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Re: PPC64 libmvec sin, cos, sincos
- From: Szabolcs Nagy <Szabolcs dot Nagy at arm dot com>
- To: GT <tnggil at protonmail dot com>, "libc-alpha at sourceware dot org" <libc-alpha at sourceware dot org>
- Cc: nd <nd at arm dot com>
- Date: Mon, 4 Mar 2019 14:07:59 +0000
- Subject: Re: PPC64 libmvec sin, cos, sincos
- References: <7IBtSR-9y3hojcUhrE1RCxG5skB9fFCI7gQ6Q1w-rxfqHNc3Cxed6OuzcO0d6MREORdF_FK7g_k9uOtn1v0-_agUgbqhM0xRY3u1aaH67zg=@protonmail.com>
On 03/03/2019 17:21, GT wrote:
> Here is a suggestion to organize the implementation of the three functions
> a little differently than was done for x86_64.
>
> Because of the trigonometric identity cos (x) = sin( x + PI/2), selecting
> either the sine or cosine polynomial series approximation should suffice to
> compute all three functions.
>
> Defining the series in a static inline function will let us call it with
> input argument x or x +/- PI/2 for sine and cosine (depending on which of the
> two series was chosen). For sincos, the function will be called twice: once
> to obtain the cosines of the inputs and a second time to get the sines.
>
> Doing that will allow us to maintain a single file which performs evaluations
> for the three functions.
>
> Any reason not to implement in this style?
i think it is better to compute
n = rint((x+pi/2)/pi) - 0.5
r = x - n*pi
sin(r)
(current x86_64 vector cos) instead of
n = rint((x+pi/2)/pi)
r = (x+pi/2) - n*pi
sin(r)
since -n*pi can be done with extra precision
(e.g. -n*pi1-n*pi2-n*pi3) but if you pass x+pi/2
down to a common implementation that may have a
large error (e.g. for x close to 0).
so the arg reduction may not be easy to share.
(and the final sign fixup)
but the polynomial can be the same i guess.