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
|
* $NetBSD: satanh.sa,v 1.2 1994/10/26 07:49:33 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.
*
* satanh.sa 3.3 12/19/90
*
* The entry point satanh computes the inverse
* hyperbolic tangent of
* an input argument; satanhd does the same except for denormalized
* input.
*
* Input: Double-extended number X in location pointed to
* by address register a0.
*
* Output: The value arctanh(X) returned in floating-point register Fp0.
*
* 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.
*
* Speed: The program satanh takes approximately 270 cycles.
*
* 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.
*
satanh IDNT 2,1 Motorola 040 Floating Point Software Package
section 8
xref t_dz
xref t_operr
xref t_frcinx
xref t_extdnrm
xref slognp1
xdef satanhd
satanhd:
*--ATANH(X) = X FOR DENORMALIZED X
bra t_extdnrm
xdef satanh
satanh:
move.l (a0),d0
move.w 4(a0),d0
ANDI.L #$7FFFFFFF,D0
CMPI.L #$3FFF8000,D0
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|
FMOVE.X FP0,FP1
FNEG.X FP1 ...-Y
FADD.X FP0,FP0 ...2Y
FADD.S #:3F800000,FP1 ...1-Y
FDIV.X FP1,FP0 ...2Y/(1-Y)
move.l (a0),d0
ANDI.L #$80000000,D0
ORI.L #$3F000000,D0 ...SIGN(X)*HALF
move.l d0,-(sp)
fmovem.x fp0,(a0) ...overwrite input
move.l d1,-(sp)
clr.l d1
bsr slognp1 ...LOG1P(Z)
fmove.l (sp)+,fpcr
FMUL.S (sp)+,FP0
bra t_frcinx
ATANHBIG:
FABS.X (a0),FP0 ...|X|
FCMP.S #:3F800000,FP0
fbgt t_operr
bra t_dz
end
|
