ref: b699be1156cb41be910dadb3c8a6df0bea12bf67
dir: /libnpe/acosh.c/
#include <math.h>
/* taken from musl */
/* acosh(x) = log(x + sqrt(x*x-1)) */
double
acosh(double x)
{
union {double f; u64int 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;
}