#include "libm.h"

#if FLT_EVAL_METHOD == 2
#undef sqrt
#define sqrt sqrtl
#endif

/* acosh(x) = log(x + sqrt(x*x-1)) */
double acosh(double x) {
  union {
    double f;
    uint64_t 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;
}