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

/*							spence.c
 *
 *	Dilogarithm
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, spence();
 *
 * y = spence( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Computes the integral
 *
 *                    x
 *                    -
 *                   | | log t
 * spence(x)  =  -   |   ----- dt
 *                 | |   t - 1
 *                  -
 *                  1
 *
 * for x >= 0.  A rational approximation gives the integral in
 * the interval (0.5, 1.5).  Transformation formulas for 1/x
 * and 1-x are employed outside the basic expansion range.
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0,4         30000       3.9e-15     5.4e-16
 *    DEC       0,4          3000       2.5e-16     4.5e-17
 *
 *
 */

/*							spence.c */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1985, 1987, 1989, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

#ifdef UNK
static double A[8] = {
    4.65128586073990045278E-5, 7.31589045238094711071E-3,
    1.33847639578309018650E-1, 8.79691311754530315341E-1,
    2.71149851196553469920E0,  4.25697156008121755724E0,
    3.29771340985225106936E0,  1.00000000000000000126E0,
};
static double B[8] = {
    6.90990488912553276999E-4, 2.54043763932544379113E-2,
    2.82974860602568089943E-1, 1.41172597751831069617E0,
    3.63800533345137075418E0,  5.03278880143316990390E0,
    3.54771340985225096217E0,  9.99999999999999998740E-1,
};
#endif
#ifdef DEC
static unsigned short A[32] = {
    0034503, 0013315, 0034120, 0157771, 0036357, 0135043, 0016766, 0150637,
    0037411, 0007533, 0005212, 0161475, 0040141, 0031563, 0023217, 0120331,
    0040455, 0104461, 0007002, 0155522, 0040610, 0034434, 0065721, 0120465,
    0040523, 0006674, 0105671, 0054427, 0040200, 0000000, 0000000, 0000000,
};
static unsigned short B[32] = {
    0035465, 0021626, 0032367, 0144157, 0036720, 0016326, 0134431, 0000406,
    0037620, 0161024, 0133701, 0120766, 0040264, 0131557, 0152055, 0064512,
    0040550, 0152424, 0051166, 0034272, 0040641, 0006233, 0014672, 0111572,
    0040543, 0006674, 0105671, 0054425, 0040200, 0000000, 0000000, 0000000,
};
#endif
#ifdef IBMPC
static unsigned short A[32] = {
    0x1bff, 0xa70a, 0x62d9, 0x3f08, 0xda34, 0x63be, 0xf744, 0x3f7d,
    0x5c68, 0x6151, 0x21eb, 0x3fc1, 0xf41b, 0x64d1, 0x266e, 0x3fec,
    0x5b6a, 0x21c0, 0xb126, 0x4005, 0x3427, 0x8d7a, 0x0723, 0x4011,
    0x2b23, 0x9177, 0x61b7, 0x400a, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
static unsigned short B[32] = {
    0xf90e, 0xc69e, 0xa472, 0x3f46, 0x2021, 0xd723, 0x039a, 0x3f9a,
    0x343f, 0x96f8, 0x1c42, 0x3fd2, 0xad29, 0xfa85, 0x966d, 0x3ff6,
    0xc717, 0x8a4e, 0x1aa2, 0x400d, 0x526f, 0x6337, 0x2193, 0x4014,
    0x2b23, 0x9177, 0x61b7, 0x400c, 0x0000, 0x0000, 0x0000, 0x3ff0,
};
#endif
#ifdef MIEEE
static unsigned short A[32] = {
    0x3f08, 0x62d9, 0xa70a, 0x1bff, 0x3f7d, 0xf744, 0x63be, 0xda34,
    0x3fc1, 0x21eb, 0x6151, 0x5c68, 0x3fec, 0x266e, 0x64d1, 0xf41b,
    0x4005, 0xb126, 0x21c0, 0x5b6a, 0x4011, 0x0723, 0x8d7a, 0x3427,
    0x400a, 0x61b7, 0x9177, 0x2b23, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
static unsigned short B[32] = {
    0x3f46, 0xa472, 0xc69e, 0xf90e, 0x3f9a, 0x039a, 0xd723, 0x2021,
    0x3fd2, 0x1c42, 0x96f8, 0x343f, 0x3ff6, 0x966d, 0xfa85, 0xad29,
    0x400d, 0x1aa2, 0x8a4e, 0xc717, 0x4014, 0x2193, 0x6337, 0x526f,
    0x400c, 0x61b7, 0x9177, 0x2b23, 0x3ff0, 0x0000, 0x0000, 0x0000,
};
#endif

#ifdef ANSIPROT
extern double fabs(double);
extern double log(double);
extern double polevl(double, void *, int);
#else
double fabs(), log(), polevl();
#endif
extern double PI, MACHEP;

double spence(x) double x;
{
  double w, y, z;
  int flag;

  if (x < 0.0) {
    mtherr("spence", DOMAIN);
    return (0.0);
  }

  if (x == 1.0)
    return (0.0);

  if (x == 0.0)
    return (PI * PI / 6.0);

  flag = 0;

  if (x > 2.0) {
    x = 1.0 / x;
    flag |= 2;
  }

  if (x > 1.5) {
    w = (1.0 / x) - 1.0;
    flag |= 2;
  }

  else if (x < 0.5) {
    w = -x;
    flag |= 1;
  }

  else
    w = x - 1.0;

  y = -w * polevl(w, A, 7) / polevl(w, B, 7);

  if (flag & 1)
    y = (PI * PI) / 6.0 - log(x) * log(1.0 - x) - y;

  if (flag & 2) {
    z = log(x);
    y = -0.5 * z * z - y;
  }

  return (y);
}