1 |
2 | stanh.sa 3.1 12/10/90
3 |
4 | The entry point sTanh computes the hyp
5 | an input argument; sTanhd does the sam
6 | input.
7 |
8 | Input: Double-extended number X in loc
9 | by address register a0.
10 |
11 | Output: The value tanh(X) returned in
12 |
13 | Accuracy and Monotonicity: The returne
14 | 64 significant bit, i.e. withi
15 | result is subsequently rounded
16 | result is provably monotonic i
17 |
18 | Speed: The program stanh takes approxi
19 |
20 | Algorithm:
21 |
22 | TANH
23 | 1. If |X| >= (5/2) log2 or |X| <= 2**(
24 |
25 | 2. (2**(-40) < |X| < (5/2) log2) Calcu
26 | sgn := sign(X), y := 2|X|, z :
27 | tanh(X) = sgn*( z/(2+z) ).
28 | Exit.
29 |
30 | 3. (|X| <= 2**(-40) or |X| >= (5/2) lo
31 | go to 7.
32 |
33 | 4. (|X| >= (5/2) log2) If |X| >= 50 lo
34 |
35 | 5. ((5/2) log2 <= |X| < 50 log2) Calcu
36 | sgn := sign(X), y := 2|X|, z :
37 | tanh(X) = sgn - [ sgn*2/(1+z)
38 | Exit.
39 |
40 | 6. (|X| >= 50 log2) Tanh(X) = +-1 (rou
41 | calculate Tanh(X) by
42 | sgn := sign(X), Tiny := 2**(-1
43 | tanh(X) := sgn - sgn*Tiny.
44 | Exit.
45 |
46 | 7. (|X| < 2**(-40)). Tanh(X) = X.
47 |
48
49 | Copyright (C) Motorola, Inc. 1
50 | All Rights Reserved
51 |
52 | For details on the license for this fi
53 | file, README, in this same directory.
54
55 |STANH idnt 2,1 | Motorola 040 Floating Po
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
69 BOUNDS1: .long 0x3FD78000,0x3FFFDDCE |
70
71 |xref t_frcinx
72 |xref t_extdnrm
73 |xref setox
74 |xref setoxm1
75
76 .global stanhd
77 stanhd:
78 |--TANH(X) = X FOR DENORMALIZED X
79
80 bra t_extdnrm
81
82 .global stanh
83 stanh:
84 fmovex (%a0),%fp0 | ...L
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
92 bcss TANHBORS
93
94 |--THIS IS THE USUAL CASE
95 |--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) *
96
97 movel X(%a6),%d0
98 movel %d0,SGN(%a6)
99 andl #0x7FFF0000,%d0
100 addl #0x00010000,%d0 | ...E
101 movel %d0,X(%a6)
102 andl #0x80000000,SGN(%a6)
103 fmovex X(%a6),%fp0
104
105 movel %d1,-(%a7)
106 clrl %d1
107 fmovemx %fp0-%fp0,(%a0)
108 bsr setoxm1 | ...F
109 movel (%a7)+,%d1
110
111 fmovex %fp0,%fp1
112 fadds #0x40000000,%fp1
113 movel SGN(%a6),%d0
114 fmovex %fp1,V(%a6)
115 eorl %d0,V(%a6)
116
117 fmovel %d1,%FPCR
118 fdivx V(%a6),%fp0
119 bra t_frcinx
120
121 TANHBORS:
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|
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 | ...E
136 movel %d0,X(%a6)
137 andl #0x80000000,SGN(%a6)
138 movel SGN(%a6),%d0
139 fmovex X(%a6),%fp0
140
141 movel %d1,-(%a7)
142 clrl %d1
143 fmovemx %fp0-%fp0,(%a0)
144 bsr setox | ...F
145 movel (%a7)+,%d1
146 movel SGN(%a6),%d0
147 fadds #0x3F800000,%fp0
148
149 eorl #0xC0000000,%d0 | ...-
150 fmoves %d0,%fp1
151 fdivx %fp0,%fp1
152
153 movel SGN(%a6),%d0
154 orl #0x3F800000,%d0 | ...S
155 fmoves %d0,%fp0
156
157 fmovel %d1,%FPCR
158 faddx %fp1,%fp0
159
160 bra t_frcinx
161
162 TANHSM:
163 movew #0x0000,XDCARE(%a6)
164
165 fmovel %d1,%FPCR
166 fmovex X(%a6),%fp0
167
168 bra t_frcinx
169
170 TANHHUGE:
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 | ...-
178
179 fmovel %d1,%FPCR
180 fadds %d0,%fp0
181
182 bra t_frcinx
183
184 |end
Linux® is a registered trademark of Linus Torvalds in the United States and other countries.
TOMOYO® is a registered trademark of NTT DATA CORPORATION.