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Re: [PATCH] Simplify pow with constant


On Fri, Aug 4, 2017 at 2:26 PM, Alexander Monakov <amonakov@ispras.ru> wrote:
> On Fri, 4 Aug 2017, Wilco Dijkstra wrote:
>> This patch simplifies pow (C, x) into exp (x * C1), where C1 = log (C).
>
> I don't think you can do that for non-positive C.

Hmm, the question is also how this interacts with other folders like
sqrt (pow (x, y)) -> pow (|x|, y * 0,5)?  Also we seem to miss
pow (2, x) -> exp2 (x) and pow (10, x) -> pow10/exp10, those may
be a better fit than exp (log (2/10) * x)?  OTOH for fast-math
canonicalization getting rid of exp2/10 and pow10 might be beneficial.

>> Do this only for fast-math as accuracy is reduced.  This is much faster
>> since pow is more complex than exp - with a current GLIBC the speedup
>> is more than 7 times for this transformation.
>
> Is it bound to be so on future glibc revisions and non-glibc platforms?

And how is accuracy affected?  I think the transform is only reasonable
for log (C) being close to e, 2 or 10 (using exp, exp2 or exp10).  Can you
provide an idea on whether there's a systematic error (with glibc) and
how that behaves over the parameter space?

Oh, and what value of C does the benchmark that triggered this have?

Richard.

> Alexander


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