Gamma.h

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// Honeycomb, Copyright (C) 2015 NewGamePlus Inc.  Distributed under the Boost Software License v1.0.
#pragma once

#include "Honey/Math/Random/Dist/Gaussian.h"

namespace honey
{

template<class Real> class GammaFunc_;
template<class Real> class GammaInc;


template<class Real>
class Gamma_ : public RandomDist<Real>
{
    typedef RandomDist<Real>    Super;
    RandomDist_imports();
    typedef Trig_<Real>         Trig;
    typedef Gaussian_<Double>   Gaussian;
    typedef GammaFunc_<Double>  GammaFunc;
    typedef GammaInc<Double>    GammaInc;
    
public:
    Gamma_(optional<RandomGen&> gen, Real a, Real b)    : Super(gen), a(a), b(b) { assert(a > 0 && b > 0); }
    Gamma_(Real a, Real b)                              : Gamma_(optnull, a, b) {}

    virtual Real next() const;
    virtual Real pdf(Real x) const;
    virtual Real cdf(Real x) const;
    virtual Real cdfComp(Real x) const;
    virtual Real cdfInv(Real P) const;
    virtual Real mean() const                   { return a*b; }
    virtual Real variance() const               { return a*Alge::sqr(b); }
    
    Real a;
    Real b;
};

typedef Gamma_<Real>      Gamma;
typedef Gamma_<Float>     Gamma_f;
typedef Gamma_<Double>    Gamma_d;

extern template class Gamma_<Float>;
extern template class Gamma_<Double>;


template<class Real>
class GammaFunc_
{
    typedef typename Numeral<Real>::Real_   Real_;
    typedef typename Real_::DoubleType      Double_;
    typedef typename Double_::Real          Double;
    typedef Alge_<Real> Alge;
public:
    static Real gamma(Real z)                   { return Alge::exp(gammaLn(z)); }
    static Real gammaLn(Real z);

    static Real factorial(Real n);
    static Real factorialLn(Real n);
    static Real choose(Real n, Real m)          { return Alge::exp(chooseLn(n,m)); }
    static Real chooseLn(Real n, Real m);
private:
    static Real series(Real z);
    static Real asymp(Real z);
    static Real gValue()                        { return 10.0; }
    static Real lanczos(Real z);
    static Real near1(Real z);
    static Real near2(Real z);
    static Real gt1(Real z);
    static Real gammaLn(Real z, int& sign);

    static const int factorialTableSize;
    static const Double factorialTable[];
};

typedef GammaFunc_<Real>    GammaFunc;
typedef GammaFunc_<Float>   GammaFunc_f;
typedef GammaFunc_<Double>  GammaFunc_d;

extern template class GammaFunc_<Float>;
extern template class GammaFunc_<Double>;

}