsr.l _dcalc_ea # calc <ea>; <ea> in %a0
cmpi.b SPCOND_FLG(%a6),&immed_flg
beq.b load_word_immed
bsr.l _dmem_read_word # fetch src operand from memory
tst.l %d1 # did dfetch fail?
bne.l facc_in_w # yes
load_word_cont:
fmov.w %d0, %fp0 # read into %fp0;convert to xprec
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
fbeq.w load_word_zero # src op is a ZERO
rts
load_word_zero:
mov.b &ZERO, STAG(%a6) # set optype tag to ZERO
rts
load_word_immed:
bsr.l _imem_read_word # fetch src operand immed data
tst.l %d1 # did ifetch fail?
bne.l funimp_iacc # yes
bra.b load_word_cont
#########################################
# load a BYTE into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 1 byte into L_SCR1 #
# (3) fmov.b into %fp0 #
#########################################
load_byte:
movq.l &0x1, %d0 # pass: 1 (byte)
bsr.l _dcalc_ea # calc <ea>; <ea> in %a0
cmpi.b SPCOND_FLG(%a6),&immed_flg
beq.b load_byte_immed
bsr.l _dmem_read_byte # fetch src operand from memory
tst.l %d1 # did dfetch fail?
bne.l facc_in_b # yes
load_byte_cont:
fmov.b %d0, %fp0 # read into %fp0;convert to xprec
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
fbeq.w load_byte_zero # src op is a ZERO
rts
load_byte_zero:
mov.b &ZERO, STAG(%a6) # set optype tag to ZERO
rts
load_byte_immed:
bsr.l _imem_read_word # fetch src operand immed data
tst.l %d1 # did ifetch fail?
bne.l funimp_iacc # yes
bra.b load_byte_cont
#########################################
# load a SGL into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 4 bytes into L_SCR1 #
# (3) fmov.s into %fp0 #
#########################################
load_sgl:
movq.l &0x4, %d0 # pass: 4 (bytes)
bsr.l _dcalc_ea # calc <ea>; <ea> in %a0
cmpi.b SPCOND_FLG(%a6),&immed_flg
beq.b load_sgl_immed
bsr.l _dmem_read_long # fetch src operand from memory
mov.l %d0, L_SCR1(%a6) # store src op on stack
tst.l %d1 # did dfetch fail?
bne.l facc_in_l # yes
load_sgl_cont:
lea L_SCR1(%a6), %a0 # pass: ptr to sgl src op
bsr.l set_tag_s # determine src type tag
mov.b %d0, STAG(%a6) # save src optype tag on stack
cmpi.b %d0, &DENORM # is it a sgl DENORM?
beq.w get_sgl_denorm # yes
cmpi.b %d0, &SNAN # is it a sgl SNAN?
beq.w get_sgl_snan # yes
fmov.s L_SCR1(%a6), %fp0 # read into %fp0;convert to xprec
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
rts
load_sgl_immed:
bsr.l _imem_read_long # fetch src operand immed data
tst.l %d1 # did ifetch fail?
bne.l funimp_iacc # yes
bra.b load_sgl_cont
# must convert sgl denorm format to an Xprec denorm fmt suitable for
# normalization...
# %a0 : points to sgl denorm
get_sgl_denorm:
clr.w FP_SRC_EX(%a6)
bfextu (%a0){&9:&23}, %d0 # fetch sgl hi(_mantissa)
lsl.l &0x8, %d0
mov.l %d0, FP_SRC_HI(%a6) # set ext hi(_mantissa)
clr.l FP_SRC_LO(%a6) # set ext lo(_mantissa)
clr.w FP_SRC_EX(%a6)
btst &0x7, (%a0) # is sgn bit set?
beq.b sgl_dnrm_norm
bset &0x7, FP_SRC_EX(%a6) # set sgn of xprec value
sgl_dnrm_norm:
lea FP_SRC(%a6), %a0
bsr.l norm # normalize number
mov.w &0x3f81, %d1 # xprec exp = 0x3f81
sub.w %d0, %d1 # exp = 0x3f81 - shft amt.
or.w %d1, FP_SRC_EX(%a6) # {sgn,exp}
mov.b &NORM, STAG(%a6) # fix src type tag
rts
# convert sgl to ext SNAN
# %a0 : points to sgl SNAN
get_sgl_snan:
mov.w &0x7fff, FP_SRC_EX(%a6) # set exp of SNAN
bfextu (%a0){&9:&23}, %d0
lsl.l &0x8, %d0 # extract and insert hi(man)
mov.l %d0, FP_SRC_HI(%a6)
clr.l FP_SRC_LO(%a6)
btst &0x7, (%a0) # see if sign of SNAN is set
beq.b no_sgl_snan_sgn
bset &0x7, FP_SRC_EX(%a6)
no_sgl_snan_sgn:
rts
#########################################
# load a DBL into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 8 bytes into L_SCR(1,2)#
# (3) fmov.d into %fp0 #
#########################################
load_dbl:
movq.l &0x8, %d0 # pass: 8 (bytes)
bsr.l _dcalc_ea # calc <ea>; <ea> in %a0
cmpi.b SPCOND_FLG(%a6),&immed_flg
beq.b load_dbl_immed
lea L_SCR1(%a6), %a1 # pass: ptr to input dbl tmp space
movq.l &0x8, %d0 # pass: # bytes to read
bsr.l _dmem_read # fetch src operand from memory
tst.l %d1 # did dfetch fail?
bne.l facc_in_d # yes
load_dbl_cont:
lea L_SCR1(%a6), %a0 # pass: ptr to input dbl
bsr.l set_tag_d # determine src type tag
mov.b %d0, STAG(%a6) # set src optype tag
cmpi.b %d0, &DENORM # is it a dbl DENORM?
beq.w get_dbl_denorm # yes
cmpi.b %d0, &SNAN # is it a dbl SNAN?
beq.w get_dbl_snan # yes
fmov.d L_SCR1(%a6), %fp0 # read into %fp0;convert to xprec
fmovm.x &0x80, FP_SRC(%a6) # return src op in FP_SRC
rts
load_dbl_immed:
lea L_SCR1(%a6), %a1 # pass: ptr to input dbl tmp space
movq.l &0x8, %d0 # pass: # bytes to read
bsr.l _imem_read # fetch src operand from memory
tst.l %d1 # did ifetch fail?
bne.l funimp_iacc # yes
bra.b load_dbl_cont
# must convert dbl denorm format to an Xprec denorm fmt suitable for
# normalization...
# %a0 : loc. of dbl denorm
get_dbl_denorm:
clr.w FP_SRC_EX(%a6)
bfextu (%a0){&12:&31}, %d0 # fetch hi(_mantissa)
mov.l %d0, FP_SRC_HI(%a6)
bfextu 4(%a0){&11:&21}, %d0 # fetch lo(_mantissa)
mov.l &0xb, %d1
lsl.l %d1, %d0
mov.l %d0, FP_SRC_LO(%a6)
btst &0x7, (%a0) # is sgn bit set?
beq.b dbl_dnrm_norm
bset &0x7, FP_SRC_EX(%a6) # set sgn of xprec value
dbl_dnrm_norm:
lea FP_SRC(%a6), %a0
bsr.l norm # normalize number
mov.w &0x3c01, %d1 # xprec exp = 0x3c01
sub.w %d0, %d1 # exp = 0x3c01 - shft amt.
or.w %d1, FP_SRC_EX(%a6) # {sgn,exp}
mov.b &NORM, STAG(%a6) # fix src type tag
rts
# convert dbl to ext SNAN
# %a0 : points to dbl SNAN
get_dbl_snan:
mov.w &0x7fff, FP_SRC_EX(%a6) # set exp of SNAN
bfextu (%a0){&12:&31}, %d0 # fetch hi(_mantissa)
mov.l %d0, FP_SRC_HI(%a6)
bfextu 4(%a0){&11:&21}, %d0 # fetch lo(_mantissa)
mov.l &0xb, %d1
lsl.l %d1, %d0
mov.l %d0, FP_SRC_LO(%a6)
btst &0x7, (%a0) # see if sign of SNAN is set
beq.b no_dbl_snan_sgn
bset &0x7, FP_SRC_EX(%a6)
no_dbl_snan_sgn:
rts
#################################################
# load a Xprec into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 12 bytes into L_SCR(1,2) #
# (3) fmov.x into %fp0 #
#################################################
load_ext:
mov.l &0xc, %d0 # pass: 12 (bytes)
bsr.l _dcalc_ea # calc <ea>
lea FP_SRC(%a6), %a1 # pass: ptr to input ext tmp space
mov.l &0xc, %d0 # pass: # of bytes to read
bsr.l _dmem_read # fetch src operand from memory
tst.l %d1 # did dfetch fail?
bne.l facc_in_x # yes
lea FP_SRC(%a6), %a0 # pass: ptr to src op
bsr.l set_tag_x # determine src type tag
cmpi.b %d0, &UNNORM # is the src op an UNNORM?
beq.b load_ext_unnorm # yes
mov.b %d0, STAG(%a6) # store the src optype tag
rts
load_ext_unnorm:
bsr.l unnorm_fix # fix the src UNNORM
mov.b %d0, STAG(%a6) # store the src optype tag
rts
#################################################
# load a packed into %fp0: #
# -number can't fault #
# (1) calc ea #
# (2) read 12 bytes into L_SCR(1,2,3) #
# (3) fmov.x into %fp0 #
#################################################
load_packed:
bsr.l get_packed
lea FP_SRC(%a6),%a0 # pass ptr to src op
bsr.l set_tag_x # determine src type tag
cmpi.b %d0,&UNNORM # is the src op an UNNORM ZERO?
beq.b load_packed_unnorm # yes
mov.b %d0,STAG(%a6) # store the src optype tag
rts
load_packed_unnorm:
bsr.l unnorm_fix # fix the UNNORM ZERO
mov.b %d0,STAG(%a6) # store the src optype tag
rts
#########################################################################
# XDEF **************************************************************** #
# fout(): move from fp register to memory or data register #
# #
# XREF **************************************************************** #
# _round() - needed to create EXOP for sgl/dbl precision #
# norm() - needed to create EXOP for extended precision #
# ovf_res() - create default overflow result for sgl/dbl precision#
# unf_res() - create default underflow result for sgl/dbl prec. #
# dst_dbl() - create rounded dbl precision result. #
# dst_sgl() - create rounded sgl precision result. #
# fetch_dreg() - fetch dynamic k-factor reg for packed. #
# bindec() - convert FP binary number to packed number. #
# _mem_write() - write data to memory. #
# _mem_write2() - write data to memory unless supv mode -(a7) exc.#
# _dmem_write_{byte,word,long}() - write data to memory. #
# store_dreg_{b,w,l}() - store data to data register file. #
# facc_out_{b,w,l,d,x}() - data access error occurred. #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 : intermediate underflow or overflow result if #
# OVFL/UNFL occurred for a sgl or dbl operand #
# #
# ALGORITHM *********************************************************** #
# This routine is accessed by many handlers that need to do an #
# opclass three move of an operand out to memory. #
# Decode an fmove out (opclass 3) instruction to determine if #
# it's b,w,l,s,d,x, or p in size. b,w,l can be stored to either a data #
# register or memory. The algorithm uses a standard "fmove" to create #
# the rounded result. Also, since exceptions are disabled, this also #
# create the correct OPERR default result if appropriate. #
# For sgl or dbl precision, overflow or underflow can occur. If #
# either occurs and is enabled, the EXOP. #
# For extended precision, the stacked <ea> must be fixed along #
# w/ the address index register as appropriate w/ _calc_ea_fout(). If #
# the source is a denorm and if underflow is enabled, an EXOP must be #
# created. #
# For packed, the k-factor must be fetched from the instruction #
# word or a data register. The <ea> must be fixed as w/ extended #
# precision. Then, bindec() is called to create the appropriate #
# packed result. #
# If at any time an access error is flagged by one of the move- #
# to-memory routines, then a special exit must be made so that the #
# access error can be handled properly. #
# #
#########################################################################
global fout
fout:
bfextu EXC_CMDREG(%a6){&3:&3},%d1 # extract dst fmt
mov.w (tbl_fout.b,%pc,%d1.w*2),%a1 # use as index
jmp (tbl_fout.b,%pc,%a1) # jump to routine
swbeg &0x8
tbl_fout:
short fout_long - tbl_fout
short fout_sgl - tbl_fout
short fout_ext - tbl_fout
short fout_pack - tbl_fout
short fout_word - tbl_fout
short fout_dbl - tbl_fout
short fout_byte - tbl_fout
short fout_pack - tbl_fout
#################################################################
# fmove.b out ###################################################
#################################################################
# Only "Unimplemented Data Type" exceptions enter here. The operand
# is either a DENORM or a NORM.
fout_byte:
tst.b STAG(%a6) # is operand normalized?
bne.b fout_byte_denorm # no
fmovm.x SRC(%a0),&0x80 # load value
fout_byte_norm:
fmov.l %d0,%fpcr # insert rnd prec,mode
fmov.b %fp0,%d0 # exec move out w/ correct rnd mode
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # fetch FPSR
or.w %d1,2+USER_FPSR(%a6) # save new exc,accrued bits
mov.b 1+EXC_OPWORD(%a6),%d1 # extract dst mode
andi.b &0x38,%d1 # is mode == 0? (Dreg dst)
beq.b fout_byte_dn # must save to integer regfile
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
bsr.l _dmem_write_byte # write byte
tst.l %d1 # did dstore fail?
bne.l facc_out_b # yes
rts
fout_byte_dn:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract Dn
andi.w &0x7,%d1
bsr.l store_dreg_b
rts
fout_byte_denorm:
mov.l SRC_EX(%a0),%d1
andi.l &0x80000000,%d1 # keep DENORM sign
ori.l &0x00800000,%d1 # make smallest sgl
fmov.s %d1,%fp0
bra.b fout_byte_norm
#################################################################
# fmove.w out ###################################################
#################################################################
# Only "Unimplemented Data Type" exceptions enter here. The operand
# is either a DENORM or a NORM.
fout_word:
tst.b STAG(%a6) # is operand normalized?
bne.b fout_word_denorm # no
fmovm.x SRC(%a0),&0x80 # load value
fout_word_norm:
fmov.l %d0,%fpcr # insert rnd prec:mode
fmov.w %fp0,%d0 # exec move out w/ correct rnd mode
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # fetch FPSR
or.w %d1,2+USER_FPSR(%a6) # save new exc,accrued bits
mov.b 1+EXC_OPWORD(%a6),%d1 # extract dst mode
andi.b &0x38,%d1 # is mode == 0? (Dreg dst)
beq.b fout_word_dn # must save to integer regfile
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
bsr.l _dmem_write_word # write word
tst.l %d1 # did dstore fail?
bne.l facc_out_w # yes
rts
fout_word_dn:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract Dn
andi.w &0x7,%d1
bsr.l store_dreg_w
rts
fout_word_denorm:
mov.l SRC_EX(%a0),%d1
andi.l &0x80000000,%d1 # keep DENORM sign
ori.l &0x00800000,%d1 # make smallest sgl
fmov.s %d1,%fp0
bra.b fout_word_norm
#################################################################
# fmove.l out ###################################################
#################################################################
# Only "Unimplemented Data Type" exceptions enter here. The operand
# is either a DENORM or a NORM.
fout_long:
tst.b STAG(%a6) # is operand normalized?
bne.b fout_long_denorm # no
fmovm.x SRC(%a0),&0x80 # load value
fout_long_norm:
fmov.l %d0,%fpcr # insert rnd prec:mode
fmov.l %fp0,%d0 # exec move out w/ correct rnd mode
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # fetch FPSR
or.w %d1,2+USER_FPSR(%a6) # save new exc,accrued bits
fout_long_write:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract dst mode
andi.b &0x38,%d1 # is mode == 0? (Dreg dst)
beq.b fout_long_dn # must save to integer regfile
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
bsr.l _dmem_write_long # write long
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
rts
fout_long_dn:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract Dn
andi.w &0x7,%d1
bsr.l store_dreg_l
rts
fout_long_denorm:
mov.l SRC_EX(%a0),%d1
andi.l &0x80000000,%d1 # keep DENORM sign
ori.l &0x00800000,%d1 # make smallest sgl
fmov.s %d1,%fp0
bra.b fout_long_norm
#################################################################
# fmove.x out ###################################################
#################################################################
# Only "Unimplemented Data Type" exceptions enter here. The operand
# is either a DENORM or a NORM.
# The DENORM causes an Underflow exception.
fout_ext:
# we copy the extended precision result to FP_SCR0 so that the reserved
# 16-bit field gets zeroed. we do this since we promise not to disturb
# what's at SRC(a0).
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
clr.w 2+FP_SCR0_EX(%a6) # clear reserved field
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
fmovm.x SRC(%a0),&0x80 # return result
bsr.l _calc_ea_fout # fix stacked <ea>
mov.l %a0,%a1 # pass: dst addr
lea FP_SCR0(%a6),%a0 # pass: src addr
mov.l &0xc,%d0 # pass: opsize is 12 bytes
# we must not yet write the extended precision data to the stack
# in the pre-decrement case from supervisor mode or else we'll corrupt
# the stack frame. so, leave it in FP_SRC for now and deal with it later...
cmpi.b SPCOND_FLG(%a6),&mda7_flg
beq.b fout_ext_a7
bsr.l _dmem_write # write ext prec number to memory
tst.l %d1 # did dstore fail?
bne.w fout_ext_err # yes
tst.b STAG(%a6) # is operand normalized?
bne.b fout_ext_denorm # no
rts
# the number is a DENORM. must set the underflow exception bit
fout_ext_denorm:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set underflow exc bit
mov.b FPCR_ENABLE(%a6),%d0
andi.b &0x0a,%d0 # is UNFL or INEX enabled?
bne.b fout_ext_exc # yes
rts
# we don't want to do the write if the exception occurred in supervisor mode
# so _mem_write2() handles this for us.
fout_ext_a7:
bsr.l _mem_write2 # write ext prec number to memory
tst.l %d1 # did dstore fail?
bne.w fout_ext_err # yes
tst.b STAG(%a6) # is operand normalized?
bne.b fout_ext_denorm # no
rts
fout_ext_exc:
lea FP_SCR0(%a6),%a0
bsr.l norm # normalize the mantissa
neg.w %d0 # new exp = -(shft amt)
andi.w &0x7fff,%d0
andi.w &0x8000,FP_SCR0_EX(%a6) # keep only old sign
or.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
fout_ext_err:
mov.l EXC_A6(%a6),(%a6) # fix stacked a6
bra.l facc_out_x
#########################################################################
# fmove.s out ###########################################################
#########################################################################
fout_sgl:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl prec
mov.l %d0,L_SCR3(%a6) # save rnd prec,mode on stack
#
# operand is a normalized number. first, we check to see if the move out
# would cause either an underflow or overflow. these cases are handled
# separately. otherwise, set the FPCR to the proper rounding mode and
# execute the move.
#
mov.w SRC_EX(%a0),%d0 # extract exponent
andi.w &0x7fff,%d0 # strip sign
cmpi.w %d0,&SGL_HI # will operand overflow?
bgt.w fout_sgl_ovfl # yes; go handle OVFL
beq.w fout_sgl_may_ovfl # maybe; go handle possible OVFL
cmpi.w %d0,&SGL_LO # will operand underflow?
blt.w fout_sgl_unfl # yes; go handle underflow
#
# NORMs(in range) can be stored out by a simple "fmov.s"
# Unnormalized inputs can come through this point.
#
fout_sgl_exg:
fmovm.x SRC(%a0),&0x80 # fetch fop from stack
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmov.s %fp0,%d0 # store does convert and round
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.w %d1,2+USER_FPSR(%a6) # set possible inex2/ainex
fout_sgl_exg_write:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract dst mode
andi.b &0x38,%d1 # is mode == 0? (Dreg dst)
beq.b fout_sgl_exg_write_dn # must save to integer regfile
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
bsr.l _dmem_write_long # write long
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
rts
fout_sgl_exg_write_dn:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract Dn
andi.w &0x7,%d1
bsr.l store_dreg_l
rts
#
# here, we know that the operand would UNFL if moved out to single prec,
# so, denorm and round and then use generic store single routine to
# write the value to memory.
#
fout_sgl_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set UNFL
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.l %a0,-(%sp)
clr.l %d0 # pass: S.F. = 0
cmpi.b STAG(%a6),&DENORM # fetch src optype tag
bne.b fout_sgl_unfl_cont # let DENORMs fall through
lea FP_SCR0(%a6),%a0
bsr.l norm # normalize the DENORM
fout_sgl_unfl_cont:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calc default underflow result
lea FP_SCR0(%a6),%a0 # pass: ptr to fop
bsr.l dst_sgl # convert to single prec
mov.b 1+EXC_OPWORD(%a6),%d1 # extract dst mode
andi.b &0x38,%d1 # is mode == 0? (Dreg dst)
beq.b fout_sgl_unfl_dn # must save to integer regfile
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
bsr.l _dmem_write_long # write long
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.b fout_sgl_unfl_chkexc
fout_sgl_unfl_dn:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract Dn
andi.w &0x7,%d1
bsr.l store_dreg_l
fout_sgl_unfl_chkexc:
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0a,%d1 # is UNFL or INEX enabled?
bne.w fout_sd_exc_unfl # yes
addq.l &0x4,%sp
rts
#
# it's definitely an overflow so call ovf_res to get the correct answer
#
fout_sgl_ovfl:
tst.b 3+SRC_HI(%a0) # is result inexact?
bne.b fout_sgl_ovfl_inex2
tst.l SRC_LO(%a0) # is result inexact?
bne.b fout_sgl_ovfl_inex2
ori.w &ovfl_inx_mask,2+USER_FPSR(%a6) # set ovfl/aovfl/ainex
bra.b fout_sgl_ovfl_cont
fout_sgl_ovfl_inex2:
ori.w &ovfinx_mask,2+USER_FPSR(%a6) # set ovfl/aovfl/ainex/inex2
fout_sgl_ovfl_cont:
mov.l %a0,-(%sp)
# call ovf_res() w/ sgl prec and the correct rnd mode to create the default
# overflow result. DON'T save the returned ccodes from ovf_res() since
# fmove out doesn't alter them.
tst.b SRC_EX(%a0) # is operand negative?
smi %d1 # set if so
mov.l L_SCR3(%a6),%d0 # pass: sgl prec,rnd mode
bsr.l ovf_res # calc OVFL result
fmovm.x (%a0),&0x80 # load default overflow result
fmov.s %fp0,%d0 # store to single
mov.b 1+EXC_OPWORD(%a6),%d1 # extract dst mode
andi.b &0x38,%d1 # is mode == 0? (Dreg dst)
beq.b fout_sgl_ovfl_dn # must save to integer regfile
mov.l EXC_EA(%a6),%a0 # stacked <ea> is correct
bsr.l _dmem_write_long # write long
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.b fout_sgl_ovfl_chkexc
fout_sgl_ovfl_dn:
mov.b 1+EXC_OPWORD(%a6),%d1 # extract Dn
andi.w &0x7,%d1
bsr.l store_dreg_l
fout_sgl_ovfl_chkexc:
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0a,%d1 # is UNFL or INEX enabled?
bne.w fout_sd_exc_ovfl # yes
addq.l &0x4,%sp
rts
#
# move out MAY overflow:
# (1) force the exp to 0x3fff
# (2) do a move w/ appropriate rnd mode
# (3) if exp still equals zero, then insert original exponent
# for the correct result.
# if exp now equals one, then it overflowed so call ovf_res.
#
fout_sgl_may_ovfl:
mov.w SRC_EX(%a0),%d1 # fetch current sign
andi.w &0x8000,%d1 # keep it,clear exp
ori.w &0x3fff,%d1 # insert exp = 0
mov.w %d1,FP_SCR0_EX(%a6) # insert scaled exp
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6) # copy hi(man)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6) # copy lo(man)
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # force fop to be rounded
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp0 # need absolute value
fcmp.b %fp0,&0x2 # did exponent increase?
fblt.w fout_sgl_exg # no; go finish NORM
bra.w fout_sgl_ovfl # yes; go handle overflow
################
fout_sd_exc_unfl:
mov.l (%sp)+,%a0
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
cmpi.b STAG(%a6),&DENORM # was src a DENORM?
bne.b fout_sd_exc_cont # no
lea FP_SCR0(%a6),%a0
bsr.l norm
neg.l %d0
andi.w &0x7fff,%d0
bfins %d0,FP_SCR0_EX(%a6){&1:&15}
bra.b fout_sd_exc_cont
fout_sd_exc:
fout_sd_exc_ovfl:
mov.l (%sp)+,%a0 # restore a0
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
fout_sd_exc_cont:
bclr &0x7,FP_SCR0_EX(%a6) # clear sign bit
sne.b 2+FP_SCR0_EX(%a6) # set internal sign bit
lea FP_SCR0(%a6),%a0 # pass: ptr to DENORM
mov.b 3+L_SCR3(%a6),%d1
lsr.b &0x4,%d1
andi.w &0x0c,%d1
swap %d1
mov.b 3+L_SCR3(%a6),%d1
lsr.b &0x4,%d1
andi.w &0x03,%d1
clr.l %d0 # pass: zero g,r,s
bsr.l _round # round the DENORM
tst.b 2+FP_SCR0_EX(%a6) # is EXOP negative?
beq.b fout_sd_exc_done # no
bset &0x7,FP_SCR0_EX(%a6) # yes
fout_sd_exc_done:
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#################################################################
# fmove.d out ###################################################
#################################################################
fout_dbl:
andi.b &0x30,%d0 # clear rnd prec
ori.b &d_mode*0x10,%d0 # insert dbl prec
mov.l %d0,L_SCR3(%a6) # save rnd prec,mode on stack
#
# operand is a normalized number. first, we check to see if the move out
# would cause either an underflow or overflow. these cases are handled
# separately. otherwise, set the FPCR to the proper rounding mode and
# execute the move.
#
mov.w SRC_EX(%a0),%d0 # extract exponent
andi.w &0x7fff,%d0 # strip sign
cmpi.w %d0,&DBL_HI # will operand overflow?
bgt.w fout_dbl_ovfl # yes; go handle OVFL
beq.w fout_dbl_may_ovfl # maybe; go handle possible OVFL
cmpi.w %d0,&DBL_LO # will operand underflow?
blt.w fout_dbl_unfl # yes; go handle underflow
#
# NORMs(in range) can be stored out by a simple "fmov.d"
# Unnormalized inputs can come through this point.
#
fout_dbl_exg:
fmovm.x SRC(%a0),&0x80 # fetch fop from stack
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmov.d %fp0,L_SCR1(%a6) # store does convert and round
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d0 # save FPSR
or.w %d0,2+USER_FPSR(%a6) # set possible inex2/ainex
mov.l EXC_EA(%a6),%a1 # pass: dst addr
lea L_SCR1(%a6),%a0 # pass: src addr
movq.l &0x8,%d0 # pass: opsize is 8 bytes
bsr.l _dmem_write # store dbl fop to memory
tst.l %d1 # did dstore fail?
bne.l facc_out_d # yes
rts # no; so we're finished
#
# here, we know that the operand would UNFL if moved out to double prec,
# so, denorm and round and then use generic store double routine to
# write the value to memory.
#
fout_dbl_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set UNFL
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.l %a0,-(%sp)
clr.l %d0 # pass: S.F. = 0
cmpi.b STAG(%a6),&DENORM # fetch src optype tag
bne.b fout_dbl_unfl_cont # let DENORMs fall through
lea FP_SCR0(%a6),%a0
bsr.l norm # normalize the DENORM
fout_dbl_unfl_cont:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calc default underflow result
lea FP_SCR0(%a6),%a0 # pass: ptr to fop
bsr.l dst_dbl # convert to single prec
mov.l %d0,L_SCR1(%a6)
mov.l %d1,L_SCR2(%a6)
mov.l EXC_EA(%a6),%a1 # pass: dst addr
lea L_SCR1(%a6),%a0 # pass: src addr
movq.l &0x8,%d0 # pass: opsize is 8 bytes
bsr.l _dmem_write # store dbl fop to memory
tst.l %d1 # did dstore fail?
bne.l facc_out_d # yes
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0a,%d1 # is UNFL or INEX enabled?
bne.w fout_sd_exc_unfl # yes
addq.l &0x4,%sp
rts
#
# it's definitely an overflow so call ovf_res to get the correct answer
#
fout_dbl_ovfl:
mov.w 2+SRC_LO(%a0),%d0
andi.w &0x7ff,%d0
bne.b fout_dbl_ovfl_inex2
ori.w &ovfl_inx_mask,2+USER_FPSR(%a6) # set ovfl/aovfl/ainex
bra.b fout_dbl_ovfl_cont
fout_dbl_ovfl_inex2:
ori.w &ovfinx_mask,2+USER_FPSR(%a6) # set ovfl/aovfl/ainex/inex2
fout_dbl_ovfl_cont:
mov.l %a0,-(%sp)
# call ovf_res() w/ dbl prec and the correct rnd mode to create the default
# overflow result. DON'T save the returned ccodes from ovf_res() since
# fmove out doesn't alter them.
tst.b SRC_EX(%a0) # is operand negative?
smi %d1 # set if so
mov.l L_SCR3(%a6),%d0 # pass: dbl prec,rnd mode
bsr.l ovf_res # calc OVFL result
fmovm.x (%a0),&0x80 # load default overflow result
fmov.d %fp0,L_SCR1(%a6) # store to double
mov.l EXC_EA(%a6),%a1 # pass: dst addr
lea L_SCR1(%a6),%a0 # pass: src addr
movq.l &0x8,%d0 # pass: opsize is 8 bytes
bsr.l _dmem_write # store dbl fop to memory
tst.l %d1 # did dstore fail?
bne.l facc_out_d # yes
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0a,%d1 # is UNFL or INEX enabled?
bne.w fout_sd_exc_ovfl # yes
addq.l &0x4,%sp
rts
#
# move out MAY overflow:
# (1) force the exp to 0x3fff
# (2) do a move w/ appropriate rnd mode
# (3) if exp still equals zero, then insert original exponent
# for the correct result.
# if exp now equals one, then it overflowed so call ovf_res.
#
fout_dbl_may_ovfl:
mov.w SRC_EX(%a0),%d1 # fetch current sign
andi.w &0x8000,%d1 # keep it,clear exp
ori.w &0x3fff,%d1 # insert exp = 0
mov.w %d1,FP_SCR0_EX(%a6) # insert scaled exp
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6) # copy hi(man)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6) # copy lo(man)
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # force fop to be rounded
fmov.l &0x0,%fpcr # clear FPCR
fabs.x %fp0 # need absolute value
fcmp.b %fp0,&0x2 # did exponent increase?
fblt.w fout_dbl_exg # no; go finish NORM
bra.w fout_dbl_ovfl # yes; go handle overflow
#########################################################################
# XDEF **************************************************************** #
# dst_dbl(): create double precision value from extended prec. #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = pointer to source operand in extended precision #
# #
# OUTPUT ************************************************************** #
# d0 = hi(double precision result) #
# d1 = lo(double precision result) #
# #
# ALGORITHM *********************************************************** #
# #
# Changes extended precision to double precision. #
# Note: no attempt is made to round the extended value to double. #
# dbl_sign = ext_sign #
# dbl_exp = ext_exp - $3fff(ext bias) + $7ff(dbl bias) #
# get rid of ext integer bit #
# dbl_mant = ext_mant{62:12} #
# #
# --------------- --------------- --------------- #
# extended -> |s| exp | |1| ms mant | | ls mant | #
# --------------- --------------- --------------- #
# 95 64 63 62 32 31 11 0 #
# | | #
# | | #
# | | #
# v v #
# --------------- --------------- #
# double -> |s|exp| mant | | mant | #
# --------------- --------------- #
# 63 51 32 31 0 #
# #
#########################################################################
dst_dbl:
clr.l %d0 # clear d0
mov.w FTEMP_EX(%a0),%d0 # get exponent
subi.w &EXT_BIAS,%d0 # subtract extended precision bias
addi.w &DBL_BIAS,%d0 # add double precision bias
tst.b FTEMP_HI(%a0) # is number a denorm?
bmi.b dst_get_dupper # no
subq.w &0x1,%d0 # yes; denorm bias = DBL_BIAS - 1
dst_get_dupper:
swap %d0 # d0 now in upper word
lsl.l &0x4,%d0 # d0 in proper place for dbl prec exp
tst.b FTEMP_EX(%a0) # test sign
bpl.b dst_get_dman # if postive, go process mantissa
bset &0x1f,%d0 # if negative, set sign
dst_get_dman:
mov.l FTEMP_HI(%a0),%d1 # get ms mantissa
bfextu %d1{&1:&20},%d1 # get upper 20 bits of ms
or.l %d1,%d0 # put these bits in ms word of double
mov.l %d0,L_SCR1(%a6) # put the new exp back on the stack
mov.l FTEMP_HI(%a0),%d1 # get ms mantissa
mov.l &21,%d0 # load shift count
lsl.l %d0,%d1 # put lower 11 bits in upper bits
mov.l %d1,L_SCR2(%a6) # build lower lword in memory
mov.l FTEMP_LO(%a0),%d1 # get ls mantissa
bfextu %d1{&0:&21},%d0 # get ls 21 bits of double
mov.l L_SCR2(%a6),%d1
or.l %d0,%d1 # put them in double result
mov.l L_SCR1(%a6),%d0
rts
#########################################################################
# XDEF **************************************************************** #
# dst_sgl(): create single precision value from extended prec #
# #
# XREF **************************************************************** #
# #
# INPUT *************************************************************** #
# a0 = pointer to source operand in extended precision #
# #
# OUTPUT ************************************************************** #
# d0 = single precision result #
# #
# ALGORITHM *********************************************************** #
# #
# Changes extended precision to single precision. #
# sgl_sign = ext_sign #
# sgl_exp = ext_exp - $3fff(ext bias) + $7f(sgl bias) #
# get rid of ext integer bit #
# sgl_mant = ext_mant{62:12} #
# #
# --------------- --------------- --------------- #
# extended -> |s| exp | |1| ms mant | | ls mant | #
# --------------- --------------- --------------- #
# 95 64 63 62 40 32 31 12 0 #
# | | #
# | | #
# | | #
# v v #
# --------------- #
# single -> |s|exp| mant | #
# --------------- #
# 31 22 0 #
# #
#########################################################################
dst_sgl:
clr.l %d0
mov.w FTEMP_EX(%a0),%d0 # get exponent
subi.w &EXT_BIAS,%d0 # subtract extended precision bias
addi.w &SGL_BIAS,%d0 # add single precision bias
tst.b FTEMP_HI(%a0) # is number a denorm?
bmi.b dst_get_supper # no
subq.w &0x1,%d0 # yes; denorm bias = SGL_BIAS - 1
dst_get_supper:
swap %d0 # put exp in upper word of d0
lsl.l &0x7,%d0 # shift it into single exp bits
tst.b FTEMP_EX(%a0) # test sign
bpl.b dst_get_sman # if positive, continue
bset &0x1f,%d0 # if negative, put in sign first
dst_get_sman:
mov.l FTEMP_HI(%a0),%d1 # get ms mantissa
andi.l &0x7fffff00,%d1 # get upper 23 bits of ms
lsr.l &0x8,%d1 # and put them flush right
or.l %d1,%d0 # put these bits in ms word of single
rts
##############################################################################
fout_pack:
bsr.l _calc_ea_fout # fetch the <ea>
mov.l %a0,-(%sp)
mov.b STAG(%a6),%d0 # fetch input type
bne.w fout_pack_not_norm # input is not NORM
fout_pack_norm:
btst &0x4,EXC_CMDREG(%a6) # static or dynamic?
beq.b fout_pack_s # static
fout_pack_d:
mov.b 1+EXC_CMDREG(%a6),%d1 # fetch dynamic reg
lsr.b &0x4,%d1
andi.w &0x7,%d1
bsr.l fetch_dreg # fetch Dn w/ k-factor
bra.b fout_pack_type
fout_pack_s:
mov.b 1+EXC_CMDREG(%a6),%d0 # fetch static field
fout_pack_type:
bfexts %d0{&25:&7},%d0 # extract k-factor
mov.l %d0,-(%sp)
lea FP_SRC(%a6),%a0 # pass: ptr to input
# bindec is currently scrambling FP_SRC for denorm inputs.
# we'll have to change this, but for now, tough luck!!!
bsr.l bindec # convert xprec to packed
# andi.l &0xcfff000f,FP_SCR0(%a6) # clear unused fields
andi.l &0xcffff00f,FP_SCR0(%a6) # clear unused fields
mov.l (%sp)+,%d0
tst.b 3+FP_SCR0_EX(%a6)
bne.b fout_pack_set
tst.l FP_SCR0_HI(%a6)
bne.b fout_pack_set
tst.l FP_SCR0_LO(%a6)
bne.b fout_pack_set
# add the extra condition that only if the k-factor was zero, too, should
# we zero the exponent
tst.l %d0
bne.b fout_pack_set
# "mantissa" is all zero which means that the answer is zero. but, the '040
# algorithm allows the exponent to be non-zero. the 881/2 do not. therefore,
# if the mantissa is zero, I will zero the exponent, too.
# the question now is whether the exponents sign bit is allowed to be non-zero
# for a zero, also...
andi.w &0xf000,FP_SCR0(%a6)
fout_pack_set:
lea FP_SCR0(%a6),%a0 # pass: src addr
fout_pack_write:
mov.l (%sp)+,%a1 # pass: dst addr
mov.l &0xc,%d0 # pass: opsize is 12 bytes
cmpi.b SPCOND_FLG(%a6),&mda7_flg
beq.b fout_pack_a7
bsr.l _dmem_write # write ext prec number to memory
tst.l %d1 # did dstore fail?
bne.w fout_ext_err # yes
rts
# we don't want to do the write if the exception occurred in supervisor mode
# so _mem_write2() handles this for us.
fout_pack_a7:
bsr.l _mem_write2 # write ext prec number to memory
tst.l %d1 # did dstore fail?
bne.w fout_ext_err # yes
rts
fout_pack_not_norm:
cmpi.b %d0,&DENORM # is it a DENORM?
beq.w fout_pack_norm # yes
lea FP_SRC(%a6),%a0
clr.w 2+FP_SRC_EX(%a6)
cmpi.b %d0,&SNAN # is it an SNAN?
beq.b fout_pack_snan # yes
bra.b fout_pack_write # no
fout_pack_snan:
ori.w &snaniop2_mask,FPSR_EXCEPT(%a6) # set SNAN/AIOP
bset &0x6,FP_SRC_HI(%a6) # set snan bit
bra.b fout_pack_write
#########################################################################
# XDEF **************************************************************** #
# fetch_dreg(): fetch register according to index in d1 #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d1 = index of register to fetch from #
# #
# OUTPUT ************************************************************** #
# d0 = value of register fetched #
# #
# ALGORITHM *********************************************************** #
# According to the index value in d1 which can range from zero #
# to fifteen, load the corresponding register file value (where #
# address register indexes start at 8). D0/D1/A0/A1/A6/A7 are on the #
# stack. The rest should still be in their original places. #
# #
#########################################################################
# this routine leaves d1 intact for subsequent store_dreg calls.
global fetch_dreg
fetch_dreg:
mov.w (tbl_fdreg.b,%pc,%d1.w*2),%d0
jmp (tbl_fdreg.b,%pc,%d0.w*1)
tbl_fdreg:
short fdreg0 - tbl_fdreg
short fdreg1 - tbl_fdreg
short fdreg2 - tbl_fdreg
short fdreg3 - tbl_fdreg
short fdreg4 - tbl_fdreg
short fdreg5 - tbl_fdreg
short fdreg6 - tbl_fdreg
short fdreg7 - tbl_fdreg
short fdreg8 - tbl_fdreg
short fdreg9 - tbl_fdreg
short fdrega - tbl_fdreg
short fdregb - tbl_fdreg
short fdregc - tbl_fdreg
short fdregd - tbl_fdreg
short fdrege - tbl_fdreg
short fdregf - tbl_fdreg
fdreg0:
mov.l EXC_DREGS+0x0(%a6),%d0
rts
fdreg1:
mov.l EXC_DREGS+0x4(%a6),%d0
rts
fdreg2:
mov.l %d2,%d0
rts
fdreg3:
mov.l %d3,%d0
rts
fdreg4:
mov.l %d4,%d0
rts
fdreg5:
mov.l %d5,%d0
rts
fdreg6:
mov.l %d6,%d0
rts
fdreg7:
mov.l %d7,%d0
rts
fdreg8:
mov.l EXC_DREGS+0x8(%a6),%d0
rts
fdreg9:
mov.l EXC_DREGS+0xc(%a6),%d0
rts
fdrega:
mov.l %a2,%d0
rts
fdregb:
mov.l %a3,%d0
rts
fdregc:
mov.l %a4,%d0
rts
fdregd:
mov.l %a5,%d0
rts
fdrege:
mov.l (%a6),%d0
rts
fdregf:
mov.l EXC_A7(%a6),%d0
rts
#########################################################################
# XDEF **************************************************************** #
# store_dreg_l(): store longword to data register specified by d1 #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = longowrd value to store #
# d1 = index of register to fetch from #
# #
# OUTPUT ************************************************************** #
# (data register is updated) #
# #
# ALGORITHM *********************************************************** #
# According to the index value in d1, store the longword value #
# in d0 to the corresponding data register. D0/D1 are on the stack #
# while the rest are in their initial places. #
# #
#########################################################################
global store_dreg_l
store_dreg_l:
mov.w (tbl_sdregl.b,%pc,%d1.w*2),%d1
jmp (tbl_sdregl.b,%pc,%d1.w*1)
tbl_sdregl:
short sdregl0 - tbl_sdregl
short sdregl1 - tbl_sdregl
short sdregl2 - tbl_sdregl
short sdregl3 - tbl_sdregl
short sdregl4 - tbl_sdregl
short sdregl5 - tbl_sdregl
short sdregl6 - tbl_sdregl
short sdregl7 - tbl_sdregl
sdregl0:
mov.l %d0,EXC_DREGS+0x0(%a6)
rts
sdregl1:
mov.l %d0,EXC_DREGS+0x4(%a6)
rts
sdregl2:
mov.l %d0,%d2
rts
sdregl3:
mov.l %d0,%d3
rts
sdregl4:
mov.l %d0,%d4
rts
sdregl5:
mov.l %d0,%d5
rts
sdregl6:
mov.l %d0,%d6
rts
sdregl7:
mov.l %d0,%d7
rts
#########################################################################
# XDEF **************************************************************** #
# store_dreg_w(): store word to data register specified by d1 #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = word value to store #
# d1 = index of register to fetch from #
# #
# OUTPUT ************************************************************** #
# (data register is updated) #
# #
# ALGORITHM *********************************************************** #
# According to the index value in d1, store the word value #
# in d0 to the corresponding data register. D0/D1 are on the stack #
# while the rest are in their initial places. #
# #
#########################################################################
global store_dreg_w
store_dreg_w:
mov.w (tbl_sdregw.b,%pc,%d1.w*2),%d1
jmp (tbl_sdregw.b,%pc,%d1.w*1)
tbl_sdregw:
short sdregw0 - tbl_sdregw
short sdregw1 - tbl_sdregw
short sdregw2 - tbl_sdregw
short sdregw3 - tbl_sdregw
short sdregw4 - tbl_sdregw
short sdregw5 - tbl_sdregw
short sdregw6 - tbl_sdregw
short sdregw7 - tbl_sdregw
sdregw0:
mov.w %d0,2+EXC_DREGS+0x0(%a6)
rts
sdregw1:
mov.w %d0,2+EXC_DREGS+0x4(%a6)
rts
sdregw2:
mov.w %d0,%d2
rts
sdregw3:
mov.w %d0,%d3
rts
sdregw4:
mov.w %d0,%d4
rts
sdregw5:
mov.w %d0,%d5
rts
sdregw6:
mov.w %d0,%d6
rts
sdregw7:
mov.w %d0,%d7
rts
#########################################################################
# XDEF **************************************************************** #
# store_dreg_b(): store byte to data register specified by d1 #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = byte value to store #
# d1 = index of register to fetch from #
# #
# OUTPUT ************************************************************** #
# (data register is updated) #
# #
# ALGORITHM *********************************************************** #
# According to the index value in d1, store the byte value #
# in d0 to the corresponding data register. D0/D1 are on the stack #
# while the rest are in their initial places. #
# #
#########################################################################
global store_dreg_b
store_dreg_b:
mov.w (tbl_sdregb.b,%pc,%d1.w*2),%d1
jmp (tbl_sdregb.b,%pc,%d1.w*1)
tbl_sdregb:
short sdregb0 - tbl_sdregb
short sdregb1 - tbl_sdregb
short sdregb2 - tbl_sdregb
short sdregb3 - tbl_sdregb
short sdregb4 - tbl_sdregb
short sdregb5 - tbl_sdregb
short sdregb6 - tbl_sdregb
short sdregb7 - tbl_sdregb
sdregb0:
mov.b %d0,3+EXC_DREGS+0x0(%a6)
rts
sdregb1:
mov.b %d0,3+EXC_DREGS+0x4(%a6)
rts
sdregb2:
mov.b %d0,%d2
rts
sdregb3:
mov.b %d0,%d3
rts
sdregb4:
mov.b %d0,%d4
rts
sdregb5:
mov.b %d0,%d5
rts
sdregb6:
mov.b %d0,%d6
rts
sdregb7:
mov.b %d0,%d7
rts
#########################################################################
# XDEF **************************************************************** #
# inc_areg(): increment an address register by the value in d0 #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = amount to increment by #
# d1 = index of address register to increment #
# #
# OUTPUT ************************************************************** #
# (address register is updated) #
# #
# ALGORITHM *********************************************************** #
# Typically used for an instruction w/ a post-increment <ea>, #
# this routine adds the increment value in d0 to the address register #
# specified by d1. A0/A1/A6/A7 reside on the stack. The rest reside #
# in their original places. #
# For a7, if the increment amount is one, then we have to #
# increment by two. For any a7 update, set the mia7_flag so that if #
# an access error exception occurs later in emulation, this address #
# register update can be undone. #
# #
#########################################################################
global inc_areg
inc_areg:
mov.w (tbl_iareg.b,%pc,%d1.w*2),%d1
jmp (tbl_iareg.b,%pc,%d1.w*1)
tbl_iareg:
short iareg0 - tbl_iareg
short iareg1 - tbl_iareg
short iareg2 - tbl_iareg
short iareg3 - tbl_iareg
short iareg4 - tbl_iareg
short iareg5 - tbl_iareg
short iareg6 - tbl_iareg
short iareg7 - tbl_iareg
iareg0: add.l %d0,EXC_DREGS+0x8(%a6)
rts
iareg1: add.l %d0,EXC_DREGS+0xc(%a6)
rts
iareg2: add.l %d0,%a2
rts
iareg3: add.l %d0,%a3
rts
iareg4: add.l %d0,%a4
rts
iareg5: add.l %d0,%a5
rts
iareg6: add.l %d0,(%a6)
rts
iareg7: mov.b &mia7_flg,SPCOND_FLG(%a6)
cmpi.b %d0,&0x1
beq.b iareg7b
add.l %d0,EXC_A7(%a6)
rts
iareg7b:
addq.l &0x2,EXC_A7(%a6)
rts
#########################################################################
# XDEF **************************************************************** #
# dec_areg(): decrement an address register by the value in d0 #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = amount to decrement by #
# d1 = index of address register to decrement #
# #
# OUTPUT ************************************************************** #
# (address register is updated) #
# #
# ALGORITHM *********************************************************** #
# Typically used for an instruction w/ a pre-decrement <ea>, #
# this routine adds the decrement value in d0 to the address register #
# specified by d1. A0/A1/A6/A7 reside on the stack. The rest reside #
# in their original places. #
# For a7, if the decrement amount is one, then we have to #
# decrement by two. For any a7 update, set the mda7_flag so that if #
# an access error exception occurs later in emulation, this address #
# register update can be undone. #
# #
#########################################################################
global dec_areg
dec_areg:
mov.w (tbl_dareg.b,%pc,%d1.w*2),%d1
jmp (tbl_dareg.b,%pc,%d1.w*1)
tbl_dareg:
short dareg0 - tbl_dareg
short dareg1 - tbl_dareg
short dareg2 - tbl_dareg
short dareg3 - tbl_dareg
short dareg4 - tbl_dareg
short dareg5 - tbl_dareg
short dareg6 - tbl_dareg
short dareg7 - tbl_dareg
dareg0: sub.l %d0,EXC_DREGS+0x8(%a6)
rts
dareg1: sub.l %d0,EXC_DREGS+0xc(%a6)
rts
dareg2: sub.l %d0,%a2
rts
dareg3: sub.l %d0,%a3
rts
dareg4: sub.l %d0,%a4
rts
dareg5: sub.l %d0,%a5
rts
dareg6: sub.l %d0,(%a6)
rts
dareg7: mov.b &mda7_flg,SPCOND_FLG(%a6)
cmpi.b %d0,&0x1
beq.b dareg7b
sub.l %d0,EXC_A7(%a6)
rts
dareg7b:
subq.l &0x2,EXC_A7(%a6)
rts
##############################################################################
#########################################################################
# XDEF **************************************************************** #
# load_fpn1(): load FP register value into FP_SRC(a6). #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = index of FP register to load #
# #
# OUTPUT ************************************************************** #
# FP_SRC(a6) = value loaded from FP register file #
# #
# ALGORITHM *********************************************************** #
# Using the index in d0, load FP_SRC(a6) with a number from the #
# FP register file. #
# #
#########################################################################
global load_fpn1
load_fpn1:
mov.w (tbl_load_fpn1.b,%pc,%d0.w*2), %d0
jmp (tbl_load_fpn1.b,%pc,%d0.w*1)
tbl_load_fpn1:
short load_fpn1_0 - tbl_load_fpn1
short load_fpn1_1 - tbl_load_fpn1
short load_fpn1_2 - tbl_load_fpn1
short load_fpn1_3 - tbl_load_fpn1
short load_fpn1_4 - tbl_load_fpn1
short load_fpn1_5 - tbl_load_fpn1
short load_fpn1_6 - tbl_load_fpn1
short load_fpn1_7 - tbl_load_fpn1
load_fpn1_0:
mov.l 0+EXC_FP0(%a6), 0+FP_SRC(%a6)
mov.l 4+EXC_FP0(%a6), 4+FP_SRC(%a6)
mov.l 8+EXC_FP0(%a6), 8+FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_1:
mov.l 0+EXC_FP1(%a6), 0+FP_SRC(%a6)
mov.l 4+EXC_FP1(%a6), 4+FP_SRC(%a6)
mov.l 8+EXC_FP1(%a6), 8+FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_2:
fmovm.x &0x20, FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_3:
fmovm.x &0x10, FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_4:
fmovm.x &0x08, FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_5:
fmovm.x &0x04, FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_6:
fmovm.x &0x02, FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
load_fpn1_7:
fmovm.x &0x01, FP_SRC(%a6)
lea FP_SRC(%a6), %a0
rts
#############################################################################
#########################################################################
# XDEF **************************************************************** #
# load_fpn2(): load FP register value into FP_DST(a6). #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# d0 = index of FP register to load #
# #
# OUTPUT ************************************************************** #
# FP_DST(a6) = value loaded from FP register file #
# #
# ALGORITHM *********************************************************** #
# Using the index in d0, load FP_DST(a6) with a number from the #
# FP register file. #
# #
#########################################################################
global load_fpn2
load_fpn2:
mov.w (tbl_load_fpn2.b,%pc,%d0.w*2), %d0
jmp (tbl_load_fpn2.b,%pc,%d0.w*1)
tbl_load_fpn2:
short load_fpn2_0 - tbl_load_fpn2
short load_fpn2_1 - tbl_load_fpn2
short load_fpn2_2 - tbl_load_fpn2
short load_fpn2_3 - tbl_load_fpn2
short load_fpn2_4 - tbl_load_fpn2
short load_fpn2_5 - tbl_load_fpn2
short load_fpn2_6 - tbl_load_fpn2
short load_fpn2_7 - tbl_load_fpn2
load_fpn2_0:
mov.l 0+EXC_FP0(%a6), 0+FP_DST(%a6)
mov.l 4+EXC_FP0(%a6), 4+FP_DST(%a6)
mov.l 8+EXC_FP0(%a6), 8+FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_1:
mov.l 0+EXC_FP1(%a6), 0+FP_DST(%a6)
mov.l 4+EXC_FP1(%a6), 4+FP_DST(%a6)
mov.l 8+EXC_FP1(%a6), 8+FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_2:
fmovm.x &0x20, FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_3:
fmovm.x &0x10, FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_4:
fmovm.x &0x08, FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_5:
fmovm.x &0x04, FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_6:
fmovm.x &0x02, FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
load_fpn2_7:
fmovm.x &0x01, FP_DST(%a6)
lea FP_DST(%a6), %a0
rts
#############################################################################
#########################################################################
# XDEF **************************************************************** #
# store_fpreg(): store an fp value to the fpreg designated d0. #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# fp0 = extended precision value to store #
# d0 = index of floating-point register #
# #
# OUTPUT ************************************************************** #
# None #
# #
# ALGORITHM *********************************************************** #
# Store the value in fp0 to the FP register designated by the #
# value in d0. The FP number can be DENORM or SNAN so we have to be #
# careful that we don't take an exception here. #
# #
#########################################################################
global store_fpreg
store_fpreg:
mov.w (tbl_store_fpreg.b,%pc,%d0.w*2), %d0
jmp (tbl_store_fpreg.b,%pc,%d0.w*1)
tbl_store_fpreg:
short store_fpreg_0 - tbl_store_fpreg
short store_fpreg_1 - tbl_store_fpreg
short store_fpreg_2 - tbl_store_fpreg
short store_fpreg_3 - tbl_store_fpreg
short store_fpreg_4 - tbl_store_fpreg
short store_fpreg_5 - tbl_store_fpreg
short store_fpreg_6 - tbl_store_fpreg
short store_fpreg_7 - tbl_store_fpreg
store_fpreg_0:
fmovm.x &0x80, EXC_FP0(%a6)
rts
store_fpreg_1:
fmovm.x &0x80, EXC_FP1(%a6)
rts
store_fpreg_2:
fmovm.x &0x01, -(%sp)
fmovm.x (%sp)+, &0x20
rts
store_fpreg_3:
fmovm.x &0x01, -(%sp)
fmovm.x (%sp)+, &0x10
rts
store_fpreg_4:
fmovm.x &0x01, -(%sp)
fmovm.x (%sp)+, &0x08
rts
store_fpreg_5:
fmovm.x &0x01, -(%sp)
fmovm.x (%sp)+, &0x04
rts
store_fpreg_6:
fmovm.x &0x01, -(%sp)
fmovm.x (%sp)+, &0x02
rts
store_fpreg_7:
fmovm.x &0x01, -(%sp)
fmovm.x (%sp)+, &0x01
rts
#########################################################################
# XDEF **************************************************************** #
# _denorm(): denormalize an intermediate result #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = points to the operand to be denormalized #
# (in the internal extended format) #
# #
# d0 = rounding precision #
# #
# OUTPUT ************************************************************** #
# a0 = pointer to the denormalized result #
# (in the internal extended format) #
# #
# d0 = guard,round,sticky #
# #
# ALGORITHM *********************************************************** #
# According to the exponent underflow threshold for the given #
# precision, shift the mantissa bits to the right in order raise the #
# exponent of the operand to the threshold value. While shifting the #
# mantissa bits right, maintain the value of the guard, round, and #
# sticky bits. #
# other notes: #
# (1) _denorm() is called by the underflow routines #
# (2) _denorm() does NOT affect the status register #
# #
#########################################################################
#
# table of exponent threshold values for each precision
#
tbl_thresh:
short 0x0
short sgl_thresh
short dbl_thresh
global _denorm
_denorm:
#
# Load the exponent threshold for the precision selected and check
# to see if (threshold - exponent) is > 65 in which case we can
# simply calculate the sticky bit and zero the mantissa. otherwise
# we have to call the denormalization routine.
#
lsr.b &0x2, %d0 # shift prec to lo bits
mov.w (tbl_thresh.b,%pc,%d0.w*2), %d1 # load prec threshold
mov.w %d1, %d0 # copy d1 into d0
sub.w FTEMP_EX(%a0), %d0 # diff = threshold - exp
cmpi.w %d0, &66 # is diff > 65? (mant + g,r bits)
bpl.b denorm_set_stky # yes; just calc sticky
clr.l %d0 # clear g,r,s
btst &inex2_bit, FPSR_EXCEPT(%a6) # yes; was INEX2 set?
beq.b denorm_call # no; don't change anything
bset &29, %d0 # yes; set sticky bit
denorm_call:
bsr.l dnrm_lp # denormalize the number
rts
#
# all bit would have been shifted off during the denorm so simply
# calculate if the sticky should be set and clear the entire mantissa.
#
denorm_set_stky:
mov.l &0x20000000, %d0 # set sticky bit in return value
mov.w %d1, FTEMP_EX(%a0) # load exp with threshold
clr.l FTEMP_HI(%a0) # set d1 = 0 (ms mantissa)
clr.l FTEMP_LO(%a0) # set d2 = 0 (ms mantissa)
rts
# #
# dnrm_lp(): normalize exponent/mantissa to specified threshhold #
# #
# INPUT: #
# %a0 : points to the operand to be denormalized #
# %d0{31:29} : initial guard,round,sticky #
# %d1{15:0} : denormalization threshold #
# OUTPUT: #
# %a0 : points to the denormalized operand #
# %d0{31:29} : final guard,round,sticky #
# #
# *** Local Equates *** #
set GRS, L_SCR2 # g,r,s temp storage
set FTEMP_LO2, L_SCR1 # FTEMP_LO copy
global dnrm_lp
dnrm_lp:
#
# make a copy of FTEMP_LO and place the g,r,s bits directly after it
# in memory so as to make the bitfield extraction for denormalization easier.
#
mov.l FTEMP_LO(%a0), FTEMP_LO2(%a6) # make FTEMP_LO copy
mov.l %d0, GRS(%a6) # place g,r,s after it
#
# check to see how much less than the underflow threshold the operand
# exponent is.
#
mov.l %d1, %d0 # copy the denorm threshold
sub.w FTEMP_EX(%a0), %d1 # d1 = threshold - uns exponent
ble.b dnrm_no_lp # d1 <= 0
cmpi.w %d1, &0x20 # is ( 0 <= d1 < 32) ?
blt.b case_1 # yes
cmpi.w %d1, &0x40 # is (32 <= d1 < 64) ?
blt.b case_2 # yes
bra.w case_3 # (d1 >= 64)
#
# No normalization necessary
#
dnrm_no_lp:
mov.l GRS(%a6), %d0 # restore original g,r,s
rts
#
# case (0<d1<32)
#
# %d0 = denorm threshold
# %d1 = "n" = amt to shift
#
# ---------------------------------------------------------
# | FTEMP_HI | FTEMP_LO |grs000.........000|
# ---------------------------------------------------------
# <-(32 - n)-><-(n)-><-(32 - n)-><-(n)-><-(32 - n)-><-(n)->
# \ \ \ \
# \ \ \ \
# \ \ \ \
# \ \ \ \
# \ \ \ \
# \ \ \ \
# \ \ \ \
# \ \ \ \
# <-(n)-><-(32 - n)-><------(32)-------><------(32)------->
# ---------------------------------------------------------
# |0.....0| NEW_HI | NEW_FTEMP_LO |grs |
# ---------------------------------------------------------
#
case_1:
mov.l %d2, -(%sp) # create temp storage
mov.w %d0, FTEMP_EX(%a0) # exponent = denorm threshold
mov.l &32, %d0
sub.w %d1, %d0 # %d0 = 32 - %d1
cmpi.w %d1, &29 # is shft amt >= 29
blt.b case1_extract # no; no fix needed
mov.b GRS(%a6), %d2
or.b %d2, 3+FTEMP_LO2(%a6)
case1_extract:
bfextu FTEMP_HI(%a0){&0:%d0}, %d2 # %d2 = new FTEMP_HI
bfextu FTEMP_HI(%a0){%d0:&32}, %d1 # %d1 = new FTEMP_LO
bfextu FTEMP_LO2(%a6){%d0:&32}, %d0 # %d0 = new G,R,S
mov.l %d2, FTEMP_HI(%a0) # store new FTEMP_HI
mov.l %d1, FTEMP_LO(%a0) # store new FTEMP_LO
bftst %d0{&2:&30} # were bits shifted off?
beq.b case1_sticky_clear # no; go finish
bset &rnd_stky_bit, %d0 # yes; set sticky bit
case1_sticky_clear:
and.l &0xe0000000, %d0 # clear all but G,R,S
mov.l (%sp)+, %d2 # restore temp register
rts
#
# case (32<=d1<64)
#
# %d0 = denorm threshold
# %d1 = "n" = amt to shift
#
# ---------------------------------------------------------
# | FTEMP_HI | FTEMP_LO |grs000.........000|
# ---------------------------------------------------------
# <-(32 - n)-><-(n)-><-(32 - n)-><-(n)-><-(32 - n)-><-(n)->
# \ \ \
# \ \ \
# \ \ -------------------
# \ -------------------- \
# ------------------- \ \
# \ \ \
# \ \ \
# \ \ \
# <-------(32)------><-(n)-><-(32 - n)-><------(32)------->
# ---------------------------------------------------------
# |0...............0|0....0| NEW_LO |grs |
# ---------------------------------------------------------
#
case_2:
mov.l %d2, -(%sp) # create temp storage
mov.w %d0, FTEMP_EX(%a0) # exponent = denorm threshold
subi.w &0x20, %d1 # %d1 now between 0 and 32
mov.l &0x20, %d0
sub.w %d1, %d0 # %d0 = 32 - %d1
# subtle step here; or in the g,r,s at the bottom of FTEMP_LO to minimize
# the number of bits to check for the sticky detect.
# it only plays a role in shift amounts of 61-63.
mov.b GRS(%a6), %d2
or.b %d2, 3+FTEMP_LO2(%a6)
bfextu FTEMP_HI(%a0){&0:%d0}, %d2 # %d2 = new FTEMP_LO
bfextu FTEMP_HI(%a0){%d0:&32}, %d1 # %d1 = new G,R,S
bftst %d1{&2:&30} # were any bits shifted off?
bne.b case2_set_sticky # yes; set sticky bit
bftst FTEMP_LO2(%a6){%d0:&31} # were any bits shifted off?
bne.b case2_set_sticky # yes; set sticky bit
mov.l %d1, %d0 # move new G,R,S to %d0
bra.b case2_end
case2_set_sticky:
mov.l %d1, %d0 # move new G,R,S to %d0
bset &rnd_stky_bit, %d0 # set sticky bit
case2_end:
clr.l FTEMP_HI(%a0) # store FTEMP_HI = 0
mov.l %d2, FTEMP_LO(%a0) # store FTEMP_LO
and.l &0xe0000000, %d0 # clear all but G,R,S
mov.l (%sp)+,%d2 # restore temp register
rts
#
# case (d1>=64)
#
# %d0 = denorm threshold
# %d1 = amt to shift
#
case_3:
mov.w %d0, FTEMP_EX(%a0) # insert denorm threshold
cmpi.w %d1, &65 # is shift amt > 65?
blt.b case3_64 # no; it's == 64
beq.b case3_65 # no; it's == 65
#
# case (d1>65)
#
# Shift value is > 65 and out of range. All bits are shifted off.
# Return a zero mantissa with the sticky bit set
#
clr.l FTEMP_HI(%a0) # clear hi(mantissa)
clr.l FTEMP_LO(%a0) # clear lo(mantissa)
mov.l &0x20000000, %d0 # set sticky bit
rts
#
# case (d1 == 64)
#
# ---------------------------------------------------------
# | FTEMP_HI | FTEMP_LO |grs000.........000|
# ---------------------------------------------------------
# <-------(32)------>
# \ \
# \ \
# \ \
# \ ------------------------------
# ------------------------------- \
# \ \
# \ \
# \ \
# <-------(32)------>
# ---------------------------------------------------------
# |0...............0|0................0|grs |
# ---------------------------------------------------------
#
case3_64:
mov.l FTEMP_HI(%a0), %d0 # fetch hi(mantissa)
mov.l %d0, %d1 # make a copy
and.l &0xc0000000, %d0 # extract G,R
and.l &0x3fffffff, %d1 # extract other bits
bra.b case3_complete
#
# case (d1 == 65)
#
# ---------------------------------------------------------
# | FTEMP_HI | FTEMP_LO |grs000.........000|
# ---------------------------------------------------------
# <-------(32)------>
# \ \
# \ \
# \ \
# \ ------------------------------
# -------------------------------- \
# \ \
# \ \
# \ \
# <-------(31)----->
# ---------------------------------------------------------
# |0...............0|0................0|0rs |
# ---------------------------------------------------------
#
case3_65:
mov.l FTEMP_HI(%a0), %d0 # fetch hi(mantissa)
and.l &0x80000000, %d0 # extract R bit
lsr.l &0x1, %d0 # shift high bit into R bit
and.l &0x7fffffff, %d1 # extract other bits
case3_complete:
# last operation done was an "and" of the bits shifted off so the condition
# codes are already set so branch accordingly.
bne.b case3_set_sticky # yes; go set new sticky
tst.l FTEMP_LO(%a0) # were any bits shifted off?
bne.b case3_set_sticky # yes; go set new sticky
tst.b GRS(%a6) # were any bits shifted off?
bne.b case3_set_sticky # yes; go set new sticky
#
# no bits were shifted off so don't set the sticky bit.
# the guard and
# the entire mantissa is zero.
#
clr.l FTEMP_HI(%a0) # clear hi(mantissa)
clr.l FTEMP_LO(%a0) # clear lo(mantissa)
rts
#
# some bits were shifted off so set the sticky bit.
# the entire mantissa is zero.
#
case3_set_sticky:
bset &rnd_stky_bit,%d0 # set new sticky bit
clr.l FTEMP_HI(%a0) # clear hi(mantissa)
clr.l FTEMP_LO(%a0) # clear lo(mantissa)
rts
#########################################################################
# XDEF **************************************************************** #
# _round(): round result according to precision/mode #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = ptr to input operand in internal extended format #
# d1(hi) = contains rounding precision: #
# ext = $0000xxxx #
# sgl = $0004xxxx #
# dbl = $0008xxxx #
# d1(lo) = contains rounding mode: #
# RN = $xxxx0000 #
# RZ = $xxxx0001 #
# RM = $xxxx0002 #
# RP = $xxxx0003 #
# d0{31:29} = contains the g,r,s bits (extended) #
# #
# OUTPUT ************************************************************** #
# a0 = pointer to rounded result #
# #
# ALGORITHM *********************************************************** #
# On return the value pointed to by a0 is correctly rounded, #
# a0 is preserved and the g-r-s bits in d0 are cleared. #
# The result is not typed - the tag field is invalid. The #
# result is still in the internal extended format. #
# #
# The INEX bit of USER_FPSR will be set if the rounded result was #
# inexact (i.e. if any of the g-r-s bits were set). #
# #
#########################################################################
global _round
_round:
#
# ext_grs() looks at the rounding precision and sets the appropriate
# G,R,S bits.
# If (G,R,S == 0) then result is exact and round is done, else set
# the inex flag in status reg and continue.
#
bsr.l ext_grs # extract G,R,S
tst.l %d0 # are G,R,S zero?
beq.w truncate # yes; round is complete
or.w &inx2a_mask, 2+USER_FPSR(%a6) # set inex2/ainex
#
# Use rounding mode as an index into a jump table for these modes.
# All of the following assumes grs != 0.
#
mov.w (tbl_mode.b,%pc,%d1.w*2), %a1 # load jump offset
jmp (tbl_mode.b,%pc,%a1) # jmp to rnd mode handler
tbl_mode:
short rnd_near - tbl_mode
short truncate - tbl_mode # RZ always truncates
short rnd_mnus - tbl_mode
short rnd_plus - tbl_mode
#################################################################
# ROUND PLUS INFINITY #
# #
# If sign of fp number = 0 (positive), then add 1 to l. #
#################################################################
rnd_plus:
tst.b FTEMP_SGN(%a0) # check for sign
bmi.w truncate # if positive then truncate
mov.l &0xffffffff, %d0 # force g,r,s to be all f's
swap %d1 # set up d1 for round prec.
cmpi.b %d1, &s_mode # is prec = sgl?
beq.w add_sgl # yes
bgt.w add_dbl # no; it's dbl
bra.w add_ext # no; it's ext
#################################################################
# ROUND MINUS INFINITY #
# #
# If sign of fp number = 1 (negative), then add 1 to l. #
#################################################################
rnd_mnus:
tst.b FTEMP_SGN(%a0) # check for sign
bpl.w truncate # if negative then truncate
mov.l &0xffffffff, %d0 # force g,r,s to be all f's
swap %d1 # set up d1 for round prec.
cmpi.b %d1, &s_mode # is prec = sgl?
beq.w add_sgl # yes
bgt.w add_dbl # no; it's dbl
bra.w add_ext # no; it's ext
#################################################################
# ROUND NEAREST #
# #
# If (g=1), then add 1 to l and if (r=s=0), then clear l #
# Note that this will round to even in case of a tie. #
#################################################################
rnd_near:
asl.l &0x1, %d0 # shift g-bit to c-bit
bcc.w truncate # if (g=1) then
swap %d1 # set up d1 for round prec.
cmpi.b %d1, &s_mode # is prec = sgl?
beq.w add_sgl # yes
bgt.w add_dbl # no; it's dbl
bra.w add_ext # no; it's ext
# *** LOCAL EQUATES ***
set ad_1_sgl, 0x00000100 # constant to add 1 to l-bit in sgl prec
set ad_1_dbl, 0x00000800 # constant to add 1 to l-bit in dbl prec
#########################
# ADD SINGLE #
#########################
add_sgl:
add.l &ad_1_sgl, FTEMP_HI(%a0)
bcc.b scc_clr # no mantissa overflow
roxr.w FTEMP_HI(%a0) # shift v-bit back in
roxr.w FTEMP_HI+2(%a0) # shift v-bit back in
add.w &0x1, FTEMP_EX(%a0) # and incr exponent
scc_clr:
tst.l %d0 # test for rs = 0
bne.b sgl_done
and.w &0xfe00, FTEMP_HI+2(%a0) # clear the l-bit
sgl_done:
and.l &0xffffff00, FTEMP_HI(%a0) # truncate bits beyond sgl limit
clr.l FTEMP_LO(%a0) # clear d2
rts
#########################
# ADD EXTENDED #
#########################
add_ext:
addq.l &1,FTEMP_LO(%a0) # add 1 to l-bit
bcc.b xcc_clr # test for carry out
addq.l &1,FTEMP_HI(%a0) # propogate carry
bcc.b xcc_clr
roxr.w FTEMP_HI(%a0) # mant is 0 so restore v-bit
roxr.w FTEMP_HI+2(%a0) # mant is 0 so restore v-bit
roxr.w FTEMP_LO(%a0)
roxr.w FTEMP_LO+2(%a0)
add.w &0x1,FTEMP_EX(%a0) # and inc exp
xcc_clr:
tst.l %d0 # test rs = 0
bne.b add_ext_done
and.b &0xfe,FTEMP_LO+3(%a0) # clear the l bit
add_ext_done:
rts
#########################
# ADD DOUBLE #
#########################
add_dbl:
add.l &ad_1_dbl, FTEMP_LO(%a0) # add 1 to lsb
bcc.b dcc_clr # no carry
addq.l &0x1, FTEMP_HI(%a0) # propogate carry
bcc.b dcc_clr # no carry
roxr.w FTEMP_HI(%a0) # mant is 0 so restore v-bit
roxr.w FTEMP_HI+2(%a0) # mant is 0 so restore v-bit
roxr.w FTEMP_LO(%a0)
roxr.w FTEMP_LO+2(%a0)
addq.w &0x1, FTEMP_EX(%a0) # incr exponent
dcc_clr:
tst.l %d0 # test for rs = 0
bne.b dbl_done
and.w &0xf000, FTEMP_LO+2(%a0) # clear the l-bit
dbl_done:
and.l &0xfffff800,FTEMP_LO(%a0) # truncate bits beyond dbl limit
rts
###########################
# Truncate all other bits #
###########################
truncate:
swap %d1 # select rnd prec
cmpi.b %d1, &s_mode # is prec sgl?
beq.w sgl_done # yes
bgt.b dbl_done # no; it's dbl
rts # no; it's ext
#
# ext_grs(): extract guard, round and sticky bits according to
# rounding precision.
#
# INPUT
# d0 = extended precision g,r,s (in d0{31:29})
# d1 = {PREC,ROUND}
# OUTPUT
# d0{31:29} = guard, round, sticky
#
# The ext_grs extract the guard/round/sticky bits according to the
# selected rounding precision. It is called by the round subroutine
# only. All registers except d0 are kept intact. d0 becomes an
# updated guard,round,sticky in d0{31:29}
#
# Notes: the ext_grs uses the round PREC, and therefore has to swap d1
# prior to usage, and needs to restore d1 to original. this
# routine is tightly tied to the round routine and not meant to
# uphold standard subroutine calling practices.
#
ext_grs:
swap %d1 # have d1.w point to round precision
tst.b %d1 # is rnd prec = extended?
bne.b ext_grs_not_ext # no; go handle sgl or dbl
#
# %d0 actually already hold g,r,s since _round() had it before calling
# this function. so, as long as we don't disturb it, we are "returning" it.
#
ext_grs_ext:
swap %d1 # yes; return to correct positions
rts
ext_grs_not_ext:
movm.l &0x3000, -(%sp) # make some temp registers {d2/d3}
cmpi.b %d1, &s_mode # is rnd prec = sgl?
bne.b ext_grs_dbl # no; go handle dbl
#
# sgl:
# 96 64 40 32 0
# -----------------------------------------------------
# | EXP |XXXXXXX| |xx | |grs|
# -----------------------------------------------------
# <--(24)--->nn\ /
# ee ---------------------
# ww |
# v
# gr new sticky
#
ext_grs_sgl:
bfextu FTEMP_HI(%a0){&24:&2}, %d3 # sgl prec. g-r are 2 bits right
mov.l &30, %d2 # of the sgl prec. limits
lsl.l %d2, %d3 # shift g-r bits to MSB of d3
mov.l FTEMP_HI(%a0), %d2 # get word 2 for s-bit test
and.l &0x0000003f, %d2 # s bit is the or of all other
bne.b ext_grs_st_stky # bits to the right of g-r
tst.l FTEMP_LO(%a0) # test lower mantissa
bne.b ext_grs_st_stky # if any are set, set sticky
tst.l %d0 # test original g,r,s
bne.b ext_grs_st_stky # if any are set, set sticky
bra.b ext_grs_end_sd # if words 3 and 4 are clr, exit
#
# dbl:
# 96 64 32 11 0
# -----------------------------------------------------
# | EXP |XXXXXXX| | |xx |grs|
# -----------------------------------------------------
# nn\ /
# ee -------
# ww |
# v
# gr new sticky
#
ext_grs_dbl:
bfextu FTEMP_LO(%a0){&21:&2}, %d3 # dbl-prec. g-r are 2 bits right
mov.l &30, %d2 # of the dbl prec. limits
lsl.l %d2, %d3 # shift g-r bits to the MSB of d3
mov.l FTEMP_LO(%a0), %d2 # get lower mantissa for s-bit test
and.l &0x000001ff, %d2 # s bit is the or-ing of all
bne.b ext_grs_st_stky # other bits to the right of g-r
tst.l %d0 # test word original g,r,s
bne.b ext_grs_st_stky # if any are set, set sticky
bra.b ext_grs_end_sd # if clear, exit
ext_grs_st_stky:
bset &rnd_stky_bit, %d3 # set sticky bit
ext_grs_end_sd:
mov.l %d3, %d0 # return grs to d0
movm.l (%sp)+, &0xc # restore scratch registers {d2/d3}
swap %d1 # restore d1 to original
rts
#########################################################################
# norm(): normalize the mantissa of an extended precision input. the #
# input operand should not be normalized already. #
# #
# XDEF **************************************************************** #
# norm() #
# #
# XREF **************************************************************** #
# none #
# #
# INPUT *************************************************************** #
# a0 = pointer fp extended precision operand to normalize #
# #
# OUTPUT ************************************************************** #
# d0 = number of bit positions the mantissa was shifted #
# a0 = the input operand's mantissa is normalized; the exponent #
# is unchanged. #
# #
#########################################################################
global norm
norm:
mov.l %d2, -(%sp) # create some temp regs
mov.l %d3, -(%sp)
mov.l FTEMP_HI(%a0), %d0 # load hi(mantissa)
mov.l FTEMP_LO(%a0), %d1 # load lo(mantissa)
bfffo %d0{&0:&32}, %d2 # how many places to shift?
beq.b norm_lo # hi(man) is all zeroes!
norm_hi:
lsl.l %d2, %d0 # left shift hi(man)
bfextu %d1{&0:%d2}, %d3 # extract lo bits
or.l %d3, %d0 # create hi(man)
lsl.l %d2, %d1 # create lo(man)
mov.l %d0, FTEMP_HI(%a0) # store new hi(man)
mov.l %d1, FTEMP_LO(%a0) # store new lo(man)
mov.l %d2, %d0 # return shift amount
mov.l (%sp)+, %d3 # restore temp regs
mov.l (%sp)+, %d2
rts
norm_lo:
bfffo %d1{&0:&32}, %d2 # how many places to shift?
lsl.l %d2, %d1 # shift lo(man)
add.l &32, %d2 # add 32 to shft amount
mov.l %d1, FTEMP_HI(%a0) # store hi(man)
clr.l FTEMP_LO(%a0) # lo(man) is now zero
mov.l %d2, %d0 # return shift amount
mov.l (%sp)+, %d3 # restore temp regs
mov.l (%sp)+, %d2
rts
#########################################################################
# unnorm_fix(): - changes an UNNORM to one of NORM, DENORM, or ZERO #
# - returns corresponding optype tag #
# #
# XDEF **************************************************************** #
# unnorm_fix() #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa #
# #
# INPUT *************************************************************** #
# a0 = pointer to unnormalized extended precision number #
# #
# OUTPUT ************************************************************** #
# d0 = optype tag - is corrected to one of NORM, DENORM, or ZERO #
# a0 = input operand has been converted to a norm, denorm, or #
# zero; both the exponent and mantissa are changed. #
# #
#########################################################################
global unnorm_fix
unnorm_fix:
bfffo FTEMP_HI(%a0){&0:&32}, %d0 # how many shifts are needed?
bne.b unnorm_shift # hi(man) is not all zeroes
#
# hi(man) is all zeroes so see if any bits in lo(man) are set
#
unnorm_chk_lo:
bfffo FTEMP_LO(%a0){&0:&32}, %d0 # is operand really a zero?
beq.w unnorm_zero # yes
add.w &32, %d0 # no; fix shift distance
#
# d0 = # shifts needed for complete normalization
#
unnorm_shift:
clr.l %d1 # clear top word
mov.w FTEMP_EX(%a0), %d1 # extract exponent
and.w &0x7fff, %d1 # strip off sgn
cmp.w %d0, %d1 # will denorm push exp < 0?
bgt.b unnorm_nrm_zero # yes; denorm only until exp = 0
#
# exponent would not go < 0. therefore, number stays normalized
#
sub.w %d0, %d1 # shift exponent value
mov.w FTEMP_EX(%a0), %d0 # load old exponent
and.w &0x8000, %d0 # save old sign
or.w %d0, %d1 # {sgn,new exp}
mov.w %d1, FTEMP_EX(%a0) # insert new exponent
bsr.l norm # normalize UNNORM
mov.b &NORM, %d0 # return new optype tag
rts
#
# exponent would go < 0, so only denormalize until exp = 0
#
unnorm_nrm_zero:
cmp.b %d1, &32 # is exp <= 32?
bgt.b unnorm_nrm_zero_lrg # no; go handle large exponent
bfextu FTEMP_HI(%a0){%d1:&32}, %d0 # extract new hi(man)
mov.l %d0, FTEMP_HI(%a0) # save new hi(man)
mov.l FTEMP_LO(%a0), %d0 # fetch old lo(man)
lsl.l %d1, %d0 # extract new lo(man)
mov.l %d0, FTEMP_LO(%a0) # save new lo(man)
and.w &0x8000, FTEMP_EX(%a0) # set exp = 0
mov.b &DENORM, %d0 # return new optype tag
rts
#
# only mantissa bits set are in lo(man)
#
unnorm_nrm_zero_lrg:
sub.w &32, %d1 # adjust shft amt by 32
mov.l FTEMP_LO(%a0), %d0 # fetch old lo(man)
lsl.l %d1, %d0 # left shift lo(man)
mov.l %d0, FTEMP_HI(%a0) # store new hi(man)
clr.l FTEMP_LO(%a0) # lo(man) = 0
and.w &0x8000, FTEMP_EX(%a0) # set exp = 0
mov.b &DENORM, %d0 # return new optype tag
rts
#
# whole mantissa is zero so this UNNORM is actually a zero
#
unnorm_zero:
and.w &0x8000, FTEMP_EX(%a0) # force exponent to zero
mov.b &ZERO, %d0 # fix optype tag
rts
#########################################################################
# XDEF **************************************************************** #
# set_tag_x(): return the optype of the input ext fp number #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision operand #
# #
# OUTPUT ************************************************************** #
# d0 = value of type tag #
# one of: NORM, INF, QNAN, SNAN, DENORM, UNNORM, ZERO #
# #
# ALGORITHM *********************************************************** #
# Simply test the exponent, j-bit, and mantissa values to #
# determine the type of operand. #
# If it's an unnormalized zero, alter the operand and force it #
# to be a normal zero. #
# #
#########################################################################
global set_tag_x
set_tag_x:
mov.w FTEMP_EX(%a0), %d0 # extract exponent
andi.w &0x7fff, %d0 # strip off sign
cmpi.w %d0, &0x7fff # is (EXP == MAX)?
beq.b inf_or_nan_x
not_inf_or_nan_x:
btst &0x7,FTEMP_HI(%a0)
beq.b not_norm_x
is_norm_x:
mov.b &NORM, %d0
rts
not_norm_x:
tst.w %d0 # is exponent = 0?
bne.b is_unnorm_x
not_unnorm_x:
tst.l FTEMP_HI(%a0)
bne.b is_denorm_x
tst.l FTEMP_LO(%a0)
bne.b is_denorm_x
is_zero_x:
mov.b &ZERO, %d0
rts
is_denorm_x:
mov.b &DENORM, %d0
rts
# must distinguish now "Unnormalized zeroes" which we
# must convert to zero.
is_unnorm_x:
tst.l FTEMP_HI(%a0)
bne.b is_unnorm_reg_x
tst.l FTEMP_LO(%a0)
bne.b is_unnorm_reg_x
# it's an "unnormalized zero". let's convert it to an actual zero...
andi.w &0x8000,FTEMP_EX(%a0) # clear exponent
mov.b &ZERO, %d0
rts
is_unnorm_reg_x:
mov.b &UNNORM, %d0
rts
inf_or_nan_x:
tst.l FTEMP_LO(%a0)
bne.b is_nan_x
mov.l FTEMP_HI(%a0), %d0
and.l &0x7fffffff, %d0 # msb is a don't care!
bne.b is_nan_x
is_inf_x:
mov.b &INF, %d0
rts
is_nan_x:
btst &0x6, FTEMP_HI(%a0)
beq.b is_snan_x
mov.b &QNAN, %d0
rts
is_snan_x:
mov.b &SNAN, %d0
rts
#########################################################################
# XDEF **************************************************************** #
# set_tag_d(): return the optype of the input dbl fp number #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = points to double precision operand #
# #
# OUTPUT ************************************************************** #
# d0 = value of type tag #
# one of: NORM, INF, QNAN, SNAN, DENORM, ZERO #
# #
# ALGORITHM *********************************************************** #
# Simply test the exponent, j-bit, and mantissa values to #
# determine the type of operand. #
# #
#########################################################################
global set_tag_d
set_tag_d:
mov.l FTEMP(%a0), %d0
mov.l %d0, %d1
andi.l &0x7ff00000, %d0
beq.b zero_or_denorm_d
cmpi.l %d0, &0x7ff00000
beq.b inf_or_nan_d
is_norm_d:
mov.b &NORM, %d0
rts
zero_or_denorm_d:
and.l &0x000fffff, %d1
bne is_denorm_d
tst.l 4+FTEMP(%a0)
bne is_denorm_d
is_zero_d:
mov.b &ZERO, %d0
rts
is_denorm_d:
mov.b &DENORM, %d0
rts
inf_or_nan_d:
and.l &0x000fffff, %d1
bne is_nan_d
tst.l 4+FTEMP(%a0)
bne is_nan_d
is_inf_d:
mov.b &INF, %d0
rts
is_nan_d:
btst &19, %d1
bne is_qnan_d
is_snan_d:
mov.b &SNAN, %d0
rts
is_qnan_d:
mov.b &QNAN, %d0
rts
#########################################################################
# XDEF **************************************************************** #
# set_tag_s(): return the optype of the input sgl fp number #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = pointer to single precision operand #
# #
# OUTPUT ************************************************************** #
# d0 = value of type tag #
# one of: NORM, INF, QNAN, SNAN, DENORM, ZERO #
# #
# ALGORITHM *********************************************************** #
# Simply test the exponent, j-bit, and mantissa values to #
# determine the type of operand. #
# #
#########################################################################
global set_tag_s
set_tag_s:
mov.l FTEMP(%a0), %d0
mov.l %d0, %d1
andi.l &0x7f800000, %d0
beq.b zero_or_denorm_s
cmpi.l %d0, &0x7f800000
beq.b inf_or_nan_s
is_norm_s:
mov.b &NORM, %d0
rts
zero_or_denorm_s:
and.l &0x007fffff, %d1
bne is_denorm_s
is_zero_s:
mov.b &ZERO, %d0
rts
is_denorm_s:
mov.b &DENORM, %d0
rts
inf_or_nan_s:
and.l &0x007fffff, %d1
bne is_nan_s
is_inf_s:
mov.b &INF, %d0
rts
is_nan_s:
btst &22, %d1
bne is_qnan_s
is_snan_s:
mov.b &SNAN, %d0
rts
is_qnan_s:
mov.b &QNAN, %d0
rts
#########################################################################
# XDEF **************************************************************** #
# unf_res(): routine to produce default underflow result of a #
# scaled extended precision number; this is used by #
# fadd/fdiv/fmul/etc. emulation routines. #
# unf_res4(): same as above but for fsglmul/fsgldiv which use #
# single round prec and extended prec mode. #
# #
# XREF **************************************************************** #
# _denorm() - denormalize according to scale factor #
# _round() - round denormalized number according to rnd prec #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precison operand #
# d0 = scale factor #
# d1 = rounding precision/mode #
# #
# OUTPUT ************************************************************** #
# a0 = pointer to default underflow result in extended precision #
# d0.b = result FPSR_cc which caller may or may not want to save #
# #
# ALGORITHM *********************************************************** #
# Convert the input operand to "internal format" which means the #
# exponent is extended to 16 bits and the sign is stored in the unused #
# portion of the extended precison operand. Denormalize the number #
# according to the scale factor passed in d0. Then, round the #
# denormalized result. #
# Set the FPSR_exc bits as appropriate but return the cc bits in #
# d0 in case the caller doesn't want to save them (as is the case for #
# fmove out). #
# unf_res4() for fsglmul/fsgldiv forces the denorm to extended #
# precision and the rounding mode to single. #
# #
#########################################################################
global unf_res
unf_res:
mov.l %d1, -(%sp) # save rnd prec,mode on stack
btst &0x7, FTEMP_EX(%a0) # make "internal" format
sne FTEMP_SGN(%a0)
mov.w FTEMP_EX(%a0), %d1 # extract exponent
and.w &0x7fff, %d1
sub.w %d0, %d1
mov.w %d1, FTEMP_EX(%a0) # insert 16 bit exponent
mov.l %a0, -(%sp) # save operand ptr during calls
mov.l 0x4(%sp),%d0 # pass rnd prec.
andi.w &0x00c0,%d0
lsr.w &0x4,%d0
bsr.l _denorm # denorm result
mov.l (%sp),%a0
mov.w 0x6(%sp),%d1 # load prec:mode into %d1
andi.w &0xc0,%d1 # extract rnd prec
lsr.w &0x4,%d1
swap %d1
mov.w 0x6(%sp),%d1
andi.w &0x30,%d1
lsr.w &0x4,%d1
bsr.l _round # round the denorm
mov.l (%sp)+, %a0
# result is now rounded properly. convert back to normal format
bclr &0x7, FTEMP_EX(%a0) # clear sgn first; may have residue
tst.b FTEMP_SGN(%a0) # is "internal result" sign set?
beq.b unf_res_chkifzero # no; result is positive
bset &0x7, FTEMP_EX(%a0) # set result sgn
clr.b FTEMP_SGN(%a0) # clear temp sign
# the number may have become zero after rounding. set ccodes accordingly.
unf_res_chkifzero:
clr.l %d0
tst.l FTEMP_HI(%a0) # is value now a zero?
bne.b unf_res_cont # no
tst.l FTEMP_LO(%a0)
bne.b unf_res_cont # no
# bset &z_bit, FPSR_CC(%a6) # yes; set zero ccode bit
bset &z_bit, %d0 # yes; set zero ccode bit
unf_res_cont:
#
# can inex1 also be set along with unfl and inex2???
#
# we know that underflow has occurred. aunfl should be set if INEX2 is also set.
#
btst &inex2_bit, FPSR_EXCEPT(%a6) # is INEX2 set?
beq.b unf_res_end # no
bset &aunfl_bit, FPSR_AEXCEPT(%a6) # yes; set aunfl
unf_res_end:
add.l &0x4, %sp # clear stack
rts
# unf_res() for fsglmul() and fsgldiv().
global unf_res4
unf_res4:
mov.l %d1,-(%sp) # save rnd prec,mode on stack
btst &0x7,FTEMP_EX(%a0) # make "internal" format
sne FTEMP_SGN(%a0)
mov.w FTEMP_EX(%a0),%d1 # extract exponent
and.w &0x7fff,%d1
sub.w %d0,%d1
mov.w %d1,FTEMP_EX(%a0) # insert 16 bit exponent
mov.l %a0,-(%sp) # save operand ptr during calls
clr.l %d0 # force rnd prec = ext
bsr.l _denorm # denorm result
mov.l (%sp),%a0
mov.w &s_mode,%d1 # force rnd prec = sgl
swap %d1
mov.w 0x6(%sp),%d1 # load rnd mode
andi.w &0x30,%d1 # extract rnd prec
lsr.w &0x4,%d1
bsr.l _round # round the denorm
mov.l (%sp)+,%a0
# result is now rounded properly. convert back to normal format
bclr &0x7,FTEMP_EX(%a0) # clear sgn first; may have residue
tst.b FTEMP_SGN(%a0) # is "internal result" sign set?
beq.b unf_res4_chkifzero # no; result is positive
bset &0x7,FTEMP_EX(%a0) # set result sgn
clr.b FTEMP_SGN(%a0) # clear temp sign
# the number may have become zero after rounding. set ccodes accordingly.
unf_res4_chkifzero:
clr.l %d0
tst.l FTEMP_HI(%a0) # is value now a zero?
bne.b unf_res4_cont # no
tst.l FTEMP_LO(%a0)
bne.b unf_res4_cont # no
# bset &z_bit,FPSR_CC(%a6) # yes; set zero ccode bit
bset &z_bit,%d0 # yes; set zero ccode bit
unf_res4_cont:
#
# can inex1 also be set along with unfl and inex2???
#
# we know that underflow has occurred. aunfl should be set if INEX2 is also set.
#
btst &inex2_bit,FPSR_EXCEPT(%a6) # is INEX2 set?
beq.b unf_res4_end # no
bset &aunfl_bit,FPSR_AEXCEPT(%a6) # yes; set aunfl
unf_res4_end:
add.l &0x4,%sp # clear stack
rts
#########################################################################
# XDEF **************************************************************** #
# ovf_res(): routine to produce the default overflow result of #
# an overflowing number. #
# ovf_res2(): same as above but the rnd mode/prec are passed #
# differently. #
# #
# XREF **************************************************************** #
# none #
# #
# INPUT *************************************************************** #
# d1.b = '-1' => (-); '0' => (+) #
# ovf_res(): #
# d0 = rnd mode/prec #
# ovf_res2(): #
# hi(d0) = rnd prec #
# lo(d0) = rnd mode #
# #
# OUTPUT ************************************************************** #
# a0 = points to extended precision result #
# d0.b = condition code bits #
# #
# ALGORITHM *********************************************************** #
# The default overflow result can be determined by the sign of #
# the result and the rounding mode/prec in effect. These bits are #
# concatenated together to create an index into the default result #
# table. A pointer to the correct result is returned in a0. The #
# resulting condition codes are returned in d0 in case the caller #
# doesn't want FPSR_cc altered (as is the case for fmove out). #
# #
#########################################################################
global ovf_res
ovf_res:
andi.w &0x10,%d1 # keep result sign
lsr.b &0x4,%d0 # shift prec/mode
or.b %d0,%d1 # concat the two
mov.w %d1,%d0 # make a copy
lsl.b &0x1,%d1 # multiply d1 by 2
bra.b ovf_res_load
global ovf_res2
ovf_res2:
and.w &0x10, %d1 # keep result sign
or.b %d0, %d1 # insert rnd mode
swap %d0
or.b %d0, %d1 # insert rnd prec
mov.w %d1, %d0 # make a copy
lsl.b &0x1, %d1 # shift left by 1
#
# use the rounding mode, precision, and result sign as in index into the
# two tables below to fetch the default result and the result ccodes.
#
ovf_res_load:
mov.b (tbl_ovfl_cc.b,%pc,%d0.w*1), %d0 # fetch result ccodes
lea (tbl_ovfl_result.b,%pc,%d1.w*8), %a0 # return result ptr
rts
tbl_ovfl_cc:
byte 0x2, 0x0, 0x0, 0x2
byte 0x2, 0x0, 0x0, 0x2
byte 0x2, 0x0, 0x0, 0x2
byte 0x0, 0x0, 0x0, 0x0
byte 0x2+0x8, 0x8, 0x2+0x8, 0x8
byte 0x2+0x8, 0x8, 0x2+0x8, 0x8
byte 0x2+0x8, 0x8, 0x2+0x8, 0x8
tbl_ovfl_result:
long 0x7fff0000,0x00000000,0x00000000,0x00000000 # +INF; RN
long 0x7ffe0000,0xffffffff,0xffffffff,0x00000000 # +EXT; RZ
long 0x7ffe0000,0xffffffff,0xffffffff,0x00000000 # +EXT; RM
long 0x7fff0000,0x00000000,0x00000000,0x00000000 # +INF; RP
long 0x7fff0000,0x00000000,0x00000000,0x00000000 # +INF; RN
long 0x407e0000,0xffffff00,0x00000000,0x00000000 # +SGL; RZ
long 0x407e0000,0xffffff00,0x00000000,0x00000000 # +SGL; RM
long 0x7fff0000,0x00000000,0x00000000,0x00000000 # +INF; RP
long 0x7fff0000,0x00000000,0x00000000,0x00000000 # +INF; RN
long 0x43fe0000,0xffffffff,0xfffff800,0x00000000 # +DBL; RZ
long 0x43fe0000,0xffffffff,0xfffff800,0x00000000 # +DBL; RM
long 0x7fff0000,0x00000000,0x00000000,0x00000000 # +INF; RP
long 0x00000000,0x00000000,0x00000000,0x00000000
long 0x00000000,0x00000000,0x00000000,0x00000000
long 0x00000000,0x00000000,0x00000000,0x00000000
long 0x00000000,0x00000000,0x00000000,0x00000000
long 0xffff0000,0x00000000,0x00000000,0x00000000 # -INF; RN
long 0xfffe0000,0xffffffff,0xffffffff,0x00000000 # -EXT; RZ
long 0xffff0000,0x00000000,0x00000000,0x00000000 # -INF; RM
long 0xfffe0000,0xffffffff,0xffffffff,0x00000000 # -EXT; RP
long 0xffff0000,0x00000000,0x00000000,0x00000000 # -INF; RN
long 0xc07e0000,0xffffff00,0x00000000,0x00000000 # -SGL; RZ
long 0xffff0000,0x00000000,0x00000000,0x00000000 # -INF; RM
long 0xc07e0000,0xffffff00,0x00000000,0x00000000 # -SGL; RP
long 0xffff0000,0x00000000,0x00000000,0x00000000 # -INF; RN
long 0xc3fe0000,0xffffffff,0xfffff800,0x00000000 # -DBL; RZ
long 0xffff0000,0x00000000,0x00000000,0x00000000 # -INF; RM
long 0xc3fe0000,0xffffffff,0xfffff800,0x00000000 # -DBL; RP
#########################################################################
# XDEF **************************************************************** #
# get_packed(): fetch a packed operand from memory and then #
# convert it to a floating-point binary number. #
# #
# XREF **************************************************************** #
# _dcalc_ea() - calculate the correct <ea> #
# _mem_read() - fetch the packed operand from memory #
# facc_in_x() - the fetch failed so jump to special exit code #
# decbin() - convert packed to binary extended precision #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# If no failure on _mem_read(): #
# FP_SRC(a6) = packed operand now as a binary FP number #
# #
# ALGORITHM *********************************************************** #
# Get the correct <ea> whihc is the value on the exception stack #
# frame w/ maybe a correction factor if the <ea> is -(an) or (an)+. #
# Then, fetch the operand from memory. If the fetch fails, exit #
# through facc_in_x(). #
# If the packed operand is a ZERO,NAN, or INF, convert it to #
# its binary representation here. Else, call decbin() which will #
# convert the packed value to an extended precision binary value. #
# #
#########################################################################
# the stacked <ea> for packed is correct except for -(An).
# the base reg must be updated for both -(An) and (An)+.
global get_packed
get_packed:
mov.l &0xc,%d0 # packed is 12 bytes
bsr.l _dcalc_ea # fetch <ea>; correct An
lea FP_SRC(%a6),%a1 # pass: ptr to super dst
mov.l &0xc,%d0 # pass: 12 bytes
bsr.l _dmem_read # read packed operand
tst.l %d1 # did dfetch fail?
bne.l facc_in_x # yes
# The packed operand is an INF or a NAN if the exponent field is all ones.
bfextu FP_SRC(%a6){&1:&15},%d0 # get exp
cmpi.w %d0,&0x7fff # INF or NAN?
bne.b gp_try_zero # no
rts # operand is an INF or NAN
# The packed operand is a zero if the mantissa is all zero, else it's
# a normal packed op.
gp_try_zero:
mov.b 3+FP_SRC(%a6),%d0 # get byte 4
andi.b &0x0f,%d0 # clear all but last nybble
bne.b gp_not_spec # not a zero
tst.l FP_SRC_HI(%a6) # is lw 2 zero?
bne.b gp_not_spec # not a zero
tst.l FP_SRC_LO(%a6) # is lw 3 zero?
bne.b gp_not_spec # not a zero
rts # operand is a ZERO
gp_not_spec:
lea FP_SRC(%a6),%a0 # pass: ptr to packed op
bsr.l decbin # convert to extended
fmovm.x &0x80,FP_SRC(%a6) # make this the srcop
rts
#########################################################################
# decbin(): Converts normalized packed bcd value pointed to by register #
# a0 to extended-precision value in fp0. #
# #
# INPUT *************************************************************** #
# a0 = pointer to normalized packed bcd value #
# #
# OUTPUT ************************************************************** #
# fp0 = exact fp representation of the packed bcd value. #
# #
# ALGORITHM *********************************************************** #
# Expected is a normal bcd (i.e. non-exceptional; all inf, zero, #
# and NaN operands are dispatched without entering this routine) #
# value in 68881/882 format at location (a0). #
# #
# A1. Convert the bcd exponent to binary by successive adds and #
# muls. Set the sign according to SE. Subtract 16 to compensate #
# for the mantissa which is to be interpreted as 17 integer #
# digits, rather than 1 integer and 16 fraction digits. #
# Note: this operation can never overflow. #
# #
# A2. Convert the bcd mantissa to binary by successive #
# adds and muls in FP0. Set the sign according to SM. #
# The mantissa digits will be converted with the decimal point #
# assumed following the least-significant digit. #
# Note: this operation can never overflow. #
# #
# A3. Count the number of leading/trailing zeros in the #
# bcd string. If SE is positive, count the leading zeros; #
# if negative, count the trailing zeros. Set the adjusted #
# exponent equal to the exponent from A1 and the zero count #
# added if SM = 1 and subtracted if SM = 0. Scale the #
# mantissa the equivalent of forcing in the bcd value: #
# #
# SM = 0 a non-zero digit in the integer position #
# SM = 1 a non-zero digit in Mant0, lsd of the fraction #
# #
# this will insure that any value, regardless of its #
# representation (ex. 0.1E2, 1E1, 10E0, 100E-1), is converted #
# consistently. #
# #
# A4. Calculate the factor 10^exp in FP1 using a table of #
# 10^(2^n) values. To reduce the error in forming factors #
# greater than 10^27, a directed rounding scheme is used with #
# tables rounded to RN, RM, and RP, according to the table #
# in the comments of the pwrten section. #
# #
# A5. Form the final binary number by scaling the mantissa by #
# the exponent factor. This is done by multiplying the #
# mantissa in FP0 by the factor in FP1 if the adjusted #
# exponent sign is positive, and dividing FP0 by FP1 if #
# it is negative. #
# #
# Clean up and return. Check if the final mul or div was inexact. #
# If so, set INEX1 in USER_FPSR. #
# #
#########################################################################
#
# PTENRN, PTENRM, and PTENRP are arrays of powers of 10 rounded
# to nearest, minus, and plus, respectively. The tables include
# 10**{1,2,4,8,16,32,64,128,256,512,1024,2048,4096}. No rounding
# is required until the power is greater than 27, however, all
# tables include the first 5 for ease of indexing.
#
RTABLE:
byte 0,0,0,0
byte 2,3,2,3
byte 2,3,3,2
byte 3,2,2,3
set FNIBS,7
set FSTRT,0
set ESTRT,4
set EDIGITS,2
global decbin
decbin:
mov.l 0x0(%a0),FP_SCR0_EX(%a6) # make a copy of input
mov.l 0x4(%a0),FP_SCR0_HI(%a6) # so we don't alter it
mov.l 0x8(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0
movm.l &0x3c00,-(%sp) # save d2-d5
fmovm.x &0x1,-(%sp) # save fp1
#
# Calculate exponent:
# 1. Copy bcd value in memory for use as a working copy.
# 2. Calculate absolute value of exponent in d1 by mul and add.
# 3. Correct for exponent sign.
# 4. Subtract 16 to compensate for interpreting the mant as all integer digits.
# (i.e., all digits assumed left of the decimal point.)
#
# Register usage:
#
# calc_e:
# (*) d0: temp digit storage
# (*) d1: accumulator for binary exponent
# (*) d2: digit count
# (*) d3: offset pointer
# ( ) d4: first word of bcd
# ( ) a0: pointer to working bcd value
# ( ) a6: pointer to original bcd value
# (*) FP_SCR1: working copy of original bcd value
# (*) L_SCR1: copy of original exponent word
#
calc_e:
mov.l &EDIGITS,%d2 # # of nibbles (digits) in fraction part
mov.l &ESTRT,%d3 # counter to pick up digits
mov.l (%a0),%d4 # get first word of bcd
clr.l %d1 # zero d1 for accumulator
e_gd:
mulu.l &0xa,%d1 # mul partial product by one digit place
bfextu %d4{%d3:&4},%d0 # get the digit and zero extend into d0
add.l %d0,%d1 # d1 = d1 + d0
addq.b &4,%d3 # advance d3 to the next digit
dbf.w %d2,e_gd # if we have used all 3 digits, exit loop
btst &30,%d4 # get SE
beq.b e_pos # don't negate if pos
neg.l %d1 # negate before subtracting
e_pos:
sub.l &16,%d1 # sub to compensate for shift of mant
bge.b e_save # if still pos, do not neg
neg.l %d1 # now negative, make pos and set SE
or.l &0x40000000,%d4 # set SE in d4,
or.l &0x40000000,(%a0) # and in working bcd
e_save:
mov.l %d1,-(%sp) # save exp on stack
#
#
# Calculate mantissa:
# 1. Calculate absolute value of mantissa in fp0 by mul and add.
# 2. Correct for mantissa sign.
# (i.e., all digits assumed left of the decimal point.)
#
# Register usage:
#
# calc_m:
# (*) d0: temp digit storage
# (*) d1: lword counter
# (*) d2: digit count
# (*) d3: offset pointer
# ( ) d4: words 2 and 3 of bcd
# ( ) a0: pointer to working bcd value
# ( ) a6: pointer to original bcd value
# (*) fp0: mantissa accumulator
# ( ) FP_SCR1: working copy of original bcd value
# ( ) L_SCR1: copy of original exponent word
#
calc_m:
mov.l &1,%d1 # word counter, init to 1
fmov.s &0x00000000,%fp0 # accumulator
#
#
# Since the packed number has a long word between the first & second parts,
# get the integer digit then skip down & get the rest of the
# mantissa. We will unroll the loop once.
#
bfextu (%a0){&28:&4},%d0 # integer part is ls digit in long word
fadd.b %d0,%fp0 # add digit to sum in fp0
#
#
# Get the rest of the mantissa.
#
loadlw:
mov.l (%a0,%d1.L*4),%d4 # load mantissa lonqword into d4
mov.l &FSTRT,%d3 # counter to pick up digits
mov.l &FNIBS,%d2 # reset number of digits per a0 ptr
md2b:
fmul.s &0x41200000,%fp0 # fp0 = fp0 * 10
bfextu %d4{%d3:&4},%d0 # get the digit and zero extend
fadd.b %d0,%fp0 # fp0 = fp0 + digit
#
#
# If all the digits (8) in that long word have been converted (d2=0),
# then inc d1 (=2) to point to the next long word and reset d3 to 0
# to initialize the digit offset, and set d2 to 7 for the digit count;
# else continue with this long word.
#
addq.b &4,%d3 # advance d3 to the next digit
dbf.w %d2,md2b # check for last digit in this lw
nextlw:
addq.l &1,%d1 # inc lw pointer in mantissa
cmp.l %d1,&2 # test for last lw
ble.b loadlw # if not, get last one
#
# Check the sign of the mant and make the value in fp0 the same sign.
#
m_sign:
btst &31,(%a0) # test sign of the mantissa
beq.b ap_st_z # if clear, go to append/strip zeros
fneg.x %fp0 # if set, negate fp0
#
# Append/strip zeros:
#
# For adjusted exponents which have an absolute value greater than 27*,
# this routine calculates the amount needed to normalize the mantissa
# for the adjusted exponent. That number is subtracted from the exp
# if the exp was positive, and added if it was negative. The purpose
# of this is to reduce the value of the exponent and the possibility
# of error in calculation of pwrten.
#
# 1. Branch on the sign of the adjusted exponent.
# 2p.(positive exp)
# 2. Check M16 and the digits in lwords 2 and 3 in decending order.
# 3. Add one for each zero encountered until a non-zero digit.
# 4. Subtract the count from the exp.
# 5. Check if the exp has crossed zero in #3 above; make the exp abs
# and set SE.
# 6. Multiply the mantissa by 10**count.
# 2n.(negative exp)
# 2. Check the digits in lwords 3 and 2 in decending order.
# 3. Add one for each zero encountered until a non-zero digit.
# 4. Add the count to the exp.
# 5. Check if the exp has crossed zero in #3 above; clear SE.
# 6. Divide the mantissa by 10**count.
#
# *Why 27? If the adjusted exponent is within -28 < expA < 28, than
# any adjustment due to append/strip zeros will drive the resultane
# exponent towards zero. Since all pwrten constants with a power
# of 27 or less are exact, there is no need to use this routine to
# attempt to lessen the resultant exponent.
#
# Register usage:
#
# ap_st_z:
# (*) d0: temp digit storage
# (*) d1: zero count
# (*) d2: digit count
# (*) d3: offset pointer
# ( ) d4: first word of bcd
# (*) d5: lword counter
# ( ) a0: pointer to working bcd value
# ( ) FP_SCR1: working copy of original bcd value
# ( ) L_SCR1: copy of original exponent word
#
#
# First check the absolute value of the exponent to see if this
# routine is necessary. If so, then check the sign of the exponent
# and do append (+) or strip (-) zeros accordingly.
# This section handles a positive adjusted exponent.
#
ap_st_z:
mov.l (%sp),%d1 # load expA for range test
cmp.l %d1,&27 # test is with 27
ble.w pwrten # if abs(expA) <28, skip ap/st zeros
btst &30,(%a0) # check sign of exp
bne.b ap_st_n # if neg, go to neg side
clr.l %d1 # zero count reg
mov.l (%a0),%d4 # load lword 1 to d4
bfextu %d4{&28:&4},%d0 # get M16 in d0
bne.b ap_p_fx # if M16 is non-zero, go fix exp
addq.l &1,%d1 # inc zero count
mov.l &1,%d5 # init lword counter
mov.l (%a0,%d5.L*4),%d4 # get lword 2 to d4
bne.b ap_p_cl # if lw 2 is zero, skip it
addq.l &8,%d1 # and inc count by 8
addq.l &1,%d5 # inc lword counter
mov.l (%a0,%d5.L*4),%d4 # get lword 3 to d4
ap_p_cl:
clr.l %d3 # init offset reg
mov.l &7,%d2 # init digit counter
ap_p_gd:
bfextu %d4{%d3:&4},%d0 # get digit
bne.b ap_p_fx # if non-zero, go to fix exp
addq.l &4,%d3 # point to next digit
addq.l &1,%d1 # inc digit counter
dbf.w %d2,ap_p_gd # get next digit
ap_p_fx:
mov.l %d1,%d0 # copy counter to d2
mov.l (%sp),%d1 # get adjusted exp from memory
sub.l %d0,%d1 # subtract count from exp
bge.b ap_p_fm # if still pos, go to pwrten
neg.l %d1 # now its neg; get abs
mov.l (%a0),%d4 # load lword 1 to d4
or.l &0x40000000,%d4 # and set SE in d4
or.l &0x40000000,(%a0) # and in memory
#
# Calculate the mantissa multiplier to compensate for the striping of
# zeros from the mantissa.
#
ap_p_fm:
lea.l PTENRN(%pc),%a1 # get address of power-of-ten table
clr.l %d3 # init table index
fmov.s &0x3f800000,%fp1 # init fp1 to 1
mov.l &3,%d2 # init d2 to count bits in counter
ap_p_el:
asr.l &1,%d0 # shift lsb into carry
bcc.b ap_p_en # if 1, mul fp1 by pwrten factor
fmul.x (%a1,%d3),%fp1 # mul by 10**(d3_bit_no)
ap_p_en:
add.l &12,%d3 # inc d3 to next rtable entry
tst.l %d0 # check if d0 is zero
bne.b ap_p_el # if not, get next bit
fmul.x %fp1,%fp0 # mul mantissa by 10**(no_bits_shifted)
bra.b pwrten # go calc pwrten
#
# This section handles a negative adjusted exponent.
#
ap_st_n:
clr.l %d1 # clr counter
mov.l &2,%d5 # set up d5 to point to lword 3
mov.l (%a0,%d5.L*4),%d4 # get lword 3
bne.b ap_n_cl # if not zero, check digits
sub.l &1,%d5 # dec d5 to point to lword 2
addq.l &8,%d1 # inc counter by 8
mov.l (%a0,%d5.L*4),%d4 # get lword 2
ap_n_cl:
mov.l &28,%d3 # point to last digit
mov.l &7,%d2 # init digit counter
ap_n_gd:
bfextu %d4{%d3:&4},%d0 # get digit
bne.b ap_n_fx # if non-zero, go to exp fix
subq.l &4,%d3 # point to previous digit
addq.l &1,%d1 # inc digit counter
dbf.w %d2,ap_n_gd # get next digit
ap_n_fx:
mov.l %d1,%d0 # copy counter to d0
mov.l (%sp),%d1 # get adjusted exp from memory
sub.l %d0,%d1 # subtract count from exp
bgt.b ap_n_fm # if still pos, go fix mantissa
neg.l %d1 # take abs of exp and clr SE
mov.l (%a0),%d4 # load lword 1 to d4
and.l &0xbfffffff,%d4 # and clr SE in d4
and.l &0xbfffffff,(%a0) # and in memory
#
# Calculate the mantissa multiplier to compensate for the appending of
# zeros to the mantissa.
#
ap_n_fm:
lea.l PTENRN(%pc),%a1 # get address of power-of-ten table
clr.l %d3 # init table index
fmov.s &0x3f800000,%fp1 # init fp1 to 1
mov.l &3,%d2 # init d2 to count bits in counter
ap_n_el:
asr.l &1,%d0 # shift lsb into carry
bcc.b ap_n_en # if 1, mul fp1 by pwrten factor
fmul.x (%a1,%d3),%fp1 # mul by 10**(d3_bit_no)
ap_n_en:
add.l &12,%d3 # inc d3 to next rtable entry
tst.l %d0 # check if d0 is zero
bne.b ap_n_el # if not, get next bit
fdiv.x %fp1,%fp0 # div mantissa by 10**(no_bits_shifted)
#
#
# Calculate power-of-ten factor from adjusted and shifted exponent.
#
# Register usage:
#
# pwrten:
# (*) d0: temp
# ( ) d1: exponent
# (*) d2: {FPCR[6:5],SM,SE} as index in RTABLE; temp
# (*) d3: FPCR work copy
# ( ) d4: first word of bcd
# (*) a1: RTABLE pointer
# calc_p:
# (*) d0: temp
# ( ) d1: exponent
# (*) d3: PWRTxx table index
# ( ) a0: pointer to working copy of bcd
# (*) a1: PWRTxx pointer
# (*) fp1: power-of-ten accumulator
#
# Pwrten calculates the exponent factor in the selected rounding mode
# according to the following table:
#
# Sign of Mant Sign of Exp Rounding Mode PWRTEN Rounding Mode
#
# ANY ANY RN RN
#
# + + RP RP
# - + RP RM
# + - RP RM
# - - RP RP
#
# + + RM RM
# - + RM RP
# + - RM RP
# - - RM RM
#
# + + RZ RM
# - + RZ RM
# + - RZ RP
# - - RZ RP
#
#
pwrten:
mov.l USER_FPCR(%a6),%d3 # get user's FPCR
bfextu %d3{&26:&2},%d2 # isolate rounding mode bits
mov.l (%a0),%d4 # reload 1st bcd word to d4
asl.l &2,%d2 # format d2 to be
bfextu %d4{&0:&2},%d0 # {FPCR[6],FPCR[5],SM,SE}
add.l %d0,%d2 # in d2 as index into RTABLE
lea.l RTABLE(%pc),%a1 # load rtable base
mov.b (%a1,%d2),%d0 # load new rounding bits from table
clr.l %d3 # clear d3 to force no exc and extended
bfins %d0,%d3{&26:&2} # stuff new rounding bits in FPCR
fmov.l %d3,%fpcr # write new FPCR
asr.l &1,%d0 # write correct PTENxx table
bcc.b not_rp # to a1
lea.l PTENRP(%pc),%a1 # it is RP
bra.b calc_p # go to init section
not_rp:
asr.l &1,%d0 # keep checking
bcc.b not_rm
lea.l PTENRM(%pc),%a1 # it is RM
bra.b calc_p # go to init section
not_rm:
lea.l PTENRN(%pc),%a1 # it is RN
calc_p:
mov.l %d1,%d0 # copy exp to d0;use d0
bpl.b no_neg # if exp is negative,
neg.l %d0 # invert it
or.l &0x40000000,(%a0) # and set SE bit
no_neg:
clr.l %d3 # table index
fmov.s &0x3f800000,%fp1 # init fp1 to 1
e_loop:
asr.l &1,%d0 # shift next bit into carry
bcc.b e_next # if zero, skip the mul
fmul.x (%a1,%d3),%fp1 # mul by 10**(d3_bit_no)
e_next:
add.l &12,%d3 # inc d3 to next rtable entry
tst.l %d0 # check if d0 is zero
bne.b e_loop # not zero, continue shifting
#
#
# Check the sign of the adjusted exp and make the value in fp0 the
# same sign. If the exp was pos then multiply fp1*fp0;
# else divide fp0/fp1.
#
# Register Usage:
# norm:
# ( ) a0: pointer to working bcd value
# (*) fp0: mantissa accumulator
# ( ) fp1: scaling factor - 10**(abs(exp))
#
pnorm:
btst &30,(%a0) # test the sign of the exponent
beq.b mul # if clear, go to multiply
div:
fdiv.x %fp1,%fp0 # exp is negative, so divide mant by exp
bra.b end_dec
mul:
fmul.x %fp1,%fp0 # exp is positive, so multiply by exp
#
#
# Clean up and return with result in fp0.
#
# If the final mul/div in decbin incurred an inex exception,
# it will be inex2, but will be reported as inex1 by get_op.
#
end_dec:
fmov.l %fpsr,%d0 # get status register
bclr &inex2_bit+8,%d0 # test for inex2 and clear it
beq.b no_exc # skip this if no exc
ori.w &inx1a_mask,2+USER_FPSR(%a6) # set INEX1/AINEX
no_exc:
add.l &0x4,%sp # clear 1 lw param
fmovm.x (%sp)+,&0x40 # restore fp1
movm.l (%sp)+,&0x3c # restore d2-d5
fmov.l &0x0,%fpcr
fmov.l &0x0,%fpsr
rts
#########################################################################
# bindec(): Converts an input in extended precision format to bcd format#
# #
# INPUT *************************************************************** #
# a0 = pointer to the input extended precision value in memory. #
# the input may be either normalized, unnormalized, or #
# denormalized. #
# d0 = contains the k-factor sign-extended to 32-bits. #
# #
# OUTPUT ************************************************************** #
# FP_SCR0(a6) = bcd format result on the stack. #
# #
# ALGORITHM *********************************************************** #
# #
# A1. Set RM and size ext; Set SIGMA = sign of input. #
# The k-factor is saved for use in d7. Clear the #
# BINDEC_FLG for separating normalized/denormalized #
# input. If input is unnormalized or denormalized, #
# normalize it. #
# #
# A2. Set X = abs(input). #
# #
# A3. Compute ILOG. #
# ILOG is the log base 10 of the input value. It is #
# approximated by adding e + 0.f when the original #
# value is viewed as 2^^e * 1.f in extended precision. #
# This value is stored in d6. #
# #
# A4. Clr INEX bit. #
# The operation in A3 above may have set INEX2. #
# #
# A5. Set ICTR = 0; #
# ICTR is a flag used in A13. It must be set before the #
# loop entry A6. #
# #
# A6. Calculate LEN. #
# LEN is the number of digits to be displayed. The #
# k-factor can dictate either the total number of digits, #
# if it is a positive number, or the number of digits #
# after the decimal point which are to be included as #
# significant. See the 68882 manual for examples. #
# If LEN is computed to be greater than 17, set OPERR in #
# USER_FPSR. LEN is stored in d4. #
# #
# A7. Calculate SCALE. #
# SCALE is equal to 10^ISCALE, where ISCALE is the number #
# of decimal places needed to insure LEN integer digits #
# in the output before conversion to bcd. LAMBDA is the #
# sign of ISCALE, used in A9. Fp1 contains #
# 10^^(abs(ISCALE)) using a rounding mode which is a #
# function of the original rounding mode and the signs #
# of ISCALE and X. A table is given in the code. #
# #
# A8. Clr INEX; Force RZ. #
# The operation in A3 above may have set INEX2. #
# RZ mode is forced for the scaling operation to insure #
# only one rounding error. The grs bits are collected in #
# the INEX flag for use in A10. #
# #
# A9. Scale X -> Y. #
# The mantissa is scaled to the desired number of #
# significant digits. The excess digits are collected #
# in INEX2. #
# #
# A10. Or in INEX. #
# If INEX is set, round error occurred. This is #
# compensated for by 'or-ing' in the INEX2 flag to #
# the lsb of Y. #
# #
# A11. Restore original FPCR; set size ext. #
# Perform FINT operation in the user's rounding mode. #
# Keep the size to extended. #
# #
# A12. Calculate YINT = FINT(Y) according to user's rounding #
# mode. The FPSP routine sintd0 is used. The output #
# is in fp0. #
# #
# A13. Check for LEN digits. #
# If the int operation results in more than LEN digits, #
# or less than LEN -1 digits, adjust ILOG and repeat from #
# A6. This test occurs only on the first pass. If the #
# result is exactly 10^LEN, decrement ILOG and divide #
# the mantissa by 10. #
# #
# A14. Convert the mantissa to bcd. #
# The binstr routine is used to convert the LEN digit #
# mantissa to bcd in memory. The input to binstr is #
# to be a fraction; i.e. (mantissa)/10^LEN and adjusted #
# such that the decimal point is to the left of bit 63. #
# The bcd digits are stored in the correct position in #
# the final string area in memory. #
# #
# A15. Convert the exponent to bcd. #
# As in A14 above, the exp is converted to bcd and the #
# digits are stored in the final string. #
# Test the length of the final exponent string. If the #
# length is 4, set operr. #
# #
# A16. Write sign bits to final string. #
# #
#########################################################################
set BINDEC_FLG, EXC_TEMP # DENORM flag
# Constants in extended precision
PLOG2:
long 0x3FFD0000,0x9A209A84,0xFBCFF798,0x00000000
PLOG2UP1:
long 0x3FFD0000,0x9A209A84,0xFBCFF799,0x00000000
# Constants in single precision
FONE:
long 0x3F800000,0x00000000,0x00000000,0x00000000
FTWO:
long 0x40000000,0x00000000,0x00000000,0x00000000
FTEN:
long 0x41200000,0x00000000,0x00000000,0x00000000
F4933:
long 0x459A2800,0x00000000,0x00000000,0x00000000
RBDTBL:
byte 0,0,0,0
byte 3,3,2,2
byte 3,2,2,3
byte 2,3,3,2
# Implementation Notes:
#
# The registers are used as follows:
#
# d0: scratch; LEN input to binstr
# d1: scratch
# d2: upper 32-bits of mantissa for binstr
# d3: scratch;lower 32-bits of mantissa for binstr
# d4: LEN
# d5: LAMBDA/ICTR
# d6: ILOG
# d7: k-factor
# a0: ptr for original operand/final result
# a1: scratch pointer
# a2: pointer to FP_X; abs(original value) in ext
# fp0: scratch
# fp1: scratch
# fp2: scratch
# F_SCR1:
# F_SCR2:
# L_SCR1:
# L_SCR2:
global bindec
bindec:
movm.l &0x3f20,-(%sp) # {%d2-%d7/%a2}
fmovm.x &0x7,-(%sp) # {%fp0-%fp2}
# A1. Set RM and size ext. Set SIGMA = sign input;
# The k-factor is saved for use in d7. Clear BINDEC_FLG for
# separating normalized/denormalized input. If the input
# is a denormalized number, set the BINDEC_FLG memory word
# to signal denorm. If the input is unnormalized, normalize
# the input and test for denormalized result.
#
fmov.l &rm_mode*0x10,%fpcr # set RM and ext
mov.l (%a0),L_SCR2(%a6) # save exponent for sign check
mov.l %d0,%d7 # move k-factor to d7
clr.b BINDEC_FLG(%a6) # clr norm/denorm flag
cmpi.b STAG(%a6),&DENORM # is input a DENORM?
bne.w A2_str # no; input is a NORM
#
# Normalize the denorm
#
un_de_norm:
mov.w (%a0),%d0
and.w &0x7fff,%d0 # strip sign of normalized exp
mov.l 4(%a0),%d1
mov.l 8(%a0),%d2
norm_loop:
sub.w &1,%d0
lsl.l &1,%d2
roxl.l &1,%d1
tst.l %d1
bge.b norm_loop
#
# Test if the normalized input is denormalized
#
tst.w %d0
bgt.b pos_exp # if greater than zero, it is a norm
st BINDEC_FLG(%a6) # set flag for denorm
pos_exp:
and.w &0x7fff,%d0 # strip sign of normalized exp
mov.w %d0,(%a0)
mov.l %d1,4(%a0)
mov.l %d2,8(%a0)
# A2. Set X = abs(input).
#
A2_str:
mov.l (%a0),FP_SCR1(%a6) # move input to work space
mov.l 4(%a0),FP_SCR1+4(%a6) # move input to work space
mov.l 8(%a0),FP_SCR1+8(%a6) # move input to work space
and.l &0x7fffffff,FP_SCR1(%a6) # create abs(X)
# A3. Compute ILOG.
# ILOG is the log base 10 of the input value. It is approx-
# imated by adding e + 0.f when the original value is viewed
# as 2^^e * 1.f in extended precision. This value is stored
# in d6.
#
# Register usage:
# Input/Output
# d0: k-factor/exponent
# d2: x/x
# d3: x/x
# d4: x/x
# d5: x/x
# d6: x/ILOG
# d7: k-factor/Unchanged
# a0: ptr for original operand/final result
# a1: x/x
# a2: x/x
# fp0: x/float(ILOG)
# fp1: x/x
# fp2: x/x
# F_SCR1:x/x
# F_SCR2:Abs(X)/Abs(X) with $3fff exponent
# L_SCR1:x/x
# L_SCR2:first word of X packed/Unchanged
tst.b BINDEC_FLG(%a6) # check for denorm
beq.b A3_cont # if clr, continue with norm
mov.l &-4933,%d6 # force ILOG = -4933
bra.b A4_str
A3_cont:
mov.w FP_SCR1(%a6),%d0 # move exp to d0
mov.w &0x3fff,FP_SCR1(%a6) # replace exponent with 0x3fff
fmov.x FP_SCR1(%a6),%fp0 # now fp0 has 1.f
sub.w &0x3fff,%d0 # strip off bias
fadd.w %d0,%fp0 # add in exp
fsub.s FONE(%pc),%fp0 # subtract off 1.0
fbge.w pos_res # if pos, branch
fmul.x PLOG2UP1(%pc),%fp0 # if neg, mul by LOG2UP1
fmov.l %fp0,%d6 # put ILOG in d6 as a lword
bra.b A4_str # go move out ILOG
pos_res:
fmul.x PLOG2(%pc),%fp0 # if pos, mul by LOG2
fmov.l %fp0,%d6 # put ILOG in d6 as a lword
# A4. Clr INEX bit.
# The operation in A3 above may have set INEX2.
A4_str:
fmov.l &0,%fpsr # zero all of fpsr - nothing needed
# A5. Set ICTR = 0;
# ICTR is a flag used in A13. It must be set before the
# loop entry A6. The lower word of d5 is used for ICTR.
clr.w %d5 # clear ICTR
# A6. Calculate LEN.
# LEN is the number of digits to be displayed. The k-factor
# can dictate either the total number of digits, if it is
# a positive number, or the number of digits after the
# original decimal point which are to be included as
# significant. See the 68882 manual for examples.
# If LEN is computed to be greater than 17, set OPERR in
# USER_FPSR. LEN is stored in d4.
#
# Register usage:
# Input/Output
# d0: exponent/Unchanged
# d2: x/x/scratch
# d3: x/x
# d4: exc picture/LEN
# d5: ICTR/Unchanged
# d6: ILOG/Unchanged
# d7: k-factor/Unchanged
# a0: ptr for original operand/final result
# a1: x/x
# a2: x/x
# fp0: float(ILOG)/Unchanged
# fp1: x/x
# fp2: x/x
# F_SCR1:x/x
# F_SCR2:Abs(X) with $3fff exponent/Unchanged
# L_SCR1:x/x
# L_SCR2:first word of X packed/Unchanged
A6_str:
tst.l %d7 # branch on sign of k
ble.b k_neg # if k <= 0, LEN = ILOG + 1 - k
mov.l %d7,%d4 # if k > 0, LEN = k
bra.b len_ck # skip to LEN check
k_neg:
mov.l %d6,%d4 # first load ILOG to d4
sub.l %d7,%d4 # subtract off k
addq.l &1,%d4 # add in the 1
len_ck:
tst.l %d4 # LEN check: branch on sign of LEN
ble.b LEN_ng # if neg, set LEN = 1
cmp.l %d4,&17 # test if LEN > 17
ble.b A7_str # if not, forget it
mov.l &17,%d4 # set max LEN = 17
tst.l %d7 # if negative, never set OPERR
ble.b A7_str # if positive, continue
or.l &opaop_mask,USER_FPSR(%a6) # set OPERR & AIOP in USER_FPSR
bra.b A7_str # finished here
LEN_ng:
mov.l &1,%d4 # min LEN is 1
# A7. Calculate SCALE.
# SCALE is equal to 10^ISCALE, where ISCALE is the number
# of decimal places needed to insure LEN integer digits
# in the output before conversion to bcd. LAMBDA is the sign
# of ISCALE, used in A9. Fp1 contains 10^^(abs(ISCALE)) using
# the rounding mode as given in the following table (see
# Coonen, p. 7.23 as ref.; however, the SCALE variable is
# of opposite sign in bindec.sa from Coonen).
#
# Initial USE
# FPCR[6:5] LAMBDA SIGN(X) FPCR[6:5]
# ----------------------------------------------
# RN 00 0 0 00/0 RN
# RN 00 0 1 00/0 RN
# RN 00 1 0 00/0 RN
# RN 00 1 1 00/0 RN
# RZ 01 0 0 11/3 RP
# RZ 01 0 1 11/3 RP
# RZ 01 1 0 10/2 RM
# RZ 01 1 1 10/2 RM
# RM 10 0 0 11/3 RP
# RM 10 0 1 10/2 RM
# RM 10 1 0 10/2 RM
# RM 10 1 1 11/3 RP
# RP 11 0 0 10/2 RM
# RP 11 0 1 11/3 RP
# RP 11 1 0 11/3 RP
# RP 11 1 1 10/2 RM
#
# Register usage:
# Input/Output
# d0: exponent/scratch - final is 0
# d2: x/0 or 24 for A9
# d3: x/scratch - offset ptr into PTENRM array
# d4: LEN/Unchanged
# d5: 0/ICTR:LAMBDA
# d6: ILOG/ILOG or k if ((k<=0)&(ILOG<k))
# d7: k-factor/Unchanged
# a0: ptr for original operand/final result
# a1: x/ptr to PTENRM array
# a2: x/x
# fp0: float(ILOG)/Unchanged
# fp1: x/10^ISCALE
# fp2: x/x
# F_SCR1:x/x
# F_SCR2:Abs(X) with $3fff exponent/Unchanged
# L_SCR1:x/x
# L_SCR2:first word of X packed/Unchanged
A7_str:
tst.l %d7 # test sign of k
bgt.b k_pos # if pos and > 0, skip this
cmp.l %d7,%d6 # test k - ILOG
blt.b k_pos # if ILOG >= k, skip this
mov.l %d7,%d6 # if ((k<0) & (ILOG < k)) ILOG = k
k_pos:
mov.l %d6,%d0 # calc ILOG + 1 - LEN in d0
addq.l &1,%d0 # add the 1
sub.l %d4,%d0 # sub off LEN
swap %d5 # use upper word of d5 for LAMBDA
clr.w %d5 # set it zero initially
clr.w %d2 # set up d2 for very small case
tst.l %d0 # test sign of ISCALE
bge.b iscale # if pos, skip next inst
addq.w &1,%d5 # if neg, set LAMBDA true
cmp.l %d0,&0xffffecd4 # test iscale <= -4908
bgt.b no_inf # if false, skip rest
add.l &24,%d0 # add in 24 to iscale
mov.l &24,%d2 # put 24 in d2 for A9
no_inf:
neg.l %d0 # and take abs of ISCALE
iscale:
fmov.s FONE(%pc),%fp1 # init fp1 to 1
bfextu USER_FPCR(%a6){&26:&2},%d1 # get initial rmode bits
lsl.w &1,%d1 # put them in bits 2:1
add.w %d5,%d1 # add in LAMBDA
lsl.w &1,%d1 # put them in bits 3:1
tst.l L_SCR2(%a6) # test sign of original x
bge.b x_pos # if pos, don't set bit 0
addq.l &1,%d1 # if neg, set bit 0
x_pos:
lea.l RBDTBL(%pc),%a2 # load rbdtbl base
mov.b (%a2,%d1),%d3 # load d3 with new rmode
lsl.l &4,%d3 # put bits in proper position
fmov.l %d3,%fpcr # load bits into fpu
lsr.l &4,%d3 # put bits in proper position
tst.b %d3 # decode new rmode for pten table
bne.b not_rn # if zero, it is RN
lea.l PTENRN(%pc),%a1 # load a1 with RN table base
bra.b rmode # exit decode
not_rn:
lsr.b &1,%d3 # get lsb in carry
bcc.b not_rp2 # if carry clear, it is RM
lea.l PTENRP(%pc),%a1 # load a1 with RP table base
bra.b rmode # exit decode
not_rp2:
lea.l PTENRM(%pc),%a1 # load a1 with RM table base
rmode:
clr.l %d3 # clr table index
e_loop2:
lsr.l &1,%d0 # shift next bit into carry
bcc.b e_next2 # if zero, skip the mul
fmul.x (%a1,%d3),%fp1 # mul by 10**(d3_bit_no)
e_next2:
add.l &12,%d3 # inc d3 to next pwrten table entry
tst.l %d0 # test if ISCALE is zero
bne.b e_loop2 # if not, loop
# A8. Clr INEX; Force RZ.
# The operation in A3 above may have set INEX2.
# RZ mode is forced for the scaling operation to insure
# only one rounding error. The grs bits are collected in
# the INEX flag for use in A10.
#
# Register usage:
# Input/Output
fmov.l &0,%fpsr # clr INEX
fmov.l &rz_mode*0x10,%fpcr # set RZ rounding mode
# A9. Scale X -> Y.
# The mantissa is scaled to the desired number of significant
# digits. The excess digits are collected in INEX2. If mul,
# Check d2 for excess 10 exponential value. If not zero,
# the iscale value would have caused the pwrten calculation
# to overflow. Only a negative iscale can cause this, so
# multiply by 10^(d2), which is now only allowed to be 24,
# with a multiply by 10^8 and 10^16, which is exact since
# 10^24 is exact. If the input was denormalized, we must
# create a busy stack frame with the mul command and the
# two operands, and allow the fpu to complete the multiply.
#
# Register usage:
# Input/Output
# d0: FPCR with RZ mode/Unchanged
# d2: 0 or 24/unchanged
# d3: x/x
# d4: LEN/Unchanged
# d5: ICTR:LAMBDA
# d6: ILOG/Unchanged
# d7: k-factor/Unchanged
# a0: ptr for original operand/final result
# a1: ptr to PTENRM array/Unchanged
# a2: x/x
# fp0: float(ILOG)/X adjusted for SCALE (Y)
# fp1: 10^ISCALE/Unchanged
# fp2: x/x
# F_SCR1:x/x
# F_SCR2:Abs(X) with $3fff exponent/Unchanged
# L_SCR1:x/x
# L_SCR2:first word of X packed/Unchanged
A9_str:
fmov.x (%a0),%fp0 # load X from memory
fabs.x %fp0 # use abs(X)
tst.w %d5 # LAMBDA is in lower word of d5
bne.b sc_mul # if neg (LAMBDA = 1), scale by mul
fdiv.x %fp1,%fp0 # calculate X / SCALE -> Y to fp0
bra.w A10_st # branch to A10
sc_mul:
tst.b BINDEC_FLG(%a6) # check for denorm
beq.w A9_norm # if norm, continue with mul
# for DENORM, we must calculate:
# fp0 = input_op * 10^ISCALE * 10^24
# since the input operand is a DENORM, we can't multiply it directly.
# so, we do the multiplication of the exponents and mantissas separately.
# in this way, we avoid underflow on intermediate stages of the
# multiplication and guarantee a result without exception.
fmovm.x &0x2,-(%sp) # save 10^ISCALE to stack
mov.w (%sp),%d3 # grab exponent
andi.w &0x7fff,%d3 # clear sign
ori.w &0x8000,(%a0) # make DENORM exp negative
add.w (%a0),%d3 # add DENORM exp to 10^ISCALE exp
subi.w &0x3fff,%d3 # subtract BIAS
add.w 36(%a1),%d3
subi.w &0x3fff,%d3 # subtract BIAS
add.w 48(%a1),%d3
subi.w &0x3fff,%d3 # subtract BIAS
bmi.w sc_mul_err # is result is DENORM, punt!!!
andi.w &0x8000,(%sp) # keep sign
or.w %d3,(%sp) # insert new exponent
andi.w &0x7fff,(%a0) # clear sign bit on DENORM again
mov.l 0x8(%a0),-(%sp) # put input op mantissa on stk
mov.l 0x4(%a0),-(%sp)
mov.l &0x3fff0000,-(%sp) # force exp to zero
fmovm.x (%sp)+,&0x80 # load normalized DENORM into fp0
fmul.x (%sp)+,%fp0
# fmul.x 36(%a1),%fp0 # multiply fp0 by 10^8
# fmul.x 48(%a1),%fp0 # multiply fp0 by 10^16
mov.l 36+8(%a1),-(%sp) # get 10^8 mantissa
mov.l 36+4(%a1),-(%sp)
mov.l &0x3fff0000,-(%sp) # force exp to zero
mov.l 48+8(%a1),-(%sp) # get 10^16 mantissa
mov.l 48+4(%a1),-(%sp)
mov.l &0x3fff0000,-(%sp)# force exp to zero
fmul.x (%sp)+,%fp0 # multiply fp0 by 10^8
fmul.x (%sp)+,%fp0 # multiply fp0 by 10^16
bra.b A10_st
sc_mul_err:
bra.b sc_mul_err
A9_norm:
tst.w %d2 # test for small exp case
beq.b A9_con # if zero, continue as normal
fmul.x 36(%a1),%fp0 # multiply fp0 by 10^8
fmul.x 48(%a1),%fp0 # multiply fp0 by 10^16
A9_con:
fmul.x %fp1,%fp0 # calculate X * SCALE -> Y to fp0
# A10. Or in INEX.
# If INEX is set, round error occurred. This is compensated
# for by 'or-ing' in the INEX2 flag to the lsb of Y.
#
# Register usage:
# Input/Output
# d0: FPCR with RZ mode/FPSR with INEX2 isolated
# d2: x/x
# d3: x/x
# d4: LEN/Unchanged
# d5: ICTR:LAMBDA
# d6: ILOG/Unchanged
# d7: k-factor/Unchanged
# a0: ptr for original operand/final result
# a1: ptr to PTENxx array/Unchanged
# a2: x/ptr to FP_SCR1(a6)
# fp0: Y/Y with lsb adjusted
# fp1: 10^ISCALE/Unchanged
# fp2: x/x
A10_st:
fmov.l %fpsr,%d0 # get FPSR
fmov.x %fp0,FP_SCR1(%a6) # move Y to memory
lea.l FP_SCR1(%a6),%a2 # load a2 with ptr to FP_SCR1
btst &9,%d0 # check if INEX2 set
beq.b A11_st # if clear, skip rest
or.l &1,8(%a2) # or in 1 to lsb of mantissa
fmov.x FP_SCR1(%a6),%fp0 # write adjusted Y back to fpu
# A11. Restore original FPCR; set size ext.
# Perform FINT operation in the user's rounding mode. Keep
# the size to extended. The sintdo entry point in the sint
# routine expects the FPCR value to be in USER_FPCR for
# mode and precision. The original FPCR is saved in L_SCR1.
A11_st:
mov.l USER_FPCR(%a6),L_SCR1(%a6) # save it for later
and.l &0x00000030,USER_FPCR(%a6) # set size to ext,
# ;block exceptions
# A12. Calculate YINT = FINT(Y) according to user's rounding mode.
# The FPSP routine sintd0 is used. The output is in fp0.
#
# Register usage:
# Input/Output
# d0: FPSR with AINEX cleared/FPCR with size set to ext
# d2: x/x/scratch
# d3: x/x
# d4: LEN/Unchanged
# d5: ICTR:LAMBDA/Unchanged
# d6: ILOG/Unchanged
# d7: k-factor/Unchanged
# a0: ptr for original operand/src ptr for sintdo
# a1: ptr to PTENxx array/Unchanged
# a2: ptr to FP_SCR1(a6)/Unchanged
# a6: temp pointer to FP_SCR1(a6) - orig value saved and restored
# fp0: Y/YINT
# fp1: 10^ISCALE/Unchanged
# fp2: x/x
# F_SCR1:x/x
# F_SCR2:Y adjusted for inex/Y with original exponent
# L_SCR1:x/original USER_FPCR
# L_SCR2:first word of X packed/Unchanged
A12_st:
movm.l &0xc0c0,-(%sp) # save regs used by sintd0 {%d0-%d1/%a0-%a1}
mov.l L_SCR1(%a6),-(%sp)
mov.l L_SCR2(%a6),-(%sp)
lea.l FP_SCR1(%a6),%a0 # a0 is ptr to FP_SCR1(a6)
fmov.x %fp0,(%a0) # move Y to memory at FP_SCR1(a6)
tst.l L_SCR2(%a6) # test sign of original operand
bge.b do_fint12 # if pos, use Y
or.l &0x80000000,(%a0) # if neg, use -Y
do_fint12:
mov.l USER_FPSR(%a6),-(%sp)
# bsr sintdo # sint routine returns int in fp0
fmov.l USER_FPCR(%a6),%fpcr
fmov.l &0x0,%fpsr # clear the AEXC bits!!!
## mov.l USER_FPCR(%a6),%d0 # ext prec/keep rnd mode
## andi.l &0x00000030,%d0
## fmov.l %d0,%fpcr
fint.x FP_SCR1(%a6),%fp0 # do fint()
fmov.l %fpsr,%d0
or.w %d0,FPSR_EXCEPT(%a6)
## fmov.l &0x0,%fpcr
## fmov.l %fpsr,%d0 # don't keep ccodes
## or.w %d0,FPSR_EXCEPT(%a6)
mov.b (%sp),USER_FPSR(%a6)
add.l &4,%sp
mov.l (%sp)+,L_SCR2(%a6)
mov.l (%sp)+,L_SCR1(%a6)
movm.l (%sp)+,&0x303 # restore regs used by sint {%d0-%d1/%a0-%a1}
mov.l L_SCR2(%a6),FP_SCR1(%a6) # restore original exponent
mov.l L_SCR1(%a6),USER_FPCR(%a6) # restore user's FPCR
# A13. Check for LEN digits.
# If the int operation results in more than LEN digits,
# or less than LEN -1 digits, adjust ILOG and repeat from
# A6. This test occurs only on the first pass. If the
# result is exactly 10^LEN, decrement ILOG and divide
# the mantissa by 10. The calculation of 10^LEN cannot
# be inexact, since all powers of ten upto 10^27 are exact
# in extended precision, so the use of a previous power-of-ten
# table will introduce no error.
#
#
# Register usage:
# Input/Output
# d0: FPCR with size set to ext/scratch final = 0
# d2: x/x
# d3: x/scratch final = x
# d4: LEN/LEN adjusted
# d5: ICTR:LAMBDA/LAMBDA:ICTR
# d6: ILOG/ILOG adjusted
# d7: k-factor/Unchanged
# a0: pointer into memory for packed bcd string formation
# a1: ptr to PTENxx array/Unchanged
# a2: ptr to FP_SCR1(a6)/Unchanged
# fp0: int portion of Y/abs(YINT) adjusted
# fp1: 10^ISCALE/Unchanged
# fp2: x/10^LEN
# F_SCR1:x/x
# F_SCR2:Y with original exponent/Unchanged
# L_SCR1:original USER_FPCR/Unchanged
# L_SCR2:first word of X packed/Unchanged
A13_st:
swap %d5 # put ICTR in lower word of d5
tst.w %d5 # check if ICTR = 0
bne not_zr # if non-zero, go to second test
#
# Compute 10^(LEN-1)
#
fmov.s FONE(%pc),%fp2 # init fp2 to 1.0
mov.l %d4,%d0 # put LEN in d0
subq.l &1,%d0 # d0 = LEN -1
clr.l %d3 # clr table index
l_loop:
lsr.l &1,%d0 # shift next bit into carry
bcc.b l_next # if zero, skip the mul
fmul.x (%a1,%d3),%fp2 # mul by 10**(d3_bit_no)
l_next:
add.l &12,%d3 # inc d3 to next pwrten table entry
tst.l %d0 # test if LEN is zero
bne.b l_loop # if not, loop
#
# 10^LEN-1 is computed for this test and A14. If the input was
# denormalized, check only the case in which YINT > 10^LEN.
#
tst.b BINDEC_FLG(%a6) # check if input was norm
beq.b A13_con # if norm, continue with checking
fabs.x %fp0 # take abs of YINT
bra test_2
#
# Compare abs(YINT) to 10^(LEN-1) and 10^LEN
#
A13_con:
fabs.x %fp0 # take abs of YINT
fcmp.x %fp0,%fp2 # compare abs(YINT) with 10^(LEN-1)
fbge.w test_2 # if greater, do next test
subq.l &1,%d6 # subtract 1 from ILOG
mov.w &1,%d5 # set ICTR
fmov.l &rm_mode*0x10,%fpcr # set rmode to RM
fmul.s FTEN(%pc),%fp2 # compute 10^LEN
bra.w A6_str # return to A6 and recompute YINT
test_2:
fmul.s FTEN(%pc),%fp2 # compute 10^LEN
fcmp.x %fp0,%fp2 # compare abs(YINT) with 10^LEN
fblt.w A14_st # if less, all is ok, go to A14
fbgt.w fix_ex # if greater, fix and redo
fdiv.s FTEN(%pc),%fp0 # if equal, divide by 10
addq.l &1,%d6 # and inc ILOG
bra.b A14_st # and continue elsewhere
fix_ex:
addq.l &1,%d6 # increment ILOG by 1
mov.w &1,%d5 # set ICTR
fmov.l &rm_mode*0x10,%fpcr # set rmode to RM
bra.w A6_str # return to A6 and recompute YINT
#
# Since ICTR <> 0, we have already been through one adjustment,
# and shouldn't have another; this is to check if abs(YINT) = 10^LEN
# 10^LEN is again computed using whatever table is in a1 since the
# value calculated cannot be inexact.
#
not_zr:
fmov.s FONE(%pc),%fp2 # init fp2 to 1.0
mov.l %d4,%d0 # put LEN in d0
clr.l %d3 # clr table index
z_loop:
lsr.l &1,%d0 # shift next bit into carry
bcc.b z_next # if zero, skip the mul
fmul.x (%a1,%d3),%fp2 # mul by 10**(d3_bit_no)
z_next:
add.l &12,%d3 # inc d3 to next pwrten table entry
tst.l %d0 # test if LEN is zero
bne.b z_loop # if not, loop
fabs.x %fp0 # get abs(YINT)
fcmp.x %fp0,%fp2 # check if abs(YINT) = 10^LEN
fbneq.w A14_st # if not, skip this
fdiv.s FTEN(%pc),%fp0 # divide abs(YINT) by 10
addq.l &1,%d6 # and inc ILOG by 1
addq.l &1,%d4 # and inc LEN
fmul.s FTEN(%pc),%fp2 # if LEN++, the get 10^^LEN
# A14. Convert the mantissa to bcd.
# The binstr routine is used to convert the LEN digit
# mantissa to bcd in memory. The input to binstr is
# to be a fraction; i.e. (mantissa)/10^LEN and adjusted
# such that the decimal point is to the left of bit 63.
# The bcd digits are stored in the correct position in
# the final string area in memory.
#
#
# Register usage:
# Input/Output
# d0: x/LEN call to binstr - final is 0
# d1: x/0
# d2: x/ms 32-bits of mant of abs(YINT)
# d3: x/ls 32-bits of mant of abs(YINT)
# d4: LEN/Unchanged
# d5: ICTR:LAMBDA/LAMBDA:ICTR
# d6: ILOG
# d7: k-factor/Unchanged
# a0: pointer into memory for packed bcd string formation
# /ptr to first mantissa byte in result string
# a1: ptr to PTENxx array/Unchanged
# a2: ptr to FP_SCR1(a6)/Unchanged
# fp0: int portion of Y/abs(YINT) adjusted
# fp1: 10^ISCALE/Unchanged
# fp2: 10^LEN/Unchanged
# F_SCR1:x/Work area for final result
# F_SCR2:Y with original exponent/Unchanged
# L_SCR1:original USER_FPCR/Unchanged
# L_SCR2:first word of X packed/Unchanged
A14_st:
fmov.l &rz_mode*0x10,%fpcr # force rz for conversion
fdiv.x %fp2,%fp0 # divide abs(YINT) by 10^LEN
lea.l FP_SCR0(%a6),%a0
fmov.x %fp0,(%a0) # move abs(YINT)/10^LEN to memory
mov.l 4(%a0),%d2 # move 2nd word of FP_RES to d2
mov.l 8(%a0),%d3 # move 3rd word of FP_RES to d3
clr.l 4(%a0) # zero word 2 of FP_RES
clr.l 8(%a0) # zero word 3 of FP_RES
mov.l (%a0),%d0 # move exponent to d0
swap %d0 # put exponent in lower word
beq.b no_sft # if zero, don't shift
sub.l &0x3ffd,%d0 # sub bias less 2 to make fract
tst.l %d0 # check if > 1
bgt.b no_sft # if so, don't shift
neg.l %d0 # make exp positive
m_loop:
lsr.l &1,%d2 # shift d2:d3 right, add 0s
roxr.l &1,%d3 # the number of places
dbf.w %d0,m_loop # given in d0
no_sft:
tst.l %d2 # check for mantissa of zero
bne.b no_zr # if not, go on
tst.l %d3 # continue zero check
beq.b zer_m # if zero, go directly to binstr
no_zr:
clr.l %d1 # put zero in d1 for addx
add.l &0x00000080,%d3 # inc at bit 7
addx.l %d1,%d2 # continue inc
and.l &0xffffff80,%d3 # strip off lsb not used by 882
zer_m:
mov.l %d4,%d0 # put LEN in d0 for binstr call
addq.l &3,%a0 # a0 points to M16 byte in result
bsr binstr # call binstr to convert mant
# A15. Convert the exponent to bcd.
# As in A14 above, the exp is converted to bcd and the
# digits are stored in the final string.
#
# Digits are stored in L_SCR1(a6) on return from BINDEC as:
#
# 32 16 15 0
# -----------------------------------------
# | 0 | e3 | e2 | e1 | e4 | X | X | X |
# -----------------------------------------
#
# And are moved into their proper places in FP_SCR0. If digit e4
# is non-zero, OPERR is signaled. In all cases, all 4 digits are
# written as specified in the 881/882 manual for packed decimal.
#
# Register usage:
# Input/Output
# d0: x/LEN call to binstr - final is 0
# d1: x/scratch (0);shift count for final exponent packing
# d2: x/ms 32-bits of exp fraction/scratch
# d3: x/ls 32-bits of exp fraction
# d4: LEN/Unchanged
# d5: ICTR:LAMBDA/LAMBDA:ICTR
# d6: ILOG
# d7: k-factor/Unchanged
# a0: ptr to result string/ptr to L_SCR1(a6)
# a1: ptr to PTENxx array/Unchanged
# a2: ptr to FP_SCR1(a6)/Unchanged
# fp0: abs(YINT) adjusted/float(ILOG)
# fp1: 10^ISCALE/Unchanged
# fp2: 10^LEN/Unchanged
# F_SCR1:Work area for final result/BCD result
# F_SCR2:Y with original exponent/ILOG/10^4
# L_SCR1:original USER_FPCR/Exponent digits on return from binstr
# L_SCR2:first word of X packed/Unchanged
A15_st:
tst.b BINDEC_FLG(%a6) # check for denorm
beq.b not_denorm
ftest.x %fp0 # test for zero
fbeq.w den_zero # if zero, use k-factor or 4933
fmov.l %d6,%fp0 # float ILOG
fabs.x %fp0 # get abs of ILOG
bra.b convrt
den_zero:
tst.l %d7 # check sign of the k-factor
blt.b use_ilog # if negative, use ILOG
fmov.s F4933(%pc),%fp0 # force exponent to 4933
bra.b convrt # do it
use_ilog:
fmov.l %d6,%fp0 # float ILOG
fabs.x %fp0 # get abs of ILOG
bra.b convrt
not_denorm:
ftest.x %fp0 # test for zero
fbneq.w not_zero # if zero, force exponent
fmov.s FONE(%pc),%fp0 # force exponent to 1
bra.b convrt # do it
not_zero:
fmov.l %d6,%fp0 # float ILOG
fabs.x %fp0 # get abs of ILOG
convrt:
fdiv.x 24(%a1),%fp0 # compute ILOG/10^4
fmov.x %fp0,FP_SCR1(%a6) # store fp0 in memory
mov.l 4(%a2),%d2 # move word 2 to d2
mov.l 8(%a2),%d3 # move word 3 to d3
mov.w (%a2),%d0 # move exp to d0
beq.b x_loop_fin # if zero, skip the shift
sub.w &0x3ffd,%d0 # subtract off bias
neg.w %d0 # make exp positive
x_loop:
lsr.l &1,%d2 # shift d2:d3 right
roxr.l &1,%d3 # the number of places
dbf.w %d0,x_loop # given in d0
x_loop_fin:
clr.l %d1 # put zero in d1 for addx
add.l &0x00000080,%d3 # inc at bit 6
addx.l %d1,%d2 # continue inc
and.l &0xffffff80,%d3 # strip off lsb not used by 882
mov.l &4,%d0 # put 4 in d0 for binstr call
lea.l L_SCR1(%a6),%a0 # a0 is ptr to L_SCR1 for exp digits
bsr binstr # call binstr to convert exp
mov.l L_SCR1(%a6),%d0 # load L_SCR1 lword to d0
mov.l &12,%d1 # use d1 for shift count
lsr.l %d1,%d0 # shift d0 right by 12
bfins %d0,FP_SCR0(%a6){&4:&12} # put e3:e2:e1 in FP_SCR0
lsr.l %d1,%d0 # shift d0 right by 12
bfins %d0,FP_SCR0(%a6){&16:&4} # put e4 in FP_SCR0
tst.b %d0 # check if e4 is zero
beq.b A16_st # if zero, skip rest
or.l &opaop_mask,USER_FPSR(%a6) # set OPERR & AIOP in USER_FPSR
# A16. Write sign bits to final string.
# Sigma is bit 31 of initial value; RHO is bit 31 of d6 (ILOG).
#
# Register usage:
# Input/Output
# d0: x/scratch - final is x
# d2: x/x
# d3: x/x
# d4: LEN/Unchanged
# d5: ICTR:LAMBDA/LAMBDA:ICTR
# d6: ILOG/ILOG adjusted
# d7: k-factor/Unchanged
# a0: ptr to L_SCR1(a6)/Unchanged
# a1: ptr to PTENxx array/Unchanged
# a2: ptr to FP_SCR1(a6)/Unchanged
# fp0: float(ILOG)/Unchanged
# fp1: 10^ISCALE/Unchanged
# fp2: 10^LEN/Unchanged
# F_SCR1:BCD result with correct signs
# F_SCR2:ILOG/10^4
# L_SCR1:Exponent digits on return from binstr
# L_SCR2:first word of X packed/Unchanged
A16_st:
clr.l %d0 # clr d0 for collection of signs
and.b &0x0f,FP_SCR0(%a6) # clear first nibble of FP_SCR0
tst.l L_SCR2(%a6) # check sign of original mantissa
bge.b mant_p # if pos, don't set SM
mov.l &2,%d0 # move 2 in to d0 for SM
mant_p:
tst.l %d6 # check sign of ILOG
bge.b wr_sgn # if pos, don't set SE
addq.l &1,%d0 # set bit 0 in d0 for SE
wr_sgn:
bfins %d0,FP_SCR0(%a6){&0:&2} # insert SM and SE into FP_SCR0
# Clean up and restore all registers used.
fmov.l &0,%fpsr # clear possible inex2/ainex bits
fmovm.x (%sp)+,&0xe0 # {%fp0-%fp2}
movm.l (%sp)+,&0x4fc # {%d2-%d7/%a2}
rts
global PTENRN
PTENRN:
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59E # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D5 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CE0 # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8E # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C7 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C17 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE5 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979B # 10 ^ 4096
global PTENRP
PTENRP:
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59E # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D6 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CE0 # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8E # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C7 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C18 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE5 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979B # 10 ^ 4096
global PTENRM
PTENRM:
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59D # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D5 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CDF # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8D # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C6 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C17 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE4 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979A # 10 ^ 4096
#########################################################################
# binstr(): Converts a 64-bit binary integer to bcd. #
# #
# INPUT *************************************************************** #
# d2:d3 = 64-bit binary integer #
# d0 = desired length (LEN) #
# a0 = pointer to start in memory for bcd characters #
# (This pointer must point to byte 4 of the first #
# lword of the packed decimal memory string.) #
# #
# OUTPUT ************************************************************** #
# a0 = pointer to LEN bcd digits representing the 64-bit integer. #
# #
# ALGORITHM *********************************************************** #
# The 64-bit binary is assumed to have a decimal point before #
# bit 63. The fraction is multiplied by 10 using a mul by 2 #
# shift and a mul by 8 shift. The bits shifted out of the #
# msb form a decimal digit. This process is iterated until #
# LEN digits are formed. #
# #
# A1. Init d7 to 1. D7 is the byte digit counter, and if 1, the #
# digit formed will be assumed the least significant. This is #
# to force the first byte formed to have a 0 in the upper 4 bits. #
# #
# A2. Beginning of the loop: #
# Copy the fraction in d2:d3 to d4:d5. #
# #
# A3. Multiply the fraction in d2:d3 by 8 using bit-field #
# extracts and shifts. The three msbs from d2 will go into d1. #
# #
# A4. Multiply the fraction in d4:d5 by 2 using shifts. The msb #
# will be collected by the carry. #
# #
# A5. Add using the carry the 64-bit quantities in d2:d3 and d4:d5 #
# into d2:d3. D1 will contain the bcd digit formed. #
# #
# A6. Test d7. If zero, the digit formed is the ms digit. If non- #
# zero, it is the ls digit. Put the digit in its place in the #
# upper word of d0. If it is the ls digit, write the word #
# from d0 to memory. #
# #
# A7. Decrement d6 (LEN counter) and repeat the loop until zero. #
# #
#########################################################################
# Implementation Notes:
#
# The registers are used as follows:
#
# d0: LEN counter
# d1: temp used to form the digit
# d2: upper 32-bits of fraction for mul by 8
# d3: lower 32-bits of fraction for mul by 8
# d4: upper 32-bits of fraction for mul by 2
# d5: lower 32-bits of fraction for mul by 2
# d6: temp for bit-field extracts
# d7: byte digit formation word;digit count {0,1}
# a0: pointer into memory for packed bcd string formation
#
global binstr
binstr:
movm.l &0xff00,-(%sp) # {%d0-%d7}
#
# A1: Init d7
#
mov.l &1,%d7 # init d7 for second digit
subq.l &1,%d0 # for dbf d0 would have LEN+1 passes
#
# A2. Copy d2:d3 to d4:d5. Start loop.
#
loop:
mov.l %d2,%d4 # copy the fraction before muls
mov.l %d3,%d5 # to d4:d5
#
# A3. Multiply d2:d3 by 8; extract msbs into d1.
#
bfextu %d2{&0:&3},%d1 # copy 3 msbs of d2 into d1
asl.l &3,%d2 # shift d2 left by 3 places
bfextu %d3{&0:&3},%d6 # copy 3 msbs of d3 into d6
asl.l &3,%d3 # shift d3 left by 3 places
or.l %d6,%d2 # or in msbs from d3 into d2
#
# A4. Multiply d4:d5 by 2; add carry out to d1.
#
asl.l &1,%d5 # mul d5 by 2
roxl.l &1,%d4 # mul d4 by 2
swap %d6 # put 0 in d6 lower word
addx.w %d6,%d1 # add in extend from mul by 2
#
# A5. Add mul by 8 to mul by 2. D1 contains the digit formed.
#
add.l %d5,%d3 # add lower 32 bits
nop # ERRATA FIX #13 (Rev. 1.2 6/6/90)
addx.l %d4,%d2 # add with extend upper 32 bits
nop # ERRATA FIX #13 (Rev. 1.2 6/6/90)
addx.w %d6,%d1 # add in extend from add to d1
swap %d6 # with d6 = 0; put 0 in upper word
#
# A6. Test d7 and branch.
#
tst.w %d7 # if zero, store digit & to loop
beq.b first_d # if non-zero, form byte & write
sec_d:
swap %d7 # bring first digit to word d7b
asl.w &4,%d7 # first digit in upper 4 bits d7b
add.w %d1,%d7 # add in ls digit to d7b
mov.b %d7,(%a0)+ # store d7b byte in memory
swap %d7 # put LEN counter in word d7a
clr.w %d7 # set d7a to signal no digits done
dbf.w %d0,loop # do loop some more!
bra.b end_bstr # finished, so exit
first_d:
swap %d7 # put digit word in d7b
mov.w %d1,%d7 # put new digit in d7b
swap %d7 # put LEN counter in word d7a
addq.w &1,%d7 # set d7a to signal first digit done
dbf.w %d0,loop # do loop some more!
swap %d7 # put last digit in string
lsl.w &4,%d7 # move it to upper 4 bits
mov.b %d7,(%a0)+ # store it in memory string
#
# Clean up and return with result in fp0.
#
end_bstr:
movm.l (%sp)+,&0xff # {%d0-%d7}
rts
#########################################################################
# XDEF **************************************************************** #
# facc_in_b(): dmem_read_byte failed #
# facc_in_w(): dmem_read_word failed #
# facc_in_l(): dmem_read_long failed #
# facc_in_d(): dmem_read of dbl prec failed #
# facc_in_x(): dmem_read of ext prec failed #
# #
# facc_out_b(): dmem_write_byte failed #
# facc_out_w(): dmem_write_word failed #
# facc_out_l(): dmem_write_long failed #
# facc_out_d(): dmem_write of dbl prec failed #
# facc_out_x(): dmem_write of ext prec failed #
# #
# XREF **************************************************************** #
# _real_access() - exit through access error handler #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# None #
# #
# ALGORITHM *********************************************************** #
# Flow jumps here when an FP data fetch call gets an error #
# result. This means the operating system wants an access error frame #
# made out of the current exception stack frame. #
# So, we first call restore() which makes sure that any updated #
# -(an)+ register gets returned to its pre-exception value and then #
# we change the stack to an acess error stack frame. #
# #
#########################################################################
facc_in_b:
movq.l &0x1,%d0 # one byte
bsr.w restore # fix An
mov.w &0x0121,EXC_VOFF(%a6) # set FSLW
bra.w facc_finish
facc_in_w:
movq.l &0x2,%d0 # two bytes
bsr.w restore # fix An
mov.w &0x0141,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_in_l:
movq.l &0x4,%d0 # four bytes
bsr.w restore # fix An
mov.w &0x0101,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_in_d:
movq.l &0x8,%d0 # eight bytes
bsr.w restore # fix An
mov.w &0x0161,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_in_x:
movq.l &0xc,%d0 # twelve bytes
bsr.w restore # fix An
mov.w &0x0161,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
################################################################
facc_out_b:
movq.l &0x1,%d0 # one byte
bsr.w restore # restore An
mov.w &0x00a1,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_out_w:
movq.l &0x2,%d0 # two bytes
bsr.w restore # restore An
mov.w &0x00c1,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_out_l:
movq.l &0x4,%d0 # four bytes
bsr.w restore # restore An
mov.w &0x0081,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_out_d:
movq.l &0x8,%d0 # eight bytes
bsr.w restore # restore An
mov.w &0x00e1,EXC_VOFF(%a6) # set FSLW
bra.b facc_finish
facc_out_x:
mov.l &0xc,%d0 # twelve bytes
bsr.w restore # restore An
mov.w &0x00e1,EXC_VOFF(%a6) # set FSLW
# here's where we actually create the access error frame from the
# current exception stack frame.
facc_finish:
mov.l USER_FPIAR(%a6),EXC_PC(%a6) # store current PC
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
mov.l (%sp),-(%sp) # store SR, hi(PC)
mov.l 0x8(%sp),0x4(%sp) # store lo(PC)
mov.l 0xc(%sp),0x8(%sp) # store EA
mov.l &0x00000001,0xc(%sp) # store FSLW
mov.w 0x6(%sp),0xc(%sp) # fix FSLW (size)
mov.w &0x4008,0x6(%sp) # store voff
btst &0x5,(%sp) # supervisor or user mode?
beq.b facc_out2 # user
bset &0x2,0xd(%sp) # set supervisor TM bit
facc_out2:
bra.l _real_access
##################################################################
# if the effective addressing mode was predecrement or postincrement,
# the emulation has already changed its value to the correct post-
# instruction value. but since we're exiting to the access error
# handler, then AN must be returned to its pre-instruction value.
# we do that here.
restore:
mov.b EXC_OPWORD+0x1(%a6),%d1
andi.b &0x38,%d1 # extract opmode
cmpi.b %d1,&0x18 # postinc?
beq.w rest_inc
cmpi.b %d1,&0x20 # predec?
beq.w rest_dec
rts
rest_inc:
mov.b EXC_OPWORD+0x1(%a6),%d1
andi.w &0x0007,%d1 # fetch An
mov.w (tbl_rest_inc.b,%pc,%d1.w*2),%d1
jmp (tbl_rest_inc.b,%pc,%d1.w*1)
tbl_rest_inc:
short ri_a0 - tbl_rest_inc
short ri_a1 - tbl_rest_inc
short ri_a2 - tbl_rest_inc
short ri_a3 - tbl_rest_inc
short ri_a4 - tbl_rest_inc
short ri_a5 - tbl_rest_inc
short ri_a6 - tbl_rest_inc
short ri_a7 - tbl_rest_inc
ri_a0:
sub.l %d0,EXC_DREGS+0x8(%a6) # fix stacked a0
rts
ri_a1:
sub.l %d0,EXC_DREGS+0xc(%a6) # fix stacked a1
rts
ri_a2:
sub.l %d0,%a2 # fix a2
rts
ri_a3:
sub.l %d0,%a3 # fix a3
rts
ri_a4:
sub.l %d0,%a4 # fix a4
rts
ri_a5:
sub.l %d0,%a5 # fix a5
rts
ri_a6:
sub.l %d0,(%a6) # fix stacked a6
rts
# if it's a fmove out instruction, we don't have to fix a7
# because we hadn't changed it yet. if it's an opclass two
# instruction (data moved in) and the exception was in supervisor
# mode, then also also wasn't updated. if it was user mode, then
# restore the correct a7 which is in the USP currently.
ri_a7:
cmpi.b EXC_VOFF(%a6),&0x30 # move in or out?
bne.b ri_a7_done # out
btst &0x5,EXC_SR(%a6) # user or supervisor?
bne.b ri_a7_done # supervisor
movc %usp,%a0 # restore USP
sub.l %d0,%a0
movc %a0,%usp
ri_a7_done:
rts
# need to invert adjustment value if the <ea> was predec
rest_dec:
neg.l %d0
bra.b rest_inc
|