梅森旋转随机数生成实例

梅森旋转演算法（Mersenne twister）是一个伪随机数发生算法。由松本真和西村拓士[1]在1997年开发，基于有限二进制字段上的矩阵线性递归

。可以快速产生高质量的伪随机数，
修正了古典随机数发生算法的很多缺陷。

Mersenne Twister这个名字来自周期长度取自梅森素数的这样一个事实。这个算法通常使用两个相近的变体，不同之处在于使用了不同的梅森素数。一个更新的和更常用的是MT19937, 32位字长。 还有一个变种是64位版的MT19937-64。 对于一个k位的长度，Mersenne
Twister会在

的区间之间生成离散型均匀分布的随机数。

优点：

最为广泛使用Mersenne Twister的一种变体是MT19937，可以产生32位整数序列。具有以下的优点:

周期非常长，达到219937−1。尽管如此长的周期并不必然意味着高质量的伪随机数，但短周期（比如许多旧版本软件包提供的232）确实会带来许多问题。
在1 ≤ k ≤ 623的维度之间都可以均等分布(参见定义).
除了在统计学意义上的不正确的随机数生成器以外，在所有伪随机数生成器法中是最快的(当时)

梅森旋转算法实现：

//************************************************************************
//  This is a slightly modified version of Equamen mersenne twister.
//
//  Copyright (C) 2009 Chipset
//
//  This program is free software: you can redistribute it and/or modify
//  it under the terms of the GNU Affero General Public License as
//  published by the Free Software Foundation, either version 3 of the
//  License, or (at your option) any later version.
//
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
//  GNU Affero General Public License for more details.
//
//  You should have received a copy of the GNU Affero General Public License
//  along with this program. If not, see <http://www.gnu.org/licenses/>.
//************************************************************************

// Original Coyright (c) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura
//
// Functions for MT19937, with initialization improved 2002/2/10.
// Coded by Takuji Nishimura and Makoto Matsumoto.
// This is a faster version by taking Shawn Cokus's optimization,
// Matthe Bellew's simplification, Isaku Wada's real version.
// C++ version by Lyell Haynes (Equamen)
//
// 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.
//

#ifndef mtrandom_HPP_
#define mtrandom_HPP_

#include <stddef.h>

class mtrandom
{
public:
mtrandom() : left(1) { init(); }

explicit mtrandom(size_t seed) : left(1) {    init(seed);    }

mtrandom(size_t* init_key, int key_length) : left(1)
{
int i = 1, j = 0;
int k = N > key_length ? N : key_length;
init();
for(; k; --k)
{
state[i]  =  (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30)) * 1664525UL))+ init_key[j] + j; // non linear
state[i] &=  4294967295UL; // for WORDSIZE > 32 machines
++i;
++j;
if(i >= N)
{
state[0] = state[N - 1];
i = 1;
}
if(j >= key_length)
j = 0;
}

for(k = N - 1; k; --k)
{
state[i] = (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30)) * 1566083941UL)) - i; // non linear
state[i] &= 4294967295UL; // for WORDSIZE > 32 machines
++i;
if(i >= N)
{
state[0] = state[N - 1];
i = 1;
}
}

state[0]  =  2147483648UL; // MSB is 1; assuring non-zero initial array
}

void reset(size_t rs)
{
init(rs);
next_state();
}

size_t rand()
{
size_t y;
if(0 == --left)
next_state();
y  = *next++;
// Tempering
y ^= (y >> 11);
y ^= (y << 7) & 0x9d2c5680UL;
y ^= (y << 15) & 0xefc60000UL;
y ^= (y >> 18);
return y;
}

double real()    {    return (double)rand() / -1UL;    }

// generates a random number on [0,1) with 53-bit resolution
double res53()
{
size_t a = rand() >> 5, b = rand() >> 6;
return (a * 67108864.0 + b) / 9007199254740992.0;
}

private:
void init(size_t seed = 19650218UL)
{
state[0] =  seed & 4294967295UL;
for(int j = 1; j < N; ++j)
{
state[j]  =  (1812433253UL * (state[j - 1] ^ (state[j - 1]  >>  30)) + j);
// See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier.
// In the previous versions, MSBs of the seed affect
// only MSBs of the array state[].
// 2002/01/09 modified by Makoto Matsumoto
state[j] &=  4294967295UL;  // for >32 bit machines
}
}

void next_state()
{
size_t* p = state;
int i;

for(i = N - M + 1; --i; ++p)
*p = (p[M] ^ twist(p[0], p[1]));

for(i = M; --i; ++p)
*p = (p[M - N] ^ twist(p[0], p[1]));
*p = p[M - N] ^ twist(p[0], state[0]);
left = N;
next = state;
}

size_t mixbits(size_t u, size_t v) const
{
return (u & 2147483648UL) | (v & 2147483647UL);
}

size_t twist(size_t u, size_t v) const
{
return ((mixbits(u, v)  >>  1) ^ (v & 1UL ? 2567483615UL : 0UL));
}

static const int N = 624, M = 397;
size_t state
;
size_t left;
size_t* next;
};

class mtrand_help
{
static mtrandom r;
public:
mtrand_help() {}
void operator()(size_t s) { r.reset(s); }
size_t operator()() const { return r.rand(); }
double operator()(double) { return r.real(); }
};
mtrandom mtrand_help:: r;

extern void mtsrand(size_t s) { mtrand_help()(s); }
extern size_t mtirand() { return mtrand_help()(); }
extern double mtdrand() { return mtrand_help()(1.0); }

#endif // mtrandom_HPP_

应用举例：

#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <stddef.h>
#include <ctime>
using namespace std;

class mtrandom
{
public:
mtrandom() : left(1) { init(); }

explicit mtrandom(size_t seed) : left(1) {    init(seed);    }

mtrandom(size_t* init_key, int key_length) : left(1)
{
int i = 1, j = 0;
int k = N > key_length ? N : key_length;
init();
for(; k; --k)
{
state[i]  =  (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30)) * 1664525UL))+ init_key[j] + j; // non linear
state[i] &=  4294967295UL; // for WORDSIZE > 32 machines
++i;
++j;
if(i >= N)
{
state[0] = state[N - 1];
i = 1;
}
if(j >= key_length)
j = 0;
}

for(k = N - 1; k; --k)
{
state[i] = (state[i] ^ ((state[i - 1] ^ (state[i - 1] >> 30)) * 1566083941UL)) - i; // non linear
state[i] &= 4294967295UL; // for WORDSIZE > 32 machines
++i;
if(i >= N)
{
state[0] = state[N - 1];
i = 1;
}
}

state[0]  =  2147483648UL; // MSB is 1; assuring non-zero initial array
}

void reset(size_t rs)
{
init(rs);
next_state();
}

size_t rand()
{
size_t y;
if(0 == --left)
next_state();
y  = *next++;
// Tempering
y ^= (y >> 11);
y ^= (y << 7) & 0x9d2c5680UL;
y ^= (y << 15) & 0xefc60000UL;
y ^= (y >> 18);
return y;
}

double real()    {    return (double)rand() / -1UL;    }

// generates a random number on [0,1) with 53-bit resolution
double res53()
{
size_t a = rand() >> 5, b = rand() >> 6;
return (a * 67108864.0 + b) / 9007199254740992.0;
}

public:
void init(size_t seed = 19650218UL)
{
state[0] =  seed & 4294967295UL;
for(int j = 1; j < N; ++j)
{
state[j]  =  (1812433253UL * (state[j - 1] ^ (state[j - 1]  >>  30)) + j);
// See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier.
// In the previous versions, MSBs of the seed affect
// only MSBs of the array state[].
// 2002/01/09 modified by Makoto Matsumoto
state[j] &=  4294967295UL;  // for >32 bit machines
}
}

void next_state()
{
size_t* p = state;
int i;

for(i = N - M + 1; --i; ++p)
*p = (p[M] ^ twist(p[0], p[1]));

for(i = M; --i; ++p)
*p = (p[M - N] ^ twist(p[0], p[1]));
*p = p[M - N] ^ twist(p[0], state[0]);
left = N;
next = state;
}

size_t mixbits(size_t u, size_t v) const
{
return (u & 2147483648UL) | (v & 2147483647UL);
}

size_t twist(size_t u, size_t v) const
{
return ((mixbits(u, v)  >>  1) ^ (v & 1UL ? 2567483615UL : 0UL));
}

static const int N = 624, M = 397;
size_t state
;
size_t left;
size_t* next;
};

class mtrand_help
{
public:
static mtrandom r;
public:
mtrand_help() {}
void operator()(size_t s) { r.reset(s); }
size_t operator()() const { return r.rand(); }
double operator()(double) { return r.real(); }
};
mtrandom mtrand_help:: r;

void mtsrand(size_t s) { mtrand_help()(s); }
size_t mtirand() { return mtrand_help()(); }
double mtdrand() { return mtrand_help()(1.0); }

int Random(int low, int high);
int Random2(double start, double end);
int Random3(double start, double end);
int main(int argc, char *argv[])
{
mtsrand(time(NULL));
int t = mtdrand()*10;//0~1.0
cout << t << endl;
for(int i=0;i<100;i++)
{
if(i%5 == 0)
cout << endl;
cout << Random(1,50)<<" ";
}
cout << endl;

return 0;
}
//[low high]
int Random(int low, int high)
{
return low + mtirand() % (high - low + 1);
}
//[start end)
int Random2(double start, double end)
{
return start+(end-start)*rand()/(RAND_MAX + 1.0);
}