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Diffstat (limited to 'libm/double/spence.c')
| -rw-r--r-- | libm/double/spence.c | 205 |
1 files changed, 205 insertions, 0 deletions
diff --git a/libm/double/spence.c b/libm/double/spence.c new file mode 100644 index 000000000..e2a56176b --- /dev/null +++ b/libm/double/spence.c @@ -0,0 +1,205 @@ +/* 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 ); +} |