126 lines
2.2 KiB
C
126 lines
2.2 KiB
C
/* spence.c
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*
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* Dilogarithm
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, spence();
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*
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* y = spence( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Computes the integral
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*
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* x
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* -
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* | | log t
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* spence(x) = - | ----- dt
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* | | t - 1
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* -
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* 1
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*
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* for x >= 0. A rational approximation gives the integral in
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* the interval (0.5, 1.5). Transformation formulas for 1/x
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* and 1-x are employed outside the basic expansion range.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,4 30000 3.9e-15 5.4e-16
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*
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*
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*/
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/* spence.c */
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/*
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* Cephes Math Library Release 2.1: January, 1989
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* Copyright 1985, 1987, 1989 by Stephen L. Moshier
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* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
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*/
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#include "mconf.h"
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static double A[8] = {
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4.65128586073990045278E-5,
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7.31589045238094711071E-3,
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1.33847639578309018650E-1,
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8.79691311754530315341E-1,
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2.71149851196553469920E0,
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4.25697156008121755724E0,
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3.29771340985225106936E0,
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1.00000000000000000126E0,
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};
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static double B[8] = {
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6.90990488912553276999E-4,
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2.54043763932544379113E-2,
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2.82974860602568089943E-1,
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1.41172597751831069617E0,
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3.63800533345137075418E0,
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5.03278880143316990390E0,
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3.54771340985225096217E0,
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9.99999999999999998740E-1,
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};
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extern double MACHEP;
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double spence(double x)
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{
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double w, y, z;
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int flag;
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if (x < 0.0) {
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sf_error("spence", SF_ERROR_DOMAIN, NULL);
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return (NAN);
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}
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if (x == 1.0)
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return (0.0);
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if (x == 0.0)
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return (M_PI * M_PI / 6.0);
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flag = 0;
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if (x > 2.0) {
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x = 1.0 / x;
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flag |= 2;
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}
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if (x > 1.5) {
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w = (1.0 / x) - 1.0;
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flag |= 2;
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}
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else if (x < 0.5) {
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w = -x;
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flag |= 1;
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}
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else
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w = x - 1.0;
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y = -w * polevl(w, A, 7) / polevl(w, B, 7);
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if (flag & 1)
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y = (M_PI * M_PI) / 6.0 - log(x) * log(1.0 - x) - y;
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if (flag & 2) {
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z = log(x);
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y = -0.5 * z * z - y;
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}
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return (y);
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}
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