CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/atanh.c

/*							atanh.c
 *
 *	Inverse hyperbolic tangent
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, atanh();
 *
 * y = atanh( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns inverse hyperbolic tangent of argument in the range
 * MINLOG to MAXLOG.
 *
 * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
 * employed.  Otherwise,
 *        atanh(x) = 0.5 * log( (1+x)/(1-x) ).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -1,1        50000       2.4e-17     6.4e-18
 *    IEEE      -1,1        30000       1.9e-16     5.2e-17
 *
 */

/*						atanh.c	*/

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

#ifdef UNK
static double P[] = {-8.54074331929669305196E-1, 1.20426861384072379242E1,
                     -4.61252884198732692637E1, 6.54566728676544377376E1,
                     -3.09092539379866942570E1};
static double Q[] = {
    /* 1.00000000000000000000E0,*/
    -1.95638849376911654834E1, 1.08938092147140262656E2,
    -2.49839401325893582852E2, 2.52006675691344555838E2,
    -9.27277618139601130017E1};
#endif
#ifdef DEC
static unsigned short P[] = {0140132, 0122235, 0105775, 0130300, 0041100,
                             0127327, 0124407, 0034722, 0141470, 0100113,
                             0115607, 0130535, 0041602, 0164721, 0003257,
                             0013673, 0141367, 0043046, 0166673, 0045750};
static unsigned short Q[] = {
    /*0040200,0000000,0000000,0000000,*/
    0141234, 0101326, 0015460, 0134564, 0041731, 0160115, 0116451,
    0032045, 0142171, 0153343, 0000532, 0167226, 0042174, 0000665,
    0077604, 0000310, 0141671, 0072235, 0031114, 0074377};
#endif

#ifdef IBMPC
static unsigned short P[] = {0xb618, 0xb17f, 0x5493, 0xbfeb, 0xe73a,
                             0xf520, 0x15da, 0x4028, 0xf62c, 0x7370,
                             0x1009, 0xc047, 0xe2f7, 0x20d5, 0x5d3a,
                             0x4050, 0x697d, 0xddb7, 0xe8c4, 0xc03e};
static unsigned short Q[] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x172f, 0xc366, 0x905a, 0xc033, 0x2685, 0xb3a5, 0x3c09,
    0x405b, 0x5dd3, 0x602b, 0x3adc, 0xc06f, 0x8019, 0xaff0,
    0x8036, 0x406f, 0x8f20, 0xa649, 0x2e93, 0xc057};
#endif

#ifdef MIEEE
static unsigned short P[] = {0xbfeb, 0x5493, 0xb17f, 0xb618, 0x4028,
                             0x15da, 0xf520, 0xe73a, 0xc047, 0x1009,
                             0x7370, 0xf62c, 0x4050, 0x5d3a, 0x20d5,
                             0xe2f7, 0xc03e, 0xe8c4, 0xddb7, 0x697d};
static unsigned short Q[] = {0xc033, 0x905a, 0xc366, 0x172f, 0x405b,
                             0x3c09, 0xb3a5, 0x2685, 0xc06f, 0x3adc,
                             0x602b, 0x5dd3, 0x406f, 0x8036, 0xaff0,
                             0x8019, 0xc057, 0x2e93, 0xa649, 0x8f20};
#endif

#ifdef ANSIPROT
extern double fabs(double);
extern double log(double x);
extern double polevl(double x, void *P, int N);
extern double p1evl(double x, void *P, int N);
#else
double fabs(), log(), polevl(), p1evl();
#endif
extern double INFINITY, NAN;

double atanh(x) double x;
{
  double s, z;

#ifdef MINUSZERO
  if (x == 0.0)
    return (x);
#endif
  z = fabs(x);
  if (z >= 1.0) {
    if (x == 1.0)
      return (INFINITY);
    if (x == -1.0)
      return (-INFINITY);
    mtherr("atanh", DOMAIN);
    return (NAN);
  }

  if (z < 1.0e-7)
    return (x);

  if (z < 0.5) {
    z = x * x;
    s = x + x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
    return (s);
  }

  return (0.5 * log((1.0 + x) / (1.0 - x)));
}