/* 
   Simple Random Number Generators
       - getuniform - uniform deviate [0,1]
       - getnorm    - gaussian (normal) deviate (mean=0, stddev=1)
       - getpoisson - poisson deviate for given expected mean lambda

   This code is adapted from SimpleRNG by John D Cook, which is
   provided in the public domain.

   The original C++ code is found here:
   http://www.johndcook.com/cpp_random_number_generation.html

   This code has been modified in the following ways compared to the
   original.
     1. convert to C from C++
     2. keep only uniform, gaussian and poisson deviates
     3. state variables are module static instead of class variables
     4. provide an srand() equivalent to initialize the state
*/
#include <math.h>
#include <stdlib.h>

#define PI 3.1415926535897932384626433832795

/* Use the standard system rand() library routine if it provides
   enough bits of information, since it probably has better randomness
   than the toy algorithm in this module. */
#if defined(RAND_MAX) && RAND_MAX > 1000000000
#define USE_SYSTEM_RAND
#endif

int simplerng_poisson_small(double lambda);
int simplerng_poisson_large(double lambda);
double simplerng_getuniform_pr(unsigned int *u, unsigned int *v);
unsigned int simplerng_getuint_pr(unsigned int *u, unsigned int *v);
double simplerng_logfactorial(int n);

/*
  These values are not magical, just the default values Marsaglia used.
  Any unit should work.
*/
static unsigned int m_u = 521288629, m_v = 362436069;

/* Set u and v state variables */
void simplerng_setstate(unsigned int u, unsigned int v)
{
    m_u = u;
    m_v = v;
}

/* Retrieve u and v state variables */
void simplerng_getstate(unsigned int *u, unsigned int *v)
{
    *u = m_u;
    *v = m_v;
}

/* srand() equivalent to seed the two state variables */
void simplerng_srand(unsigned int seed)
{
#ifdef USE_SYSTEM_RAND
  srand(seed);
#else
  simplerng_setstate(seed ^ 521288629, seed ^ 362436069);
#endif
}

/* Private routine to get uniform deviate */
double simplerng_getuniform_pr(unsigned int *u, unsigned int *v)
{
  /* 0 <= u <= 2^32 */
  unsigned int z = simplerng_getuint_pr(u, v);
  /* The magic number is 1/(2^32) and so result is positive and less than 1. */
  return z*2.328306435996595e-10;
}

/* Private routine to get unsigned integer */
/* Marsaglia multiply-with-carry algorithm (MWC) */
unsigned int simplerng_getuint_pr(unsigned int *u, unsigned int *v)
{
  *v = 36969*((*v) & 65535) + ((*v) >> 16);
  *u = 18000*((*u) & 65535) + ((*u) >> 16);
  return ((*v) << 16) + (*u);
}

/* Get uniform deviate [0,1] */
double simplerng_getuniform(void)
{
#ifdef USE_SYSTEM_RAND
  return rand()*(1.0 / ((double)RAND_MAX + 1));
#else
  return simplerng_getuniform_pr(&m_u, &m_v);
#endif
}

/* Get unsigned integer [0, UINT_MAX] */
unsigned int simplerng_getuint()
{
  /* WARNING: no option for calling rand() here.  Will need to provide
     a scalar to make the uint in the [0,UINT_MAX] range */
  return simplerng_getuint_pr(&m_u, &m_v);
}
    
/* Get normal (Gaussian) random sample with mean=0, stddev=1 */
double simplerng_getnorm()
{
  double u1, u2, r, theta;
  static int saved = 0;
  static double y;

  /* Since you get two deviates for "free" with each calculation, save
     one of them for later */

  if (saved == 0) {
    /* Use Box-Muller algorithm */
    u1 = simplerng_getuniform();
    u2 = simplerng_getuniform();
    r = sqrt( -2.0*log(u1) );
    theta = 2.0*PI*u2;
    /* save second value for next call */
    y = r*cos(theta);
    saved = 1;
    return r*sin(theta);

  } else {
    /* We already saved a value from the last call so use it */
    saved = 0;
    return y;
  }
}

/* Poisson deviate for expected mean value lambda.
   lambda should be in the range [0, infinity]
   
   For small lambda, a simple rejection method is used
   For large lambda, an approximation is used
*/
int simplerng_getpoisson(double lambda)
{
  if (lambda < 0) lambda = 0;
  return ((lambda < 15.0) 
	  ? simplerng_poisson_small(lambda) 
	  : simplerng_poisson_large(lambda));
}

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

int simplerng_poisson_large(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. */
  static double beta, alpha, k;
  static double old_lambda = -999999.;

  if (lambda != old_lambda) {
    double c = 0.767 - 3.36/lambda;
    beta = PI/sqrt(3.0*lambda);
    alpha = beta*lambda;
    k = log(c) - lambda - log(beta);
    old_lambda = lambda;
  }

  for(;;) { /* forever */
    double u, x, v, y, temp, lhs, rhs;
    int n;

    u = simplerng_getuniform();
    x = (alpha - log((1.0 - u)/u))/beta;
    n = (int) floor(x + 0.5);
    if (n < 0) continue;

    v = simplerng_getuniform();
    y = alpha - beta*x;
    temp = 1.0 + exp(y);
    lhs = y + log(v/(temp*temp));
    rhs = k + n*log(lambda) - simplerng_logfactorial(n);
    if (lhs <= rhs) return n;
  }

}

/* Lookup table for log-gamma function */
static 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,
            309.164193580146900,
            313.652829949878990,
            318.152639620209300,
            322.663499126726210,
            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,
            405.622296161144900,
            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,
            481.872979229887900,
            486.709261136839360,
            491.553448223298010,
            496.405478487217580,
            501.265290891579240,
            506.132825342034830,
            511.008022665236070,
            515.890824587822520,
            520.781173716044240,
            525.679013515995050,
            530.584288294433580,
            535.496943180169520,
            540.416924105997740,
            545.344177791154950,
            550.278651724285620,
            555.220294146894960,
            560.169054037273100,
            565.124881094874350,
            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,
            691.183401114410800,
            696.307365093814040,
            701.437263808737160,
            706.573062245787470,
            711.714725802289990,
            716.862220279103440,
            722.015511873601330,
            727.174567172815840,
            732.339353146739310,
            737.509837141777440,
            742.685986874351220,
            747.867770424643370,
            753.055156230484160,
            758.248113081374300,
            763.446610112640200,
            768.650616799717000,
            773.860102952558460,
            779.075038710167410,
            784.295394535245690,
            789.521141208958970,
            794.752249825813460,
            799.988691788643450,
            805.230438803703120,
            810.477462875863580,
            815.729736303910160,
            820.987231675937890,
            826.249921864842800,
            831.517780023906310,
            836.790779582469900,
            842.068894241700490,
            847.352097970438420,
            852.640365001133090,
            857.933669825857460,
            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,
};

double simplerng_logfactorial(int n)
{
  if (n < 0) return 0;
  if (n > 254) {
    double x = n + 1;
    return (x - 0.5)*log(x) - x + 0.5*log(2*PI) + 1.0/(12.0*x);
  }
  return lf[n];
}