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使用随机数生成器对 Pi 进行 C++ 近似，输出在我运行 Ubuntu 的 AMD 64 机器上完全符合预期，但是在我的学校机器上，我实现的第二个算法被破坏了，并且希望了解原因。代码如下：

#ifndef RANDOMNUMBER_H_
#define RANDOMNUMBER_H_

class RandomNumber {
public:
RandomNumber() {
    x = time(NULL);
    m = pow(2, 19); //some constant value
    M = 65915 * 7915; //multiply of some simple numbers p and q
    method = 1;
}
RandomNumber(int seed) {
    x = ((seed > 0) ? seed : time(NULL));
    m = pow(2, 19); //some constant value
    method = 1; //method number
    M = 6543 * 7915; //multiply of some simple numbers p and q
}
void setSeed(long int seed) {
    x = seed; //set start value
}

void chooseMethod(int method) {
    this->method = ((method > 0 && method <= 2) ? method : 1); //choose one of     two method
}

long int linearCongruential() { //first generator, that uses linear congruential method
    long int c = 0; // some constant
    long int a = 69069; //some constant
    x = (a * x + c) % m; //solution next value
    return x;
}

long int BBS() { //algorithm Blum - Blum - Shub
    x = (long int) (pow(x, 2)) % M;
    return x;
}
double nextPoint() { //return random number in range (-1;1)
    double point;
    if (method == 1) //use first method
        point = linearCongruential() / double(m);
    else
        point = BBS() / double(M);
    return point;
}
private:
long int x; //current value
long int m; // some range for first method
long int M; //some range for second method
int method; //method number
};

#endif /* RANDOMNUMBER_H_ */

和测试类：

#include <iostream>
#include <stdlib.h>
#include <math.h>
#include <iomanip>
#include "RandomNumber.h"
using namespace std;

int main(int argc, char* argv[]) {
cout.setf(ios::fixed);
cout.precision(6);
RandomNumber random;
random.setSeed(argc);
srand((unsigned) time(NULL));
cout << "---------------------------------" << endl;
cout << "   Monte Carlo Pi Approximation" << endl;
cout << "---------------------------------" << endl;
cout << " Enter number of points: ";
long int k1;
cin >> k1;
cout << "Select generator number: ";
int method;
cin >> method;
random.chooseMethod(method);
cout << "---------------------------------" << endl;
long int k2 = 0;
double sumX = 0;
double sumY = 0;
for (long int i = 0; i < k1; i++) {
    double x = pow(-1, int(random.nextPoint() * 10) % 2)
            * random.nextPoint();
    double y = pow(-1, int(random.nextPoint() * 10) % 2)
            * random.nextPoint();
    sumX += x;
    sumY += y;
    if ((pow(x, 2) + pow(y, 2)) <= 1)
        k2++;

}
double pi = 4 * (double(k2) / k1);
cout << "M(X)  = " << setw(10) << sumX / k1 << endl; //mathematical expectation of x
cout << "M(Y)  = " << setw(10) << sumY / k1 << endl; //mathematical expectation of y
cout << endl << "Pi = " << pi << endl << endl; //approximate Pi

return 0;
}

第二种方法在我的实验室机器上始终返回 4.000，但在我的个人机器上返回相当接近的近似值。

4

1 回答 1

4

一方面，您使用的 BBS 生成器将始终返回1.

由于您的程序不带任何参数，因此它argc可能是1. 你作为种子传递argc（为什么？），所以初始x值为1。

BBS()有以下逻辑：

x = (long int) (pow(x, 2)) % M;

显然，1平方模M给出1，所以x永远不会改变。

当您使用这样的生成器运行模拟时，您的程序将始终输出4.

x0PS Wikipedia对Blum Blum Shub的初始值有以下说法：

种子x0应该是一个与M（即不是 的因数）p而不是or互质的整数。qx010

于 2012-11-27T20:45:19.953 回答