Re: [PATCH v3 5/7] math: Remove powerpc e_hypot

[Wilco Dijkstra via Libc-alpha <libc-alpha@sourceware.org>]

Hi Adhemerval,

>>> Another option is to use the powerpc implementation which favor FP over integer
>>> as the default one.
>> 
>> That is the fastest implementation. It is less accurate though (~1.04ULP with FMA
>> and ~1.21ULP without FMA), so I'm not sure that would be acceptable.
>
> This should not be worse than the current default (the powerpc one is essentially
> the same as default using FP operations).

The generic version carefully computes x * x + y * y with higher accuracy so that
the sqrt stays below 1.0ULP. The powerpc version doesn't and so goes over 1.0ULP.

>> I did some quick optimizations on the new algorithm, on Neoverse N1 my fastest
>> version is less than 10% slower than the powerpc version, and has ~0.94 ULP error.
>
> Do you mean besides the optimized nan/inf checks? I can check if it helps on
> powerpc.

Yes. I avoid the unnecessary checks at the end by doing everything in the 3 main
cases. The division can be made independent of the sqrt so they run in parallel on
modern cores.

However we can do even better with FMA and remove the division entirely by 
special casing the difficult case where x and y are really close. This has only 3.5%
higher latency than the powerpc version, so that's the fastest option below 1.0ULP.
I'll see whether it could work without FMA too and send you something to benchmark
if it passes the testsuite.

Cheers,
Wilco