Hi,
Observing following performance:
In []: m= 1e5
In []: n= 1e2
In []: o= ones(n)
In []: M= randn(m, n)
In []: timeit M.sum(1)
10 loops, best of 3: 38.3 ms per loop In []: timeit dot(M, o)
10 loops, best of 3: 21.1 ms per loop In []: m= 1e2
In []: n= 1e5
In []: o= ones(n)
In []: M= randn(m, n)
In []: timeit M.sum(1)
100 loops, best of 3: 18.3 ms per loop In []: timeit dot(M, o)
10 loops, best of 3: 21.2 ms per loop One would expect sum to outperform dot with a clear marginal. Does there exixts any 'tricks' to increase the performance of sum?
In []: sys.version
Out[]: '2.7.1 (r271:86832, Nov 27 2010, 18:30:46) [MSC v.1500 32 bit (Intel)]' # installed binaries from http://python.org/
In []: np.version.version
Out[]: '1.5.1' Regards,
eat
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On Thu, Feb 10, 2011 at 8:29 AM, eat <[hidden email]> wrote:
I'm not surprised, much depends on the version of ATLAS or MKL you are linked to. If you aren't linked to either and just using numpy's version then the results are a bit strange. With numpy development I get In [1]: m= 1e5 In [2]: n= 1e2 In [3]: o= ones(n) In [4]: M= randn(m, n) In [5]: timeit M.sum(1) 100 loops, best of 3: 19.2 ms per loop In [6]: timeit dot(M, o) 100 loops, best of 3: 15 ms per loop In [7]: m= 1e2 In [8]: n= 1e5 In [9]: o= ones(n) In [10]: M= randn(m, n) In [11]: timeit M.sum(1) 100 loops, best of 3: 17.4 ms per loop In [12]: timeit dot(M, o) 100 loops, best of 3: 14.2 ms per loop Chuck _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
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 ;-).
Regards,
eat
On Thu, Feb 10, 2011 at 7:10 PM, Charles R Harris <[hidden email]> wrote:
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On Thu, Feb 10, 2011 at 11:53, eat <[hidden email]> 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. Additionally, the number of instructions in your dot() probably isn't that many more than the sum(). The sum() is pretty dumb 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. If you were willing to spend that amount of developer time and code complexity to make platform-specific backends to sum(), you could make it go really fast, too. Typically, it's not all that important to make it worthwhile, though. One thing that might be worthwhile is to make implementations of sum() and cumsum() that avoid the ufunc machinery and do their iterations more quickly, at least for some common combinations of dtype and contiguity. -- 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 _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
Thu, 10 Feb 2011 12:16:12 -0600, Robert Kern wrote:
[clip] > One thing that might be worthwhile is to make > implementations of sum() and cumsum() that avoid the ufunc machinery and > do their iterations more quickly, at least for some common combinations > of dtype and contiguity. I wonder what is the balance between the iterator overhead and the time taken in the reduction inner loop. This should be straightforward to benchmark. Apparently, some overhead decreased with the new iterators, since current Numpy master outperforms 1.5.1 by a factor of 2 for this benchmark: In [8]: %timeit M.sum(1) # Numpy 1.5.1 10 loops, best of 3: 85 ms per loop In [8]: %timeit M.sum(1) # Numpy master 10 loops, best of 3: 49.5 ms per loop I don't think this is explainable by the new memory layout optimizations, since M is C-contiguous. Perhaps there would be room for more optimization, even within the ufunc framework? -- Pauli Virtanen _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Robert Kern-2
Hi Robert,
On Thu, Feb 10, 2011 at 8:16 PM, Robert Kern <[hidden email]> wrote:
Can't we have this as well with simple sum?
Additionally, the number But does it need to be?
and just does a linear accumulation Couldn't sum benefit with similar logic?
If you were willing to spend that amount of developer time and code Actually I would, but I'm not competent at all in that detailed level (:, But I'm willing to spend more on my own time for example for testing, debugging, analysing various improvements and suggestions if such emerge.
, you could make Well I'm allready perplexd before reaching that 'ufunc machinery', it's actually anyway trivial (for us more mortal ;-) to figure out what's happening with sum on fromnumeric.py!
Regards,
eat
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In reply to this post by Pauli Virtanen-3
Hi Pauli,
On Thu, Feb 10, 2011 at 8:31 PM, Pauli Virtanen <[hidden email]> wrote: Thu, 10 Feb 2011 12:16:12 -0600, Robert Kern wrote: I hope so. Please suggest if there's anything that I can do to further advance this. (My C skills are allready bit rusty, but at any higher level I'll try my best to contribute).
Thanks,
eat
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On Thu, 10 Feb 2011 22:38:52 +0200, eat wrote:
[clip] > I hope so. Please suggest if there's anything that I can do to further > advance this. (My C skills are allready bit rusty, but at any higher > level I'll try my best to contribute). If someone wants to try to improve the situation, here's a possible plan of attack: 1. Check first if the bottleneck is in the inner reduction loop (function DOUBLE_add in loops.c.src:712) or in the outer iteration (function PyUFunc_ReductionOp in ufunc_object.c:2781). 2. If it's in the inner loop, some optimizations are possible, e.g. specialized cases for sizeof(item) strides. Think how to add them cleanly. 3. If it's in the outer iteration, try to think how to make it faster. This will be a more messy problem to solve. -- Pauli Virtanen _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
Maybe I'm missing something, but why not just implement sum() using
dot() and ones() ? --Josh On Thu, Feb 10, 2011 at 11:49 AM, Pauli Virtanen <[hidden email]> wrote: > On Thu, 10 Feb 2011 22:38:52 +0200, eat wrote: > [clip] >> I hope so. Please suggest if there's anything that I can do to further >> advance this. (My C skills are allready bit rusty, but at any higher >> level I'll try my best to contribute). > > If someone wants to try to improve the situation, here's a possible plan > of attack: > > 1. Check first if the bottleneck is in the inner reduction loop > (function DOUBLE_add in loops.c.src:712) or in the outer iteration > (function PyUFunc_ReductionOp in ufunc_object.c:2781). > > 2. If it's in the inner loop, some optimizations are possible, e.g. > specialized cases for sizeof(item) strides. Think how to add them cleanly. > > 3. If it's in the outer iteration, try to think how to make it faster. > This will be a more messy problem to solve. > > -- > Pauli Virtanen > > _______________________________________________ > NumPy-Discussion mailing list > [hidden email] > http://mail.scipy.org/mailman/listinfo/numpy-discussion > NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by eat-3
On Thu, Feb 10, 2011 at 14:29, eat <[hidden email]> wrote:
> Hi Robert, > > On Thu, Feb 10, 2011 at 8:16 PM, Robert Kern <[hidden email]> wrote: >> >> On Thu, Feb 10, 2011 at 11:53, eat <[hidden email]> 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 _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Joshua Holbrook
On Thu, Feb 10, 2011 at 14:51, Joshua Holbrook <[hidden email]> wrote:
> Maybe I'm missing something, but why not just implement sum() using > dot() and ones() ? You can't do everything that sum() does with just dot() and ones(). -- 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 _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Pauli Virtanen-3
On Thu, Feb 10, 2011 at 10:31 AM, Pauli Virtanen <[hidden email]> wrote:
Thu, 10 Feb 2011 12:16:12 -0600, Robert Kern wrote: I played around with this in einsum, where it's a bit easier to specialize this case than in the ufunc machinery. What I found made the biggest difference is to use SSE prefetching instructions to prepare the cache in advance. Here are the kind of numbers I get, all from the current Numpy master:
In [7]: timeit M.sum(1) 10 loops, best of 3: 44.6 ms per loop In [8]: timeit dot(M, o) 10 loops, best of 3: 36.8 ms per loop
In [9]: timeit einsum('ij->i', M) 10 loops, best of 3: 32.1 ms per loop ... In [14]: timeit M.sum(1) 10 loops, best of 3: 41.5 ms per loop In [15]: timeit dot(M, o) 10 loops, best of 3: 42.1 ms per loop In [16]: timeit einsum('ij->i', M) 10 loops, best of 3: 30 ms per loop -Mark _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Robert Kern-2
Hi Robert,
On Thu, Feb 10, 2011 at 10:58 PM, Robert Kern <[hidden email]> wrote:
Yes I acknowledge this. But didn't they then ignore them something simpler, like sum (but which actually could benefit exactly similiar optimizations).
and cause substantial headaches for people I appreciate this. No doubt at all.
However, they are frequently worth it But here I have to disagree; I'll think that at least I (if not even the majority of numpy users) don't like (nor I'm be capable/ or have enough time/ resources) go to dwell such details. I'm sorry but I'll have to restate that it's quite reasonable to expect that sum outperforms dot in any case. Lets now to start make such movements, which enables sum to outperform dot.
You can gain speed by specializing to just your use case, e.g. Yes, I would really like to specialize into my case, but 'without going out the python realm.'
Thanks,
eat
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On Thu, Feb 10, 2011 at 15:32, eat <[hidden email]> wrote:
> Hi Robert, > > On Thu, Feb 10, 2011 at 10:58 PM, Robert Kern <[hidden email]> wrote: >> >> On Thu, Feb 10, 2011 at 14:29, eat <[hidden email]> wrote: >> > Hi Robert, >> > >> > On Thu, Feb 10, 2011 at 8:16 PM, Robert Kern <[hidden email]> >> > wrote: >> >> >> >> On Thu, Feb 10, 2011 at 11:53, eat <[hidden email]> 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 > > Yes I acknowledge this. But didn't they then ignore them something simpler, > like sum (but which actually could benefit exactly similiar optimizations). Let's set aside the fact that the people who optimized the implementation of dot() (the authors of ATLAS or the MKL or whichever optimized BLAS library you linked to) are different from those who implemented sum() (the numpy devs). Let me repeat a reason why one would put a lot of effort into optimizing dot() but not sum(): """ >> However, they are frequently worth it >> because those operations are often bottlenecks in whole applications. >> sum(), even in its stupidest implementation, rarely is. """ I don't know if I'm just not communicating very clearly, or if you just reply to individual statements before reading the whole email. >> and cause substantial headaches for people >> building and installing numpy. > > I appreciate this. No doubt at all. >> >> 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. > > But here I have to disagree; I'll think that at least I (if not even the > majority of numpy users) don't like (nor I'm be capable/ or have enough > time/ resources) go to dwell such details. And you think we have the time and resources to do it for you? > I'm sorry but I'll have to > restate that it's quite reasonable to expect that sum outperforms dot in any > case. You don't optimize a function just because you are capable of it. You optimize a function because it is taking up a significant portion of total runtime in your real application. Anything else is a waste of time. > Lets now to start make such movements, which enables sum to outperform > dot. Sorry, you don't get to volunteer anyone's time or set anyone's priorities but your own. There are some sensible things one could do to optimize sums or even general ufunc reductions, as outlined my Mark, Pauli and myself, but please stop using the accelerated-BLAS dot() as your benchmark. It's a completely inappropriate comparison. >> 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. > > Yes, I would really like to specialize into my case, but 'without going out > the python realm.' The Bottleneck project is a good place for such things. It's a nice middle-ground for somewhat-specialized routines that are still pretty common but not general enough to be in numpy yet. http://pypi.python.org/pypi/Bottleneck If you're not willing to learn how to implement it yourself in Cython, I'm afraid that you're stuck waiting for someone to do it for you. But please don't expect anyone to feel obligated to do so. -- 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 _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Mark Wiebe
On Thu, Feb 10, 2011 at 2:26 PM, Mark Wiebe <[hidden email]> wrote:
I get an even bigger speedup: In [5]: timeit M.sum(1) 10 loops, best of 3: 19.2 ms per loop In [6]: timeit dot(M, o) 100 loops, best of 3: 15.2 ms per loop In [7]: timeit einsum('ij->i', M) 100 loops, best of 3: 11.4 ms per loop <snip> Chuck _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Robert Kern-2
On Thu, Feb 10, 2011 at 3:08 PM, Robert Kern <[hidden email]> wrote:
Heh. Reminds me of a passage in General Bradley's A Soldier's Story where he admonished one of his officers in North Africa for taking a hill and suffering casualties, telling him that one didn't take a hill because one could, but because doing so served a purpose in the larger campaign. <snip> Chuck _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by Robert Kern-2
Hi,
On Fri, Feb 11, 2011 at 12:08 AM, Robert Kern <[hidden email]> wrote:
You are communicating very well. It's me who's not communicating so well.
My intention was not to suggest anything like that.
OK. Lets compare sum to itself:
In []: M= randn(1e5, 1e2)
In []: timeit M.sum(0)
10 loops, best of 3: 169 ms per loop In []: timeit M.sum(1)
10 loops, best of 3: 37.5 ms per loop In []: timeit M.sum()
10 loops, best of 3: 18.1 ms per loop In []: timeit sum(M.sum(0))
10 loops, best of 3: 169 ms per loop In []: timeit sum(M.sum(1))
10 loops, best of 3: 37.7 ms per loop In []: timeit M.T.sum(0)
10 loops, best of 3: 37.7 ms per loop In []: timeit M.T.sum(1)
10 loops, best of 3: 171 ms per loop In []: timeit M.T.sum()
1 loops, best of 3: 288 ms per loop In []: timeit sum(M.T.sum(0))
10 loops, best of 3: 37.7 ms per loop In []: timeit sum(M.T.sum(1))
10 loops, best of 3: 170 ms per loop In []: 288./ 18.1
Out[]: 15.91160220994475
Perhaps my bad wordings, but I do not expect anyone to do it for me. I also think that there exists some real substance I addressed (as demonstrated now with comparing sum to itself).
Regards,
eat
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In reply to this post by Pauli Virtanen-3
Thu, 10 Feb 2011 20:49:28 +0000, Pauli Virtanen wrote:
[clip] > 1. Check first if the bottleneck is in the inner reduction loop > (function DOUBLE_add in loops.c.src:712) or in the outer iteration > (function PyUFunc_ReductionOp in ufunc_object.c:2781). > 2. If it's in the inner loop, some optimizations are possible, e.g. > specialized cases for sizeof(item) strides. Think how to add them > cleanly. A quick check (just replace the inner loop with a no-op) shows that for 100 items, the bottleneck is in the inner loop. The cross-over between inner loop time and strided iterator overhead apparently occurs around ~20-30 items (on the machine I used for testing). Anyway, spending time for optimizing the inner loop for a 30% speed gain (max) seems questionable... -- Pauli Virtanen _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
In reply to this post by eat-3
Den 10.02.2011 16:29, skrev eat:
> One would expect sum to outperform dot with a clear marginal. Does > there exixts any 'tricks' to increase the performance of sum? I see that others have ansvered already. The ufunc np.sum is not going going to beat np.dot. You are racing the heavy machinery of NumPy (array iterators, type chekcs, bound checks, etc.) against level-3 BLAS routine DGEMM, the most heavily optimized numerical kernel ever written. Also beware that computation is much cheaper than memory access. Although DGEMM does more arithmetics, and even is O(N3) in that respect, it is always faster except for very sparse arrays. If you need fast loops, you can always write your own Fortran or C, and even insert OpenMP pragmas. But don't expect that to beat optimized high-level BLAS kernels by any margin. The first chapters of "Numerical Methods in Fortran 90" might be worth reading. It deals with several of these issues, including dimensional expansion, which is important for writing fast numerical code -- but not intuitively obvious. "I expect this to be faster because it does less work" is a fundamental misconception in numerical computing. Whatever cause less traffic on the memory BUS (the real bottleneck) will almost always be faster, regardless of the amount of work done by the CPU. A good advice is to use high-level BLAS whenever you can. The only exception, as mentioned, is when matrices get very sparse. Sturla _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
Hi Sturla,
On Sat, Feb 12, 2011 at 5:38 PM, Sturla Molden <[hidden email]> wrote: Den 10.02.2011 16:29, skrev eat: First of all, thanks for you still replying. Well, I'm still a little bit unsure how I should proceed with this discussion... I may have used bad wordings and created unneccessary mayhyem with my original question (:. Trust me, I'm only trying to discuss here with a positive criticism in my mind.
Now, I'm not pretending to know what kind of a person a 'typical' numpy user is. But I'm assuming that there just exists more than me with roughly similar questions in their (our) minds and who wish to utilize numpy more 'pythonic; all batteries included' way. Ocassionally I (we) may ask really stupid questions, but please beare with us.
Said that, I'm still very confident that (from a users point of view) there's some real substance on the issue I addressed.
I see that others have ansvered already. The ufunc np.sum is not going Fair enough.
Also Sure, that's exactly where I expected the performance boost to emerge.
Although That's a very important potential, but surely not all numpy users are expected to master that ;-)
But don't expect that to beat optimized high-level BLAS kernels by any And I'm totally aware of it, and actually it was exactly the original intended logic of my question: "how bout if the sum could follow the steps of dot; then, since less instructions it must be bounded below of the execution time of dot". But as R. Kern gently pointed out allready it's not fruitfull enough avenue to proceed. And I'm able to live with that.
Regards,
eat
A good advice is to use high-level BLAS whenever _______________________________________________ NumPy-Discussion mailing list [hidden email] http://mail.scipy.org/mailman/listinfo/numpy-discussion |
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