什么是次正规浮点数?

2022-01-09 00:00:00 floating-point ieee-754 c++ c++11

isnormal() 参考页面说:

判断给定的浮点数 arg 是否正常，即是既不是零、次正规、无限，也不是 NaN.

Determines if the given floating point number arg is normal, i.e. is neither zero, subnormal, infinite, nor NaN.

很清楚数字为零、无限或 NaN 的含义.但它也说不正常.什么时候是次正规数?

It's clear what a number being zero, infinite or NaN means. But it also says subnormal. When is a number subnormal?

推荐答案

在IEEE754标准中，浮点数用二进制科学记数法表示，x = M × 2^e.这里M是尾数，e是指数.在数学上，您始终可以选择指数，以便 1 ≤ M < 2.* 但是，由于在计算机表示中，指数只能具有有限范围，因此是一些大于零但小于 1.0 × 2^e_min 的数字.这些数字是 subnormals 或 denormals.

In the IEEE754 standard, floating point numbers are represented as binary scientific notation, x = M × 2^e. Here M is the mantissa and e is the exponent. Mathematically, you can always choose the exponent so that 1 ≤ M < 2.* However, since in the computer representation the exponent can only have a finite range, there are some numbers which are bigger than zero, but smaller than 1.0 × 2^e_min. Those numbers are the subnormals or denormals.

实际上，尾数的存储没有前导 1，因为总是有前导 1，除了对于次正规数(和零).因此解释是，如果指数是非最小的，则有一个隐含的前导 1，如果指数是最小的，则没有，并且该数字是次正规的.

Practically, the mantissa is stored without the leading 1, since there is always a leading 1, except for subnormal numbers (and zero). Thus the interpretation is that if the exponent is non-minimal, there is an implicit leading 1, and if the exponent is minimal, there isn't, and the number is subnormal.

_{*) 更一般地说，1 ≤ M < B 对于任何基础-B 科学记数法.}

_{*) More generally, 1 ≤ M < B for any base-B scientific notation.}

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