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1da177e4 LT |
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 | | | |
e00d82d0 MW |
52 | | For details on the license for this file, please see the |
53 | | file, README, in this same directory. | |
1da177e4 LT |
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 | ||
69 | BOUNDS1: .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 | |
77 | stanhd: | |
78 | |--TANH(X) = X FOR DENORMALIZED X | |
79 | ||
80 | bra t_extdnrm | |
81 | ||
82 | .global stanh | |
83 | stanh: | |
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 | ||
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|, 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 | ||
162 | TANHSM: | |
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 | ||
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 | ...-SIGN(X)*EPS | |
178 | ||
179 | fmovel %d1,%FPCR |restore users exceptions | |
180 | fadds %d0,%fp0 | |
181 | ||
182 | bra t_frcinx | |
183 | ||
184 | |end |