EPI 5.1 COMPUTING PARITY

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本文介绍了一种高效实现整数奇偶性判断的方法，通过位操作优化了传统的判断方式，实现了更快的执行速度。文章详细阐述了三种不同的实现方式，并通过测试验证了它们的正确性和性能表现。

#include <iostream>
#include <cassert>
using namespace std;

int parity1(unsigned long long n) {
    int p = 0;
    while (n) {
        p ^= (n & 1);
        n >>= 1;
    }
    return p;
}

int parity2(unsigned long long n) {
    int p = 0;
    while (n) {
        p ^= 1;
        n &= (n - 1); // Drop the lowest set bit of n
    }
    return p;
}

int precomputed_parity[1 << 16];

int parity3(unsigned long long n) {
    return precomputed_parity[(n >> 48) & 0xffff] ^
           precomputed_parity[(n >> 32) & 0xffff] ^
           precomputed_parity[(n >> 16) & 0xffff] ^
           precomputed_parity[n & 0xffff];
}

int main(int argc, char *argv[]) {
    for (int i = 0; i < (1 << 16); i++) {
        precomputed_parity[i] = parity2(i);
    }
    srand(time(nullptr));
    if (argc == 2) {
        unsigned long long n = atol(argv[1]);
        assert(parity1(n) == parity2(n));
        assert(parity2(n) == parity3(n));
        cout << "n = " << n << ", parity = " << parity3(n) << endl;
    } else {
        for (int i = 0; i < 100; i++) {
            unsigned long long n = rand();
            assert(parity1(n) == parity2(n));
            assert(parity2(n) == parity3(n));
            cout << "n = " << n << ", parity = " << parity3(n) << endl;
        }
    }
    return 0;
}