[Cfp-interest 2149] Re: supernormal numbers (was: WG14 IEEE 754-C binding meeting minutes) 2021/08/17

[Vincent Lefevre]

On 2021-09-13 16:43:25 -0700, Jim Thomas wrote:
> > With GCC on PowerPC (double-double), where the precision is 106,
> 
> The double-double described in 
> 
> http://mrob.com/pub/math/f161.html <http://mrob.com/pub/math/f161.html>
> 
> claims the precision is 107, with the extra bit coming from the way
> the sign of the low component is used.

This is not a specification. With a specification, you have additional
issues, such as what happens in unusual cases, e.g. for the maximum
exponent. The fact is that LDBL_MANT_DIG = 106 on PowerPC.

[...]
> I believe “floating-point number” was originally intended to refer to a model number. 5.2.4.2.2 still says that clearly:
> 
> For each floating-point type, a floating-point number (x) is defined by the following model:
> 
> An implementation could include other values in floating types, but defining and describing how such values fit into the specification for model numbers would be the implementation’s job. 
> 
> However, it’s easy and natural to interpret “floating-point number” as any number in a floating type. And efforts to support double-double formats have used that interpretation, e.g., in the definitions of FLT_MAX and FLT_NORM_MAX.
> 
> So what is a floating-point number? A number defined by the model, or a number in a floating type? Or is it one or the other depending on context?
> 
> What’s feasible for CFP to do about this?

Well, whatever the choice for the meaning of "floating-point number",
the definition of some macros such as LDBL_MANT_DIG should be defined
in terms of the numbers defined by the model.

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Vincent Lefèvre <vincent at vinc17.net> - Web: <https://www.vinc17.net/>
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