| #include "libm.h" |
| |
| /* cosh(x) = (exp(x) + 1/exp(x))/2 |
| * = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x) |
| * = 1 + x*x/2 + o(x^4) |
| */ |
| double cosh(double x) { |
| union { |
| double f; |
| uint64_t i; |
| } u = {.f = x}; |
| uint32_t w; |
| double t; |
| |
| /* |x| */ |
| u.i &= (uint64_t)-1 / 2; |
| x = u.f; |
| w = u.i >> 32; |
| |
| /* |x| < log(2) */ |
| if (w < 0x3fe62e42) { |
| if (w < 0x3ff00000 - (26 << 20)) { |
| /* raise inexact if x!=0 */ |
| FORCE_EVAL(x + 0x1p120f); |
| return 1; |
| } |
| t = expm1(x); |
| return 1 + t * t / (2 * (1 + t)); |
| } |
| |
| /* |x| < log(DBL_MAX) */ |
| if (w < 0x40862e42) { |
| t = exp(x); |
| /* note: if x>log(0x1p26) then the 1/t is not needed */ |
| return 0.5 * (t + 1 / t); |
| } |
| |
| /* |x| > log(DBL_MAX) or nan */ |
| /* note: the result is stored to handle overflow */ |
| t = __expo2(x); |
| return t; |
| } |
