inf和NaN的内部表示是什么？ [英] What is the internal representation of inf and NaN?

问题描述

朋友&我正在辩论今天午餐时如何储存Inf和NaN。

以Fortran 90为例。 4字节的实数可以获得Inf或NaN的值。这是如何存储在内部的？据推测，一个4字节的实数是由一个32位二进制数字内部表示的数字。 Inf和NaN是以33位二进制数存储的吗？

pbs.edu/general/software/packages/ieee/ieee.phprel =noreferrer> link ：

IEEE单精度浮点标准表示需要一个32位字，它可以表示为从0到31的编号，从左到右。第一位是符号位， S ，接下来的八位是指数位，' E '，最后的23位是小数点' F '：

 
 EEEEEEEE FFFFFFFFFFFFFFFFFFFFFFF 
 0 1 8 9 31 
 

由该词表示的 V 可以如下确定：

• 如果 E = 255 和 F 非零，则 V = NaN （不是数字）


• code> E = 255 和 F 为零且 S 为 1 ，然后 V = -Infinity


• 如果 E = 255 和 F 为零且 S 为 0 ，则 V = Infinity


• 如果 0 然后 V =（ - 1）** S * 2 **（E-127）*（1.F）其中 1.F 旨在表示通过用隐式前导1和二进制前缀F创建的二进制数
点。如果 E = 0 且 F 不为零，则 V =（ - 1）** S * 2 **（-126）*（0.F）这些
是非标准化值。


• 如果 E = 0 且 F 为零且 S 是 1 ，然后 V = -0


• 如果 E = 0 且 F 为零且 S 0 ，然后 V = 0

A friend & I were debating how Inf's and NaN's are stored during lunch today.

Take Fortran 90 for example. 4-byte reals can obtain the value of Inf or NaN. How is this stored internally? Presumably, a 4-byte real is a number represented internally by a 32 digit binary number. Are Inf's and NaN's stored as 33 bit binary numbers?

解决方案

Specifically from Pesto's link:

The IEEE single precision floating point standard representation requires a 32 bit word, which may be represented as numbered from 0 to 31, left to right. The first bit is the sign bit, S, the next eight bits are the exponent bits, 'E', and the final 23 bits are the fraction 'F':

S EEEEEEEE FFFFFFFFFFFFFFFFFFFFFFF  
0 1      8 9                    31  

The value V represented by the word may be determined as follows:

• If E=255 and F is nonzero, then V=NaN ("Not a number")
• If E=255 and F is zero and S is 1, then V=-Infinity
• If E=255 and F is zero and S is 0, then V=Infinity
• If 0<E<255 then V=(-1)**S * 2 ** (E-127) * (1.F) where "1.F" is intended to represent the binary number created by prefixing F with an implicit leading 1 and a binary point.
• If E=0 and F is nonzero, then V=(-1)**S * 2 ** (-126) * (0.F) These are "unnormalized" values.
• If E=0 and F is zero and S is 1, then V=-0
• If E=0 and F is zero and S is 0, then V=0

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