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

[Joseph Myers <joseph at codesourcery dot com>]

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.

> 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.  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.

> 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.

> Lastly, is there anything to say about floating-point exceptions?  From

Only that these functions raise no exceptions except for sNaNs.

-- 
Joseph S. Myers
joseph@codesourcery.com