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/* spencef.c
*
* Dilogarithm
*
*
*
* SYNOPSIS:
*
* float x, y, spencef();
*
* y = spencef( 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 4.4e-7 6.3e-8
*
*
*/
/* 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 <math.h>
static float A[8] = {
4.65128586073990045278E-5,
7.31589045238094711071E-3,
1.33847639578309018650E-1,
8.79691311754530315341E-1,
2.71149851196553469920E0,
4.25697156008121755724E0,
3.29771340985225106936E0,
1.00000000000000000126E0,
};
static float B[8] = {
6.90990488912553276999E-4,
2.54043763932544379113E-2,
2.82974860602568089943E-1,
1.41172597751831069617E0,
3.63800533345137075418E0,
5.03278880143316990390E0,
3.54771340985225096217E0,
9.99999999999999998740E-1,
};
extern float PIF, MACHEPF;
/* pi * pi / 6 */
#define PIFS 1.64493406684822643647
float logf(float), polevlf(float, float *, int);
float spencef(float xx)
{
float x, w, y, z;
int flag;
x = xx;
if( x < 0.0 )
{
mtherr( "spencef", DOMAIN );
return(0.0);
}
if( x == 1.0 )
return( 0.0 );
if( x == 0.0 )
return( PIFS );
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 * polevlf( w, A, 7) / polevlf( w, B, 7 );
if( flag & 1 )
y = PIFS - logf(x) * logf(1.0-x) - y;
if( flag & 2 )
{
z = logf(x);
y = -0.5 * z * z - y;
}
return( y );
}
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