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libreoffice/sc/source/core/opencl/opinlinefun_statistical.cxx
Tor Lillqvist 4afa88f289 No need for own implementation of erfc() in OpenCL 
The own code was copied from the C++ one we used to have in
sal/rtl/math.cxx but which was removed in
a62bc6a65a. However, it did not work
correctly on some machines at least, like my AMD A10-7800 running
Windows 10. I was unable to figure out why not. This lead to OpenCL
being disabled by the Desktop::CheckOpenCLCompute() code we now run
early on startup.

Anyway, as OpenCL has erfc(), just use that.

Change-Id: I7ba6104fc4975cd570358760fa97a19390a54cce
2016-07-25 19:26:25 +03:00

1367 lines
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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
* This file is part of the LibreOffice project.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*/
#ifndef SC_OPENCL_OPINLINFUN_statistical
#define SC_OPENCL_OPINLINFUN_statistical
std::string MinDecl = "#define Min 2.22507e-308\n";
std::string F_PIDecl="#define F_PI 3.1415926\n";
std::string fBigInvDecl ="#define fBigInv 2.22045e-016\n";
std::string fMachEpsDecl ="#define fMachEps 2.22045e-016\n";
std::string fLogDblMaxDecl ="#define fLogDblMax log(1.79769e+308)\n";
std::string fHalfMachEpsDecl ="#define fHalfMachEps 0.5*2.22045e-016\n";
std::string fMaxGammaArgumentDecl=
"#define fMaxGammaArgument 171.624376956302\n";
std::string GetValueDecl=
"double GetValue( double x,double fp,double fDF );\n";
std::string GetValue=
"double GetValue( double x,double fp,double fDF )\n"
"{\n"
" return fp - 2 * GetTDist(x, fDF);\n"
"}\n";
std::string GetGammaSeriesDecl=
"double GetGammaSeries( double fA, double fX );\n";
std::string GetGammaSeries =
"double GetGammaSeries( double fA, double fX )\n"
"{\n"
" double fDenomfactor = fA;\n"
" double fSummand = 1.0/fA;\n"
" double fSum = fSummand;\n"
" int nCount=1;\n"
" do\n"
" {\n"
" fDenomfactor = fDenomfactor + 1.0;\n"
" fSummand = fSummand * fX/fDenomfactor;\n"
" fSum = fSum + fSummand;\n"
" nCount = nCount+1;\n"
" } while ( fSummand/fSum > fHalfMachEps && nCount<=10000);\n"
" if (nCount>10000)\n"
" {\n"
" }\n"
" return fSum;\n"
"}\n";
std::string GetGammaContFractionDecl = "double GetGammaContFraction( double "
"fA, double fX );\n";
std::string GetGammaContFraction =
"double GetGammaContFraction( double fA, double fX )\n"
"{\n"
" double fBig = 1.0/fBigInv;\n"
" double fCount = 0.0;\n"
" double fNum = 0.0;\n"
" double fY = 1.0 - fA;\n"
" double fDenom = fX + 2.0-fA;\n"
" double fPk = 0.0;\n"
" double fPkm1 = fX + 1.0;\n"
" double fPkm2 = 1.0;\n"
" double fQk = 1.0;\n"
" double fQkm1 = fDenom * fX;\n"
" double fQkm2 = fX;\n"
" double fApprox = fPkm1/fQkm1;\n"
" bool bFinished = false;\n"
" double fR = 0.0;\n"
" do\n"
" {\n"
" fCount = fCount +1.0;\n"
" fY = fY+ 1.0;\n"
" fNum = fY * fCount;\n"
" fDenom = fDenom +2.0;\n"
" fPk = fPkm1 * fDenom - fPkm2 * fNum;\n"
" fQk = fQkm1 * fDenom - fQkm2 * fNum;\n"
" if (fQk != 0.0)\n"
" {\n"
" fR = fPk/fQk;\n"
" bFinished = (fabs( (fApprox - fR)/fR ) <= fHalfMachEps);\n"
" fApprox = fR;\n"
" }\n"
" fPkm2 = fPkm1;\n"
" fPkm1 = fPk;\n"
" fQkm2 = fQkm1;\n"
" fQkm1 = fQk;\n"
" if (fabs(fPk) > fBig)\n"
" {\n"
" fPkm2 = fPkm2 * fBigInv;\n"
" fPkm1 = fPkm1 * fBigInv;\n"
" fQkm2 = fQkm2 * fBigInv;\n"
" fQkm1 = fQkm1 * fBigInv;\n"
" }\n"
" } while (!bFinished && fCount<10000);\n"
" if (!bFinished)\n"
" {\n"
" }\n"
" return fApprox;\n"
"}\n";
std::string GetLowRegIGammaDecl = "double GetLowRegIGamma( double "
"fA, double fX );\n";
std::string GetLowRegIGamma =
"double GetLowRegIGamma( double fA, double fX )\n"
"{\n"
" double fLnFactor = fA * log(fX) - fX - lgamma(fA);\n"
" double fFactor = exp(fLnFactor);\n"
" if (fX>fA+1.0) \n"
" return 1.0 - fFactor * GetGammaContFraction(fA,fX);\n"
" else\n"
" return fFactor * GetGammaSeries(fA,fX);\n"
"}\n";
std::string GetGammaDistDecl = "double GetGammaDist( double fX, double "
"fAlpha, double fLambda );\n";
std::string GetGammaDist =
"double GetGammaDist( double fX, double fAlpha, double fLambda )\n"
"{\n"
" if (fX <= 0.0)\n"
" return 0.0;\n"
" else\n"
" return GetLowRegIGamma( fAlpha, fX / fLambda);\n"
"}\n";
std::string GetGammaDistPDFDecl = "double GetGammaDistPDF( double fX"
", double fAlpha, double fLambda );\n";
std::string GetGammaDistPDF =
"double GetGammaDistPDF( double fX, double fAlpha, double fLambda )\n"
"{\n"
" if (fX < 0.0)\n"
" return 0.0;\n"
" else if (fX == 0)\n"
" {\n"
" if (fAlpha < 1.0)\n"
" {\n"
" return HUGE_VAL;\n"
" }\n"
" else if (fAlpha == 1)\n"
" {\n"
" return (1.0 / fLambda);\n"
" }\n"
" else\n"
" {\n"
" return 0.0;\n"
" }\n"
" }\n"
" else\n"
" {\n"
" double fXr = fX / fLambda;\n"
" if (fXr > 1.0)\n"
" {\n"
" if (log(fXr) * (fAlpha-1.0) < fLogDblMax &&"
"fAlpha < fMaxGammaArgument)\n"
" {\n"
" return pow( fXr, fAlpha-1.0) * exp(-fXr) / "
"fLambda / tgamma(fAlpha);\n"
" }\n"
" else\n"
" {\n"
" return exp( (fAlpha-1.0) * log(fXr) - fXr - "
"log(fLambda) - lgamma(fAlpha));\n"
" }\n"
" }\n"
" else\n"
" {\n"
" if (fAlpha<fMaxGammaArgument)\n"
" {\n"
" return pow( fXr, fAlpha-1.0) * exp(-fXr) / "
"fLambda / tgamma(fAlpha);\n"
" }\n"
" else\n"
" {\n"
" return pow( fXr, fAlpha-1.0) * exp(-fXr) / "
"fLambda / exp( lgamma(fAlpha));\n"
" }\n"
" }\n"
" }\n"
"}\n";
std::string GetBetaDistDecl =
"double GetBetaDist(double fXin, double fAlpha, double fBeta);\n";
std::string GetBetaDist =
"double GetBetaDist(double fXin, double fAlpha, double fBeta)\n"
"{\n"
" if (fXin <= 0.0)\n"
" return 0.0;\n"
" if (fXin >= 1.0)\n"
" return 1.0;\n"
" if (fBeta == 1.0)\n"
" return pow(fXin, fAlpha);\n"
" if (fAlpha == 1.0)\n"
" return -expm1(fBeta * log1p(-fXin));\n"
" double fResult;\n"
" double fY = (0.5-fXin)+0.5;\n"
" double flnY = log1p(-fXin);\n"
" double fX = fXin;\n"
" double flnX = log(fXin);\n"
" double fA = fAlpha;\n"
" double fB = fBeta;\n"
" bool bReflect = fXin > fAlpha*pow((fAlpha+fBeta),-1.0);\n"
" if (bReflect)\n"
" {\n"
" fA = fBeta;\n"
" fB = fAlpha;\n"
" fX = fY;\n"
" fY = fXin;\n"
" flnX = flnY;\n"
" flnY = log(fXin);\n"
" }\n"
" fResult = lcl_GetBetaHelperContFrac(fX,fA,fB)*pow(fA,-1.0);\n"
" double fP = fA*pow((fA+fB),-1.0);\n"
" double fQ = fB*pow((fA+fB),-1.0);\n"
" if (fA > 1.0 && fB > 1.0 && fP < 0.97 && fQ < 0.97)\n"
" fResult *= GetBetaDistPDF(fX,fA,fB)*fX*fY;\n"
" else\n"
" fResult *= pow(exp(1.0),(fA*flnX + fB*flnY - GetLogBeta(fA,fB)));\n"
" if (bReflect)\n"
" fResult = 0.5 - fResult + 0.5;\n"
" if (fResult > 1.0)\n"
" fResult = 1.0;\n"
" if (fResult < 0.0)\n"
" fResult = 0.0;\n"
" return fResult;\n"
"}\n";
std::string GetFDistDecl =
"double GetFDist(double x, double fF1, double fF2);\n";
std::string GetFDist =
"double GetFDist(double x, double fF1, double fF2)\n"
"{\n"
" double arg = fF2*pow((fF2+fF1*x),-1.0);\n"
" double alpha = fF2*pow(2.0,-1.0);\n"
" double beta = fF1*pow(2.0,-1.0);\n"
" return (GetBetaDist(arg, alpha, beta));\n"
"}\n";
std::string GetGammaInvValueDecl = "double"
" GetGammaInvValue(double fAlpha,double fBeta,double fX1 );\n";
std::string GetGammaInvValue =
"double GetGammaInvValue(double fAlpha,double fBeta,double fX1 )\n"
"{\n"
" if (fX1 <= 0.0)\n"
" return 0.0;\n"
" else\n"
" {\n"
" double fX=fX1*pow(fBeta,-1.0);\n"
" double fLnFactor = fAlpha * log(fX) - fX - lgamma(fAlpha);\n"
" double fFactor = exp(fLnFactor);\n"
" if (fX>fAlpha+1.0)\n"
" return 1.0 - fFactor * GetGammaContFraction(fAlpha,fX);\n"
" else\n"
" return fFactor * GetGammaSeries(fAlpha,fX);\n"
" }\n"
"}\n";
std::string GetFInvValueDecl = "double GetFInvValue(double fF1,double fF2"
",double fX1 );";
std::string GetFInvValue =
"double GetFInvValue(double fF1,double fF2,double fX1 )\n"
"{\n"
" double arg = fF2*pow((fF2+fF1*fX1),-1.0);\n"
" double alpha = fF2*pow(2.0,-1.0);\n"
" double beta = fF1*pow(2.0,-1.0);\n"
" double fXin,fAlpha,fBeta;\n"
" fXin=arg;fAlpha=alpha;fBeta=beta;\n"
" if (fXin <= 0.0)\n"
" return 0.0;\n"
" if (fXin >= 1.0)\n"
" return 1.0;\n"
" if (fBeta == 1.0)\n"
" return pow(fXin, fAlpha);\n"
" if (fAlpha == 1.0)\n"
" return -expm1(fBeta * log1p(-fXin));\n"
" double fResult;\n"
" double fY = (0.5-fXin)+0.5;\n"
" double flnY = log1p(-fXin);\n"
" double fX = fXin;\n"
" double flnX = log(fXin);\n"
" double fA = fAlpha;\n"
" double fB = fBeta;\n"
" bool bReflect = fXin > fAlpha*pow((fAlpha+fBeta),-1.0);\n"
" if (bReflect)\n"
" {\n"
" fA = fBeta;\n"
" fB = fAlpha;\n"
" fX = fY;\n"
" fY = fXin;\n"
" flnX = flnY;\n"
" flnY = log(fXin);\n"
" }\n"
" fResult = lcl_GetBetaHelperContFrac(fX,fA,fB);\n"
" fResult = fResult*pow(fA,-1.0);\n"
" double fP = fA*pow((fA+fB),-1.0);\n"
" double fQ = fB*pow((fA+fB),-1.0);\n"
" double fTemp;\n"
" if (fA > 1.0 && fB > 1.0 && fP < 0.97 && fQ < 0.97)\n"
" fTemp = GetBetaDistPDF(fX,fA,fB)*fX*fY;\n"
" else\n"
" fTemp = exp(fA*flnX + fB*flnY - GetLogBeta(fA,fB));\n"
" fResult *= fTemp;\n"
" if (bReflect)\n"
" fResult = 0.5 - fResult + 0.5;\n"
" if (fResult > 1.0)\n"
" fResult = 1.0;\n"
" if (fResult < 0.0)\n"
" fResult = 0.0;\n"
" return fResult;\n"
"}\n";
std::string GetBinomDistPMFDecl =
"double GetBinomDistPMF(double x, double n, double p);";
std::string GetBinomDistPMF =
"double GetBinomDistPMF(double x, double n, double p)\n"
"{\n"
" double q = (0.5 - p) + 0.5;\n"
" double fFactor = pow(q, n);\n"
" if (fFactor <= Min)\n"
" {\n"
" fFactor = pow(p, n);\n"
" if (fFactor <= Min)\n"
" return GetBetaDistPDF(p, x + 1.0, n - x + 1.0)*pow((n + 1.0),-1.0);\n"
" else\n"
" {\n"
" uint max = (uint)(n - x);\n"
" for (uint i = 0; i < max && fFactor > 0.0; ++i)\n"
" fFactor *= (n - i)*pow((i + 1),-1.0)*q*pow(p,-1.0);\n"
" return fFactor;\n"
" }\n"
" }\n"
" else\n"
" {\n"
" uint max = (uint)x;\n"
" for (uint i = 0; i < max && fFactor > 0.0; ++i)\n"
" fFactor *= (n - i)*pow((i + 1),-1.0)*p*pow(q,-1.0);\n"
" return fFactor;\n"
" }\n"
"}\n";
std::string lcl_GetBinomDistRangeDecl =
"double lcl_GetBinomDistRange(double n, \n"
"double xs, double xe, double fFactor, double p, double q);";
std::string lcl_GetBinomDistRange=
"double lcl_GetBinomDistRange(double n, double xs, double xe,\n"
" double fFactor, double p, double q)\n"
"{\n"
" uint i;\n"
" double fSum;\n"
" uint nXs = (uint)xs;\n"
" for (i = 1; i <= nXs && fFactor > 0.0; ++i)\n"
" fFactor *= (n - i + 1)*pow(i,-1.0)*p*pow(q,-1.0);\n"
" fSum = fFactor;\n"
" uint nXe =(uint)xe;\n"
" for (i = nXs + 1; i <= nXe && fFactor > 0.0; ++i)\n"
" {\n"
" fFactor *= (n - i + 1)*pow(i,-1.0)*p*pow(q,-1.0);\n"
" fSum += fFactor;\n"
" }\n"
" return (fSum > 1.0) ? 1.0 : fSum;\n"
"}\n";
std::string GetLogGammaDecl = "double GetLogGamma(double fZ);\n";
std::string GetLogGamma =
"double GetLogGamma(double fZ)\n"
"{\n"
" if (fZ >= fMaxGammaArgument)\n"
" return lcl_GetLogGammaHelper(fZ);\n"
" if (fZ >= 1.0)\n"
" return log(lcl_GetGammaHelper(fZ));\n"
" if (fZ >= 0.5)\n"
" return log( lcl_GetGammaHelper(fZ+1) *pow(fZ,-1.0));\n"
" return lcl_GetLogGammaHelper(fZ+2) - log(fZ+1) - log(fZ);\n"
"}\n";
std::string GetChiDistDecl = "double GetChiDist(double fX, double fDF);\n";
std::string GetChiDist =
"double GetChiDist(double fX, double fDF)\n"
"{\n"
" if (fX <= 0.0)\n"
" return 1.0;\n"
" else\n"
" return GetUpRegIGamma( fDF*pow(2.0,-1.0), fX*pow(2.0,-1.0));\n"
"}\n";
std::string GetChiSqDistCDFDecl =
"double GetChiSqDistCDF(double fX, double fDF);\n";
std::string GetChiSqDistCDF =
"double GetChiSqDistCDF(double fX, double fDF)\n"
"{\n"
" if (fX <= 0.0)\n"
" return 0.0;"
" else\n"
" return GetLowRegIGamma( fDF*pow(2.0,-1.0), fX*pow(2.0,-1.0));\n"
"}\n";
std::string GetChiSqDistPDFDecl=
"double GetChiSqDistPDF(double fX, double fDF);\n";
std::string GetChiSqDistPDF =
"double GetChiSqDistPDF(double fX, double fDF)\n"
"{\n"
" double fValue;\n"
" if (fX <= 0.0)\n"
" return 0.0;\n"
" if (fDF*fX > 1391000.0)\n"
" {\n"
" fValue = exp((0.5*fDF - 1) * log(fX*0.5) - 0.5 * fX - log(2.0)"
" - lgamma(0.5*fDF));\n"
" }\n"
" else\n"
" {\n"
" double fCount;\n"
" if (fmod(fDF,2.0)<0.5)\n"
" {\n"
" fValue = 0.5;\n"
" fCount = 2.0;\n"
" }\n"
" else\n"
" {\n"
" fValue = pow(sqrt(fX*2*F_PI),-1.0);\n"
" fCount = 1.0;\n"
" }\n"
" while ( fCount < fDF)\n"
" {\n"
" fValue *= (fX *pow(fCount,-1.0));\n"
" fCount += 2.0;\n"
" }\n"
" if (fX>=1425.0)\n"
" fValue = exp(log(fValue)-fX*pow(2,-1.0));\n"
" else\n"
" fValue *= exp(-fX*pow(2,-1.0));\n"
" }\n"
" return fValue;\n"
"}\n";
std::string lcl_IterateInverseBetaInvDecl =
"static double lcl_IterateInverseBetaInv(double fp, double fAlpha, \n"
" double fBeta, double fAx, double fBx, bool *rConvError );\n";
std::string lcl_IterateInverseBetaInv =
"static double lcl_IterateInverseBetaInv(double fp, double fAlpha, \n"
" double fBeta, double fAx, double fBx, bool *rConvError )\n"
"{\n"
" *rConvError = false;\n"
" double fYEps = 1.0E-307;\n"
" double fXEps = fMachEps;\n"
" if(!(fAx < fBx))\n"
" {\n"
" //print error\n"
" }\n"
" double fAy = fp - GetBetaDist(fAx, fAlpha, fBeta);\n"
" double fBy = fp - GetBetaDist(fBx, fAlpha, fBeta);\n"
" double fTemp;\n"
" unsigned short nCount;\n"
" for (nCount = 0; nCount < 1000 && !lcl_HasChangeOfSign(fAy,fBy);"
" nCount++)\n"
" {\n"
" if (fabs(fAy) <= fabs(fBy))\n"
" {\n"
" fTemp = fAx;\n"
" fAx += 2.0 * (fAx - fBx);\n"
" if (fAx < 0.0)\n"
" fAx = 0.0;\n"
" fBx = fTemp;\n"
" fBy = fAy;\n"
" fAy = fp - GetBetaDist(fAx, fAlpha, fBeta);\n"
" }\n"
" else\n"
" {\n"
" fTemp = fBx;\n"
" fBx += 2.0 * (fBx - fAx);\n"
" fAx = fTemp;\n"
" fAy = fBy;\n"
" fBy = fp - GetBetaDist(fBx, fAlpha, fBeta);\n"
" }\n"
" }\n"
" if (fAy == 0.0)\n"
" return fAx;\n"
" if (fBy == 0.0)\n"
" return fBx;\n"
" if (!lcl_HasChangeOfSign( fAy, fBy))\n"
" {\n"
" *rConvError = true;\n"
" return 0.0;\n"
" }\n"
" double fPx = fAx;\n"
" double fPy = fAy;\n"
" double fQx = fBx;\n"
" double fQy = fBy;\n"
" double fRx = fAx;\n"
" double fRy = fAy;\n"
" double fSx = 0.5 * (fAx + fBx);\n"
" bool bHasToInterpolate = true;\n"
" nCount = 0;\n"
" while ( nCount < 500 && fabs(fRy) > fYEps &&\n"
" (fBx-fAx) > fmax( fabs(fAx), fabs(fBx)) * fXEps )\n"
" {\n"
" if (bHasToInterpolate)\n"
" {\n"
" if (fPy!=fQy && fQy!=fRy && fRy!=fPy)\n"
" {\n"
" fSx = fPx*fRy*fQy*pow(fRy-fPy,-1.0)*pow(fQy-fPy,-1.0)\n"
" + fRx*fQy*fPy*pow(fQy-fRy,-1.0)*pow(fPy-fRy,-1.0)\n"
" + fQx*fPy*fRy*pow(fPy-fQy,-1.0)*pow(fRy-fQy,-1.0);\n"
" bHasToInterpolate = (fAx < fSx) && (fSx < fBx);\n"
" }\n"
" else\n"
" bHasToInterpolate = false;\n"
" }\n"
" if(!bHasToInterpolate)\n"
" {\n"
" fSx = 0.5 * (fAx + fBx);\n"
" fPx = fAx; fPy = fAy;\n"
" fQx = fBx; fQy = fBy;\n"
" bHasToInterpolate = true;\n"
" }\n"
" fPx = fQx; fQx = fRx; fRx = fSx;\n"
" fPy = fQy; fQy = fRy; fRy = fp - GetBetaDist(fSx, fAlpha, fBeta);\n"
" if (lcl_HasChangeOfSign( fAy, fRy))\n"
" {\n"
" fBx = fRx; fBy = fRy;\n"
" }\n"
" else\n"
" {\n"
" fAx = fRx; fAy = fRy;\n"
" }\n"
" bHasToInterpolate = bHasToInterpolate && (fabs(fRy) *"
" 2.0 <= fabs(fQy));\n"
" ++nCount;\n"
" }\n"
" return fRx;\n"
"}\n";
std::string lcl_IterateInverseChiInvDecl =
"static double lcl_IterateInverseChiInv"
"(double fp, double fdf, double fAx, double fBx, bool *rConvError);\n";
std::string lcl_IterateInverseChiInv =
"static double lcl_IterateInverseChiInv"
"(double fp, double fdf, double fAx, double fBx, bool *rConvError)\n"
"{\n"
" *rConvError = false;\n"
" double fYEps = 1.0E-307;\n"
" double fXEps = fMachEps;\n"
" if(!(fAx < fBx))\n"
" {\n"
" //print error\n"
" }"
" double fAy = fp - GetChiDist(fAx, fdf);\n"
" double fBy = fp - GetChiDist(fBx, fdf);\n"
" double fTemp;\n"
" unsigned short nCount;\n"
" for (nCount = 0; nCount < 1000 && "
"!lcl_HasChangeOfSign(fAy,fBy); nCount++)\n"
" {\n"
" if (fabs(fAy) <= fabs(fBy))\n"
" {\n"
" fTemp = fAx;\n"
" fAx += 2.0 * (fAx - fBx);\n"
" if (fAx < 0.0)\n"
" fAx = 0.0;\n"
" fBx = fTemp;\n"
" fBy = fAy;\n"
" fAy = fp - GetChiDist(fAx, fdf);\n"
" }\n"
" else\n"
" {\n"
" fTemp = fBx;\n"
" fBx += 2.0 * (fBx - fAx);\n"
" fAx = fTemp;\n"
" fAy = fBy;\n"
" fBy = fp - GetChiDist(fBx, fdf);\n"
" }\n"
" }\n"
" if (fAy == 0.0)\n"
" return fAx;\n"
" if (fBy == 0.0)\n"
" return fBx;\n"
" if (!lcl_HasChangeOfSign( fAy, fBy))\n"
" {\n"
" *rConvError = true;\n"
" return 0.0;\n"
" }\n"
" double fPx = fAx;\n"
" double fPy = fAy;\n"
" double fQx = fBx;\n"
" double fQy = fBy;\n"
" double fRx = fAx;\n"
" double fRy = fAy;\n"
" double fSx = 0.5 * (fAx + fBx);\n"
" bool bHasToInterpolate = true;\n"
" nCount = 0;\n"
" while ( nCount < 500 && fabs(fRy) > fYEps &&\n"
" (fBx-fAx) > fmax( fabs(fAx), fabs(fBx)) * fXEps )\n"
" {\n"
" if (bHasToInterpolate)\n"
" {\n"
" if (fPy!=fQy && fQy!=fRy && fRy!=fPy)\n"
" {\n"
" fSx = fPx * fRy * fQy*pow(fRy-fPy,-1.0)*pow(fQy-fPy,-1.0)\n"
" + fRx * fQy * fPy*pow(fQy-fRy,-1.0)*pow(fPy-fRy,-1.0)\n"
" + fQx * fPy * fRy*pow(fPy-fQy,-1.0)*pow(fRy-fQy,-1.0);\n"
" bHasToInterpolate = (fAx < fSx) && (fSx < fBx);\n"
" }\n"
" else\n"
" bHasToInterpolate = false;\n"
" }\n"
" if(!bHasToInterpolate)\n"
" {\n"
" fSx = 0.5 * (fAx + fBx);\n"
" fPx = fAx; fPy = fAy;\n"
" fQx = fBx; fQy = fBy;\n"
" bHasToInterpolate = true;\n"
" }\n"
" fPx = fQx; fQx = fRx; fRx = fSx;\n"
" fPy = fQy; fQy = fRy; fRy = fp - GetChiDist(fSx, fdf);\n"
" if (lcl_HasChangeOfSign( fAy, fRy))\n"
" {\n"
" fBx = fRx; fBy = fRy;\n"
" }\n"
" else\n"
" {\n"
" fAx = fRx; fAy = fRy;\n"
" }\n"
" bHasToInterpolate = bHasToInterpolate && (fabs(fRy)"
" * 2.0 <= fabs(fQy));\n"
" ++nCount;\n"
" }\n"
" return fRx;\n"
"}\n";
std::string lcl_IterateInverseChiSQInvDecl =
"static double lcl_IterateInverseChiSQInv( double fp, double fdf, \n"
" double fAx, double fBx, bool *rConvError );\n";
std::string lcl_IterateInverseChiSQInv =
"static double lcl_IterateInverseChiSQInv( double fp, double fdf, \n"
" double fAx, double fBx, bool *rConvError )\n"
"{\n"
" *rConvError = false;\n"
" double fYEps = 1.0E-307;\n"
" double fXEps = fMachEps;\n"
" if(!(fAx < fBx))\n"
" {\n"
" //print error\n"
" }\n"
" double fAy = fp - GetChiSqDistCDF(fAx, fdf);\n"
" double fBy = fp - GetChiSqDistCDF(fBx, fdf);\n"
" double fTemp;\n"
" unsigned short nCount;\n"
" for (nCount = 0; nCount < 1000 && !lcl_HasChangeOfSign(fAy,fBy);"
" nCount++)\n"
" {\n"
" if (fabs(fAy) <= fabs(fBy))\n"
" {\n"
" fTemp = fAx;\n"
" fAx += 2.0 * (fAx - fBx);\n"
" if (fAx < 0.0)\n"
" fAx = 0.0;\n"
" fBx = fTemp;\n"
" fBy = fAy;\n"
" fAy = fp - GetChiSqDistCDF(fAx, fdf);\n"
" }\n"
" else\n"
" {\n"
" fTemp = fBx;\n"
" fBx += 2.0 * (fBx - fAx);\n"
" fAx = fTemp;\n"
" fAy = fBy;\n"
" fBy = fp - GetChiSqDistCDF(fBx, fdf);\n"
" }\n"
" }\n"
" if (fAy == 0.0)\n"
" return fAx;\n"
" if (fBy == 0.0)\n"
" return fBx;\n"
" if (!lcl_HasChangeOfSign( fAy, fBy))\n"
" {\n"
" *rConvError = true;\n"
" return 0.0;\n"
" }\n"
" double fPx = fAx;\n"
" double fPy = fAy;\n"
" double fQx = fBx;\n"
" double fQy = fBy;\n"
" double fRx = fAx;\n"
" double fRy = fAy;\n"
" double fSx = 0.5 * (fAx + fBx);\n"
" bool bHasToInterpolate = true;\n"
" nCount = 0;\n"
" while ( nCount < 500 && fabs(fRy) > fYEps &&\n"
" (fBx-fAx) > fmax( fabs(fAx), fabs(fBx)) * fXEps )\n"
" {\n"
" if (bHasToInterpolate)\n"
" {\n"
" if (fPy!=fQy && fQy!=fRy && fRy!=fPy)\n"
" {\n"
" fSx = fPx * fRy * fQy / (fRy-fPy) / (fQy-fPy)\n"
" + fRx * fQy * fPy / (fQy-fRy) / (fPy-fRy)\n"
" + fQx * fPy * fRy / (fPy-fQy) / (fRy-fQy);\n"
" bHasToInterpolate = (fAx < fSx) && (fSx < fBx);\n"
" }\n"
" else\n"
" bHasToInterpolate = false;\n"
" }\n"
" if(!bHasToInterpolate)\n"
" {\n"
" fSx = 0.5 * (fAx + fBx);\n"
" fPx = fAx; fPy = fAy;\n"
" fQx = fBx; fQy = fBy;\n"
" bHasToInterpolate = true;\n"
" }\n"
" fPx = fQx; fQx = fRx; fRx = fSx;\n"
" fPy = fQy; fQy = fRy; fRy = fp - GetChiSqDistCDF(fSx, fdf);\n"
" if (lcl_HasChangeOfSign( fAy, fRy))\n"
" {\n"
" fBx = fRx; fBy = fRy;\n"
" }\n"
" else\n"
" {\n"
" fAx = fRx; fAy = fRy;\n"
" }\n"
" bHasToInterpolate = bHasToInterpolate && (fabs(fRy) * 2.0"
" <= fabs(fQy));\n"
" ++nCount;\n"
" }\n"
" return fRx;\n"
"}\n";
std::string gaussinvDecl = "double gaussinv(double x);\n";
std::string gaussinv =
"double gaussinv(double x)\n"
"{\n"
" double q,t,z;\n"
" q=x-0.5;\n"
" if(fabs(q)<=.425)\n"
" {\n"
" t=0.180625-q*q;\n"
" z=\n"
" q*\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" t*2509.0809287301226727+33430.575583588128105\n"
" )\n"
" *t+67265.770927008700853\n"
" )\n"
" *t+45921.953931549871457\n"
" )\n"
" *t+13731.693765509461125\n"
" )\n"
" *t+1971.5909503065514427\n"
" )\n"
" *t+133.14166789178437745\n"
" )\n"
" *t+3.387132872796366608\n"
" )\n"
" *pow\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" t*5226.495278852854561+28729.085735721942674\n"
" )\n"
" *t+39307.89580009271061\n"
" )\n"
" *t+21213.794301586595867\n"
" )\n"
" *t+5394.1960214247511077\n"
" )\n"
" *t+687.1870074920579083\n"
" )\n"
" *t+42.313330701600911252\n"
" )\n"
" *t+1.0\n"
" , -1.0);\n"
" }\n"
" else\n"
" {\n"
" if(q>0) t=1-x;\n"
" else t=x;\n"
" t=sqrt(-log(t));\n"
" if(t<=5.0)\n"
" {\n"
" t+=-1.6;\n"
" z=\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" t*7.7454501427834140764e-4+0.0227238449892691845833\n"
" )\n"
" *t+0.24178072517745061177\n"
" )\n"
" *t+1.27045825245236838258\n"
" )\n"
" *t+3.64784832476320460504\n"
" )\n"
" *t+5.7694972214606914055\n"
" )\n"
" *t+4.6303378461565452959\n"
" )\n"
" *t+1.42343711074968357734\n"
" )\n"
" *pow\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" t*1.05075007164441684324e-9+5.475938084995344946e-4\n"
" )\n"
" *t+0.0151986665636164571966\n"
" )\n"
" *t+0.14810397642748007459\n"
" )\n"
" *t+0.68976733498510000455\n"
" )\n"
" *t+1.6763848301838038494\n"
" )\n"
" *t+2.05319162663775882187\n"
" )\n"
" *t+1.0\n"
" , -1.0);\n"
" }\n"
" else\n"
" {\n"
" t+=-5.0;\n"
" z=\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" t*2.01033439929228813265e-7+2.71155556874348757815e-5\n"
" )\n"
" *t+0.0012426609473880784386\n"
" )\n"
" *t+0.026532189526576123093\n"
" )\n"
" *t+0.29656057182850489123\n"
" )\n"
" *t+1.7848265399172913358\n"
" )\n"
" *t+5.4637849111641143699\n"
" )\n"
" *t+6.6579046435011037772\n"
" )\n"
" *pow\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" (\n"
" t*2.04426310338993978564e-15+1.4215117583164458887e-7\n"
" )\n"
" *t+1.8463183175100546818e-5\n"
" )\n"
" *t+7.868691311456132591e-4\n"
" )\n"
" *t+0.0148753612908506148525\n"
" )\n"
" *t+0.13692988092273580531\n"
" )\n"
" *t+0.59983220655588793769\n"
" )\n"
" *t+1.0\n"
" , -1.0);\n"
" }\n"
" if(q<0.0) z=-z;\n"
" }\n"
" return z;\n"
"}\n";
std::string lcl_GetLogGammaHelperDecl=
"static double lcl_GetLogGammaHelper(double fZ);\n";
std::string lcl_GetLogGammaHelper =
"static double lcl_GetLogGammaHelper(double fZ)\n"
"{\n"
" double fg = 6.024680040776729583740234375;\n"
" double fZgHelp = fZ + fg - 0.5;\n"
" return log( lcl_getLanczosSum(fZ)) + (fZ-0.5) * log(fZgHelp) - fZgHelp;\n"
"}\n";
std::string lcl_GetGammaHelperDecl=
"static double lcl_GetGammaHelper(double fZ);\n";
std::string lcl_GetGammaHelper =
"static double lcl_GetGammaHelper(double fZ)\n"
"{\n"
" double fGamma = lcl_getLanczosSum(fZ);\n"
" double fg = 6.024680040776729583740234375;\n"
" double fZgHelp = fZ + fg - 0.5;\n"
" double fHalfpower = pow( fZgHelp, fZ*pow(2,-1.0) - 0.25);\n"
" fGamma *= fHalfpower;\n"
" fGamma = fGamma*pow(exp(fZgHelp),-1.0);\n"
" fGamma *= fHalfpower;\n"
" fGamma = 120.4;\n"
" if (fZ <= 20.0 && fZ == (int)fZ)\n"
" {\n"
" fGamma = (int)(fGamma+0.5);\n"
" }\n"
" return fGamma;\n"
"}\n";
std::string lcl_getLanczosSumDecl=
"static double lcl_getLanczosSum(double fZ);\n";
std::string lcl_getLanczosSum =
"static double lcl_getLanczosSum(double fZ) \n"
"{ \n"
" double fNum[13] ={ \n"
" 23531376880.41075968857200767445163675473, \n"
" 42919803642.64909876895789904700198885093, \n"
" 35711959237.35566804944018545154716670596, \n"
" 17921034426.03720969991975575445893111267, \n"
" 6039542586.35202800506429164430729792107, \n"
" 1439720407.311721673663223072794912393972, \n"
" 248874557.8620541565114603864132294232163, \n"
" 31426415.58540019438061423162831820536287, \n"
" 2876370.628935372441225409051620849613599, \n"
" 186056.2653952234950402949897160456992822, \n"
" 8071.672002365816210638002902272250613822, \n"
" 210.8242777515793458725097339207133627117, \n"
" 2.506628274631000270164908177133837338626 \n"
" }; \n"
" double fDenom[13] = { \n"
" 0,\n"
" 39916800,\n"
" 120543840,\n"
" 150917976,\n"
" 105258076,\n"
" 45995730,\n"
" 13339535,\n"
" 2637558,\n"
" 357423,\n"
" 32670,\n"
" 1925,\n"
" 66,\n"
" 1\n"
" };\n"
" double fSumNum;\n"
" double fSumDenom;\n"
" int nI;\n"
" if (fZ<=1.0)\n"
" {\n"
" fSumNum = fNum[12];\n"
" fSumDenom = fDenom[12];\n"
" nI = 11;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 10;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 9;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 8;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 7;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 6;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 5;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 4;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 3;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 2;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 1;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" nI = 0;\n"
" fSumNum = fSumNum*fZ+fNum[nI];\n"
" fSumDenom = fSumDenom*fZ+fDenom[nI];\n"
" }\n"
" if (fZ>1.0)\n"
" {\n"
" double fZInv = pow(fZ,-1.0);\n"
" fSumNum = fNum[0];\n"
" fSumDenom = fDenom[0];\n"
" nI = 1;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 2;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 3;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 4;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 5;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 6;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 7;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 8;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 9;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 10;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 11;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" nI = 12;\n"
" fSumNum = fSumNum*fZInv+fNum[nI];\n"
" fSumDenom = fSumDenom*fZInv+fDenom[nI];\n"
" }\n"
" return fSumNum*pow(fSumDenom,-1.0);\n"
"}\n";
std::string GetUpRegIGammaDecl=
" double GetUpRegIGamma( double fA, double fX ) ;\n";
std::string GetUpRegIGamma =
"double GetUpRegIGamma( double fA, double fX )\n"
"{\n"
" double fLnFactor= fA*log(fX)-fX-lgamma(fA);\n"
" double fFactor = exp(fLnFactor); \n"
" if (fX>fA+1.0) \n"
" return fFactor * GetGammaContFraction(fA,fX);\n"
" else \n"
" return 1.0 -fFactor * GetGammaSeries(fA,fX);\n"
"}\n";
std::string lcl_HasChangeOfSignDecl=
"static inline bool lcl_HasChangeOfSign( double u, double w );\n";
std::string lcl_HasChangeOfSign =
"static inline bool lcl_HasChangeOfSign( double u, double w )\n"
"{\n"
" return (u < 0.0 && w > 0.0) || (u > 0.0 && w < 0.0);\n"
"}\n";
std::string GetTDistDecl=" double GetTDist(double T, double fDF);\n";
std::string GetTDist =
"double GetTDist(double T, double fDF)\n"
"{\n"
" return 0.5 * GetBetaDist(fDF*pow(fDF+T*T,-1.0),fDF*pow(2.0,-1.0), 0.5);\n"
"}\n";
std::string GetBetaDecl=" double GetBeta(double fAlpha, double fBeta);\n";
std::string GetBeta =
"double GetBeta(double fAlpha, double fBeta)\n"
"{\n"
" double fA;\n"
" double fB;\n"
" fAlpha>fBeta?(fA = fAlpha,fB = fBeta):(fA = fBeta,fB = fAlpha);\n"
" double fAB = fA + fB;\n"
" if (fAB < fMaxGammaArgument)\n"
" return tgamma(fA)*pow(tgamma(fAB),-1.0)*tgamma(fB);\n"
" double fgm = 5.524680040776729583740234375;\n"
" double fLanczos = lcl_getLanczosSum(fA)*lcl_getLanczosSum(fB)\n"
" *pow(lcl_getLanczosSum(fAB),-1.0);\n"
" fLanczos *= sqrt(((fAB + fgm)*pow(fA + fgm,-1.0))*pow(fB + fgm,-1.0));\n"
" return fLanczos * pow(exp(1.0),(-fA*log1p(fB*pow(fA + fgm,-1.0)))"
" - fB*log1p(fA*pow(fB + fgm,-1.0)) - fgm);\n"
"}\n";
std::string GetLogBetaDecl=
" double GetLogBeta(double fAlpha, double fBeta);\n";
std::string GetLogBeta =
"double GetLogBeta(double fAlpha, double fBeta)\n"
"{\n"
" double fA;\n"
" double fB;\n"
" fAlpha>fBeta?(fA = fAlpha,fB = fBeta):(fA = fBeta,fB = fAlpha);\n"
" double fgm = 5.524680040776729583740234375;\n"
" double fLanczos = lcl_getLanczosSum(fA)*lcl_getLanczosSum(fB)*\n"
" pow(lcl_getLanczosSum(fA + fB),-1.0);\n"
" double fResult= -fA *log1p(fB*pow(fA + fgm,-1.0))"
"-fB *log1p(fA*pow(fB + fgm,-1.0))-fgm;\n"
" fResult += log(fLanczos)+0.5*(log(fA + fB + fgm) - log(fA + fgm)\n"
" - log(fB + fgm));\n"
" return fResult;\n"
"}\n";
std::string GetBetaDistPDFDecl=
"double GetBetaDistPDF(double fX, double fA, double fB);\n";
std::string GetBetaDistPDF =
"double GetBetaDistPDF(double fX, double fA, double fB)\n"
"{\n"
" if (fA == 1.0) \n"
" {\n"
" if (fB == 1.0)\n"
" return 1.0;\n"
" if (fB == 2.0)\n"
" return -2.0*fX + 2.0;\n"
" if (fX == 1.0 && fB < 1.0)\n"
" {\n"
" return HUGE_VAL;\n"
" }\n"
" if (fX <= 0.01)\n"
" return fB + fB * expm1((fB-1.0) * log1p(-fX));\n"
" else \n"
" return fB * pow(0.5-fX+0.5,fB-1.0);\n"
" }\n"
" if (fB == 1.0) \n"
" {\n"
" if (fA == 2.0)\n"
" return fA * fX;\n"
" if (fX == 0.0 && fA < 1.0)\n"
" {\n"
" return HUGE_VAL;\n"
" }\n"
" return fA * pow(fX,fA-1);\n"
" }\n"
" if (fX <= 0.0)\n"
" {\n"
" if (fA < 1.0 && fX == 0.0)\n"
" {\n"
" return HUGE_VAL;\n"
" }\n"
" else\n"
" return 0.0;\n"
" }\n"
" if (fX >= 1.0)\n"
" {\n"
" if (fB < 1.0 && fX == 1.0)\n"
" {\n"
" return HUGE_VAL;\n"
" }\n"
" else \n"
" return 0.0;\n"
" }\n"
" double fLogDblMax = log( 1.79769e+308 );\n"
" double fLogDblMin = log( 2.22507e-308 );\n"
" double fLogY = (fX < 0.1) ? log1p(-fX) : log(0.5-fX+0.5);\n"
" double fLogX = log(fX);\n"
" double fAm1LogX = (fA-1.0) * fLogX;\n"
" double fBm1LogY = (fB-1.0) * fLogY;\n"
" double fLogBeta = GetLogBeta(fA,fB);\n"
" if ( fAm1LogX < fLogDblMax && fAm1LogX > fLogDblMin\n"
" && fBm1LogY < fLogDblMax && fBm1LogY > fLogDblMin\n"
" && fLogBeta < fLogDblMax && fLogBeta > fLogDblMin\n"
" && fAm1LogX + fBm1LogY < fLogDblMax && fAm1LogX + fBm1LogY > \n"
" fLogDblMin)\n"
" return pow(fX,fA-1.0)*pow(0.5-fX+0.5,fB-1.0)"
"*pow(GetBeta(fA,fB),-1.0);\n"
" else \n"
" return exp( fAm1LogX + fBm1LogY - fLogBeta);\n"
"}\n";
std::string lcl_GetBetaHelperContFracDecl=
"double lcl_GetBetaHelperContFrac(double fX, double fA, double fB);\n";
std::string lcl_GetBetaHelperContFrac =
"double lcl_GetBetaHelperContFrac(double fX, double fA, double fB)\n"
"{ \n"
" double a1, b1, a2, b2, fnorm, apl2m, d2m, d2m1, cfnew, cf;\n"
" a1 = 1.0; b1 = 1.0;\n"
" b2 = 1.0 - (fA+fB)*pow(fA+1.0,-1.0)*fX;\n"
" b2==0.0?(a2 = 0.0,fnorm = 1.0,cf = 1.0):\n"
" (a2 = 1.0,fnorm = pow(b2,-1.0),cf = a2*fnorm);\n"
" cfnew = 1.0;\n"
" double rm = 1.0;\n"
" double fMaxIter = 50000.0;\n"
" bool bfinished = false;\n"
" do\n"
" {\n"
" apl2m = fA + 2.0*rm;\n"
" d2m = (rm*(fB-rm))*fX*pow(apl2m*(apl2m-1.0),-1.0);\n"
" d2m1 = -((fA+rm)*(fA+rm+fB))*fX*pow(apl2m*(apl2m+1.0),-1.0);\n"
" a1 = (a2+d2m*a1)*fnorm;\n"
" b1 = (b2+d2m*b1)*fnorm;\n"
" a2 = a1 + d2m1*a2*fnorm;\n"
" b2 = b1 + d2m1*b2*fnorm;\n"
" if (b2 != 0.0) \n"
" {\n"
" fnorm = pow(b2,-1.0);\n"
" cfnew = a2*fnorm;\n"
" bfinished = (fabs(cf-cfnew) < fabs(cf)*fMachEps);\n"
" }\n"
" cf = cfnew;\n"
" rm += 1.0;\n"
" }\n"
" while (rm < fMaxIter && !bfinished);\n"
" return cf;\n"
"}\n";
std::string lcl_IterateInverseDecl=
"double lcl_IterateInverse("
"double fAx, double fBx, bool* rConvError,double fp,double fDF );\n";
std::string lcl_IterateInverse =
"double lcl_IterateInverse( "
"double fAx, double fBx, bool* rConvError,double fp,double fDF )\n"
"{\n"
" *rConvError = false;\n"
" double fYEps = 1.0E-307;\n"
" double fXEps =DBL_EPSILON;\n"
" if(fAx>fBx)\n"
" return DBL_MAX;\n"
" double fAy = GetValue(fAx,fp,fDF);\n"
" double fBy = GetValue(fBx,fp,fDF);\n"
" double fTemp;\n"
" unsigned short nCount;\n"
" double inter;\n"
" bool sign;\n"
" for (nCount =0;nCount<1000&&!lcl_HasChangeOfSign(fAy,fBy);nCount++)\n"
" {\n"
" inter = 2.0 * (fAx - fBx);\n"
" if (fabs(fAy) <= fabs(fBy)) \n"
" {\n"
" sign = true;\n"
" fTemp = fAx;\n"
" fAx += inter;\n"
" if (fAx < 0.0)\n"
" fAx = 0.0;\n"
" fBx = fTemp;\n"
" fBy = fAy;\n"
" fTemp = fAx;\n"
" }\n"
" else\n"
" {\n"
" sign = false;\n"
" fTemp = fBx;\n"
" fBx -= inter;\n"
" fAx = fTemp;\n"
" fAy = fBy;\n"
" fTemp = fBx;\n"
" }\n"
" fTemp = GetValue(fTemp,fp,fDF);\n"
" sign?(fAy = fTemp):(fBy = fTemp);\n"
" }\n"
" if (fAy == 0.0)\n"
" return fAx;\n"
" if (fBy == 0.0)\n"
" return fBx;\n"
" if (!lcl_HasChangeOfSign( fAy, fBy))\n"
" {\n"
" *rConvError = true;\n"
" return 0.0;\n"
" }\n"
" double fPx = fAx;\n"
" double fPy = fAy;\n"
" double fQx = fBx;\n"
" double fQy = fBy;\n"
" double fRx = fAx;\n"
" double fRy = fAy;\n"
" double fSx = 0.5 * (fAx + fBx); \n"
" bool bHasToInterpolate = true;\n"
" nCount = 0;\n"
" while ( nCount < 500 && fabs(fRy) > fYEps &&\n"
" (fBx-fAx) > max( fabs(fAx), fabs(fBx)) * fXEps )\n"
" {\n"
" if (bHasToInterpolate)\n"
" {\n"
" if (fPy!=fQy && fQy!=fRy && fRy!=fPy)\n"
" {\n"
" fSx = fPx * fRy * fQy * pow(fRy-fPy,-1.0)*pow(fQy-fPy,-1.0)\n"
" + fRx * fQy * fPy * pow(fQy-fRy,-1.0)*pow(fPy-fRy,-1.0)\n"
" + fQx * fPy * fRy * pow(fPy-fQy,-1.0)*pow(fRy-fQy,-1.0);\n"
" bHasToInterpolate = (fAx < fSx) && (fSx < fBx);\n"
" }\n"
" else\n"
" bHasToInterpolate = false;\n"
" }\n"
" if(!bHasToInterpolate)\n"
" {\n"
" fSx = 0.5 * (fAx + fBx);\n"
" \n"
" fPx = fAx; fPy = fAy;\n"
" fQx = fBx; fQy = fBy;\n"
" bHasToInterpolate = true;\n"
" }\n"
" fPx = fQx; fQx = fRx; fRx = fSx;\n"
" fPy = fQy; fQy = fRy; fRy = GetValue(fSx,fp,fDF);\n"
" lcl_HasChangeOfSign( fAy, fRy)?(fBx = fRx,fBy = fRy):\n"
" (fAx = fRx,fAy = fRy);\n"
" bHasToInterpolate =\n"
" bHasToInterpolate && (fabs(fRy) * 2.0 <= fabs(fQy));\n"
" ++nCount;\n"
" }\n"
" return fRx;\n"
"}\n";
std::string phiDecl=
"double phi(double x);\n";
std::string phi =
"double phi(double x)\n"
"{\n"
" return 0.39894228040143268 * exp(-(x * x) / 2.0);\n"
"}\n";
std::string taylorDecl =
"double taylor(double* pPolynom, uint nMax, double x);\n";
std::string taylor =
"double taylor(double* pPolynom, uint nMax, double x)\n"
"{\n"
" double nVal = pPolynom[nMax];\n"
" for (short i = nMax-1; i >= 0; i--)\n"
" {\n"
" nVal = pPolynom[i] + (nVal * x);\n"
" }\n"
" return nVal;\n"
"}";
std::string gaussDecl = "double gauss(double x);\n";
std::string gauss =
"double gauss(double x)\n"
"{\n"
" double xAbs = fabs(x);\n"
" uint xShort = (uint)(floor(xAbs));\n"
" double nVal = 0.0;\n"
" if (xShort == 0)\n"
" {\n"
" double t0[] =\n"
" { 0.39894228040143268, -0.06649038006690545, 0.00997355701003582,\n"
" -0.00118732821548045, 0.00011543468761616, -0.00000944465625950,\n"
" 0.00000066596935163, -0.00000004122667415, 0.00000000227352982,\n"
" 0.00000000011301172, 0.00000000000511243, -0.00000000000021218 };\n"
" nVal = taylor(t0, 11, (xAbs * xAbs)) * xAbs;\n"
" }\n"
" else if ((xShort >= 1) && (xShort <= 2))\n"
" {\n"
" double t2[] =\n"
" { 0.47724986805182079, 0.05399096651318805, -0.05399096651318805,\n"
" 0.02699548325659403, -0.00449924720943234, -0.00224962360471617,\n"
" 0.00134977416282970, -0.00011783742691370, -0.00011515930357476,\n"
" 0.00003704737285544, 0.00000282690796889, -0.00000354513195524,\n"
" 0.00000037669563126, 0.00000019202407921, -0.00000005226908590,\n"
" -0.00000000491799345, 0.00000000366377919, -0.00000000015981997,\n"
" -0.00000000017381238, 0.00000000002624031, 0.00000000000560919,\n"
" -0.00000000000172127, -0.00000000000008634, 0.00000000000007894 };\n"
" nVal = taylor(t2, 23, (xAbs - 2.0));\n"
" }\n"
" else if ((xShort >= 3) && (xShort <= 4))\n"
" {\n"
" double t4[] =\n"
" { 0.49996832875816688, 0.00013383022576489, -0.00026766045152977,\n"
" 0.00033457556441221, -0.00028996548915725, 0.00018178605666397,\n"
" -0.00008252863922168, 0.00002551802519049, -0.00000391665839292,\n"
" -0.00000074018205222, 0.00000064422023359, -0.00000017370155340,\n"
" 0.00000000909595465, 0.00000000944943118, -0.00000000329957075,\n"
" 0.00000000029492075, 0.00000000011874477, -0.00000000004420396,\n"
" 0.00000000000361422, 0.00000000000143638, -0.00000000000045848 };\n"
" nVal = taylor(t4, 20, (xAbs - 4.0));\n"
" }\n"
" else\n"
" {\n"
" double asympt[] = { -1.0, 1.0, -3.0, 15.0, -105.0 };\n"
" nVal = 0.5 + phi(xAbs) * taylor(asympt, 4, 1.0/(xAbs * xAbs))/xAbs;\n"
" }\n"
" if (x < 0.0)\n"
" return -nVal;\n"
" else\n"
" return nVal;\n"
"}\n";
#endif
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
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