#include <cmath>
#include <stdexcept>
#include <sstream>
#include <iostream>
#include "SimpleRNG.h"

#define PI 3.1415926535897932384626433832795

SimpleRNG::SimpleRNG()
{
    // These values are not magical, just the default values Marsaglia used.
    // Any unit should work.
    m_u = 521288629;
    m_v = 362436069;
}

void SimpleRNG::SetState(unsigned int u, unsigned int v)
{
    m_u = u;
    m_v = v;
}

void SimpleRNG::GetState(unsigned int& u, unsigned int& v)
{
    u = m_u;
    v = m_v;
}

double SimpleRNG::GetUniform(unsigned int& u, unsigned int& v)
{
    // 0 <= u <= 2^32
    unsigned int z = GetUint(u, v);
    // The magic number is 1/(2^32 + 1) and so result is positive and less than 1.
    return z*2.328306435996595e-10;
}

unsigned int SimpleRNG::GetUint(unsigned int& u, unsigned int& v)
{
    v = 36969*(v & 65535) + (v >> 16);
    u = 18000*(u & 65535) + (u >> 16);
    return (v << 16) + u;
}

double SimpleRNG::GetUniform()
{
    return GetUniform(m_u, m_v);
}

unsigned int SimpleRNG::GetUint()
{
    return GetUint(m_u, m_v);
}
    
// Get normal (Gaussian) random sample with specified mean and standard deviation
double SimpleRNG::GetNormal(double mean = 0.0, double standardDeviation = 1.0)
{
    if (standardDeviation <= 0.0)
    {
        std::stringstream os;
        os << "Standard deviation must be positive." << "\n" 
           << "Received standard deviation " << standardDeviation;
        throw std::invalid_argument( os.str() );
    }
        // Use Box-Muller algorithm
    double u1 = GetUniform();
    double u2 = GetUniform();
    double r = sqrt( -2.0*log(u1) );
    double theta = 2.0*PI*u2;
    return mean + standardDeviation*r*sin(theta);
}
        
// Get exponential random sample with specified mean
double SimpleRNG::GetExponential(double mean = 1.0)
{
    if (mean <= 0.0)
    {
        std::stringstream os;
        os << "Exponential mean must be positive." << "\n" 
           << "Received standard deviation " << mean;
        throw std::invalid_argument( os.str() );
    }
    return -mean*log( GetUniform() );
}

double SimpleRNG::GetGamma(double shape, double scale)
{
    // Implementation based on "A Simple Method for Generating Gamma Variables"
    // by George Marsaglia and Wai Wan Tsang.  ACM Transactions on Mathematical Software
    // Vol 26, No 3, September 2000, pages 363-372.

    double d, c, x, xsquared, v, u;

    if (shape >= 1.0)
    {
        d = shape - 1.0/3.0;
        c = 1.0/sqrt(9.0*d);
        for (;;)
        {
            do
            {
                x = GetNormal();
                v = 1.0 + c*x;
            }
            while (v <= 0.0);
            v = v*v*v;
            u = GetUniform();
            xsquared = x*x;
            if (u < 1.0 -.0331*xsquared*xsquared || log(u) < 0.5*xsquared + d*(1.0 - v + log(v)))
                return scale*d*v;
        }
    }
    else if (shape <= 0.0)
    {
        std::stringstream os;
        os << "Shape parameter must be positive." << "\n"
           << "Received shape parameter " << shape;
        throw std::invalid_argument( os.str() );
    }
    else
    {
        double g = GetGamma(shape+1.0, 1.0);
        double w = GetUniform();
        return scale*g*pow(w, 1.0/shape);
    }
}

double SimpleRNG::GetChiSquare(double degreesOfFreedom)
{
    // A chi squared distribution with n degrees of freedom
    // is a gamma distribution with shape n/2 and scale 2.
    return GetGamma(0.5 * degreesOfFreedom, 2.0);
}

double SimpleRNG::GetInverseGamma(double shape, double scale)
{
    // If X is gamma(shape, scale) then
    // 1/Y is inverse gamma(shape, 1/scale)
    return 1.0 / GetGamma(shape, 1.0 / scale);
}

double SimpleRNG::GetWeibull(double shape, double scale)
{
    if (shape <= 0.0 || scale <= 0.0)
    {
        std::stringstream os;
        os << "Shape and scale parameters must be positive." << "\n" 
           << "Received shape " << shape << " and scale " << scale;
        throw std::invalid_argument( os.str() );
    }
    return scale * pow(-log(GetUniform()), 1.0 / shape);
}

double SimpleRNG::GetCauchy(double median, double scale)
{
    if (scale <= 0)
    {
        std::stringstream os;
        os << "Shape parameter must be positive." << "\n"
           << "Received shape parameter " << scale;
        throw std::invalid_argument( os.str() );
    }

    double p = GetUniform();

    // Apply inverse of the Cauchy distribution function to a uniform
    return median + scale*tan(PI*(p - 0.5));
}

double SimpleRNG::GetStudentT(double degreesOfFreedom)
{
    if (degreesOfFreedom <= 0)
    {
        std::stringstream os;
        os << "Degrees of freedom must be positive." << "\n" 
           << "Received shape parameter " << degreesOfFreedom;
        throw std::invalid_argument( os.str() );
    }

    // See Seminumerical Algorithms by Knuth
    double y1 = GetNormal();
    double y2 = GetChiSquare(degreesOfFreedom);
    return y1 / sqrt(y2 / degreesOfFreedom);
}

// The Laplace distribution is also known as the double exponential distribution.
double SimpleRNG::GetLaplace(double mean, double scale)
{
    double u = GetUniform();
    return (u < 0.5) ?
        mean + scale*log(2.0*u) :
        mean - scale*log(2*(1-u));
}

double SimpleRNG::GetLogNormal(double mu, double sigma)
{
    return exp(GetNormal(mu, sigma));
}

double SimpleRNG::GetBeta(double a, double b)
{
    if (a <= 0.0 || b <= 0.0)
    {
        std::stringstream os;
        os << "Beta parameters must be positive." << "\n" 
           << "Received parameters " << a << " and " << b;
        throw std::invalid_argument( os.str() );
    }

    // There are more efficient methods for generating beta samples.
    // However such methods are a little more efficient and much more complicated.
    // For an explanation of why the following method works, see
    // http://www.johndcook.com/distribution_chart.html#gamma_beta

    double u = GetGamma(a, 1.0);
    double v = GetGamma(b, 1.0);
    return u / (u + v);
}

int SimpleRNG::GetPoisson(double lambda)
{
    return (lambda < 30.0) ? PoissonSmall(lambda) : PoissonLarge(lambda);
}

int SimpleRNG::PoissonSmall(double lambda)
{
    // Algorithm due to Donald Knuth, 1969.
    double p = 1.0, L = exp(-lambda);
    int k = 0;
    do
    {
        k++;
        p *= GetUniform();
    }
    while (p > L);
    return k - 1;
}

int SimpleRNG::PoissonLarge(double lambda)
{
    // "Rejection method PA" from "The Computer Generation of Poisson Random Variables" by A. C. Atkinson
    // Journal of the Royal Statistical Society Series C (Applied Statistics) Vol. 28, No. 1. (1979)
    // The article is on pages 29-35. The algorithm given here is on page 32.

    double c = 0.767 - 3.36/lambda;
    double beta = PI/sqrt(3.0*lambda);
    double alpha = beta*lambda;
    double k = log(c) - lambda - log(beta);

    for(;;)
    {
        double u = GetUniform();
        double x = (alpha - log((1.0 - u)/u))/beta;
        int n = (int) floor(x + 0.5);
        if (n < 0)
            continue;
        double v = GetUniform();
        double y = alpha - beta*x;
        double temp = 1.0 + exp(y);
        double lhs = y + log(v/(temp*temp));
        double rhs = k + n*log(lambda) - LogFactorial(n);
        if (lhs <= rhs)
            return n;
    }
}

double SimpleRNG::LogFactorial(int n)
{

    if (n < 0)
    {
        std::stringstream os;
        os << "Invalid input argument (" << n 
        << "); may not be negative";
        throw std::invalid_argument( os.str() );
            
    }
    else if (n > 254)
    {
        double x = n + 1;
        return (x - 0.5)*log(x) - x + 0.5*log(2*PI) + 1.0/(12.0*x);
    }
    else
    {
        double lf[] =        
        {
            0.000000000000000,
            0.000000000000000,
            0.693147180559945,
            1.791759469228055,
            3.178053830347946,
            4.787491742782046,
            6.579251212010101,
            8.525161361065415,
            10.604602902745251,
            12.801827480081469,
            15.104412573075516,
            17.502307845873887,
            19.987214495661885,
            22.552163853123421,
            25.191221182738683,
            27.899271383840894,
            30.671860106080675,
            33.505073450136891,
            36.395445208033053,
            39.339884187199495,
            42.335616460753485,
            45.380138898476908,
            48.471181351835227,
            51.606675567764377,
            54.784729398112319,
            58.003605222980518,
            61.261701761002001,
            64.557538627006323,
            67.889743137181526,
            71.257038967168000,
            74.658236348830158,
            78.092223553315307,
            81.557959456115029,
            85.054467017581516,
            88.580827542197682,
            92.136175603687079,
            95.719694542143202,
            99.330612454787428,
            102.968198614513810,
            106.631760260643450,
            110.320639714757390,
            114.034211781461690,
            117.771881399745060,
            121.533081515438640,
            125.317271149356880,
            129.123933639127240,
            132.952575035616290,
            136.802722637326350,
            140.673923648234250,
            144.565743946344900,
            148.477766951773020,
            152.409592584497350,
            156.360836303078800,
            160.331128216630930,
            164.320112263195170,
            168.327445448427650,
            172.352797139162820,
            176.395848406997370,
            180.456291417543780,
            184.533828861449510,
            188.628173423671600,
            192.739047287844900,
            196.866181672889980,
            201.009316399281570,
            205.168199482641200,
            209.342586752536820,
            213.532241494563270,
            217.736934113954250,
            221.956441819130360,
            226.190548323727570,
            230.439043565776930,
            234.701723442818260,
            238.978389561834350,
            243.268849002982730,
            247.572914096186910,
            251.890402209723190,
            256.221135550009480,
            260.564940971863220,
            264.921649798552780,
            269.291097651019810,
            273.673124285693690,
            278.067573440366120,
            282.474292687630400,
            286.893133295426990,
            291.323950094270290,
            295.766601350760600,
            300.220948647014100,
            304.686856765668720,
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            327.185287703775200,
            331.717887196928470,
            336.261181979198450,
            340.815058870798960,
            345.379407062266860,
            349.954118040770250,
            354.539085519440790,
            359.134205369575340,
            363.739375555563470,
            368.354496072404690,
            372.979468885689020,
            377.614197873918670,
            382.258588773060010,
            386.912549123217560,
            391.575988217329610,
            396.248817051791490,
            400.930948278915760,
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            410.322776526937280,
            415.032306728249580,
            419.750805599544780,
            424.478193418257090,
            429.214391866651570,
            433.959323995014870,
            438.712914186121170,
            443.475088120918940,
            448.245772745384610,
            453.024896238496130,
            457.812387981278110,
            462.608178526874890,
            467.412199571608080,
            472.224383926980520,
            477.044665492585580,
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            530.584288294433580,
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            560.169054037273100,
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            570.087725725134190,
            575.057539024710200,
            580.034272767130800,
            585.017879388839220,
            590.008311975617860,
            595.005524249382010,
            600.009470555327430,
            605.020105849423770,
            610.037385686238740,
            615.061266207084940,
            620.091704128477430,
            625.128656730891070,
            630.172081847810200,
            635.221937855059760,
            640.278183660408100,
            645.340778693435030,
            650.409682895655240,
            655.484856710889060,
            660.566261075873510,
            665.653857411105950,
            670.747607611912710,
            675.847474039736880,
            680.953419513637530,
            686.065407301994010,
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            768.650616799717000,
            773.860102952558460,
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            784.295394535245690,
            789.521141208958970,
            794.752249825813460,
            799.988691788643450,
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            815.729736303910160,
            820.987231675937890,
            826.249921864842800,
            831.517780023906310,
            836.790779582469900,
            842.068894241700490,
            847.352097970438420,
            852.640365001133090,
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            863.231987192405430,
            868.535292100464630,
            873.843559797865740,
            879.156765776907600,
            884.474885770751830,
            889.797895749890240,
            895.125771918679900,
            900.458490711945270,
            905.796028791646340,
            911.138363043611210,
            916.485470574328820,
            921.837328707804890,
            927.193914982476710,
            932.555207148186240,
            937.921183163208070,
            943.291821191335660,
            948.667099599019820,
            954.046996952560450,
            959.431492015349480,
            964.820563745165940,
            970.214191291518320,
            975.612353993036210,
            981.015031374908400,
            986.422203146368590,
            991.833849198223450,
            997.249949600427840,
            1002.670484599700300,
            1008.095434617181700,
            1013.524780246136200,
            1018.958502249690200,
            1024.396581558613400,
            1029.838999269135500,
            1035.285736640801600,
            1040.736775094367400,
            1046.192096209724900,
            1051.651681723869200,
            1057.115513528895000,
            1062.583573670030100,
            1068.055844343701400,
            1073.532307895632800,
            1079.012946818975000,
            1084.497743752465600,
            1089.986681478622400,
            1095.479742921962700,
            1100.976911147256000,
            1106.478169357800900,
            1111.983500893733000,
            1117.492889230361000,
            1123.006317976526100,
            1128.523770872990800,
            1134.045231790853000,
            1139.570684729984800,
            1145.100113817496100,
            1150.633503306223700,
            1156.170837573242400,
        };
        return lf[n];
    }
}