fusl/src/math/atanhf.c

#include "libm.h"

/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
float atanhf(float x) {
  union {
    float f;
    uint32_t i;
  } u = {.f = x};
  unsigned s = u.i >> 31;
  float_t y;

  /* |x| */
  u.i &= 0x7fffffff;
  y = u.f;

  if (u.i < 0x3f800000 - (1 << 23)) {
    if (u.i < 0x3f800000 - (32 << 23)) {
      /* handle underflow */
      if (u.i < (1 << 23))
        FORCE_EVAL((float)(y * y));
    } else {
      /* |x| < 0.5, up to 1.7ulp error */
      y = 0.5f * log1pf(2 * y + 2 * y * y / (1 - y));
    }
  } else {
    /* avoid overflow */
    y = 0.5f * log1pf(2 * (y / (1 - y)));
  }
  return s ? -y : y;
}