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

/*							asinh.c
 *
 *	Inverse hyperbolic sine
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, asinh();
 *
 * y = asinh( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns inverse hyperbolic sine of argument.
 *
 * If |x| < 0.5, the function is approximated by a rational
 * form  x + x**3 P(x)/Q(x).  Otherwise,
 *
 *     asinh(x) = log( x + sqrt(1 + x*x) ).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC      -3,3         75000       4.6e-17     1.1e-17
 *    IEEE     -1,1         30000       3.7e-16     7.8e-17
 *    IEEE      1,3         30000       2.5e-16     6.7e-17
 *
 */

/*						asinh.c	*/

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

#include "mconf.h"

#ifdef UNK
static double P[] = {-4.33231683752342103572E-3, -5.91750212056387121207E-1,
                     -4.37390226194356683570E0, -9.09030533308377316566E0,
                     -5.56682227230859640450E0};
static double Q[] = {
    /* 1.00000000000000000000E0,*/
    1.28757002067426453537E1, 4.86042483805291788324E1,
    6.95722521337257608734E1, 3.34009336338516356383E1};
#endif

#ifdef DEC
static unsigned short P[] = {0136215, 0173033, 0110410, 0105475, 0140027,
                             0076361, 0020056, 0164520, 0140613, 0173401,
                             0160136, 0053142, 0141021, 0070744, 0000503,
                             0176261, 0140662, 0021550, 0073106, 0133351};
static unsigned short Q[] = {
    /* 0040200,0000000,0000000,0000000,*/
    0041116, 0001336, 0034120, 0173054, 0041502, 0065300, 0013144, 0021231,
    0041613, 0022376, 0035516, 0153063, 0041405, 0115216, 0054265, 0004557};
#endif

#ifdef IBMPC
static unsigned short P[] = {0x1168, 0x7221, 0xbec3, 0xbf71, 0xdd2a,
                             0x2405, 0xef9e, 0xbfe2, 0xcacc, 0x3c0b,
                             0x7ee0, 0xc011, 0x7f96, 0x8028, 0x2e3c,
                             0xc022, 0xd6dd, 0x0ec8, 0x446d, 0xc016};
static unsigned short Q[] = {
    /* 0x0000,0x0000,0x0000,0x3ff0,*/
    0x1ec5, 0xc70a, 0xc05b, 0x4029, 0x8453, 0x02cc, 0x4d58, 0x4048,
    0xdac6, 0xc769, 0x649f, 0x4051, 0xa12e, 0xcb16, 0xb351, 0x4040};
#endif

#ifdef MIEEE
static unsigned short P[] = {0xbf71, 0xbec3, 0x7221, 0x1168, 0xbfe2,
                             0xef9e, 0x2405, 0xdd2a, 0xc011, 0x7ee0,
                             0x3c0b, 0xcacc, 0xc022, 0x2e3c, 0x8028,
                             0x7f96, 0xc016, 0x446d, 0x0ec8, 0xd6dd};
static unsigned short Q[] = {0x4029, 0xc05b, 0xc70a, 0x1ec5, 0x4048, 0x4d58,
                             0x02cc, 0x8453, 0x4051, 0x649f, 0xc769, 0xdac6,
                             0x4040, 0xb351, 0xcb16, 0xa12e};
#endif

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

double asinh(xx) double xx;
{
  double a, z, x;
  int sign;

#ifdef MINUSZERO
  if (xx == 0.0)
    return (xx);
#endif
  if (xx < 0.0) {
    sign = -1;
    x = -xx;
  } else {
    sign = 1;
    x = xx;
  }

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

  z = x * x;
  if (x < 0.5) {
    a = (polevl(z, P, 4) / p1evl(z, Q, 4)) * z;
    a = a * x + x;
    if (sign < 0)
      a = -a;
    return (a);
  }

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