数论-Miller-Rabin素数测试

 

据说测试的数字 a 取素数比较好，当 a 取遍 [1, 50] 之间的素数（共 15 个）时，可以保证 long long 范围内没有差错。

 

测试题目：LOJ143 质数判定 

 

#include <cstdio>
#include <algorithm>

using namespace std;

#define SC(a, b) (static_cast<a>(b))

typedef long long LL;
typedef long double LD;

 LL test[16] = {0,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}, test_cnt = 15;

LL mul(LL a, LL b, LL n)
{
    LL t = a * b - SC(LL, SC(LD, a) * b / n + 0.5) * n;//注意这里 +0.5 非常重要！
    return t < 0 ? t + n : t;
}

LL mont(LL a, LL b, LL n)
{
    LL t = 1;
    a %= n;
    while (b) {
        if (b & 1) t = mul(t, a, n);
        b >>= 1, a = mul(a, a, n);
    }
    return t;
}

bool check(LL n)
{
    if (n == 2) return true;
    if (n < 2 || n & 1 ^ 1) return false;
    LL d = n - 1, r = 0;// n-1 = d * 2^r
    while (d & 1 ^ 1) d >>= 1, ++r;
    for (int i = 1; i <= test_cnt; ++i) {
        if (test[i] == n) return true;
        LL a = test[i];
        LL x = mont(a, d, n), y;
        for (LL j = 1; j <= r; ++j) {
            y = mul(x, x, n);
            if (y == 1 && x != 1 && x != n-1) return false;
            x = y;
        }
        if (x != 1) return false;
    }
    return true;
}

int main()
{
    LL n;
    while (scanf("%lld", &n) != EOF) {
        if (check(n)) printf("Y\n");
        else printf("N\n");
    }
    return 0;
}