Toom-8 testing (mpz level)

[Niels Möller]

Torbjorn Granlund <tg at gmplib.org> writes:

> I think the updated graphs might be better.  I've refined the measure-
> ment code, and updated the underlying GMP.  There are now also diagrams
> for 3 different machine types, so that one may see patterns better.

Looks a lot more like sectors now. Some observations:

Borders are a lot sharper for Core 2 than Athlon. In the Athlon
figure, the border between toom52 and toom62 and the upper border for
toom52 partial are sharper than others.

On Core 2 and Pentium 4, the area for toom42 is quite small, almost
overtaken by toom53. Hmm, you're including toom43 now? Its area is
smaller than toom44 and toom53.

The region where FFT wins looks like (an + bn) > THRESHOLD, which
makes sense (I would'n say it's "expected", since this is quite
complex). And then current FFT-performance is not as smooth as one
would wish.

The region where base case wins looks like bn < THRESHOLD, which is
nice. I.e., it could use a threshold on the size of the smaller factor
only.

Have you tried matching nice rational numbers to the slopes of the
borders?

Regards,
/Niels