/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2003 Ferdinando Ametrano

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <https://www.quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT

 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS

 FOR A PARTICULAR PURPOSE.  See the license for more details.

*/

/*

    The implementation of the algorithm was inspired by

    "Numerical Recipes in C", 2nd edition,

    Press, Teukolsky, Vetterling, Flannery, chapter 6

*/

#include <ql/math/incompletegamma.hpp>

#include <ql/math/distributions/gammadistribution.hpp>

namespace QuantLib {

    Real incompleteGammaFunction(Real a, Real x, Real accuracy,

                                 Integer maxIteration) {

        QL_REQUIRE(a>0.0, "non-positive a is not allowed");

        QL_REQUIRE(x>=0.0, "negative x non allowed");

        if (x < (a+1.0)) {

            // Use the series representation

            return incompleteGammaFunctionSeriesRepr(a, x,

                accuracy, maxIteration);

        } else {

            // Use the continued fraction representation

            return 1.0-incompleteGammaFunctionContinuedFractionRepr(a, x,

                accuracy, maxIteration);

        }

    }

    Real incompleteGammaFunctionSeriesRepr(Real a, Real x, Real accuracy,

                                           Integer maxIteration) {

        if (x==0.0) return 0.0;

        Real gln = GammaFunction().logValue(a);

        Real ap=a;

        Real del=1.0/a;

        Real sum=del;

        for (Integer n=1; n<=maxIteration; n++) {

            ++ap;

            del *= x/ap;

            sum += del;

            if (std::fabs(del) < std::fabs(sum)*accuracy) {

                return sum*std::exp(-x+a*std::log(x)-gln);

            }

        }

        QL_FAIL("accuracy not reached");

    }

    Real incompleteGammaFunctionContinuedFractionRepr(Real a, Real x,

                                                      Real accuracy,

                                                      Integer maxIteration) {

        Integer i;

        Real an, b, c, d, del, h;

        Real gln = GammaFunction().logValue(a);

        b=x+1.0-a;

        c=1.0/QL_EPSILON;

        d=1.0/b;

        h=d;

        for (i=1; i<=maxIteration; i++) {

            an = -i*(i-a);

            b += 2.0;

            d=an*d+b;

            if (std::fabs(d) < QL_EPSILON) d=QL_EPSILON;

            c=b+an/c;

            if (std::fabs(c) < QL_EPSILON) c=QL_EPSILON;

            d=1.0/d;

            del=d*c;

            h *= del;

            if (std::fabs(del-1.0) < accuracy) {

                return std::exp(-x+a*std::log(x)-gln)*h;

            }

        }

        QL_FAIL("accuracy not reached");

    }

}