半precision转换 [英] Half precision conversion

问题描述

怎么来了 0 11110 1111111111 等于半precision格式 1.1111111111 * 2 ^ 15 ？两者应为65504。

How comes that 0 11110 1111111111 is equal to the half precision format 1.1111111111 * 2^15? Both should be 65504.

这里的符号位为0的指数是11101和小数部分1111111111.但是，这并不像 1.1111111111 * 2 ^ 15 可言。

The sign bit here is a 0. The exponent would be 11101 and the fractional part 1111111111. But that doesn't look like 1.1111111111 * 2^15 at all.

有人可以解释这样对我？

Can someone explain that to me?

推荐答案

下面是你半precision数的布局：

Here is the layout of your half-precision number:

该指数的值是11110 ₂ ，这是30 ₁₀ 。半precision数字有指数的偏置的15 <子> 10 ，所以我们需要从30 _{10 10} >获得15 _{10 。}

The exponent's value is 11110₂, which is 30₁₀. Half-precision numbers have exponent bias of 15₁₀, so we need to subtract 15₁₀ from 30₁₀ to get the actual exponent of 15₁₀.

有一个隐含的1 ₂ pre-挂起的分数，因此实际分数在它的前面有一个额外的1。该二进制小数点紧靠隐式1后，使得这个样子的号码：

There is an implicit 1₂ pre-pended to the fraction, so the actual fraction has one extra 1 in front of it. The binary fraction point is located immediately after that implicit 1, making the number look like this:

1.1111111111

为了申请15 ₁₀ 的二进制指数，我们需要十五个位置移动分数点的权利。这将产生数1111111111100000 ₂ ，这是转换后相当于65504 ₁₀ 。

In order to apply the binary exponent of 15₁₀, we need to move the fraction point fifteen positions to the right. This produces the number 1111111111100000₂, which is equal to 65504₁₀ after the conversion.

这篇关于半precision转换的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！