mingw-w64-crt/complex/catanh.def.h

/*
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*/

__FLT_TYPE __complex__ __cdecl
__FLT_ABI(catanh) (__FLT_TYPE __complex__ z)
{
  __complex__ __FLT_TYPE ret;
  __FLT_TYPE i2, n, d;
  int r_class = fpclassify (__real__ z);
  int i_class = fpclassify (__imag__ z);

  if (r_class == FP_INFINITE || r_class == FP_NAN || i_class == FP_INFINITE || i_class == FP_NAN)
  {
    if (i_class == FP_INFINITE)
    {
      __real__ ret = __FLT_ABI(copysign) (__FLT_CST(0.0), __real__ z);
      __imag__ ret = __FLT_ABI(copysign) (__FLT_PI_2, __imag__ z);
      return ret;
    }

    if (r_class == FP_INFINITE || r_class == FP_ZERO)
    {
      __real__ ret = __FLT_ABI(copysign) (__FLT_CST(0.0), __real__ z);
      __imag__ ret = ((i_class != FP_NAN && i_class != FP_INFINITE)
        ? __FLT_ABI(copysign) (__FLT_PI_2, __imag__ z) : __FLT_NAN);
      return ret;
    }

    __real__ ret = __FLT_NAN;
    __imag__ ret = __FLT_NAN;
    return ret;
  }

  if (r_class == FP_ZERO && i_class == FP_ZERO)
    return z;

  /* catanh(z) = 1/2 * clog(1+z) - 1/2 * clog(1-z) = 1/2 * clog((1+z)/(1-z)) */

  /* Use identity clog(c) = 1/2*log(|c|^2) + i*arg(c) to calculate real and
  imaginary parts separately. */

  /* real part */
  /* |c|^2 = (Im(z)^2 + (1+Re(z))^2)/(Im(z)^2 + (1-Re(z))^2) */
  i2 = __imag__ z * __imag__ z;

  if (__FLT_ABI(fabs) (__real__ z) <= __FLT_EPSILON)
  {
    /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + O(Re(z)^2)  (Taylor series) */
    __real__ ret = __FLT_CST(0.25) *
      __FLT_ABI(log1p) (__FLT_CST(4.0)*(__real__ z) / (__FLT_CST(1.0) + i2));
  }
  else if ((__real__ z)*(__real__ z) <= __FLT_EPSILON)
  {
    /* |c|^2 = 1 + 4*Re(z)/(1+Im(z)^2) + 8*Re(z)^2/(1+Im(z)^2)^2 + O(Re(z)^3)  (Taylor series) */
    d = __real__ z / (__FLT_CST(1.0) + i2);
    __real__ ret = __FLT_CST(0.25) *
      __FLT_ABI(log1p) (__FLT_CST(4.0) * d * (__FLT_CST(1.0) + __FLT_CST(2.0) * d));
  }
  else
  {
    n = __FLT_CST(1.0) + __real__ z;
    n = i2 + n * n;

    d = __FLT_CST(1.0) - __real__ z;
    d = i2 + d * d;

    __real__ ret = __FLT_CST(0.25) * (__FLT_ABI(log) (n) - __FLT_ABI(log) (d));
  }

  /* imaginary part */
  /* z = (1 - Re(z)^2 - Im(z)^2 + 2i * Im(z) / ((1-Re(z))^2 + Im(z)^2) */
  d = __FLT_CST(1.0) - __real__ z * __real__ z - i2;

  __imag__ ret = __FLT_CST(0.5) * __FLT_ABI(atan2) (__FLT_CST(2.0) * __imag__ z, d);

  return ret;
}