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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(x)
double x;
{
double w, y, z;
int flag;
if (x < 0.0) {
mtherr("spence", DOMAIN);
return (NPY_NAN);
}
if (x == 1.0)
return (0.0);
if (x == 0.0)
return (NPY_PI * NPY_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 = (NPY_PI * NPY_PI) / 6.0 - log(x) * log(1.0 - x) - y;
if (flag & 2) {
z = log(x);
y = -0.5 * z * z - y;
}
return (y);
}
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