[PATCH] Define 3-argument overloads of std::hypot for C++17 (P0030R1)

[Ed Smith-Rowland]

On 09/28/2016 07:37 AM, Jonathan Wakely wrote:
> On 28/09/16 13:31 +0200, Marc Glisse wrote:
>> On Wed, 28 Sep 2016, Jonathan Wakely wrote:
>>
>>> On 27/09/16 23:28 +0000, Joseph Myers wrote:
>>>> On Tue, 27 Sep 2016, Jonathan Wakely wrote:
>>>>
>>>>> This adds the new 3D std::hypot() functions. This implementation 
>>>>> seems
>>>>> to be faster than the naïve sqrt(x*x + y*y + z*z) implementation, or
>>>>> hypot(hypot(x, y), z), and should be a bit more accurate at very 
>>>>> large
>>>>> or very small values due to reducing the arguments by the largest 
>>>>> one.
>>>>> Improvements welcome though, as this is not my forte.
>>>>
>>>> Should I take it from this implementation that C++ is not concerned by
>>>> certain considerations that would arise for C: spurious underflow
>>>> exceptions from the scaling when some arguments much larger than 
>>>> others;
>>>> spurious "invalid" exceptions from the comparisons when any 
>>>> argument is
>>>> (quiet) NaN; handling of mixed (quiet) NaN and Inf arguments (where 
>>>> ISO C
>>>> Annex F has Inf returned, not NaN)?
>>>
>>> The entire spec from the C++ draft is:  Returns: √ x^2 + y^2 + z^2
>>>
>>> It doesn't mention "without undue overflow or underflow" as the C
>>> standard does for hypot(x, y). Handling those conditions would of
>>> course be nice, but I'm not capable of doing so, and I'd rather have a
>>> poor implementation than none.
>>
>> p0030r0 had "In addition to the two-argument versions of certain math
>> functions in <cmath> and its float and long double overloads, C++ adds
>> three-argument versions of these functions that follow similar semantics
>> as their two-argument counterparts."
>>
>> One could interpret that as an intent to follow the C semantics. On the
>> other hand, the paper mentions speed and convenience as the main selling
>> points. Maybe LWG could clarify the intent?
>
> I expect the answer will be that it's QoI.
>
>
I would expect hypot3 to treat broader range of arguments without under 
or overflow.

In other words, I think correctness is more important than speed.  
Jonathans scaling algo is what I would expect to find and it will work 
for very tiny and very huge args (see attached toy which is essentially 
the same thing).  I would be very surprised if hypot and hypot3 had 
different philosophies.

Anyone can do sqrt(x^2 + y^2 + z^2) (and they do).

I interpret this function to act like the other special math functions 
in terms of its treatment of nan and inf.

I was working on this and will pick up *PR77776* 
<https://gcc.gnu.org/bugzilla/show_bug.cgi?id=77776>

*Ed
* <https://gcc.gnu.org/bugzilla/show_bug.cgi?id=77776>

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