1/**
 2 * This file has no copyright assigned and is placed in the Public Domain.
 3 * This file is part of the mingw-w64 runtime package.
 4 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
 5 */
 6#include <math.h>
 7#include <errno.h>
 8#include "fastmath.h"
 9
10/* atanh (x) = 0.5 * log ((1.0 + x)/(1.0 - x)) */
11long double atanhl (long double x)
12{
13  long double z;
14  if (isnan (x))
15    return x;
16  z = fabsl (x);
17  if (z == 1.0L)
18    {
19      errno  = ERANGE;
20      return (x > 0 ? INFINITY : -INFINITY);
21    }
22  if ( z > 1.0L)
23    {
24      errno = EDOM;
25      return nanl("");
26    }
27  /* Rearrange formula to avoid precision loss for small x.
28  atanh(x) = 0.5 * log ((1.0 + x)/(1.0 - x))
29 	   = 0.5 * log1p ((1.0 + x)/(1.0 - x) - 1.0)
30           = 0.5 * log1p ((1.0 + x - 1.0 + x) /(1.0 - x)) 
31           = 0.5 * log1p ((2.0 * x ) / (1.0 - x))  */
32  z = 0.5L * __fast_log1pl ((z + z) / (1.0L - z));
33  return copysignl(z, x); //ensure 0.0 -> 0.0 and -0.0 -> -0.0.
34}