Gaussian.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/Uniform.h"

namespace honey
{


template<class Real>
class Gaussian_ : public RandomDist<Real>
{
    typedef RandomDist<Real>    Super;
    RandomDist_imports();
    typedef Trig_<Double>       Trig_d;
    
public:
    Gaussian_(optional<RandomGen&> gen, Real mu = 0, Real sigma = 1)    : Super(gen), mu(mu), sigma(sigma) { assert(sigma > 0); }
    Gaussian_(Real mu = 0, Real sigma = 1)                              : Gaussian_(optnull, mu, sigma) {}

    virtual Real next() const;
    virtual Real pdf(Real x) const;
    virtual Real cdf(Real x) const;
    virtual Real cdfInv(Real P) const;
    virtual Real mean() const               { return mu; }
    virtual Real variance() const           { return Alge::sqr(sigma); }
    
    static Real erf(Real x)                 { return 2*Gaussian_().cdf(Double(x)*Double_::sqrtTwo) - 1; }
    static Real erfComp(Real x)             { return 2*Gaussian_().cdf(-Double(x)*Double_::sqrtTwo); }
    static Real erfInv(Real y)              { return Gaussian_().cdfInv(Double(y+1)/2) / Double_::sqrtTwo; }
    static Real erfCompInv(Real y)          { return -Gaussian_().cdfInv(Double(y)/2) / Double_::sqrtTwo; }

    Real mu;
    Real sigma;
};

typedef Gaussian_<Real>      Gaussian;
typedef Gaussian_<Float>     Gaussian_f;
typedef Gaussian_<Double>    Gaussian_d;

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

}