fusl/src/math/atanh.c

#include "libm.h"

/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
double atanh(double x) {
  union {
    double f;
    uint64_t i;
  } u = {.f = x};
  unsigned e = u.i >> 52 & 0x7ff;
  unsigned s = u.i >> 63;
  double_t y;

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

  if (e < 0x3ff - 1) {
    if (e < 0x3ff - 32) {
      /* handle underflow */
      if (e == 0)
        FORCE_EVAL((float)y);
    } else {
      /* |x| < 0.5, up to 1.7ulp error */
      y = 0.5 * log1p(2 * y + 2 * y * y / (1 - y));
    }
  } else {
    /* avoid overflow */
    y = 0.5 * log1p(2 * (y / (1 - y)));
  }
  return s ? -y : y;
}