[Cfp-interest] Normalized numbers

[Jim Thomas]

> On Aug 28, 2018, at 1:26 PM, Fred J. Tydeman <tydeman at tybor.com> wrote:
> 
> On Tue, 28 Aug 2018 13:13:45 -0500 Rajan Bhakta wrote:
>> 
>>   Fred: Give reference to the C DR for normalized double double meaning 
>> bits can be changed.
> 
> C defect (change) request 432 has:
> 
> Proposed Change
> 
> The first sentence in 5.2.4.2.2 #3 should be changed to:
> 
>  Floating types shall be able to represent normalized
>  floating-point numbers (f1 > 0) and (positive or unsigned) zero. In
>  addition, floating types may be able to contain other kinds of
>  floating-point numbers, such as negative zero and subnormal …

Good to have zero! Suggest changing “negative zero and subnormal floating-point numbers (x ̸= 0, e = emin, f1 = 0) and unnormalized ...” to “negative zero, subnormal floating-point numbers (x ̸= 0, e = emin, f1 = 0), and unnormalized ...”. 
> 
> 
> C defect (change) request 467 has:
> 
> Proposed Change
> 
> In §5.2.4.2.2#1 after the definition of the floating point model
> parameters, add:
> 
>  For each floating-point type: b, emin, emax, p are fixed constants. 

Paragraph 2 says they’re parameters for each floating-point type (not for each floating-point number). Isn’t that sufficient? Has anyone interpreted this incorrectly?
> 
> In §5.2.4.2.2#3 change:
> 
>  In addition to normalized floating-point numbers ( f1 > 0 if x != 0), 
> 
> to:
> 
>  In addition to normalized floating-point numbers ( f1 > 0 if x != 0),
>  all possible fk digits result in values representable in the
>  type [footnote].

What happens to the rest if the original sentence? The proposed words suggest that normalized floating-point numbers don’t include representations with all possible fk digits. I believe the common interpretation is that a floating-point type must include all normalized floating-point numbers in the model, i.e., all values of the formula for f1 > 0.
> 
>  footnote: Some implementations may have types with numeric values
>  which are not covered by this model.

What is the intention of the footnote? We already say “floating types may contain other kinds of  floating-point numbers”.
> 
> In 5.2.4.2.2#12, first item change the phrase
> 
>  maximum representable finite floating-point number, [ math formula ] 
> 
> to
> 
>  maximum representable finite floating-point number; if that value is
>  normalized, its value is [ math formula ],

The standard refers to "normalized floating-point number", not "normalized floating-point value".

> 
> In 5.2.4.2.2#13, first item change the phrase
> 
>  the difference between 1 and the least value greater than 1 
> 
> to
> 
>  the difference between 1 and the least normalized value greater than 1

As above, use “number" instead of “value”.

If this is intended to fit double-double into the standard, how are e and p defined for double-double?


Jim Thomas

> 
> 
> 
> ---
> Fred J. Tydeman        Tydeman Consulting
> tydeman at tybor.com      Testing, numerics, programming
> +1 (702) 608-6093      Vice-chair of PL22.11 (ANSI "C")
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