#include "libm.h"

/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
float asinhf(float x) {
  union {
    float f;
    uint32_t i;
  } u = {.f = x};
  uint32_t i = u.i & 0x7fffffff;
  unsigned s = u.i >> 31;

  /* |x| */
  u.i = i;
  x = u.f;

  if (i >= 0x3f800000 + (12 << 23)) {
    /* |x| >= 0x1p12 or inf or nan */
    x = logf(x) + 0.693147180559945309417232121458176568f;
  } else if (i >= 0x3f800000 + (1 << 23)) {
    /* |x| >= 2 */
    x = logf(2 * x + 1 / (sqrtf(x * x + 1) + x));
  } else if (i >= 0x3f800000 - (12 << 23)) {
    /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
    x = log1pf(x + x * x / (sqrtf(x * x + 1) + 1));
  } else {
    /* |x| < 0x1p-12, raise inexact if x!=0 */
    FORCE_EVAL(x + 0x1p120f);
  }
  return s ? -x : x;
}