Hi all,

I just did some timings of MPIR 5.1.3 vs MPIR 2.6.0 to see if we could
benefit from using any of the GMP (balanced) integer multiplication code,
especially toom6, which we don't currently have.

I did timings on an AMD k10 and and Intel Core2 Penryn in the following
ranges:

basecase
karatsuba
toom3
toom4
toom6h (GMP only)
toom8h
fft (up to 100000 limbs)

In the basecase range we are usually slightly faster on both machines, with
only a handful of exceptions where GMP has a slight win. There's nothing we
can do about those exceptions.

In the karatsuba, toom3 and toom4 ranges we always win, as far as I can see.

GMP's does not use toom6h on Penryn. On the K10 our toom4 was faster than
GMP's toom6h in the relevant range. Even if we had toom6h, it would
essentially not be used.

Our toom8h is exactly the same as in GMP, but because of our faster
basecase, we still win in this range.

Our FFT is usually faster, with GMP having some wins at around 20000 limbs
on both machines and 30000 limbs on the Penryn. After this point our FFT
becomes a lot faster than the current GMP FFT.

So it seems that we can't do anything to speed up balanced multiplication.

As our division code is now quite a bit faster after the two new algorithms
I implemented, I think we are in reasonable shape for basic operations.

I'll also take a look at squaring and report back. I had the impression we
we slower in the basecase range, which we may be able to fix.

Bill.

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