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// @(#)root/mathcore:$Id$
// Authors: Andras Zsenei & Lorenzo Moneta 06/2005
/**********************************************************************
* *
* Copyright (c) 2005 , LCG ROOT MathLib Team *
* *
* *
**********************************************************************/
#if defined(__sun) || defined(__sgi) || defined(_WIN32) || defined(_AIX)
#define NOT_HAVE_TGAMMA
#endif
#include "SpecFuncCephes.h"
#include <cmath>
#include <limits>
#ifndef PI
#define PI 3.14159265358979323846264338328 /* pi */
#endif
// use cephes for functions which are also in C99
#define USE_CEPHES
// platforms not implemening C99
// #if defined(__sun) || defined(__sgi) || defined(_WIN32) || defined(_AIX)
// #define USE_CEPHES
// #endif
namespace ROOT {
namespace Math {
// (26.x.21.2) complementary error function
double erfc(double x) {
#ifdef USE_CEPHES
// use cephes implementation
return ROOT::Math::Cephes::erfc(x);
#else
return ::erfc(x);
#endif
}
// (26.x.21.1) error function
double erf(double x) {
#ifdef USE_CEPHES
return ROOT::Math::Cephes::erf(x);
#else
return ::erf(x);
#endif
}
double lgamma(double z) {
#ifdef USE_CEPHES
return ROOT::Math::Cephes::lgam(z);
#else
return ::lgamma(z);
#endif
}
// (26.x.18) gamma function
double tgamma(double x) {
#ifdef USE_CEPHES
return ROOT::Math::Cephes::gamma(x);
#else
return ::tgamma(x);
#endif
}
double inc_gamma( double a, double x) {
return ROOT::Math::Cephes::igam(a,x);
}
double inc_gamma_c( double a, double x) {
return ROOT::Math::Cephes::igamc(a,x);
}
// [5.2.1.3] beta function
// (26.x.19)
double beta(double x, double y) {
return std::exp(lgamma(x)+lgamma(y)-lgamma(x+y));
}
double inc_beta( double x, double a, double b) {
return ROOT::Math::Cephes::incbet(a,b,x);
}
// Sine integral
// Translated from CERNLIB SININT (C336) by B. List 29.4.2010
double sinint(double x) {
static const double z1 = 1, r8 = z1/8;
static const double pih = PI/2;
static const double s[16] = {
+1.95222097595307108, -0.68840423212571544,
+0.45518551322558484, -0.18045712368387785,
+0.04104221337585924, -0.00595861695558885,
+0.00060014274141443, -0.00004447083291075,
+0.00000253007823075, -0.00000011413075930,
+0.00000000418578394, -0.00000000012734706,
+0.00000000000326736, -0.00000000000007168,
+0.00000000000000136, -0.00000000000000002};
static const double p[29] = {
+0.96074783975203596, -0.03711389621239806,
+0.00194143988899190, -0.00017165988425147,
+0.00002112637753231, -0.00000327163256712,
+0.00000060069211615, -0.00000012586794403,
+0.00000002932563458, -0.00000000745695921,
+0.00000000204105478, -0.00000000059502230,
+0.00000000018322967, -0.00000000005920506,
+0.00000000001996517, -0.00000000000699511,
+0.00000000000253686, -0.00000000000094929,
+0.00000000000036552, -0.00000000000014449,
+0.00000000000005851, -0.00000000000002423,
+0.00000000000001025, -0.00000000000000442,
+0.00000000000000194, -0.00000000000000087,
+0.00000000000000039, -0.00000000000000018,
+0.00000000000000008};
static const double q[25] = {
+0.98604065696238260, -0.01347173820829521,
+0.00045329284116523, -0.00003067288651655,
+0.00000313199197601, -0.00000042110196496,
+0.00000006907244830, -0.00000001318321290,
+0.00000000283697433, -0.00000000067329234,
+0.00000000017339687, -0.00000000004786939,
+0.00000000001403235, -0.00000000000433496,
+0.00000000000140273, -0.00000000000047306,
+0.00000000000016558, -0.00000000000005994,
+0.00000000000002237, -0.00000000000000859,
+0.00000000000000338, -0.00000000000000136,
+0.00000000000000056, -0.00000000000000024,
+0.00000000000000010};
double h;
if (std::abs(x) <= 8) {
double y = r8*x;
h = 2*y*y-1;
double alfa = h+h;
double b0 = 0;
double b1 = 0;
double b2 = 0;
for (int i = 15; i >= 0; --i) {
b0 = s[i]+alfa*b1-b2;
b2 = b1;
b1 = b0;
}
h = y*(b0-b2);
} else {
double r = 1/x;
h = 128*r*r-1;
double alfa = h+h;
double b0 = 0;
double b1 = 0;
double b2 = 0;
for (int i = 28; i >= 0; --i) {
b0 = p[i]+alfa*b1-b2;
b2 = b1;
b1 = b0;
}
double pp = b0-h*b2;
b1 = 0;
b2 = 0;
for (int i = 24; i >= 0; --i) {
b0 = q[i]+alfa*b1-b2;
b2 = b1;
b1 = b0;
}
h = (x > 0 ? pih : -pih)-r*(r*pp*std::sin(x)+(b0-h*b2)*std::cos(x));
}
return h;
}
// Real part of the cosine integral
// Translated from CERNLIB COSINT (C336) by B. List 29.4.2010
double cosint(double x) {
static const double z1 = 1, r32 = z1/32;
static const double ce = 0.57721566490153286;
static const double c[16] = {
+1.94054914648355493, +0.94134091328652134,
-0.57984503429299276, +0.30915720111592713,
-0.09161017922077134, +0.01644374075154625,
-0.00197130919521641, +0.00016925388508350,
-0.00001093932957311, +0.00000055223857484,
-0.00000002239949331, +0.00000000074653325,
-0.00000000002081833, +0.00000000000049312,
-0.00000000000001005, +0.00000000000000018};
static const double p[29] = {
+0.96074783975203596, -0.03711389621239806,
+0.00194143988899190, -0.00017165988425147,
+0.00002112637753231, -0.00000327163256712,
+0.00000060069211615, -0.00000012586794403,
+0.00000002932563458, -0.00000000745695921,
+0.00000000204105478, -0.00000000059502230,
+0.00000000018322967, -0.00000000005920506,
+0.00000000001996517, -0.00000000000699511,
+0.00000000000253686, -0.00000000000094929,
+0.00000000000036552, -0.00000000000014449,
+0.00000000000005851, -0.00000000000002423,
+0.00000000000001025, -0.00000000000000442,
+0.00000000000000194, -0.00000000000000087,
+0.00000000000000039, -0.00000000000000018,
+0.00000000000000008};
static const double q[25] = {
+0.98604065696238260, -0.01347173820829521,
+0.00045329284116523, -0.00003067288651655,
+0.00000313199197601, -0.00000042110196496,
+0.00000006907244830, -0.00000001318321290,
+0.00000000283697433, -0.00000000067329234,
+0.00000000017339687, -0.00000000004786939,
+0.00000000001403235, -0.00000000000433496,
+0.00000000000140273, -0.00000000000047306,
+0.00000000000016558, -0.00000000000005994,
+0.00000000000002237, -0.00000000000000859,
+0.00000000000000338, -0.00000000000000136,
+0.00000000000000056, -0.00000000000000024,
+0.00000000000000010};
double h = 0;
if(x == 0) {
h = - std::numeric_limits<double>::infinity();
} else if (std::abs(x) <= 8) {
h = r32*x*x-1;
double alfa = h+h;
double b0 = 0;
double b1 = 0;
double b2 = 0;
for (int i = 15; i >= 0; --i) {
b0 = c[i]+alfa*b1-b2;
b2 = b1;
b1 = b0;
}
h = ce+std::log(std::abs(x))-b0+h*b2;
} else {
double r = 1/x;
h = 128*r*r-1;
double alfa = h+h;
double b0 = 0;
double b1 = 0;
double b2 = 0;
for (int i = 28; i >= 0; --i) {
b0 = p[i]+alfa*b1-b2;
b2 = b1;
b1 = b0;
}
double pp = b0-h*b2;
b1 = 0;
b2 = 0;
for (int i = 24; i >= 0; --i) {
b0 = q[i]+alfa*b1-b2;
b2 = b1;
b1 = b0;
}
h = r*((b0-h*b2)*std::sin(x)-r*pp*std::cos(x));
}
return h;
}
} // namespace Math
} // namespace ROOT
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