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

/*							acosh.c
 *
 *	Inverse hyperbolic cosine
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, acosh();
 *
 * y = acosh( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns inverse hyperbolic cosine of argument.
 *
 * If 1 <= x < 1.5, a rational approximation
 *
 *	sqrt(z) * P(z)/Q(z)
 *
 * where z = x-1, is used.  Otherwise,
 *
 * acosh(x)  =  log( x + sqrt( (x-1)(x+1) ).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       1,3         30000       4.2e-17     1.1e-17
 *    IEEE      1,3         30000       4.6e-16     8.7e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * acosh domain       |x| < 1            NAN
 *
 */

/*							acosh.c	*/

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/

/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */

#include "mconf.h"

#ifdef UNK
static double P[] = {1.18801130533544501356E2, 3.94726656571334401102E3,
                     3.43989375926195455866E4, 1.08102874834699867335E5,
                     1.10855947270161294369E5};
static double Q[] = {
    /* 1.00000000000000000000E0,*/
    1.86145380837903397292E2, 4.15352677227719831579E3,
    2.97683430363289370382E4, 8.29725251988426222434E4,
    7.83869920495893927727E4};
#endif

#ifdef DEC
static unsigned short P[] = {0041755, 0115055, 0144002, 0146444, 0043166,
                             0132103, 0155150, 0150302, 0044006, 0057360,
                             0003021, 0162753, 0044323, 0021557, 0175225,
                             0056253, 0044330, 0101771, 0040046, 0006636};
static unsigned short Q[] = {
    /*0040200,0000000,0000000,0000000,*/
    0042072, 0022467, 0126670, 0041232, 0043201, 0146066, 0152142,
    0034015, 0043750, 0110257, 0121165, 0026100, 0044242, 0007103,
    0034667, 0033173, 0044231, 0014576, 0175573, 0017472};
#endif

#ifdef IBMPC
static unsigned short P[] = {0x59a4, 0xb900, 0xb345, 0x405d, 0x1a18,
                             0x7b4d, 0xd688, 0x40ae, 0x3cbd, 0x00c2,
                             0xcbde, 0x40e0, 0xab95, 0xff52, 0x646d,
                             0x40fa, 0xc1b4, 0x2804, 0x107f, 0x40fb};
static unsigned short Q[] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x0853, 0xf5b7, 0x44a6, 0x4067, 0x4702, 0xda8c, 0x3986,
    0x40b0, 0xa588, 0xf44e, 0x1215, 0x40dd, 0xe6cf, 0x6736,
    0x41c8, 0x40f4, 0x63e7, 0xdf6f, 0x232f, 0x40f3};
#endif

#ifdef MIEEE
static unsigned short P[] = {0x405d, 0xb345, 0xb900, 0x59a4, 0x40ae,
                             0xd688, 0x7b4d, 0x1a18, 0x40e0, 0xcbde,
                             0x00c2, 0x3cbd, 0x40fa, 0x646d, 0xff52,
                             0xab95, 0x40fb, 0x107f, 0x2804, 0xc1b4};
static unsigned short Q[] = {
    0x4067, 0x44a6, 0xf5b7, 0x0853, 0x40b0, 0x3986, 0xda8c,
    0x4702, 0x40dd, 0x1215, 0xf44e, 0xa588, 0x40f4, 0x41c8,
    0x6736, 0xe6cf, 0x40f3, 0x232f, 0xdf6f, 0x63e7,
};
#endif

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double log(double);
extern double sqrt(double);
#else
double log(), sqrt(), polevl(), p1evl();
#endif
extern double LOGE2, INFINITY, NAN;

double acosh(x) double x;
{
  double a, z;

  if (x < 1.0) {
    mtherr("acosh", DOMAIN);
    return (NAN);
  }

  if (x > 1.0e8) {
#ifdef INFINITIES
    if (x == INFINITY)
      return (INFINITY);
#endif
    return (log(x) + LOGE2);
  }

  z = x - 1.0;

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

  a = sqrt(z * (x + 1.0));
  return (log(x + a));
}