diff options
author | Theo de Raadt <deraadt@cvs.openbsd.org> | 1995-10-18 08:53:40 +0000 |
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committer | Theo de Raadt <deraadt@cvs.openbsd.org> | 1995-10-18 08:53:40 +0000 |
commit | d6583bb2a13f329cf0332ef2570eb8bb8fc0e39c (patch) | |
tree | ece253b876159b39c620e62b6c9b1174642e070e /sys/arch/m68k/fpsp/stan.sa |
initial import of NetBSD tree
Diffstat (limited to 'sys/arch/m68k/fpsp/stan.sa')
-rw-r--r-- | sys/arch/m68k/fpsp/stan.sa | 480 |
1 files changed, 480 insertions, 0 deletions
diff --git a/sys/arch/m68k/fpsp/stan.sa b/sys/arch/m68k/fpsp/stan.sa new file mode 100644 index 00000000000..9bc9904a000 --- /dev/null +++ b/sys/arch/m68k/fpsp/stan.sa @@ -0,0 +1,480 @@ +* $NetBSD: stan.sa,v 1.3 1994/10/26 07:50:10 cgd Exp $ + +* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP +* M68000 Hi-Performance Microprocessor Division +* M68040 Software Package +* +* M68040 Software Package Copyright (c) 1993, 1994 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. + +* +* stan.sa 3.3 7/29/91 +* +* The entry point stan computes the tangent of +* an input argument; +* stand does the same except for denormalized input. +* +* Input: Double-extended number X in location pointed to +* by address register a0. +* +* Output: The value tan(X) returned in floating-point register Fp0. +* +* 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. +* +* Speed: The program sTAN takes approximately 170 cycles for +* input argument X such that |X| < 15Pi, which is the the usual +* situation. +* +* 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. +* + +STAN IDNT 2,1 Motorola 040 Floating Point Software Package + + section 8 + + include fpsp.h + +BOUNDS1 DC.L $3FD78000,$4004BC7E +TWOBYPI DC.L $3FE45F30,$6DC9C883 + +TANQ4 DC.L $3EA0B759,$F50F8688 +TANP3 DC.L $BEF2BAA5,$A8924F04 + +TANQ3 DC.L $BF346F59,$B39BA65F,$00000000,$00000000 + +TANP2 DC.L $3FF60000,$E073D3FC,$199C4A00,$00000000 + +TANQ2 DC.L $3FF90000,$D23CD684,$15D95FA1,$00000000 + +TANP1 DC.L $BFFC0000,$8895A6C5,$FB423BCA,$00000000 + +TANQ1 DC.L $BFFD0000,$EEF57E0D,$A84BC8CE,$00000000 + +INVTWOPI DC.L $3FFC0000,$A2F9836E,$4E44152A,$00000000 + +TWOPI1 DC.L $40010000,$C90FDAA2,$00000000,$00000000 +TWOPI2 DC.L $3FDF0000,$85A308D4,$00000000,$00000000 + +*--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. + xdef PITBL +PITBL: + DC.L $C0040000,$C90FDAA2,$2168C235,$21800000 + DC.L $C0040000,$C2C75BCD,$105D7C23,$A0D00000 + DC.L $C0040000,$BC7EDCF7,$FF523611,$A1E80000 + DC.L $C0040000,$B6365E22,$EE46F000,$21480000 + DC.L $C0040000,$AFEDDF4D,$DD3BA9EE,$A1200000 + DC.L $C0040000,$A9A56078,$CC3063DD,$21FC0000 + DC.L $C0040000,$A35CE1A3,$BB251DCB,$21100000 + DC.L $C0040000,$9D1462CE,$AA19D7B9,$A1580000 + DC.L $C0040000,$96CBE3F9,$990E91A8,$21E00000 + DC.L $C0040000,$90836524,$88034B96,$20B00000 + DC.L $C0040000,$8A3AE64F,$76F80584,$A1880000 + DC.L $C0040000,$83F2677A,$65ECBF73,$21C40000 + DC.L $C0030000,$FB53D14A,$A9C2F2C2,$20000000 + DC.L $C0030000,$EEC2D3A0,$87AC669F,$21380000 + DC.L $C0030000,$E231D5F6,$6595DA7B,$A1300000 + DC.L $C0030000,$D5A0D84C,$437F4E58,$9FC00000 + DC.L $C0030000,$C90FDAA2,$2168C235,$21000000 + DC.L $C0030000,$BC7EDCF7,$FF523611,$A1680000 + DC.L $C0030000,$AFEDDF4D,$DD3BA9EE,$A0A00000 + DC.L $C0030000,$A35CE1A3,$BB251DCB,$20900000 + DC.L $C0030000,$96CBE3F9,$990E91A8,$21600000 + DC.L $C0030000,$8A3AE64F,$76F80584,$A1080000 + DC.L $C0020000,$FB53D14A,$A9C2F2C2,$1F800000 + DC.L $C0020000,$E231D5F6,$6595DA7B,$A0B00000 + DC.L $C0020000,$C90FDAA2,$2168C235,$20800000 + DC.L $C0020000,$AFEDDF4D,$DD3BA9EE,$A0200000 + DC.L $C0020000,$96CBE3F9,$990E91A8,$20E00000 + DC.L $C0010000,$FB53D14A,$A9C2F2C2,$1F000000 + DC.L $C0010000,$C90FDAA2,$2168C235,$20000000 + DC.L $C0010000,$96CBE3F9,$990E91A8,$20600000 + DC.L $C0000000,$C90FDAA2,$2168C235,$1F800000 + DC.L $BFFF0000,$C90FDAA2,$2168C235,$1F000000 + DC.L $00000000,$00000000,$00000000,$00000000 + DC.L $3FFF0000,$C90FDAA2,$2168C235,$9F000000 + DC.L $40000000,$C90FDAA2,$2168C235,$9F800000 + DC.L $40010000,$96CBE3F9,$990E91A8,$A0600000 + DC.L $40010000,$C90FDAA2,$2168C235,$A0000000 + DC.L $40010000,$FB53D14A,$A9C2F2C2,$9F000000 + DC.L $40020000,$96CBE3F9,$990E91A8,$A0E00000 + DC.L $40020000,$AFEDDF4D,$DD3BA9EE,$20200000 + DC.L $40020000,$C90FDAA2,$2168C235,$A0800000 + DC.L $40020000,$E231D5F6,$6595DA7B,$20B00000 + DC.L $40020000,$FB53D14A,$A9C2F2C2,$9F800000 + DC.L $40030000,$8A3AE64F,$76F80584,$21080000 + DC.L $40030000,$96CBE3F9,$990E91A8,$A1600000 + DC.L $40030000,$A35CE1A3,$BB251DCB,$A0900000 + DC.L $40030000,$AFEDDF4D,$DD3BA9EE,$20A00000 + DC.L $40030000,$BC7EDCF7,$FF523611,$21680000 + DC.L $40030000,$C90FDAA2,$2168C235,$A1000000 + DC.L $40030000,$D5A0D84C,$437F4E58,$1FC00000 + DC.L $40030000,$E231D5F6,$6595DA7B,$21300000 + DC.L $40030000,$EEC2D3A0,$87AC669F,$A1380000 + DC.L $40030000,$FB53D14A,$A9C2F2C2,$A0000000 + DC.L $40040000,$83F2677A,$65ECBF73,$A1C40000 + DC.L $40040000,$8A3AE64F,$76F80584,$21880000 + DC.L $40040000,$90836524,$88034B96,$A0B00000 + DC.L $40040000,$96CBE3F9,$990E91A8,$A1E00000 + DC.L $40040000,$9D1462CE,$AA19D7B9,$21580000 + DC.L $40040000,$A35CE1A3,$BB251DCB,$A1100000 + DC.L $40040000,$A9A56078,$CC3063DD,$A1FC0000 + DC.L $40040000,$AFEDDF4D,$DD3BA9EE,$21200000 + DC.L $40040000,$B6365E22,$EE46F000,$A1480000 + DC.L $40040000,$BC7EDCF7,$FF523611,$21E80000 + DC.L $40040000,$C2C75BCD,$105D7C23,$20D00000 + DC.L $40040000,$C90FDAA2,$2168C235,$A1800000 + +INARG equ FP_SCR4 + +TWOTO63 equ L_SCR1 +ENDFLAG equ L_SCR2 +N equ L_SCR3 + + xref t_frcinx + xref t_extdnrm + + xdef stand +stand: +*--TAN(X) = X FOR DENORMALIZED X + + bra t_extdnrm + + xdef stan +stan: + FMOVE.X (a0),FP0 ...LOAD INPUT + + MOVE.L (A0),D0 + MOVE.W 4(A0),D0 + ANDI.L #$7FFFFFFF,D0 + + CMPI.L #$3FD78000,D0 ...|X| >= 2**(-40)? + BGE.B TANOK1 + BRA.W TANSM +TANOK1: + CMPI.L #$4004BC7E,D0 ...|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. + FMOVE.X FP0,FP1 + FMUL.D TWOBYPI,FP1 ...X*2/PI + +*--HIDE THE NEXT TWO INSTRUCTIONS + lea.l PITBL+$200,a1 ...TABLE OF N*PI/2, N = -32,...,32 + +*--FP1 IS NOW READY + FMOVE.L FP1,D0 ...CONVERT TO INTEGER + + ASL.L #4,D0 + ADDA.L D0,a1 ...ADDRESS N*PIBY2 IN Y1, Y2 + + FSUB.X (a1)+,FP0 ...X-Y1 +*--HIDE THE NEXT ONE + + FSUB.S (a1),FP0 ...FP0 IS R = (X-Y1)-Y2 + + ROR.L #5,D0 + ANDI.L #$80000000,D0 ...D0 WAS ODD IFF D0 < 0 + +TANCONT: + + TST.L D0 + BLT.W NODD + + FMOVE.X FP0,FP1 + FMUL.X FP1,FP1 ...S = R*R + + FMOVE.D TANQ4,FP3 + FMOVE.D TANP3,FP2 + + FMUL.X FP1,FP3 ...SQ4 + FMUL.X FP1,FP2 ...SP3 + + FADD.D TANQ3,FP3 ...Q3+SQ4 + FADD.X TANP2,FP2 ...P2+SP3 + + FMUL.X FP1,FP3 ...S(Q3+SQ4) + FMUL.X FP1,FP2 ...S(P2+SP3) + + FADD.X TANQ2,FP3 ...Q2+S(Q3+SQ4) + FADD.X TANP1,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,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 #:3F800000,FP1 ...1+S(Q1+...) + + FMOVE.L d1,fpcr ;restore users exceptions + FDIV.X FP1,FP0 ;last inst - possible exception set + + bra t_frcinx + +NODD: + FMOVE.X FP0,FP1 + FMUL.X FP0,FP0 ...S = R*R + + FMOVE.D TANQ4,FP3 + FMOVE.D TANP3,FP2 + + FMUL.X FP0,FP3 ...SQ4 + FMUL.X FP0,FP2 ...SP3 + + FADD.D TANQ3,FP3 ...Q3+SQ4 + FADD.X TANP2,FP2 ...P2+SP3 + + FMUL.X FP0,FP3 ...S(Q3+SQ4) + FMUL.X FP0,FP2 ...S(P2+SP3) + + FADD.X TANQ2,FP3 ...Q2+S(Q3+SQ4) + FADD.X TANP1,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,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 #:3F800000,FP0 ...1+S(Q1+...) + + + FMOVE.X FP1,-(sp) + EORI.L #$80000000,(sp) + + FMOVE.L d1,fpcr ;restore users exceptions + FDIV.X (sp)+,FP0 ;last inst - possible exception set + + bra t_frcinx + +TANBORS: +*--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION. +*--IF |X| < 2**(-40), RETURN X OR 1. + CMPI.L #$3FFF8000,D0 + BGT.B REDUCEX + +TANSM: + + FMOVE.X FP0,-(sp) + FMOVE.L d1,fpcr ;restore users exceptions + FMOVE.X (sp)+,FP0 ;last inst - posibble exception set + + bra t_frcinx + + +REDUCEX: +*--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. + + FMOVEM.X FP2-FP5,-(A7) ...save FP2 through FP5 + MOVE.L D2,-(A7) + FMOVE.S #:00000000,FP1 + +*--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. + cmpi.l #$7ffeffff,d0 ;is argument dangerously large? + bne.b LOOP + move.l #$7ffe0000,FP_SCR2(a6) ;yes +* ;create 2**16383*PI/2 + move.l #$c90fdaa2,FP_SCR2+4(a6) + clr.l FP_SCR2+8(a6) + ftst.x fp0 ;test sign of argument + move.l #$7fdc0000,FP_SCR3(a6) ;create low half of 2**16383* +* ;PI/2 at FP_SCR3 + move.l #$85a308d3,FP_SCR3+4(a6) + clr.l FP_SCR3+8(a6) + fblt.w red_neg + or.w #$8000,FP_SCR2(a6) ;positive arg + or.w #$8000,FP_SCR3(a6) +red_neg: + fadd.x FP_SCR2(a6),fp0 ;high part of reduction is exact + fmove.x fp0,fp1 ;save high result in fp1 + fadd.x FP_SCR3(a6),fp0 ;low part of reduction + fsub.x fp0,fp1 ;determine low component of result + fadd.x FP_SCR3(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: + FMOVE.X FP0,INARG(a6) ...+-2**K * F, 1 <= F < 2 + MOVE.W INARG(a6),D0 + MOVE.L D0,A1 ...save a copy of D0 + ANDI.L #$00007FFF,D0 + SUBI.L #$00003FFF,D0 ...D0 IS K + CMPI.L #28,D0 + BLE.B LASTLOOP +CONTLOOP: + SUBI.L #27,D0 ...D0 IS L := K-27 + CLR.L ENDFLAG(a6) + BRA.B WORK +LASTLOOP: + CLR.L D0 ...D0 IS L := 0 + MOVE.L #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) + + MOVE.L #$00003FFE,D2 ...BIASED EXPO OF 2/PI + SUB.L D0,D2 ...BIASED EXPO OF 2**(-L)*(2/PI) + + MOVE.L #$A2F9836E,FP_SCR1+4(a6) + MOVE.L #$4E44152A,FP_SCR1+8(a6) + MOVE.W D2,FP_SCR1(a6) ...FP_SCR1 is 2**(-L)*(2/PI) + + FMOVE.X FP0,FP2 + FMUL.X FP_SCR1(a6),FP2 +*--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. + +*--HIDE SIX CYCLES OF INSTRUCTION + MOVE.L A1,D2 + SWAP D2 + ANDI.L #$80000000,D2 + ORI.L #$5F000000,D2 ...D2 IS SIGN(INARG)*2**63 IN SGL + MOVE.L D2,TWOTO63(a6) + + MOVE.L D0,D2 + ADDI.L #$00003FFF,D2 ...BIASED EXPO OF 2**L * (PI/2) + +*--FP2 IS READY + FADD.S TWOTO63(a6),FP2 ...THE FRACTIONAL PART OF FP1 IS ROUNDED + +*--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2 + MOVE.W D2,FP_SCR2(a6) + CLR.W FP_SCR2+2(a6) + MOVE.L #$C90FDAA2,FP_SCR2+4(a6) + CLR.L FP_SCR2+8(a6) ...FP_SCR2 is 2**(L) * Piby2_1 + +*--FP2 IS READY + FSUB.S TWOTO63(a6),FP2 ...FP2 is N + + ADDI.L #$00003FDD,D0 + MOVE.W D0,FP_SCR3(a6) + CLR.W FP_SCR3+2(a6) + MOVE.L #$85A308D3,FP_SCR3+4(a6) + CLR.L FP_SCR3+8(a6) ...FP_SCR3 is 2**(L) * Piby2_2 + + MOVE.L ENDFLAG(a6),D0 + +*--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and +*--P2 = 2**(L) * Piby2_2 + FMOVE.X FP2,FP4 + FMul.X FP_SCR2(a6),FP4 ...W = N*P1 + FMove.X FP2,FP5 + FMul.X FP_SCR3(a6),FP5 ...w = N*P2 + FMove.X FP4,FP3 +*--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 is P + FSub.X FP3,FP4 ...W-P + + FSub.X FP3,FP0 ...FP0 is A := R - P + FAdd.X FP5,FP4 ...FP4 is p = (W-P)+w + + FMove.X FP0,FP3 ...FP3 A + FSub.X FP4,FP1 ...FP1 is 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 is R := A+a +*--No need to calculate r if this is the last loop + TST.L D0 + BGT.W RESTORE + +*--Need to calculate r + FSub.X FP0,FP3 ...A-R + FAdd.X FP3,FP1 ...FP1 is r := (A-R)+a + BRA.W LOOP + +RESTORE: + FMOVE.L FP2,N(a6) + MOVE.L (A7)+,D2 + FMOVEM.X (A7)+,FP2-FP5 + + + MOVE.L N(a6),D0 + ROR.L #1,D0 + + + BRA.W TANCONT + + end |