| #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; |
| } |
