#include "libm.h"

/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
double asinh(double x) {
  union {
    double f;
    uint64_t i;
  } u = {.f = x};
  unsigned e = u.i >> 52 & 0x7ff;
  unsigned s = u.i >> 63;

  /* |x| */
  u.i &= (uint64_t)-1 / 2;
  x = u.f;

  if (e >= 0x3ff + 26) {
    /* |x| >= 0x1p26 or inf or nan */
    x = log(x) + 0.693147180559945309417232121458176568;
  } else if (e >= 0x3ff + 1) {
    /* |x| >= 2 */
    x = log(2 * x + 1 / (sqrt(x * x + 1) + x));
  } else if (e >= 0x3ff - 26) {
    /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
    x = log1p(x + x * x / (sqrt(x * x + 1) + 1));
  } else {
    /* |x| < 0x1p-26, raise inexact if x != 0 */
    FORCE_EVAL(x + 0x1p120f);
  }
  return s ? -x : x;
}