Okay, I was stupid. I just checked in a new version that does the
same operation in 30 seconds on my mac. Tile size is larger (64x64),
and I avoid calculating offsets with PP macros inside the hottest loop
- it walks through using dimincs in the summation direction. So the
$a x $b case below now runs in 30 seconds, a factor-of-2.7 improvement
(on my platform) over yesterday morning.
Cheers,
Craig
On May 8, 2010, at 6:30 AM, Chris Marshall wrote:
> On 5/8/2010 3:44 AM, Craig DeForest wrote:
>>
>> Er, sorry, I was noodling around and may have jumped the gun. I just
>> checked in a small speed improvement for matmult. It just evaluates
>> the terms in the matrix product in tiled order (multiplying 32x32
>> tiles) rather than in direct threading order; that fits each tile
>> into
>> 16k in the double-precision case, which is small enough to fit in L1
>> cache of most performance CPUs. Unsurprisingly, it helps.
>> Surprisingly, not so very much. On my PowerBook:
>>
>> perldl> $a = random(2000,2000);
>> perldl> $b = random(2000,2000);
>> perldl> {$t0=time; $c = $a->dummy(1)->inner($b->xchg(0,1)-
>> >dummy(2));
>> ..{> $t1=time; print $t1-$t0,"\n";}
>> 82
>>
>> perldl> {$t0=time; $d = $a x $b;
>> ..{> $t1=time; print $t1-$t0,"\n";}
>> 70
>>
>> perldl> print all($d==$c)
>> 1
>>
>> I am a bit puzzled how these other packages manage to go so much
>> faster...
>
> The tiled calculation optimizes the memory accesses
> but, if I understand correctly, the tile code still
> uses the existing inner product algorithm.
>
> If so the total memory ops is still N**3 rather than
> the optimal N**2, they've just been moved to a different
> level of the memory hierarchy.
>
> Another possibility is that a 32x32 tile is not
> big enough to hide the memory access time for the
> data behind the floating point calculations.
>
> As to other packages performance, I'm sure an
> optimized C matrix multiply routine that did the
> entire optimization would be very fast. I don't
> know how much threading would/could be supported.
>
> --Chris
>> Cheers,
>> Craig
>>
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