| #include "libm.h" |
| |
| #if FLT_EVAL_METHOD == 2 |
| #undef sqrt |
| #define sqrt sqrtl |
| #endif |
| |
| /* acosh(x) = log(x + sqrt(x*x-1)) */ |
| double acosh(double x) { |
| union { |
| double f; |
| uint64_t i; |
| } u = {.f = x}; |
| unsigned e = u.i >> 52 & 0x7ff; |
| |
| /* x < 1 domain error is handled in the called functions */ |
| |
| if (e < 0x3ff + 1) /* |x| < 2, up to 2ulp error in [1,1.125] */ |
| return log1p(x - 1 + sqrt((x - 1) * (x - 1) + 2 * (x - 1))); |
| if (e < 0x3ff + 26) /* |x| < 0x1p26 */ |
| return log(2 * x - 1 / (x + sqrt(x * x - 1))); |
| /* |x| >= 0x1p26 or nan */ |
| return log(x) + 0.693147180559945309417232121458176568; |
| } |
