On 23 October 2013 16:27, Fredrik Johansson <fredrik.johans...@gmail.com>wrote:

> On Wed, Oct 23, 2013 at 4:17 PM, Bill Hart <goodwillh...@googlemail.com>
> wrote:
> > I have made a number of speedups to the precomputed inverse code I
> announced
> > earlier, and removed two unneeeded functions. It is now up to 20% faster
> > than ordinary 2n x n division for n = 1 limb and from n = 3-15 limbs and
> up
> > to 2.2 times as fast above n = 120 limbs.
>
> So it's slower for n = 2 limbs? Could you hardcode this case?
>

Yeah, you could. But it wouldn't make much difference. I tried various
things, but they always either didn't improve things, or made it slower.


>
> > There's nothing more I can do for it now. The gaps that remain are
> essential
> > gaps, due to the raw speed of the division code in the mpir trunk (the
> code
> > in mpir-2.6.0 is substantially slower).
>
> Seems like a pretty good improvement, even if there is a gap!
>
> > Unfortunately, in those gaps, the ordinary division code is up to 20%
> faster
> > than using a precomputed inverse. We could eventually close the gaps by
> > rewriting mullow and mulhigh in mpir, but this is a lot of work,
> including
> > lots of assembly code and much careful thought about algorithms.
>
> Assembly optimised basecase mullow and mulhigh would be very useful
> for many other things too. Few people have the skills to do this,
> though, and you are probably right to prioritise other things...
>

Yep.


>
> > As it is, it is possible to switch on mpir's mullow code for one of the
> > multiplications and it slows it down, again due to the raw speed of
> mpir's
> > ordinary multiplication code.
>
> Fredrik
>
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