1#include "libm.h"
2
3#if FLT_EVAL_METHOD==2
4#undef sqrt
5#define sqrt sqrtl
6#endif
7
8/* acosh(x) = log(x + sqrt(x*x-1)) */
9double acosh(double x)
10{
11 union {double f; uint64_t i;} u = {.f = x};
12 unsigned e = u.i >> 52 & 0x7ff;
13
14 /* x < 1 domain error is handled in the called functions */
15
16 if (e < 0x3ff + 1)
17 /* |x| < 2, up to 2ulp error in [1,1.125] */
18 return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)));
19 if (e < 0x3ff + 26)
20 /* |x| < 0x1p26 */
21 return log(2*x - 1/(x+sqrt(x*x-1)));
22 /* |x| >= 0x1p26 or nan */
23 return log(x) + 0.693147180559945309417232121458176568;
24}