什么是亚正规浮点数？ [英] What is a subnormal floating point number?

问题描述

isnormal（）参考页告诉您：

确定给定的浮点数arg是否正常，即
既不为零，也不为正，无穷大，也不为NaN。

数字为零，无限或NaN清楚什么意思。但它也说subnormal。在IEEE754标准中，浮点数用二进制科学记数法表示，

  =  M ×  2 ^e 。这里 M 是尾数， e 是指数。在数学上，您可以随时选择指数，以便1 <2>。但是，由于在计算机表示中，指数只能具有有限范围是大于零，但小于1.0 ×  2 _^min 的一些数字。这些数字是子字幕或。

实际上，尾数存储时没有前导1，始终为前1，除非为正常数字（和零）。因此，解释是如果指数是非最小的，则存在隐式前导1，并且如果指数最小，则不存在，并且数字是次正常的。

_{*）更一般地说，1    M  <  B 对于任何基本的 科学记数法。}

isnormal() reference page tells :

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

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

解决方案

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.

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.

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

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