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

/*							exp.c
 *
 *	Exponential function
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, exp();
 *
 * y = exp( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns e (2.71828...) raised to the x power.
 *
 * Range reduction is accomplished by separating the argument
 * into an integer k and fraction f such that
 *
 *     x    k  f
 *    e  = 2  e.
 *
 * A Pade' form  1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
 * of degree 2/3 is used to approximate exp(f) in the basic
 * interval [-0.5, 0.5].
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       +- 88       50000       2.8e-17     7.0e-18
 *    IEEE      +- 708      40000       2.0e-16     5.6e-17
 *
 *
 * Error amplification in the exponential function can be
 * a serious matter.  The error propagation involves
 * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
 * which shows that a 1 lsb error in representing X produces
 * a relative error of X times 1 lsb in the function.
 * While the routine gives an accurate result for arguments
 * that are exactly represented by a double precision
 * computer number, the result contains amplified roundoff
 * error for large arguments not exactly represented.
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * exp underflow    x < MINLOG         0.0
 * exp overflow     x > MAXLOG         INFINITY
 *
 */

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

/*	Exponential function	*/

#include "mconf.h"

#ifdef UNK

static double P[] = {
    1.26177193074810590878E-4,
    3.02994407707441961300E-2,
    9.99999999999999999910E-1,
};
static double Q[] = {
    3.00198505138664455042E-6,
    2.52448340349684104192E-3,
    2.27265548208155028766E-1,
    2.00000000000000000009E0,
};
static double C1 = 6.93145751953125E-1;
static double C2 = 1.42860682030941723212E-6;
#endif

#ifdef DEC
static unsigned short P[] = {
    0035004, 0047156, 0127442, 0057502, 0036770, 0033210,
    0063121, 0061764, 0040200, 0000000, 0000000, 0000000,
};
static unsigned short Q[] = {
    0033511, 0072665, 0160662, 0176377, 0036045, 0070715, 0124105, 0132777,
    0037550, 0134114, 0142077, 0001637, 0040400, 0000000, 0000000, 0000000,
};
static unsigned short sc1[] = {0040061, 0071000, 0000000, 0000000};
#define C1 (*(double *)sc1)
static unsigned short sc2[] = {0033277, 0137216, 0075715, 0057117};
#define C2 (*(double *)sc2)
#endif

#ifdef IBMPC
static unsigned short P[] = {
    0x4be8, 0xd5e4, 0x89cd, 0x3f20, 0x2c7e, 0x0cca,
    0x06d1, 0x3f9f, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
static unsigned short Q[] = {
    0x5fa0, 0xbc36, 0x2eb6, 0x3ec9, 0xb6c0, 0xb508, 0xae39, 0x3f64,
    0xe074, 0x9887, 0x1709, 0x3fcd, 0x0000, 0x0000, 0x0000, 0x4000,
};
static unsigned short sc1[] = {0x0000, 0x0000, 0x2e40, 0x3fe6};
#define C1 (*(double *)sc1)
static unsigned short sc2[] = {0xabca, 0xcf79, 0xf7d1, 0x3eb7};
#define C2 (*(double *)sc2)
#endif

#ifdef MIEEE
static unsigned short P[] = {
    0x3f20, 0x89cd, 0xd5e4, 0x4be8, 0x3f9f, 0x06d1,
    0x0cca, 0x2c7e, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
static unsigned short Q[] = {
    0x3ec9, 0x2eb6, 0xbc36, 0x5fa0, 0x3f64, 0xae39, 0xb508, 0xb6c0,
    0x3fcd, 0x1709, 0x9887, 0xe074, 0x4000, 0x0000, 0x0000, 0x0000,
};
static unsigned short sc1[] = {0x3fe6, 0x2e40, 0x0000, 0x0000};
#define C1 (*(double *)sc1)
static unsigned short sc2[] = {0x3eb7, 0xf7d1, 0xcf79, 0xabca};
#define C2 (*(double *)sc2)
#endif

#ifdef ANSIPROT
extern double polevl(double, void *, int);
extern double p1evl(double, void *, int);
extern double floor(double);
extern double ldexp(double, int);
extern int isnan(double);
extern int isfinite(double);
#else
double polevl(), p1evl(), floor(), ldexp();
int isnan(), isfinite();
#endif
extern double LOGE2, LOG2E, MAXLOG, MINLOG, MAXNUM;
#ifdef INFINITIES
extern double INFINITY;
#endif

double exp(x) double x;
{
  double px, xx;
  int n;

#ifdef NANS
  if (isnan(x))
    return (x);
#endif
  if (x > MAXLOG) {
#ifdef INFINITIES
    return (INFINITY);
#else
    mtherr("exp", OVERFLOW);
    return (MAXNUM);
#endif
  }

  if (x < MINLOG) {
#ifndef INFINITIES
    mtherr("exp", UNDERFLOW);
#endif
    return (0.0);
  }

  /* Express e**x = e**g 2**n
   *   = e**g e**( n loge(2) )
   *   = e**( g + n loge(2) )
   */
  px = floor(LOG2E * x + 0.5); /* floor() truncates toward -infinity. */
  n = px;
  x -= px * C1;
  x -= px * C2;

  /* rational approximation for exponential
   * of the fractional part:
   * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
   */
  xx = x * x;
  px = x * polevl(xx, P, 2);
  x = px / (polevl(xx, Q, 3) - px);
  x = 1.0 + 2.0 * x;

  /* multiply by power of 2 */
  x = ldexp(x, n);
  return (x);
}