| #include "libm.h" |
| |
| /* sinh(x) = (exp(x) - 1/exp(x))/2 |
| * = (exp(x)-1 + (exp(x)-1)/exp(x))/2 |
| * = x + x^3/6 + o(x^5) |
| */ |
| double sinh(double x) |
| { |
| union {double f; uint64_t i;} u = {.f = x}; |
| uint32_t w; |
| double t, h, absx; |
| |
| h = 0.5; |
| if (u.i >> 63) |
| h = -h; |
| /* |x| */ |
| u.i &= (uint64_t)-1/2; |
| absx = u.f; |
| w = u.i >> 32; |
| |
| /* |x| < log(DBL_MAX) */ |
| if (w < 0x40862e42) { |
| t = expm1(absx); |
| if (w < 0x3ff00000) { |
| if (w < 0x3ff00000 - (26<<20)) |
| /* note: inexact and underflow are raised by expm1 */ |
| /* note: this branch avoids spurious underflow */ |
| return x; |
| return h*(2*t - t*t/(t+1)); |
| } |
| /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */ |
| return h*(t + t/(t+1)); |
| } |
| |
| /* |x| > log(DBL_MAX) or nan */ |
| /* note: the result is stored to handle overflow */ |
| t = 2*h*__expo2(absx); |
| return t; |
| } |
