[Cfp-interest 2093] Re: number classification macros, fpclassify and normal numbers

[Jim Thomas]

> On Aug 13, 2021, at 2:08 PM, Fred J. Tydeman <tydeman at tybor.com> wrote:
> 
> On Fri, 13 Aug 2021 13:49:09 -0700 Jim Thomas wrote:
>> 
>>> Note that for a strict floating-point format, "normal" should be
>>> the same as "normalized".
>> 
>> I think this would be a natural resolution, really just a clarification, and might (appear to) be the most helpful resolution for analysis.
> 
> That thinking only applies to IEEE-754 binary floating-point (FP).
> 
> The 32-bit decimal FP has 7 versions of the value 1:
> 0000001e0
> 0000010e-1
> 0000100e-2
> 0001000e-3
> 0010000e-4
> 0100000e-5
> 1000000e-6
> 
> Only the value with a leading non-zero digit is normalized.
> So, the other six are unnormals.

I don’t think we’ve said this explicitly, but it’s a reasonable interpretation. The object representation is not the model representation, but since these representations have different semantics it makes sense to view them as different model representations, albeit with the same numerical value.

>  But, they should be
> considered normal floating-point numbers.
> 

This seems to be another argument for (2) or (3) (in my previous message).

- Jim Thomas

> 
> 
> ---
> Fred J. Tydeman        Tydeman Consulting
> tydeman at tybor.com      Testing, numerics, programming
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