1#include "libm.h" 2 3/* sinh(x) = (exp(x) - 1/exp(x))/2 4 * = (exp(x)-1 + (exp(x)-1)/exp(x))/2 5 * = x + x^3/6 + o(x^5) 6 */ 7double sinh(double x) { 8 union { 9 double f; 10 uint64_t i; 11 } u = {.f = x}; 12 uint32_t w; 13 double t, h, absx; 14 15 h = 0.5; 16 if (u.i >> 63) 17 h = -h; 18 /* |x| */ 19 u.i &= (uint64_t)-1 / 2; 20 absx = u.f; 21 w = u.i >> 32; 22 23 /* |x| < log(DBL_MAX) */ 24 if (w < 0x40862e42) { 25 t = expm1(absx); 26 if (w < 0x3ff00000) { 27 if (w < 0x3ff00000 - (26 << 20)) /* note: inexact and underflow are raised by expm1 */ 28 /* note: this branch avoids spurious underflow */ 29 return x; 30 return h * (2 * t - t * t / (t + 1)); 31 } 32 /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */ 33 return h * (t + t / (t + 1)); 34 } 35 36 /* |x| > log(DBL_MAX) or nan */ 37 /* note: the result is stored to handle overflow */ 38 t = 2 * h * __expo2(absx); 39 return t; 40} 41