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

/*

 Copyright (C) 2002, 2003 Sadruddin Rejeb

 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

 <http://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.

*/

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

namespace QuantLib {

    Real CumulativeGammaDistribution::operator()(Real x) const {

        if (x <= 0.0) return 0.0;

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

        if (x<(a_+1.0)) {

            Real ap = a_;

            Real del = 1.0/a_;

            Real sum = del;

            for (Size n=1; n<=100; n++) {

                ap += 1.0;

                del *= x/ap;

                sum += del;

                if (std::fabs(del) < std::fabs(sum)*3.0e-7)

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

            }

        } else {

            Real b = x + 1.0 - a_;

            Real c = QL_MAX_REAL;

            Real d = 1.0/b;

            Real h = d;

            for (Size n=1; n<=100; n++) {

                Real an = -1.0*n*(n-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;

                Real del = d*c;

                h *= del;

                if (std::fabs(del - 1.0)<QL_EPSILON)

                    return 1.0-h*std::exp(-x + a_*std::log(x) - gln);

            }

        }

        QL_FAIL("too few iterations");

    }

    const Real GammaFunction::c1_ = 76.18009172947146;

    const Real GammaFunction::c2_ = -86.50532032941677;

    const Real GammaFunction::c3_ = 24.01409824083091;

    const Real GammaFunction::c4_ = -1.231739572450155;

    const Real GammaFunction::c5_ = 0.1208650973866179e-2;

    const Real GammaFunction::c6_ = -0.5395239384953e-5;

    Real GammaFunction::logValue(Real x) const {

        QL_REQUIRE(x>0.0, "positive argument required");

        Real temp = x + 5.5;

        temp -= (x + 0.5)*std::log(temp);

        Real ser=1.000000000190015;

        ser += c1_/(x + 1.0);

        ser += c2_/(x + 2.0);

        ser += c3_/(x + 3.0);

        ser += c4_/(x + 4.0);

        ser += c5_/(x + 5.0);

        ser += c6_/(x + 6.0);

        return -temp+std::log(2.5066282746310005*ser/x);

    }

    Real GammaFunction::value(Real x) const {

        if (x >= 1.0) {

            return std::exp(logValue(x));

        }

        else {

            if (x > -20.0) {

                // \Gamma(x) = \frac{\Gamma(x+1)}{x}

                return value(x+1.0)/x;

            }

            else {

                // \Gamma(-x) = -\frac{\pi}{\Gamma(x)\sin(\pi x) x}

                return -M_PI/(value(-x)*x*std::sin(M_PI*x));

            }

        }

    }

}