乱数の発生

/*************************/
/* 乱数の発生            */
/*      coded Y.Suganuma */
/*************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double exp_d(double);
double norm_d(double, double);
double unifm_d();

int main()
{
	double a, b, m, r, mean, sd;
	int i1, n = 10000, seed;

	printf("乱数の初期値を入力してください ");
	scanf("%d", &seed);

	srand(seed);   // 乱数の初期設定
/*
          [a b] 区間の一様乱数
*/
	mean = 0.0;
	sd   = 0.0;
	a    = 2.0;
	b    = 4.0;

	for (i1 = 0; i1 < n; i1++) {
		r     = a + (b - a) * unifm_d();
		mean += r;
		sd   += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("一様分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);
/*
          平均 m の指数分布
*/
	mean = 0.0;
	sd   = 0.0;
	m    = 0.5;

	for (i1 = 0; i1 < n; i1++) {
		r     = exp_d(m);
		mean += r;
		sd   += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("指数分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);
/*
          標準正規分布
*/
	mean = 0.0;
	sd   = 0.0;

	for (i1 = 0; i1 < n; i1++) {
		r     = norm_d(0.0, 1.0);
		mean += r;
		sd   += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("標準正規分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);

	return 0;
}

/******************************/
/* [0, 1]区間の一様乱数の発生 */
/*      rerutn : 乱数         */
/******************************/
double unifm_d()
{
	double x;

	while ((x = (double)rand() / RAND_MAX) == 0.0)
		;

	return x;
}

/*****************************/
/* 平均値 m の指数乱数の発生 */
/*      m : 平均             */
/*****************************/
#include <math.h>

double exp_d(double m)
{
	return -m * log(unifm_d());
}

/***********************************/
/* 正規分布変量の発生              */
/*      m : 平均                   */
/*      s : 標準偏差               */
/*           return : 正規分布変量 */
/***********************************/
double norm_d(double m, double s)
{
	double x;
	int i1;

	x = 0.0;

	for (i1 = 0; i1 < 12; i1++)
		x += unifm_d();

	x = s * (x - 6.0) + m;

	return x;
}
		

　　上のプログラムにおいては，標準関数の rand を使用していますが，rand は，16 ビットを使用しているためその周期が短く（最大でも，32767 ），あまり質が良い乱数を生成してくれません．そこで，メルセンヌ・ツイスタを使用した例（ MT.h を含む）も添付しておきます．メルセンヌ・ツイスタでは，以下に示すような乱数を生成できます．C++11 の場合は，メルセンヌ・ツイスタ法を使用した乱数生成関数が，標準ライブラリ内に含まれています．

genrand_int32() //符号なし32ビット長整数

genrand_int31() //符号なし31ビット長整数

genrand_real1() //一様実乱数[0,1] (32ビット精度)

genrand_real2() //一様実乱数[0,1) (32ビット精度)

genrand_real3() //一様実乱数(0,1) (32ビット精度)

genrand_res53() //一様実乱数[0,1) (53ビット精度)

-----------------------使用方法--------------------

/**********************************/
/* メルセンヌ・ツイスタの使用方法 */
/*      coded by Y.Suganuma       */
/**********************************/
#include <stdio.h>
#include <time.h>
#include <math.h>
#include "MT.h"
 
int main()
{
/*
			初期設定
*/
	init_genrand((unsigned)time(NULL));
/*
			符号なし32ビット長整数乱数の生成
*/
	for (int i1 = 0; i1 < 10; i1++)
		printf("%lld\n",(unsigned long long)genrand_int32());

	return 0;
}

-----------------------乱数の発生--------------------

/*************************/
/* 乱数の発生            */
/*      coded Y.Suganuma */
/*************************/
#include <stdio.h>
#include <math.h>
#include <time.h>
#include "MT.h"

double exp_d(double);
double norm_d(double, double);

int main()
{
	double a, b, m, r, mean, sd;
	int i1, n = 10000;

	init_genrand((unsigned)time(NULL));   // 乱数の初期設定
/*
          [a b] 区間の一様乱数
*/
	mean = 0.0;
	sd   = 0.0;
	a    = 2.0;
	b    = 4.0;

	for (i1 = 0; i1 < n; i1++) {
		r     = a + (b - a) * genrand_real3();
		mean += r;
		sd   += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("一様分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);
/*
          平均 m の指数分布
*/
	mean = 0.0;
	sd   = 0.0;
	m    = 0.5;

	for (i1 = 0; i1 < n; i1++) {
		r     = exp_d(m);
		mean += r;
		sd   += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("指数分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);
/*
          標準正規分布
*/
	mean = 0.0;
	sd   = 0.0;

	for (i1 = 0; i1 < n; i1++) {
		r     = norm_d(0.0, 1.0);
		mean += r;
		sd   += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("標準正規分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);

	return 0;
}

/*****************************/
/* 平均値 m の指数乱数の発生 */
/*      m : 平均             */
/*****************************/
#include <math.h>

double exp_d(double m)
{
	return -m * log(genrand_real3());
}

/***********************************/
/* 正規分布変量の発生              */
/*      m : 平均                   */
/*      s : 標準偏差               */
/*           return : 正規分布変量 */
/***********************************/
double norm_d(double m, double s)
{
	double x;
	int i1;

	x = 0.0;

	for (i1 = 0; i1 < 12; i1++)
		x += genrand_real3();

	x = s * (x - 6.0) + m;

	return x;
}

-----------------------MT.h--------------------

/*
   A C-program for MT19937, with initialization improved 2002/1/26.
   Coded by Takuji Nishimura and Makoto Matsumoto.

   Before using, initialize the state by using init_genrand(seed)  
   or init_by_array(init_key, key_length).

   Copyright (C) 1997 - 2002, 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.


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

/*
   The original version of http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c was modified by Takahiro Omi as
   - delete line 47 "#include<stdio.h>"
   - delete line 174 int main(void){...}
   - change N -> MT_N
   - change N -> MT_N
   - change the file name "mt19937ar.c" -> "MT.h"
*/


/* Period parameters */  
#define MT_N 624
#define MT_M 397
#define MATRIX_A 0x9908b0dfUL   /* constant vector a */
#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
#define LOWER_MASK 0x7fffffffUL /* least significant r bits */

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

/* initializes mt[MT_N] with a seed */
void init_genrand(unsigned long s)
{
    mt[0]= s & 0xffffffffUL;
    for (mti=1; mti<MT_N; mti++) {
        mt[mti] = 
	    (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); 
        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
        /* In the previous versions, MSBs of the seed affect   */
        /* only MSBs of the array mt[].                        */
        /* 2002/01/09 modified by Makoto Matsumoto             */
        mt[mti] &= 0xffffffffUL;
        /* for >32 bit machines */
    }
}

/* initialize by an array with array-length */
/* init_key is the array for initializing keys */
/* key_length is its length */
/* slight change for C++, 2004/2/26 */
void init_by_array(unsigned long init_key[], int key_length)
{
    int i, j, k;
    init_genrand(19650218UL);
    i=1; j=0;
    k = (MT_N>key_length ? MT_N : key_length);
    for (; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
          + init_key[j] + j; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++; j++;
        if (i>=MT_N) { mt[0] = mt[MT_N-1]; i=1; }
        if (j>=key_length) j=0;
    }
    for (k=MT_N-1; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
          - i; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++;
        if (i>=MT_N) { mt[0] = mt[MT_N-1]; i=1; }
    }

    mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ 
}

/* generates a random number on [0,0xffffffff]-interval */
unsigned long genrand_int32(void)
{
    unsigned long y;
    static unsigned long mag01[2]={0x0UL, MATRIX_A};
    /* mag01[x] = x * MATRIX_A  for x=0,1 */

    if (mti >= MT_N) { /* generate N words at one time */
        int kk;

        if (mti == MT_N+1)   /* if init_genrand() has not been called, */
            init_genrand(5489UL); /* a default initial seed is used */

        for (kk=0;kk<MT_N-MT_M;kk++) {
            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
            mt[kk] = mt[kk+MT_M] ^ (y >> 1) ^ mag01[y & 0x1UL];
        }
        for (;kk<MT_N-1;kk++) {
            y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
            mt[kk] = mt[kk+(MT_M-MT_N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
        }
        y = (mt[MT_N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
        mt[MT_N-1] = mt[MT_M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

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

    /* Tempering */
    y ^= (y >> 11);
    y ^= (y << 7) & 0x9d2c5680UL;
    y ^= (y << 15) & 0xefc60000UL;
    y ^= (y >> 18);

    return y;
}

/* generates a random number on [0,0x7fffffff]-interval */
long genrand_int31(void)
{
    return (long)(genrand_int32()>>1);
}

/* generates a random number on [0,1]-real-interval */
double genrand_real1(void)
{
    return genrand_int32()*(1.0/4294967295.0); 
    /* divided by 2^32-1 */ 
}

/* generates a random number on [0,1)-real-interval */
double genrand_real2(void)
{
    return genrand_int32()*(1.0/4294967296.0); 
    /* divided by 2^32 */
}

/* generates a random number on (0,1)-real-interval */
double genrand_real3(void)
{
    return (((double)genrand_int32()) + 0.5)*(1.0/4294967296.0); 
    /* divided by 2^32 */
}

/* generates a random number on [0,1) with 53-bit resolution*/
double genrand_res53(void) 
{ 
    unsigned long a=genrand_int32()>>5, b=genrand_int32()>>6; 
    return(a*67108864.0+b)*(1.0/9007199254740992.0); 
} 
/* These real versions are due to Isaku Wada, 2002/01/09 added */

		

---------------------（C++11）乱数-------------------------

　　参考のため，標準ライブラリ内の関数 uniform_real_distribution，exponential_distribution，normal_distribution を使用した例を示しておきます．

/*************************/
/* 乱数の発生            */
/*      coded Y.Suganuma */
/*************************/
#include <stdio.h>
#include <random>
#include <cmath>

using namespace std;

int main()
{
	random_device rsd;   // 予測不能な乱数生成器(class)，初期設定のために使用
	mt19937 rnd(rsd());   // 乱数生成期の定義とその初期設定
/*
          [2, 4] 区間の一様乱数
*/
	double mean = 0.0;
	double sd   = 0.0;
	int n       = 10000;

	uniform_real_distribution<> uniform_r(2.0, 4.0);   // コンストラクタ

	for (int i1 = 0; i1 < n; i1++) {
		double r = uniform_r(rnd);
		mean    += r;
		sd      += r * r;
	}

	mean = mean / n;
	sd   = sqrt(abs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("一様分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);
/*
          平均 0.5 の指数分布
*/
	mean     = 0.0;
	sd       = 0.0;

	exponential_distribution<> exponent(0.5);   // コンストラクタ

	for (int i1 = 0; i1 < n; i1++) {
		double r = exponent(rnd);
		mean    += r;
		sd      += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("指数分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);
/*
          標準正規分布
*/
	mean = 0.0;
	sd   = 0.0;

	normal_distribution<> normal(0.0, 1.0);   // コンストラクタ

	for (int i1 = 0; i1 < n; i1++) {
		double r = normal(rnd);
		mean    += r;
		sd      += r * r;
	}

	mean = mean / n;
	sd   = sqrt(fabs(n /(n - 1.0) * (sd / n - mean * mean)));

	printf("標準正規分布\n");
	printf("   平均 %f 標準偏差 %f\n", mean, sd);

	return 0;
}
		

----------------------（C++11）乱数終わり--------------------