spence.c

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/*                                                     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
 *
 *
 */

/*                                                     spence.c */
 
 
/*
 * Cephes Math Library Release 2.1:  January, 1989
 * Copyright 1985, 1987, 1989 by Stephen L. Moshier
 * Direct inquiries to 30 Frost Street, Cambridge, MA 02140
 */
 
#include "mconf.h"
 
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,
};
 
extern double MACHEP;
 
double spence(double x)
{
    double w, y, z;
    int flag;
 
    if (x < 0.0) {
        sf_error("spence", SF_ERROR_DOMAIN, NULL);
        return (NAN);
    }
 
    if (x == 1.0)
        return (0.0);
 
    if (x == 0.0)
        return (M_PI * M_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 = (M_PI * M_PI) / 6.0 - log(x) * log(1.0 - x) - y;
 
    if (flag & 2) {
        z = log(x);
        y = -0.5 * z * z - y;
    }
 
    return (y);
}