[Cfp-interest 2260] Re: meaning of "nearest" in case of overflow

[Jim Thomas]

Right. The definition in 3.9 does not account for infinities. A minimal way of dealing with this might be to append a note to 3.9, something like:

	Note 2 to entry: IEC 60559 or implementation-defined rules apply for extreme magnitude results if the result format contains infinity.

- Jim Thomas

> On Oct 29, 2021, at 6:31 AM, Vincent Lefevre <vincent at vinc17.net> wrote:
> 
> In IEEE 754, there is a special rule for the rounding to nearest in
> case of overflow:
> 
>  4.3.1 Rounding-direction attributes to nearest
> 
>  In the following two rounding-direction attributes, an infinitely
>  precise result with magnitude at least b^emax × (b − ½b^(1−p))
>  shall round to ∞ with no change in sign [...]
> 
> But in the C2x draft (N2731), there is no explicit meaning and there
> may be disagreements. For instance:
> 
>  3.9
>  correctly rounded result
> 
>  representation in the result format that is nearest in value,
>  subject to the current rounding mode, to what the result would
>  be given unlimited range and precision
> 
> Note that "correctly rounded" is used even in contexts that do not
> imply IEEE 754 support. So it is not clear whether the IEEE 754 rule
> should be used.
> 
>  6.4.4.2 Floating constants
> [...]
>  4   [...] the result is either the nearest representable value,
>      or the larger or smaller representable value immediately
>      adjacent to the nearest representable value, chosen in an
>      implementation-defined manner. For hexadecimal floating
>      constants when FLT_RADIX is a power of 2, the result is
>      correctly rounded.
> 
> In the last sentence, I would expect the IEEE 754 rule, though there
> is no mention of IEEE 754 (this rule remains valid without IEEE 754
> support).
> 
> And about "nearest representable value" earlier, in case of overflow
> (i.e. an inexact ∞ result for IEEE 754), the question is whether the
> C standard means also ∞ or the largest finite value (e.g. DBL_MAX for
> the double type), i.e. whether nextdown(DBL_MAX) is an acceptable
> result (as being adjacent to DBL_MAX if DBL_MAX is assumed to be the
> nearest representable value) or not.
> 
> For the context:
> 
> In https://groups.google.com/g/comp.std.c/c/XCzEiwD9n_A/m/Q7XScZMoBAAJ
> (2021-10-26 18:53:34), James Kuyper says:
>> No definition by the standard is needed; the conventional mathematical
>> definitions of "nearest" are sufficient. If infinity is representable,
>> DBL_MAX is always nearer to any finite value than infinity is.
>> Regardless of whether infinity is representable, any finite value
>> greater than DBL_MAX is closer to DBL_MAX than it is to any other
>> representable value.
> 
> -- 
> Vincent Lefèvre <vincent at vinc17.net> - Web: <https://www.vinc17.net/>
> 100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/>
> Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)
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