File: simplerng.c

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/* 
   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,
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            959.431492015349480,
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            970.214191291518320,
            975.612353993036210,
            981.015031374908400,
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            1100.976911147256000,
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            1111.983500893733000,
            1117.492889230361000,
            1123.006317976526100,
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            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];
}