CocoRoboDesktop/pdf1.js/node_modules/cephes/cephes/exp2.c

/*							exp2.c
 *
 *	Base 2 exponential function
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, exp2();
 *
 * y = exp2( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns 2 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
 *    2  = 2  2.
 *
 * A Pade' form
 *
 *   1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
 *
 * approximates 2**x in the basic range [-0.5, 0.5].
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE    -1022,+1024   30000       1.8e-16     5.4e-17
 *
 *
 * See exp.c for comments on error amplification.
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * exp underflow    x < -MAXL2        0.0
 * exp overflow     x > MAXL2         MAXNUM
 *
 * For DEC arithmetic, MAXL2 = 127.
 * For IEEE arithmetic, MAXL2 = 1024.
 */

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

#include "mconf.h"

#ifdef UNK
static double P[] = {
    2.30933477057345225087E-2,
    2.02020656693165307700E1,
    1.51390680115615096133E3,
};
static double Q[] = {
    /* 1.00000000000000000000E0,*/
    2.33184211722314911771E2,
    4.36821166879210612817E3,
};
#define MAXL2 1024.0
#define MINL2 -1024.0
#endif

#ifdef DEC
static unsigned short P[] = {
    0036675, 0027102, 0122327, 0053227, 0041241, 0116724,
    0115412, 0157355, 0042675, 0036404, 0101733, 0132226,
};
static unsigned short Q[] = {
    /*0040200,0000000,0000000,0000000,*/
    0042151, 0027450, 0077732, 0160744, 0043210, 0100661, 0077550, 0056560,
};
#define MAXL2 127.0
#define MINL2 -127.0
#endif

#ifdef IBMPC
static unsigned short P[] = {
    0xead3, 0x549a, 0xa5c8, 0x3f97, 0x5bde, 0x9361,
    0x33ba, 0x4034, 0x7693, 0x907b, 0xa7a0, 0x4097,
};
static unsigned short Q[] = {
    /*0x0000,0x0000,0x0000,0x3ff0,*/
    0x5c3c, 0x0ffb, 0x25e5, 0x406d, 0x0bae, 0x2fed, 0x1036, 0x40b1,
};
#define MAXL2 1024.0
#define MINL2 -1022.0
#endif

#ifdef MIEEE
static unsigned short P[] = {
    0x3f97, 0xa5c8, 0x549a, 0xead3, 0x4034, 0x33ba,
    0x9361, 0x5bde, 0x4097, 0xa7a0, 0x907b, 0x7693,
};
static unsigned short Q[] = {
    /*0x3ff0,0x0000,0x0000,0x0000,*/
    0x406d, 0x25e5, 0x0ffb, 0x5c3c, 0x40b1, 0x1036, 0x2fed, 0x0bae,
};
#define MAXL2 1024.0
#define MINL2 -1022.0
#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
#ifdef INFINITIES
extern double INFINITY;
#endif
extern double MAXNUM;

double exp2(x) double x;
{
  double px, xx;
  short n;

#ifdef NANS
  if (isnan(x))
    return (x);
#endif
  if (x > MAXL2) {
#ifdef INFINITIES
    return (INFINITY);
#else
    mtherr("exp2", OVERFLOW);
    return (MAXNUM);
#endif
  }

  if (x < MINL2) {
#ifndef INFINITIES
    mtherr("exp2", UNDERFLOW);
#endif
    return (0.0);
  }

  xx = x; /* save x */
  /* separate into integer and fractional parts */
  px = floor(x + 0.5);
  n = px;
  x = x - px;

  /* rational approximation
   * exp2(x) = 1 +  2xP(xx)/(Q(xx) - P(xx))
   * where xx = x**2
   */
  xx = x * x;
  px = x * polevl(xx, P, 2);
  x = px / (p1evl(xx, Q, 2) - px);
  x = 1.0 + ldexp(x, 1);

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