为什么这是真的？ [英] Why is this true?

问题描述

这是IEEE 754标准问题。我不完全理解它背后的机制。

This is IEEE 754 standard question. I don't completely understand the mechanics behind it.

public class Gray {  
    public static void main(String[] args){
        System.out.println( (float) (2000000000) == (float) (2000000000 + 50));
    }
}

推荐答案

float 只能保留7到8有效数字。也就是说，它没有足够的位来表示数字2000000050，所以它被四舍五入到2000000000。

Because a float can only hold about 7 to 8 significant digits. That is, it doesn't have enough bits to represent the number 2000000050 exactly, so it gets rounded to 2000000000.

具体来说， float 由三部分组成：

Specifically speaking, a float consists of three parts:

• 符号位（1位）


• 指数（8位）


• 有效位数（24位，但只存储23位，因为有效位数的MSB始终为1）

您可以将浮点视为计算机以科学记数法的方式，但是以二进制。

You can think of floating point as the computer's way doing scientific notation, but in binary.

> precision 等于 log（2 ^有效数位数）。这意味着 float 可以保存 log（2 ^ 24）= 7.225 有效数字。

The precision is equal to log(2 ^ number of significand bits). That means a float can hold log(2 ^ 24) = 7.225 significant digits.

数字2,000,000,050有9个有效数字。上面的计算告诉我们，24位有效位数不能容纳那么多有效数字。

The number 2,000,000,050 has 9 significant digits. The calculation above tells us that a 24-bit significand can't hold that many significant digits. The reason why 2,000,000,000 works because there's only 1 significant digit, so it fits in the significand.

要解决这个问题，您需要使用 double ，因为它有一个52位有效位数，足以代表每个可能的32位数字。

To solve the problem, you would use a double since it has a 52-bit significand, which is more than enough to represent every possible 32-bit number.

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