On Wednesday 21 May 2008, Bill Hart wrote:
> Hi Martin,
>
> I downloaded the clean tarball and added an extra test, but I get:
>
> mul: m: 4096, l: 3528, n: 4096, k: 0, cutoff: 1024
> FAIL: Strassen != M4RM
> FAIL: Strassen != Naive
>
> :-(
>
> Also I later replaced the following lines of strassen.c:
>
> a -= a%RADIX;
> b -= b%RADIX;
> c -= c%RADIX;
>
> with
>
> unsigned long mult = 1;
> unsigned long width = a;
> while (width > 2*cutoff)
> {
> width/=2;
> mult*=2;
> }
> a -= a%(RADIX*mult);
> b -= b%(RADIX*mult);
> c -= c%(RADIX*mult);
>
> and this sped up the 32000x32000 multiplication by a further 5% or so.
> The other times didn't change (the 10000x10000 may have been slightly
> quicker).
>
> :-)
>
> Bill.
I've uploaded a new version to
http://m4ri.sagemath.org/downloads/m4ri-20080521.tar.gz
which
- fixes the bug described above
- adds your code snipped
- fixes a couple of other problems reported by Valgrind.
It seems the last bugfix also speeds up the thing (on my notebook) since we
computed too much stuff and wrote it to unallocated memory. Updated
performance figures:
64-bit Debian/GNU Linux, 2.33Ghz Core2Duo (Macbook Pro, 2nd Gen.)
Matrix Dimension Magma GAP M4RI
10,000 x 10,000 2.920 6.691 1.760
16,384 x 16,384 11.140 36.063 6.760
20,000 x 20,000 20.370 - 12.200
32,000 x 32,000 74.260 - 51.510
I'm having trouble believing those figures but all tests pass (including some
equality checks with Magma via Sage). On sage.math things don't seem to get
any better but it is hard to tell since it is often so loaded. Also, this
version only enables SSE2 on Intel CPUs and has a configure switch for OpenMP
(--enable-openmp).
Martin
PS: One thing that seems significant on sage.math: The systime is
considerable, e.g.:
sage: A = random_matrix(GF(2),32000,32000)
sage: B = random_matrix(GF(2),32000,32000)
sage: time C = A._multiply_strassen(B,cutoff=2^11)
CPU times: user 108.02 s, sys: 5.03 s, total: 113.05 s
Wall time: 113.05
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
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