如何添加两个数字，而无需使用++或+或者其他算术运算符 [英] How to add two numbers without using ++ or + or another arithmetic operator

问题描述

我如何添加两个数字，而无需使用++或+或任何其他算术运算符？

How do I add two numbers without using ++ or + or any other arithmetic operator?

这是一个问题很久以前在一些校园里采访要求。不管怎么说，今天有人问对于一些位操作的问题，并在回答一个美丽的quide的 斯坦福位操作 被提到。我花了一些时间来研究它，并认为有实际上可能是一个问题的答案。我不知道，我无法找到一个。有没有一个答案存在？

It was a question asked a long time ago in some campus interview. Anyway, today someone asked a question regarding some bit-manipulations, and in answers a beautiful quide Stanford bit twiddling was referred. I spend some time studying it and thought that there actually might be an answer to the question. I don't know, I could not find one. Does an answer exist?

推荐答案

这是我已经写了前一段时间的乐趣。它采用了补重新presentation和使用重复的变化与进位实现此外，在实施其他运营商大多在除了方面

This is something I have written a while ago for fun. It uses a two's complement representation and implements addition using repeated shifts with a carry bit, implementing other operators mostly in terms of addition.

#include <stdlib.h> /* atoi() */
#include <stdio.h>  /* (f)printf */
#include <assert.h> /* assert() */

int add(int x, int y) {
    int carry = 0;
    int result = 0;
    int i;

    for(i = 0; i < 32; ++i) {
        int a = (x >> i) & 1;
        int b = (y >> i) & 1;
        result |= ((a ^ b) ^ carry) << i;
        carry = (a & b) | (b & carry) | (carry & a);
    }

    return result;
}

int negate(int x) {
    return add(~x, 1);
}

int subtract(int x, int y) {
    return add(x, negate(y));
}

int is_even(int n) {
    return !(n & 1);
}

int divide_by_two(int n) {
    return n >> 1;
}

int multiply_by_two(int n) {
    return n << 1;
}

int multiply(int x, int y) {
    int result = 0;

    if(x < 0 && y < 0) {
        return multiply(negate(x), negate(y));
    }

    if(x >= 0 && y < 0) {
        return multiply(y, x);
    }

    while(y > 0) {
        if(is_even(y)) {
            x = multiply_by_two(x);
            y = divide_by_two(y);
        } else {
            result = add(result, x);
            y = add(y, -1);
        }
    }

    return result;
}

int main(int argc, char **argv) {
    int from = -100, to = 100;
    int i, j;

    for(i = from; i <= to; ++i) {
        assert(0 - i == negate(i));
        assert(((i % 2) == 0) == is_even(i));
        assert(i * 2 == multiply_by_two(i));
        if(is_even(i)) {
            assert(i / 2 == divide_by_two(i));
        }
    }

    for(i = from; i <= to; ++i) {
        for(j = from; j <= to; ++j) {
            assert(i + j == add(i, j));
            assert(i - j == subtract(i, j));
            assert(i * j == multiply(i, j));
        }
    }

    return 0;
}

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