[Cfp-interest 1773] Re: Exact subnormal results

[Jim Thomas]

> On Sep 1, 2020, at 12:09 PM, Fred J. Tydeman <tydeman at tybor.com> wrote:
> 
> Attached is the rewrite on range errors and exact subnormal results.
> 
> 
> ---
> Fred J. Tydeman        Tydeman Consulting
> tydeman at tybor.com <mailto:tydeman at tybor.com>      Testing, numerics, programming
> +1 (702) 608-6093      Vice-chair of PL22.11 (ANSI "C")
> Sample C99+FPCE tests: http://www.tybor.com <http://www.tybor.com/>
> Savers sleep well, investors eat well, spenders work forever.
> 
> 
> Submitter:CFP group
> Submission Date: 2020-??-??
> Document: WG14 N25??
> Title: N25??: Exact subnormal results
> Reference Documents:N2506
> 
> Summary
> 
> This is a follow on to N2506 that was accepted (except for three math functions). Those three functions [fmod(), remainder(), and remquo()] can produce exact subnormal results and there was a question on should they underflow.
> 
> 7.12.1 Treatment of error conditions has two "requirements" related to this issue.
> 
> #4 has:
> 
> Likewise, a range error occurs if and only if the mathematical result of the function cannot be represented in an object of the specified type, due to extreme magnitude.
> #6 has:
> 
> The result underflows if the magnitude of the mathematical result is nonzero and less than the minimum normal number in the type.243)
> So, if an exact subnormal result is produced, is it an underflow range error?
> 
> Since it is exact, it is representable, so does not meet the condition in paragraph 4.
> 
> Since it is subnormal, it meets the condition of paragraph 6.
> 
> So what is it?
> 
> Assuming exact subnormal results are underflow, here are proposed wording changes to the C standard.
> 
> Note: Since what happens on underflow is implementation defined, these changes do not cause any existing implementation to change.
> 
> C2x changes:
> 
> 7.12.1 Treatment of error conditions
> Add to 7.12.1#4 after the first sentance.
> 
> Also, a range error occurs if the mathematical result is beyond the range where all values can be represented in an object of the specified type, to the full precision of the type.footnote
> footnote: Exact subnormal results are a range error.
> 
Consider changing the footnote to “A range error occurs if the function result is subnormal, even if the mathematical result is represented exactly in the type.”


- Jim Thomas
> The fmod functions
> Add to 7.12.10.1#2
> 
> A range error occurs if x is finite, both x and y are nonzero, and either is too close to zero.
> The remainder functions
> Add to 7.12.10.2#2
> 
> A range error occurs if x is finite, both x and y are nonzero, and either is too close to zero.
> The fdim functions
> Change 7.12.12.1#2
> 
> A range error may occur.
> to:
> 
> A range error may occuroccurs if positive finite x-y is either too large or too close to zero.
> Change F.10.9.1 The fdim functions
> 
> No aditional requirements.
> to:
> 
> No aditional requirements. When subnormal results are supported, the returned value is exact and is independent of the current rounding direction mode.
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