使用32位无符号整数将64位数字相乘的算法 [英] algorithm to multiply 64 bit numbers using 32 bit unsigned integers

问题描述

我有64位数字(63位+符号位)，表示为二进制补码，存储在两个无符号的32位整数中.

I have 64 bit numbers (63 bits + sign bit), represented as two's complement numbers, stored in two unsigned 32 bit integers.

struct Long
{
    uint32 high;
    uint32 low;
}

我该如何仅使用32位数字来实现乘法算法，并检查结果是否适合63位，如果结果不合适，我想返回一个指示溢出的错误代码.

How can i implement a multiplication algorithm, using just 32 bit numbers, and check that the result fits in 63 bits, i want to return an error code indicating overflow if the result doesn't fit.

推荐答案

通常，您需要2 * n位来存储两个n位数字的乘积(最大结果是(2 ^ n)^ 2 = 2 ^(2 * n))，所以我最好的主意是将数字分成四个16位部分，将它们一一相乘，然后相加.总共有16个乘法，但是错误检查是微不足道的.

Generally you need 2*n bits to store the product of two n bit numbers (largest result is (2^n)^2 = 2^(2*n)), so my best idea is to split up the number into four 16-bit parts, multiply them one by one and add them together. 16 multiplications all in all, but error checking is trivial.

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