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)) */
acosh(double x)9 double 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 }
25