两个整数相乘溢出导致负数

Multiplication of two ints overflowing to result in a negative number(两个整数相乘溢出导致负数)

问题描述

考虑一下 Java 语言规范中的这段代码.

Consider this snippet from the Java language specification.

class Test {
    public static void main(String[] args) {
        int i = 1000000;
        System.out.println(i * i);
        long l = i;
        System.out.println(l * l);
    }
}

输出是

-727379968
1000000000000

为什么 (i*i) 的结果是 -727379968?理想情况下应该是 1000000000000.

Why is the result -727379968 for (i*i)? Ideally it should be 1000000000000.

我知道 Integer 的范围是从 –2147483648 到 2147483647.所以显然 1000000000000不在给定范围内.

I know the range of Integer is from –2147483648 to 2147483647. so obviously 1000000000000 is not in the given range.

为什么结果会变成-727379968?

推荐答案

Java(就像现在的大多数计算机架构一样)使用一种叫做 二进制补码算法，它使用整数的最高有效位来表示一个数字是否为负数.如果你将两个大数相乘，你会得到一个大到设置最高位的数，结果是负数.

Java (like most computer architectures these days) uses something called two's complement arithmetic, which uses the most significant bit of an integer to signify that a number is negative. If you multiply two big numbers, you end up with a number that's so big it sets that highest bit, and the result ends up negative.

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