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

/*

 Copyright (C) 2008 Roland Lichters

 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.

*/

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

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

#include <ql/math/beta.hpp>

namespace QuantLib {

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

        static GammaFunction G;

        Real g1 = std::exp (G.logValue(0.5 * (n_ + 1)));

        Real g2 = std::exp (G.logValue(0.5 * n_));

        Real power = std::pow (1. + x*x / n_, 0.5 * (n_ + 1));

        return g1 / (g2 * power * std::sqrt (M_PI * n_));

    }

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

        Real xx = 1.0 * n_ / (x*x + n_);

        Real sig = (x > 0 ? 1.0 : - 1.0);

        return 0.5 + 0.5 * sig * ( incompleteBetaFunction (0.5 * n_, 0.5, 1.0)

                                   -incompleteBetaFunction (0.5 * n_, 0.5, xx));

    }

    Real InverseCumulativeStudent::operator()(Real y) const {

        QL_REQUIRE (y >= 0 && y <= 1, "argument out of range [0, 1]");

        Real x = 0;

        Size count = 0;

        // do a few newton steps to find x

        do {

            x -= (f_(x) - y) / d_(x);

            count++;

        }

        while (std::fabs(f_(x) - y) > accuracy_ && count < maxIterations_);

        QL_REQUIRE (count < maxIterations_,

                    "maximum number of iterations " << maxIterations_

                    << " reached in InverseCumulativeStudent, "

                    << "y=" << y << ", x=" << x);

        return x;

    }

}