ExtendedMath.h

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#ifndef EXTENDEDMATH_H
#define EXTENDEDMATH_H

#include <iostream> //std::istream and std::stringstream
#include <fstream> //std::fstream
#include <cmath> 
#include <limits>

#include "Vector.h"

/*
 * \brief
 */
namespace constants
{
    //Values from WolframAlpha
    const Mdouble pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068;
    const Mdouble sqrt_pi = 1.772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665;
    const Mdouble sqr_pi = 9.869604401089358618834490999876151135313699407240790626413349376220044822419205243001773403718552232;
    const Mdouble sqrt_2 = 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573;
    const Mdouble sqrt_3 = 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576;
}

namespace mathsFunc
{
    Mdouble gamma(Mdouble gamma_in);
    
    Mdouble chi_squared(const Mdouble x, const unsigned int k);
    
    Mdouble chi_squared_prob(const Mdouble x, const unsigned int k);
    
    Mdouble goldenSectionSearch(Mdouble (*function)(const Mdouble), Mdouble min, Mdouble cur, Mdouble max, Mdouble endCondition, Mdouble curVal = std::numeric_limits<Mdouble>::quiet_NaN());

    template<typename T> int sign(T val)
    {
        return (T(0) < val) - (val < T(0));
    }

    template<typename T> T square(T val)
    {
        return val * val;
    }

    template<typename T> T cubic(T val)
    {
        return val * val * val;
    }

    bool isEqual(Mdouble v1,Mdouble v2, Mdouble absError);
    bool isEqual(Vec3D v1, Vec3D v2, Mdouble absError);

    template<typename T> constexpr T factorial(const T t)
    {
        return (t == 0) ? 1 : t * factorial(t - 1);
    }

    //platform independent implementation of sine and cosine, taken from
    // http://stackoverflow.com/questions/18662261/fastest-implementation-of-sine-cosine-and-square-root-in-c-doesnt-need-to-b
    // (cosine was implemented wrongly on the website, here is a corrected version)

    // sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
    Mdouble sin(Mdouble x);

    // cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...
    Mdouble cos(Mdouble x);

    Mdouble exp(Mdouble Exponent);

    Mdouble log(Mdouble Power);


    // tan=sin/cos
    template<typename T> T tan(T x) {
        return sin(x)/cos(x);
    }


    Mdouble chebyshev(Mdouble x, const Mdouble coef[], int N);
    
    Mdouble I0_exp(Mdouble x);
    
    Mdouble I0(Mdouble x);

}

#endif