C++实现的Miller-Rabin素性测试程序

Miller-Rabin素性测试算法是概率算法，不是确定算法。然而测试的计算速度快，比较有效，被广泛使用。

另外一个值得介绍的算法是AKS算法，是三位印度人发明的，AKS是他们的姓氏首字母。ASK算法是确定算法，其时间复杂度相当于多项式的，属于可计算的算法。

代码来自Sanfoundry的C++ Program to Implement Miller Rabin Primality Test。

源程序如下：

/* 
 * C++ Program to Implement Miller Rabin Primality Test
 */

#include <iostream>
#include <cstring>
#include <cstdlib>
#define ll long long

using namespace std;
  
/* 
 * calculates (a * b) % c taking into account that a * b might overflow 
 */

ll mulmod(ll a, ll b, ll mod)
{
    ll x = 0,y = a % mod;
    while (b > 0)
    {
        if (b % 2 == 1)
        {    
            x = (x + y) % mod;
        }
        y = (y * 2) % mod;
        b /= 2;
    }
    return x % mod;
}

/* 
 * modular exponentiation
 */
ll modulo(ll base, ll exponent, ll mod)
{
    ll x = 1;
    ll y = base;
    while (exponent > 0)
    {
        if (exponent % 2 == 1)
            x = (x * y) % mod;
        y = (y * y) % mod;
        exponent = exponent / 2;
    }
    return x % mod;
}
   
/*
 * Miller-Rabin primality test, iteration signifies the accuracy
 */
bool Miller(ll p,int iteration)
{
    if (p < 2)
    {
        return false;
    }
    if (p != 2 && p % 2==0)
    {
        return false;
    }

    ll s = p - 1;
    while (s % 2 == 0)
    {
        s /= 2;
    }
    for (int i = 0; i < iteration; i++)
    {
        ll a = rand() % (p - 1) + 1, temp = s;
        ll mod = modulo(a, temp, p);
        while (temp != p - 1 && mod != 1 && mod != p - 1)
        {
            mod = mulmod(mod, mod, p);
            temp *= 2;
        }
        if (mod != p - 1 && temp % 2 == 0)
        {
            return false;
        }
    }
    return true;
}

//Main
int main()
{
    int iteration = 5;
    ll num;

    cout<<"Enter integer to test primality: ";
    cin>>num;

    if (Miller(num, iteration))
        cout<<num<<" is prime"<<endl;
    else
        cout<<num<<" is not prime"<<endl;

    return 0;
}