Jason moorepants.info +01 530-601-9791
On Fri, Aug 29, 2014 at 2:38 AM, James Crist <crist...@umn.edu> wrote: > I was planning on going to bed, but ended up working on this instead. I > have no self control... > > Anyway, I've uncovered some things: > > 1. Addition of the restrict keyword to tell the compiler we're not > aliasing offers marginal gains. Gain a couple microseconds here and there. > This requires a c99 compiler, but it's 2014, everyone should have one by > now. > > 2. Inlining the function call resulted in smaller gains than 1, but still > *slightly* measurable. I suspect that for larger expression sizes this will > be negligible to none. > > 3. Here's the big one: For small powers, pow(c, n) is considerably slower > than c*c*c*c... Changing the ccode Pow handler to print all pows less than > 5 (arbitrary number) out as multiplication I was able to match/beat > (slightly) all of jason's benchmarks with the C + numpy ufuncs. > Oh yes! I knew that. In fact, I feel like I read in the current code somewhere. I forget, but that seems like a standard way we should be handling pows in C. Nice find! > > > On Thursday, August 28, 2014 1:38:30 PM UTC-5, Tim Lahey wrote: > >> On why Fortran is faster, Fortran semantics ensure that function >> arguments never alias, this allows the optimizer to make assumptions about >> the function and the arguments. This the main advantage of Fortran over C. >> But, because of this, it can lead to more memory usage. I know that the >> newer C++ standards have a keyword to mark arguments to indicate that they >> won't be aliased, but that requires that the code generator and the >> compiler support them. >> >> Cheers, >> >> Tim. >> >> On 2014-08-28, at 2:17 PM, Jason Moore <moore...@gmail.com> wrote: >> >> > Jim and others, >> > >> > Here are the benchmarks I made yesterday: >> > >> > http://www.moorepants.info/blog/fast-matrix-eval.html >> > >> > The working code is here: https://gist.github.com/moorepants/ >> 6ef8ab450252789a1411 >> > >> > Any feedback is welcome. >> > >> > >> > Jason >> > moorepants.info >> > +01 530-601-9791 >> > >> > >> > On Wed, Aug 27, 2014 at 11:44 PM, James Crist <cris...@umn.edu> wrote: >> > I was wondering about that. I wasn't sure if the overhead from looping >> through the inputs multiple times would outweigh improvements from fast C >> loops. Glad that in your case it does. >> > >> > I've thrown a WIP PR up: https://github.com/sympy/sympy/pull/7929 >> > >> > For some reason, creating the functions in python with numpy calls >> still seems to be faster (for micro-benchmarks). This probably has >> something to do with function complexity (the example function above is >> simple), but I'd still think it'd be faster in pure C. I tried inlining the >> call, which was a small improvement, but it was still slower than the pure >> numpy-python version. Something to look into. >> > >> > >> > On Wed, Aug 27, 2014 at 10:28 PM, Jason Moore <moore...@gmail.com> >> wrote: >> > Yeh, but if you simply create a ufunc for each expression in a matrix >> you still get substantial speedups. I wrote a bunch of test cases that I'll >> post to my blog tomorrow. >> > >> > >> > Jason >> > moorepants.info >> > +01 530-601-9791 >> > >> > >> > On Wed, Aug 27, 2014 at 11:26 PM, James Crist <cris...@umn.edu> wrote: >> > Not yet. I wrote it this morning during an extremely boring meeting, >> and haven't had a chance to clean it up. This doesn't solve your problem >> about broadcasting a matrix calculation though... >> > >> > >> > On Wed, Aug 27, 2014 at 10:23 PM, Jason Moore <moore...@gmail.com> >> wrote: >> > Awesome. I was working on this today but it looks like you've by passed >> what I had working. Do you have a PR with this? >> > >> > >> > Jason >> > moorepants.info >> > +01 530-601-9791 >> > >> > >> > On Wed, Aug 27, 2014 at 11:11 PM, Matthew Rocklin <mroc...@gmail.com> >> wrote: >> > Cool >> > >> > >> > On Wed, Aug 27, 2014 at 8:07 PM, James Crist <cris...@umn.edu> wrote: >> > I still need to do some cleanups and add tests, but I finally have this >> working and thought I'd share. I'm really happy with this: >> > >> > In [1]: from sympy import * >> > >> > In [2]: a, b, c = symbols('a, b, c') >> > >> > In [3]: expr = (sin(a) + sqrt(b)*c**2)/2 >> > >> > In [4]: from sympy.utilities.autowrap import ufuncify >> > >> > In [5]: func = ufuncify((a, b, c), expr) >> > >> > In [6]: func(1, 2, 3) >> > Out[6]: 6.7846965230828769 >> > >> > In [7]: func([1, 2, 3, 4, 5], [6, 7, 8, 9, 10], 3) >> > Out[7]: array([ 11.44343933, 12.36052961, 12.79848207, 13.12159875, >> 13.75078733]) >> > >> > In [8]: from numpy import arange >> > >> > In [9]: a = arange(10).reshape((2, 5)) >> > >> > In [10]: c = arange(10, 20).reshape((2, 5)) >> > >> > In [11]: b = 25 >> > >> > In [12]: func(a, b, c) >> > Out[12]: >> > array([[ 250. , 302.92073549, 360.45464871, 422.57056 , >> > 489.62159875], >> > [ 562.02053786, 639.86029225, 722.8284933 , 810.49467912, >> > 902.70605924]]) >> > >> > In [13]: type(func) >> > Out[13]: numpy.ufunc >> > >> > This now does everything a numpy `ufunc` does normally, as it *is* a >> ufunc. Codegen is hooked up to numpy api. Type conversion and broadcasting >> are done automagically. >> > >> > Caveats: only functions with a single output are accepted (this could >> be changed to accept multi-output without much effort though). Also, as >> with all unfuncs, input/outputs must all be scalars (no matrix/Indexed >> operations allowed). >> > >> > -- >> > You received this message because you are subscribed to the Google >> Groups "sympy" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> an email to sympy+un...@googlegroups.com. >> > To post to this group, send email to sy...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sympy. >> > To view this discussion on the web visit https://groups.google.com/d/ >> msgid/sympy/76e0fbbe-5ce4-43b7-855b-6ac821f6b8ae%40googlegroups.com. >> > For more options, visit https://groups.google.com/d/optout. >> > >> > >> > -- >> > You received this message because you are subscribed to the Google >> Groups "sympy" group. >> > To unsubscribe from this group and stop receiving emails from it, send >> an email to sympy+un...@googlegroups.com. >> > To post to this group, send email to sy...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sympy. >> > To view this discussion on the web visit https://groups.google.com/d/ >> msgid/sympy/CAJ8oX-EHZXbd5aFFNRy7gJ0hcydpAsG2qxv7 >> Py65DQ9cA9VUUA%40mail.gmail.com. >> > >> > For more options, visit https://groups.google.com/d/optout. >> > >> > >> > -- >> > You received this message because you are subscribed to a topic in the >> Google Groups "sympy" group. >> > To unsubscribe from this topic, visit https://groups.google.com/d/ >> topic/sympy/azVZHLOv9Vc/unsubscribe. >> > To unsubscribe from this group and all its topics, send an email to >> sympy+un...@googlegroups.com. >> > >> > To post to this group, send email to sy...@googlegroups.com. >> > Visit this group at http://groups.google.com/group/sympy. >> > To view this discussion on the web visit https://groups.google.com/d/ >> msgid/sympy/CAP7f1AieaeoOFtc_S4XPxWOX2jr2zmda9VCRpWpzHMTGLk >> mHPQ%40mail.gmail.com. >> > >> > For more options, visit https://groups.google.com/d/optout. >> > >> 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