source:
asp3_tinet_ecnl_rx/trunk/musl-1.1.18/src/math/tanh.c
Last change on this file was 337, checked in by , 6 years ago | |
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File size: 996 bytes |
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[337] | 1 | #include "libm.h" |
2 | ||
3 | /* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x)) | |
4 | * = (exp(2*x) - 1)/(exp(2*x) - 1 + 2) | |
5 | * = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2) | |
6 | */ | |
7 | double tanh(double x) | |
8 | { | |
9 | union {double f; uint64_t i;} u = {.f = x}; | |
10 | uint32_t w; | |
11 | int sign; | |
12 | double_t t; | |
13 | ||
14 | /* x = |x| */ | |
15 | sign = u.i >> 63; | |
16 | u.i &= (uint64_t)-1/2; | |
17 | x = u.f; | |
18 | w = u.i >> 32; | |
19 | ||
20 | if (w > 0x3fe193ea) { | |
21 | /* |x| > log(3)/2 ~= 0.5493 or nan */ | |
22 | if (w > 0x40340000) { | |
23 | /* |x| > 20 or nan */ | |
24 | /* note: this branch avoids raising overflow */ | |
25 | t = 1 - 0/x; | |
26 | } else { | |
27 | t = expm1(2*x); | |
28 | t = 1 - 2/(t+2); | |
29 | } | |
30 | } else if (w > 0x3fd058ae) { | |
31 | /* |x| > log(5/3)/2 ~= 0.2554 */ | |
32 | t = expm1(2*x); | |
33 | t = t/(t+2); | |
34 | } else if (w >= 0x00100000) { | |
35 | /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */ | |
36 | t = expm1(-2*x); | |
37 | t = -t/(t+2); | |
38 | } else { | |
39 | /* |x| is subnormal */ | |
40 | /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */ | |
41 | FORCE_EVAL((float)x); | |
42 | t = x; | |
43 | } | |
44 | return sign ? -t : t; | |
45 | } |
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