IEEE 754：究竟它是如何工作的？ [英] IEEE 754: How exactly does it work?

问题描述

为什么以下code的行为因为它使用C？

Why does the following code behave as it does in C?

float x = 2147483647; //2^31
printf("%f\n", x); //Outputs 2147483648

下面是我的思维过程：

2147483647 =   0      1001 1101      1111 1111 1111 1111 1111 111

   (0.11111111111111111111111)base2 = (1-(0.5)^23)base10
=> (1.11111111111111111111111)base2 = (1 + 1-(0.5)^23)base10 = (1.99999988)base10

因此​​，对IEEE转换754记号回十进制： 1.99999988 * 2 ^ 30 = 2147483520

所以从技术上来说，C程序必须打印出来2147483520，对吧？

So technically, the C program must have printed out 2147483520, right?

推荐答案

的价值进行重新presented是2147483647，可重新psented这样$ P $接下来的两个值是2147483520和2147483648

The value to be represented would be 2147483647. the next two values which can be represented this way are 2147483520 and 2147483648.

由于后者更靠近unre presentable理想的，它被使用：在浮点，值得圆形，不截断

As the latter is closer to the unrepresentable "ideal one", it gets used: in floating point, the values get rounded, not truncated.

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