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    union {
11        double f;
12        uint64_t i;
13    } u = {.f = x};
14    unsigned e = u.i >> 52 & 0x7ff;
15
16    /* x < 1 domain error is handled in the called functions */
17
18    if (e < 0x3ff + 1) /* |x| < 2, up to 2ulp error in [1,1.125] */
19        return log1p(x - 1 + sqrt((x - 1) * (x - 1) + 2 * (x - 1)));
20    if (e < 0x3ff + 26) /* |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