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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
* 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 <math.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 );
}
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