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Re: [PATCH v3] Add nextup and nextdown math functions

On 06/07/2016 10:24 AM, Joseph Myers wrote:
> On Tue, 7 Jun 2016, Rical Jasan wrote:
>>> +the function returns the positive number of least magnitude in the type of
>>> +@var{x}.  If @var{x} is @code{NaN}, @code{NaN} is returned.  @code{nextup}
>> To adhere to the majority style of the Arithmetic chapter, those NaNs
>> would not be enclosed in @code{} (57:2).  In fact, their appearance in
>> @code{} in nextafter is the only place in the chapter that happens (and
>> only one other time in Mathematics).  Personally, I thought it was
>> strange they were all unformatted, and they probably should be
>> @code{NaN}, but I wanted to mention it for the sake of consistent style.
> I don't think any should use @code, because it's not a literal sequence of 
> characters in source code, but a value, that's being referred to.

True, thanks for pointing that out.

>> I've attached the beginnings of how I would approach it, but there are
>> some questions embedded as comments in there, which I also mention
>> below.  The general strategy is to attempt to address the functions'
>> behaviour when given any of the classifications of floating-point
>> numbers, as outlined in fpclassify, 20.4 Floating-Point Number
>> Classification Functions (NaN, infinity, 0, subnormal, normal).
>> Hopefully my understanding of the target values is correct, and I am
>> referencing the Floating Point Parameters in Appendix A correctly.
> I think in general that's a bad approach, and very repetitive.

Good to know.

> A function 
> has semantics from which you can deduce what it does for all those values.  
> Some of those semantics may come from general rules; for example, that a 
> function with a signaling NaN input raises the "invalid" exception, other 
> than for a few non-arithmetic functions such as fabs and copysign; a 
> function raising the "invalid" exception and returning a floating-point 
> result returns a quiet NaN; and a function with a quiet NaN argument 
> returns a quiet NaN without raising any exceptions if it does not have any 
> signaling NaN arguments (except for a few special cases such as hypot 
> (Inf, NaN), and the possibility of fma (0, Inf, NaN) raising "invalid").  
> Pretty much no functions should do anything special for subnormals, or for 
> 0, and the result for infinity are generally the limits of the 
> mathematical function for finite arguments.

Yes, it's quite clear now.  How did I miss all that about signalling
NaNs and quiet NaNs?  :)  Did you write this chapter?

Really, though, there was a moment where I debated taking the more
verbose approach because, as I mentioned, there was definitely a sense
of minimalism to the function descriptions which seemed to rely on the
fact the underlying material was presented thoroughly throughout the
rest of the chapter---and it generally is.

I don't believe quiet NaNs are mentioned, though, so if that just means
a normal NaN that doesn't make noise by signalling like a sNaN, it might
not hurt to introduce that language in the Infinity and NaN section.

Even weirder, I don't see "quiet" in the entire manual...

$ grep -i quiet manual/*.texi

>> It seems like the really interesting case is what nextup and nextdown do
>> when they should increment away from their respective infinities.  I can
>> reason returning both infinity or the next largest value, and I can't
>> find anything in your documentation about those cases, so I definitely
>> think those need clarification.
> They do what the nextUp and nextDown operations in IEEE 754-2008 do.  
> That's the exact point of these functions.  The most relevant case to 
> mention for infinities would seem to be nextup(+Inf) and nextdown(-Inf), 
> as the cases where there aren't any more representable values in the 
> relevant direction.  (And the other special cases to mention are for zero 
> - that a zero result has the sign of the argument and a zero argument of 
> either sign results in a nonzero result.)

>> Are subnormals treated differently than normals?  It sounds like
>> subnormals have their own special representation, and I'm not sure if
>> the step sizes between them are different than for normals.  If they
> If you aren't familiar with subnormals and other aspects of the set of 
> values of an IEEE floating-point type, you aren't likely to have a use for 
> these functions.
> The functions that are the odd cases out are nextafter / nexttoward, that 
> raise "inexact" and "underflow" for subnormal results despite those 
> results not depending on the rounding mode.

So it sounds like the whole NaN issue isn't worth mentioning within
functions unless they deviate from the norm in some way, which these
don't, the infinity behaviour seems expected (though I still think
nextup(-Inf) is more interesting :), as well as the subnormal, but is
the zero behaviour you just described abnormal in some way? That seems
to be what I would expect it to do, which leaves me wondering whether
there is anything to say about these functions at all... besides "read
the rest of the chapter"...

>> Lastly, is there anything to say about floating-point exceptions?  From
> Only that these functions raise no exceptions except for sNaNs.

Well there's something!  ;)

Thank you for your feedback.  I appreciate hearing your views on
documentation and formatting, and I really appreciate your taking the
time to elucidate the extra information about this whole topic.  I'll
quit hijacking this thread and let the actual developer do their thing.


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