rand.c

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "rand.h"

#define NN 312
#define MM 156
#define MATRIX_A 0xB5026F5AA96619E9ULL
#define UM 0xFFFFFFFF80000000ULL /* Most significant 33 bits */
#define LM 0x7FFFFFFFULL /* Least significant 31 bits */


/* 
   A C-program for MT19937-64 (2004/9/29 version).
   Coded by Takuji Nishimura and Makoto Matsumoto.

   This is a 64-bit version of Mersenne Twister pseudorandom number
   generator.

   Before using, initialize the state by using init_genrand64(seed)  
   or init_by_array64(init_key, key_length).

   Copyright (C) 2004, Makoto Matsumoto and Takuji Nishimura,
   All rights reserved.                          

   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions
   are met:

     1. Redistributions of source code must retain the above copyright
        notice, this list of conditions and the following disclaimer.

     2. Redistributions in binary form must reproduce the above copyright
        notice, this list of conditions and the following disclaimer in the
        documentation and/or other materials provided with the distribution.

     3. The names of its contributors may not be used to endorse or promote 
        products derived from this software without specific prior written 
        permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
   CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

   References:
   T. Nishimura, ``Tables of 64-bit Mersenne Twisters''
     ACM Transactions on Modeling and 
     Computer Simulation 10. (2000) 348--357.
   M. Matsumoto and T. Nishimura,
     ``Mersenne Twister: a 623-dimensionally equidistributed
       uniform pseudorandom number generator''
     ACM Transactions on Modeling and 
     Computer Simulation 8. (Jan. 1998) 3--30.

   Any feedback is very welcome.
   http://www.math.hiroshima-u.ac.jp/~m-mat/MT/emt.html
   email: m-mat @ math.sci.hiroshima-u.ac.jp (remove spaces)
*/


/* The array for the state vector */
static unsigned long long mt[NN]; 
/* mti==NN+1 means mt[NN] is not initialized */
static int mti=NN+1; 

/* initializes mt[NN] with a seed */
void init_genrand64(unsigned long long seed)
{
    mt[0] = seed;
    for (mti=1; mti<NN; mti++) 
        mt[mti] =  (6364136223846793005ULL * (mt[mti-1] ^ (mt[mti-1] >> 62)) + mti);
}

/* initialize by an array with array-length */
/* init_key is the array for initializing keys */
/* key_length is its length */
void init_by_array64(unsigned long long init_key[],
		     unsigned long long key_length)
{
    unsigned long long i, j, k;
    init_genrand64(19650218ULL);
    i=1; j=0;
    k = (NN>key_length ? NN : key_length);
    for (; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 62)) * 3935559000370003845ULL))
          + init_key[j] + j; /* non linear */
        i++; j++;
        if (i>=NN) { mt[0] = mt[NN-1]; i=1; }
        if (j>=key_length) j=0;
    }
    for (k=NN-1; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 62)) * 2862933555777941757ULL))
          - i; /* non linear */
        i++;
        if (i>=NN) { mt[0] = mt[NN-1]; i=1; }
    }

    mt[0] = 1ULL << 63; /* MSB is 1; assuring non-zero initial array */ 
}

/* generates a random number on [0, 2^64-1]-interval */
unsigned long long genrand64_int64(void)
{
    int i;
    unsigned long long x;
    static unsigned long long mag01[2]={0ULL, MATRIX_A};

    if (mti >= NN) { /* generate NN words at one time */

        /* if init_genrand64() has not been called, */
        /* a default initial seed is used     */
        if (mti == NN+1) 
            init_genrand64(5489ULL); 

        for (i=0;i<NN-MM;i++) {
            x = (mt[i]&UM)|(mt[i+1]&LM);
            mt[i] = mt[i+MM] ^ (x>>1) ^ mag01[(int)(x&1ULL)];
        }
        for (;i<NN-1;i++) {
            x = (mt[i]&UM)|(mt[i+1]&LM);
            mt[i] = mt[i+(MM-NN)] ^ (x>>1) ^ mag01[(int)(x&1ULL)];
        }
        x = (mt[NN-1]&UM)|(mt[0]&LM);
        mt[NN-1] = mt[MM-1] ^ (x>>1) ^ mag01[(int)(x&1ULL)];

        mti = 0;
    }
  
    x = mt[mti++];

    x ^= (x >> 29) & 0x5555555555555555ULL;
    x ^= (x << 17) & 0x71D67FFFEDA60000ULL;
    x ^= (x << 37) & 0xFFF7EEE000000000ULL;
    x ^= (x >> 43);

    return x;
}

/* generates a random number on [0, 2^63-1]-interval */
long long genrand64_int63(void)
{
    return (long long)(genrand64_int64() >> 1);
}

/* generates a random number on [0,1]-real-interval */
double genrand64_real1(void)
{
    return (genrand64_int64() >> 11) * (1.0/9007199254740991.0);
}

/* generates a random number on [0,1)-real-interval */
double genrand64_real2(void)
{
    return (genrand64_int64() >> 11) * (1.0/9007199254740992.0);
}

/* generates a random number on (0,1)-real-interval */
double genrand64_real3(void)
{
    return ((genrand64_int64() >> 12) + 0.5) * (1.0/4503599627370496.0);
}
/*

int main(void)
{
    int i;
    unsigned long long init[4]={0x12345ULL, 0x23456ULL, 0x34567ULL, 0x45678ULL}, length=4;
    init_by_array64(init, length);
    printf("1000 outputs of genrand64_int64()\n");
    for (i=0; i<1000; i++) {
      printf("%20llu ", genrand64_int64());
      if (i%5==4) printf("\n");
    }
    printf("\n1000 outputs of genrand64_real2()\n");
    for (i=0; i<1000; i++) {
      printf("%10.8f ", genrand64_real2());
      if (i%5==4) printf("\n");
    }
    return 0;
}
*/





/*-------------  UNIFORM [0, 1) RANDOM NUMBER GENERATOR  -------------*/
double uniform(void)
  {
	//return drand48();

	return genrand64_real2();
  }


/*-------------  UNIFORM (0, 1) RANDOM NUMBER GENERATOR  -------------*/
double uniform_pos(void)
{
	double g;

	g = uniform();
	while (g == 0.0)
		g = uniform();

	return g;

/*
	return genrand64_real3();
*/
}


/*--------------------------  SET SEED  --------------------------*/
void seed( long int n)
    { /* set seed to n  */
	//srand48(n);
	
	unsigned long long init[4]={n, n+3, n+5, n+13}, length=4;
    	init_by_array64(init, length);
    }

/*------------  UNIFORM [a, b) RANDOM VARIATE GENERATOR  -------------*/
double uniform_ab(double a, double b)
    { /* 'uniform' returns a psuedo-random variate from a uniform     */
      /* distribution with lower bound a and upper bound b.           */
      if (a>b)  printf("uniform Argument Error: a > b\n");
      return(a+(b-a)*uniform());
    }

/*--------------------  RANDOM INTEGER GENERATOR  --------------------*/
int uniform_int(int i, int n)
    { /* 'random' returns an integer equiprobably selected from the   */
      /* set of integers i, i+1, i+2, . . , n.                        */
      if (i>n)  printf("random Argument Error: i > n\n");
      n-=i; n=(n+1.0)*uniform();
      return(i+n);
    }

/*--------------  EXPONENTIAL RANDOM VARIATE GENERATOR  --------------*/
/* The exponential distribution has the form

   p(x) dx = exp(-x/landa) dx/landa

   for x = 0 ... +infty 
*/


double exponential(double landa)
{ 
	/* 'exponential' returns a psuedo-random variate from a negative     */
      	/* exponential distribution with mean 1/landa.                        */

 	double u = uniform_pos();	
	double mean = 1.0 / landa;


 	return -mean * log(1-u);
}

/*----------------  ERLANG RANDOM VARIATE GENERATOR  -----------------*/
double erlang(double x, double s)
    { /* 'erlang' returns a psuedo-random variate from an erlang      */
      /* distribution with mean x and standard deviation s.           */
      int i,k; double z;
      if (s>x)  printf("erlang Argument Error: s > x\n");
      z=x/s; k=(int)z*z;
      z=1.0; for (i=0; i<k; i++) z*=uniform_pos();
      return(-(x/k)*log(z));
    }

/*-----------  HYPEREXPONENTIAL RANDOM VARIATE GENERATION  -----------*/
double hyperx(double x, double s)
    { /* 'hyperx' returns a psuedo-random variate from Morse's two-   */
      /* stage hyperexponential distribution with mean x and standard */
      /* deviation s, s>x.  */
      double cv,z,p;
      if (s<=x)  printf("hyperx Argument Error: s not > x\n");
      cv=s/x; z=cv*cv; p=0.5*(1.0-sqrt((z-1.0)/(z+1.0)));
      z=(uniform_pos()>p)? (x/(1.0-p)):(x/p);
      return(-0.5*z*log(uniform_pos()));
    }

/*-----------------  NORMAL RANDOM VARIATE GENERATOR  ----------------*/
double normal(double x, double s)
    { /* 'normal' returns a psuedo-random variate from a normal dis-  */
      /* tribution with mean x and standard deviation s.              */
      double v1,v2,w,z1; static double z2=0.0;
      if (z2!=0.0)
         {z1=z2; z2=0.0;}  /* use value from previous call */
        else
          {
            do
              {v1=2.0*uniform_pos()-1.0; v2=2.0*uniform_pos()-1.0; w=v1*v1+v2*v2;}
            while (w>=1.0);
            w=sqrt((-2.0*log(w))/w); z1=v1*w; z2=v2*w;
          }
      return(x+z1*s);
  }



/* The Weibull distribution has the form,

   p(x) dx = (k/a) (x/a)^(k-1) exp(-(x/a)^k) dx

   k = shape
  a = landa = scale
 */

double ran_weibull ( const double k, const double a)
{
  double x = uniform_pos ();

  double z = pow (-log (x), 1 / k);

  return a * z;
}



/* The Gamma distribution 

   k = shape
   b = teta = scale

   p(x) dx = {1 / \Gamma(k) b^a } x^{k-1} e^{-x/b} dx

   for x>0.  If X and Y are independent gamma-distributed random
   variables of order a1 and a2 with the same scale parameter b, then
   X+Y has gamma distribution of order a1+a2.

   The algorithms below are from Knuth, vol 2, 2nd ed, p. 129. */

double ran_gamma (const double k, const double b)
{
  /* assume a > 0 */
   unsigned int na = floor (k);

  if (k == na)
    {
      return b * ran_gamma_int (na);
    }
  else if (na == 0)
    {
      return b * gamma_frac (k);
    }
  else
    {
      return b * (ran_gamma_int (na) + gamma_frac (k - na)) ;
    }
}

double ran_gamma_int (const unsigned int a)
{
  if (a < 12)
    {
      unsigned int i;
      double prod = 1;

      for (i = 0; i < a; i++)
        {
          prod *= uniform_pos ();
        }

      /* Note: for 12 iterations we are safe against underflow, since
         the smallest positive random number is O(2^-32). This means
         the smallest possible product is 2^(-12*32) = 10^-116 which
         is within the range of double precision. */

      return -log (prod);
    }
  else
    {
      return gamma_large ((double) a);
    }
}

static double gamma_large (const double a)
{
  /* Works only if a > 1, and is most efficient if a is large

     This algorithm, reported in Knuth, is attributed to Ahrens.  A
     faster one, we are told, can be found in: J. H. Ahrens and
     U. Dieter, Computing 12 (1974) 223-246 begin_of_the_skype_highlighting              12 (1974) 223-246      end_of_the_skype_highlighting.  */

  double sqa, x, y, v;
  sqa = sqrt (2 * a - 1);
  do
    {
      do
        {
          y = tan (M_PI * uniform ());
          x = sqa * y + a - 1;
        }
      while (x <= 0);
      v = uniform ();
    }
  while (v > (1 + y * y) * exp ((a - 1) * log (x / (a - 1)) - sqa * y));

  return x;
}

static double gamma_frac (const double a)
{
  /* This is exercise 16 from Knuth; see page 135, and the solution is
     on page 551.  */

  double p, q, x, u, v;
  p = M_E / (a + M_E);
  do
    {
      u = uniform ();
      v = uniform_pos ();

      if (u < p)
        {
          x = exp ((1 / a) * log (v));
          q = exp (-x);
        }
      else
        {
          x = 1 - log (v);
          q = exp ((a - 1) * log (x));
        }
    }
  while (uniform () >= q);

  return x;
}