1|
2| stanh.sa 3.1 12/10/90
3|
4| The entry point sTanh computes the hyperbolic tangent of
5| an input argument; sTanhd does the same except for denormalized
6| input.
7|
8| Input: Double-extended number X in location pointed to
9| by address register a0.
10|
11| Output: The value tanh(X) returned in floating-point register Fp0.
12|
13| Accuracy and Monotonicity: The returned result is within 3 ulps in
14| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
15| result is subsequently rounded to double precision. The
16| result is provably monotonic in double precision.
17|
18| Speed: The program stanh takes approximately 270 cycles.
19|
20| Algorithm:
21|
22| TANH
23| 1. If |X| >= (5/2) log2 or |X| <= 2**(-40), go to 3.
24|
25| 2. (2**(-40) < |X| < (5/2) log2) Calculate tanh(X) by
26| sgn := sign(X), y := 2|X|, z := expm1(Y), and
27| tanh(X) = sgn*( z/(2+z) ).
28| Exit.
29|
30| 3. (|X| <= 2**(-40) or |X| >= (5/2) log2). If |X| < 1,
31| go to 7.
32|
33| 4. (|X| >= (5/2) log2) If |X| >= 50 log2, go to 6.
34|
35| 5. ((5/2) log2 <= |X| < 50 log2) Calculate tanh(X) by
36| sgn := sign(X), y := 2|X|, z := exp(Y),
37| tanh(X) = sgn - [ sgn*2/(1+z) ].
38| Exit.
39|
40| 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we
41| calculate Tanh(X) by
42| sgn := sign(X), Tiny := 2**(-126),
43| tanh(X) := sgn - sgn*Tiny.
44| Exit.
45|
46| 7. (|X| < 2**(-40)). Tanh(X) = X. Exit.
47|
48
49| Copyright (C) Motorola, Inc. 1990
50| All Rights Reserved
51|
52| For details on the license for this file, please see the
53| file, README, in this same directory.
54
55|STANH idnt 2,1 | Motorola 040 Floating Point Software Package
56
57 |section 8
58
59#include "fpsp.h"
60
61 .set X,FP_SCR5
62 .set XDCARE,X+2
63 .set XFRAC,X+4
64
65 .set SGN,L_SCR3
66
67 .set V,FP_SCR6
68
69BOUNDS1: .long 0x3FD78000,0x3FFFDDCE | ... 2^(-40), (5/2)LOG2
70
71 |xref t_frcinx
72 |xref t_extdnrm
73 |xref setox
74 |xref setoxm1
75
76 .global stanhd
77stanhd:
78|--TANH(X) = X FOR DENORMALIZED X
79
80 bra t_extdnrm
81
82 .global stanh
83stanh:
84 fmovex (%a0),%fp0 | ...LOAD INPUT
85
86 fmovex %fp0,X(%a6)
87 movel (%a0),%d0
88 movew 4(%a0),%d0
89 movel %d0,X(%a6)
90 andl #0x7FFFFFFF,%d0
91 cmp2l BOUNDS1(%pc),%d0 | ...2**(-40) < |X| < (5/2)LOG2 ?
92 bcss TANHBORS
93
94|--THIS IS THE USUAL CASE
95|--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
96
97 movel X(%a6),%d0
98 movel %d0,SGN(%a6)
99 andl #0x7FFF0000,%d0
100 addl #0x00010000,%d0 | ...EXPONENT OF 2|X|
101 movel %d0,X(%a6)
102 andl #0x80000000,SGN(%a6)
103 fmovex X(%a6),%fp0 | ...FP0 IS Y = 2|X|
104
105 movel %d1,-(%a7)
106 clrl %d1
107 fmovemx %fp0-%fp0,(%a0)
108 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y)
109 movel (%a7)+,%d1
110
111 fmovex %fp0,%fp1
112 fadds #0x40000000,%fp1 | ...Z+2
113 movel SGN(%a6),%d0
114 fmovex %fp1,V(%a6)
115 eorl %d0,V(%a6)
116
117 fmovel %d1,%FPCR |restore users exceptions
118 fdivx V(%a6),%fp0
119 bra t_frcinx
120
121TANHBORS:
122 cmpl #0x3FFF8000,%d0
123 blt TANHSM
124
125 cmpl #0x40048AA1,%d0
126 bgt TANHHUGE
127
128|-- (5/2) LOG2 < |X| < 50 LOG2,
129|--TANH(X) = 1 - (2/[EXP(2X)+1]). LET Y = 2|X|, SGN = SIGN(X),
130|--TANH(X) = SGN - SGN*2/[EXP(Y)+1].
131
132 movel X(%a6),%d0
133 movel %d0,SGN(%a6)
134 andl #0x7FFF0000,%d0
135 addl #0x00010000,%d0 | ...EXPO OF 2|X|
136 movel %d0,X(%a6) | ...Y = 2|X|
137 andl #0x80000000,SGN(%a6)
138 movel SGN(%a6),%d0
139 fmovex X(%a6),%fp0 | ...Y = 2|X|
140
141 movel %d1,-(%a7)
142 clrl %d1
143 fmovemx %fp0-%fp0,(%a0)
144 bsr setox | ...FP0 IS EXP(Y)
145 movel (%a7)+,%d1
146 movel SGN(%a6),%d0
147 fadds #0x3F800000,%fp0 | ...EXP(Y)+1
148
149 eorl #0xC0000000,%d0 | ...-SIGN(X)*2
150 fmoves %d0,%fp1 | ...-SIGN(X)*2 IN SGL FMT
151 fdivx %fp0,%fp1 | ...-SIGN(X)2 / [EXP(Y)+1 ]
152
153 movel SGN(%a6),%d0
154 orl #0x3F800000,%d0 | ...SGN
155 fmoves %d0,%fp0 | ...SGN IN SGL FMT
156
157 fmovel %d1,%FPCR |restore users exceptions
158 faddx %fp1,%fp0
159
160 bra t_frcinx
161
162TANHSM:
163 movew #0x0000,XDCARE(%a6)
164
165 fmovel %d1,%FPCR |restore users exceptions
166 fmovex X(%a6),%fp0 |last inst - possible exception set
167
168 bra t_frcinx
169
170TANHHUGE:
171|---RETURN SGN(X) - SGN(X)EPS
172 movel X(%a6),%d0
173 andl #0x80000000,%d0
174 orl #0x3F800000,%d0
175 fmoves %d0,%fp0
176 andl #0x80000000,%d0
177 eorl #0x80800000,%d0 | ...-SIGN(X)*EPS
178
179 fmovel %d1,%FPCR |restore users exceptions
180 fadds %d0,%fp0
181
182 bra t_frcinx
183
184 |end
185

source code of linux/arch/m68k/fpsp040/stanh.S