[Numpy-discussion] odd performance of sum?

Robert Kern robert.kern@gmail....
Thu Feb 10 14:58:55 CST 2011


On Thu, Feb 10, 2011 at 14:29, eat <e.antero.tammi@gmail.com> wrote:
> Hi Robert,
>
> On Thu, Feb 10, 2011 at 8:16 PM, Robert Kern <robert.kern@gmail.com> wrote:
>>
>> On Thu, Feb 10, 2011 at 11:53, eat <e.antero.tammi@gmail.com> wrote:
>> > Thanks Chuck,
>> >
>> > for replying. But don't you still feel very odd that dot outperforms sum
>> > in
>> > your machine? Just to get it simply; why sum can't outperform dot?
>> > Whatever
>> > architecture (computer, cache) you have, it don't make any sense at all
>> > that
>> > when performing significantly less instructions, you'll reach to spend
>> > more
>> > time ;-).
>>
>> These days, the determining factor is less often instruction count
>> than memory latency, and the optimized BLAS implementations of dot()
>> heavily optimize the memory access patterns.
>
> Can't we have this as well with simple sum?

It's technically feasible to accomplish, but as I mention later, it
entails quite a large cost. Those optimized BLASes represent many
man-years of effort and cause substantial headaches for people
building and installing numpy. However, they are frequently worth it
because those operations are often bottlenecks in whole applications.
sum(), even in its stupidest implementation, rarely is. In the places
where it is a significant bottleneck, an ad hoc implementation in C or
Cython or even FORTRAN for just that application is pretty easy to
write. You can gain speed by specializing to just your use case, e.g.
contiguous data, summing down to one number, or summing along one axis
of only 2D data, etc. There's usually no reason to try to generalize
that implementation to put it back into numpy.

>> Additionally, the number
>> of instructions in your dot() probably isn't that many more than the
>> sum(). The sum() is pretty dumb
>
> But does it need to be?

As I also allude to later in my email, no, but there are still costs involved.

>> and just does a linear accumulation
>> using the ufunc reduce mechanism, so (m*n-1) ADDs plus quite a few
>> instructions for traversing the array in a generic manner. With fused
>> multiply-adds, being able to assume contiguous data and ignore the
>> numpy iterator overhead, and applying divide-and-conquer kernels to
>> arrange sums, the optimized dot() implementations could have a
>> comparable instruction count.
>
> Couldn't sum benefit with similar logic?

Etc. I'm not going to keep repeating myself.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
  -- Umberto Eco


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