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}