[Cfp-interest 1489] Re: Range errors

[Jim Thomas]

> On Jan 16, 2020, at 7:10 PM, Fred J. Tydeman <tydeman at tybor.com> wrote:
> 
> Attached is the latest version of my range error paper.
> 
> 
> ---
> 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:Fred Tydeman
> Submission Date: 2019-10-??
> Document: WG14 Nxxxx
> Reference Documents:
> 
> Summary
> 
> The standard has a few incorrect, missing, or ambiguous statements about range errors in some of the math functions.
> 
> Does "too large" mean close to +infinity or +/-infinity?
> 
> Does "too small" mean close to -infinity or +/-zero?
> 
> Some implementations incorrectly treat f(infinity) as a range error based upon the text: A range error occurs if [the magnitude of] x is too large. While this is covered by 7.12.1#5 about overflows, the CFP group believes it is better to be explicit in each math function where it matters.
> 
> Possible Technical Corrigendum:
> 
> The asin functions
> Add to 7.12.4.2#2
> 
> A range error occurs if nonzero x is too close to zero.
> The atan functions
> Add to 7.12.4.3#2
> 
> A range error occurs if nonzero x is too close to zero.
> The atan2 functions
> Add to 7.12.4.4#2
> 
> A range error occurs if x is positive and nonzero y/x is too close to zero.
> The sin functions
> Add to 7.12.4.6#2
> 
> A range error occurs if nonzero x is too close to zero.
> The tan functions
> Add to 7.12.4.7#2
> 
> A range error occurs if nonzero x is too close to zero.
> The asinpi functions
> Change 7.12.4.9#2
> 
> A range error occurs if the magnitude of nonzero x is too small.
> to:
> A range error occurs if the magnitude nonzero x is too smallclose to zero.
> The atanpi functions
> Change 7.12.4.10#2
> 
> A range error occurs if the magnitude of nonzero x is too small.
> to:
> A range error occurs if the magnitude nonzero x is too smallclose to zero.
> The atan2pi functions
> Change 7.12.4.11#2
> 
> A range error occurs if x is positive and the magnitude of nonzero y/x is too close to small.
> to:
> A range error occurs if x is positive and the magnitude ofnonzero y/x is too close to smallzero.
> The sinpi functions
> Add to 7.12.4.13#2
> 
> A range error occurs if nonzero x is too close to zero.
> The tanpi functions
> Add to 7.12.4.14#2
> 
> A range error occurs if nonzero x is too close to zero.
> The asinh functions
> Add to 7.12.5.2#2
> 
> A range error occurs if nonzero x is too close to zero.
> The atanh functions
> Add to 7.12.5.3#2
> 
> A range error occurs if nonzero x is too close to zero.
> The cosh functions
> Change 7.12.5.4#2 from
> 
> A range error occurs if the magnitude of x is too large.
> to
> 
> A range error occurs if the magnitude of (positive or negative) finite x is too large.
“the magnitude of” cannot be deleted here.
> The sinh functions
> Change 7.12.5.5#2 from
> 
> A range error occurs if the magnitude of x is too large.
> to
> 
> A range error occurs if the magnitude of (positive or negative) finite x is too large or if nonzero x is too close to zero.
“the magnitude of” cannot be deleted here.
> The tanh functions
> Add to 7.12.5.6#2
> 
> A range error occurs if nonzero x is too close to zero.
> The exp functions
> Change 7.12.6.1#2 from
> 
> A range error occurs if the magnitude of x is too large.
> to
> 
> A range error occurs if the magnitude of positive finite x is too large or if negative finite x is too large.
“the magnitude of” is needed in the negative cases:

	• A range error occurs if positive finite x is too large or if the magnitude of negative finite x is too large.
> The exp10 functions
> Change 7.12.6.2#2 from
> 
> A range error occurs if the magnitude of x is too large.
> to
> 
> A range error occurs if the magnitude of positive finite x is too large or if negative finite x is too large.
“the magnitude of” is needed in the negative cases:

	• A range error occurs if positive finite x is too large or if the magnitude of negative finite x is too large.
> The exp10m1 functions
> Change 7.12.6.3#2 from
> 
> A range error occurs if finite x is too large or if the magnitude of nonzero x is too small.
> to
> 
> A range error occurs if positive finite x is too large or if the magnitude of positive nonzero x is too smallclose to zero or if negative nonzero x is too close to zero.
Reconsidering, I think it’s ok to say “… if nonzero x is too close to zero.” See tgamma.
> The exp2 functions
> Change 7.12.6.4#2 from
> 
> A range error occurs if the magnitude of x is too large.
> to
> 
> A range error occurs if the magnitude of positive finite x is too large or if negative finite x is too large.
“the magnitude of” is needed in the negative cases:

	• A range error occurs if positive finite x is too large or if the magnitude of negative finite x is too large.
> The exp2m1 functions
> Change 7.12.6.5#2 from
> 
> A range error occurs if the magnitude of x is too large or if the magnitude of nonzero x is too small.
> to
> 
> A range error occurs if the magnitude of positive finite x is too large or if the magnitude ofpositive nonzero x is too smallclose to zero or if negative nonzero x is too close to zero.
I think it’s ok to say “… if nonzero x is too close to zero.”
> The expm1 functions
> Change 7.12.6.6#2 from
> 
> A range error occurs if positive x is too large.252)
> to
> 
> A range error occurs if positive finite x is too large or if positive nonzero x is too close to zero or if negavie nonzero x is too close to zero.252)
I think it’s ok to say “… if nonzero x is too close to zero."
> The ldexp functions
> Change 7.12.6.9#2 from
> 
> A range error may occur.
> to
> 
> A range error may occuroccurs for some finite x, depending on p.
> The log10p1 function
> Change 7.12.6.13#2
> 
> A range error occurs if the magnitude of nonzero x is too small.
> to:
> A range error occurs if the magnitude positive nonzero x is too smallclose to zero or if negative nonzero x is too close to zero.
I think it’s ok to say “… if nonzero x is too close to zero."
> The log1p and logp1 functions
> Add to 7.12.6.14#2
> 
> A range error occurs if positive nonzero x is too close to zero or if negative nonzero x is too close to zero.
I think it’s ok to say “… if nonzero x is too close to zero."
> The log2p1 functions
> Add to 7.12.6.16#2
> 
> A range error occurs if positive nonzero x is too close to zero or it negative nonzero x is too close to zero.
I think it’s ok to say “… if nonzero x is too close to zero."
> The scalbn and scalbln functions
> Change 7.12.6.19#2 from
> 
> A range error may occur.
> to
> 
> A range error may occur occurs for some finite x, depending on n.
> The compoundn functions
> Change 7.12.7.2#2 from
> 
> A range error may occur if n is too large, depending on x.
> to
> 
> A range error may occuroccurs if positive finite x n is too large or if negative x is too near -1, depending on nx.
> The hypot functions
> Change 7.12.7.4#2 from
> 
> A range error may occur.
> to
> 
> A range error may occuroccurs for some finite arguments.
> The pow functions
> Change 7.12.7.5#2 from
> 
> A range error may occur.
> to
> 
> A range error may occurocurs if (positive or negative) nonzero finite x is too large or too near zero, depending on y.
	• A range error occurs if the magnitude of (positive or negative) nonzero finite x is too large or too near zero, depending on y.
> The pown functions
> Change 7.12.7.6#2 from
> 
> A range error may occur.
> to
> 
> A range error may occuroccurs if (positive or negative) nonzero finite x if too large or too near zero, depending on n.
	• A range error ocurs if the magnitude of (positive or negative) nonzero finite x is too large or too near zero, depending on n.

> The powr functions
> Change 7.12.7.7#2 from
> 
> A range error may occur.
> to
> 
> A range error may occuroccurs if positive nonzero finite x is too large or too near zero, depending on y.
> The rootn functions
> Change 7.12.7.8#2 from
> 
> A range error may occur if n is -1.
> to
> 
> A range error may occuroccurs if (positive or negative) nonzero finite x is too large or too near zero and if n is -1.
	• A range error occurs if the magnitude of (positive or negative) nonzero finite x is too large or too near zero and if n is -1.
> The erf functions
> Add to 7.12.8.1#2
> 
> A range error occurs if nonzero x is too close to zero.
> The erfc functions
> Change 7.12.8.2#2
> 
> A range error occurs if positive x is too large.
> to:
> 
> A range error occurs if positive finite x is too large.
> The lgamma functions
> Change 7.12.8.3#2
> 
> A range error occurs if positive x is too large.
> to:
> 
> A range error occurs if positive finite x is too large.
> The tgamma functions
> Change 7.12.8.4#2
> 
> A range error occurs if the magnitude of x is too large and may occur if the magnitude of x is too small.
> to:
> 
> A range error occurs for some negative finite x, and if the magnitude ofpositive finite x is too large, and may occur if the magnitude of nonzero x is too smallclose to zero.
> 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 x-y is too large or too small.
> The fma functions
> Change 7.12.13.1#2
> 
> A range error may occur.
> to:
> 
> A range error may occuroccurs for some finite arguments.
> _______________________________________________
> Cfp-interest mailing list
> Cfp-interest at oakapple.net <mailto:Cfp-interest at oakapple.net>
> http://mailman.oakapple.net/mailman/listinfo/cfp-interest <http://mailman.oakapple.net/mailman/listinfo/cfp-interest>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mailman.oakapple.net/pipermail/cfp-interest/attachments/20200218/018a75b1/attachment-0003.html