两个整数的乘法溢出导致负数 [英] Multiplication of two ints overflowing to result in a negative number

问题描述

考虑Java语言规范中的这个片段。

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

-727379968
1000000000000

为什么（i * i）的结果 -727379968 ？理想情况下它应该是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）使用了一种名为 二的补充算术 ，它使用整数的最高有效位表示数字为负数。如果你乘以两个大数字，你最终会得到一个如此大的数字，它设置最高位，结果最终为负数。

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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