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path: root/src/math/tanh.c
blob: 0e766c5cbeb195b9e8d27df8f4c008d965025075 (plain)
 ```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 ``` ``````#include "libm.h" /* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x)) * = (exp(2*x) - 1)/(exp(2*x) - 1 + 2) * = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2) */ double tanh(double x) { union {double f; uint64_t i;} u = {.f = x}; uint32_t w; int sign; double t; /* x = |x| */ sign = u.i >> 63; u.i &= (uint64_t)-1/2; x = u.f; w = u.i >> 32; if (w > 0x3fe193ea) { /* |x| > log(3)/2 ~= 0.5493 or nan */ if (w > 0x40340000) { /* |x| > 20 or nan */ /* note: this branch avoids raising overflow */ /* raise inexact if x!=+-inf and handle nan */ t = 1 + 0/(x + 0x1p-120f); } else { t = expm1(2*x); t = 1 - 2/(t+2); } } else if (w > 0x3fd058ae) { /* |x| > log(5/3)/2 ~= 0.2554 */ t = expm1(2*x); t = t/(t+2); } else { /* |x| is small, up to 2ulp error in [0.1,0.2554] */ t = expm1(-2*x); t = -t/(t+2); } return sign ? -t : t; } ``````