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. 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 <javascript:>> > 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 > <javascript:>> 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 > <javascript:>> 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 > <javascript:>> 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 > <javascript:>> 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 > <javascript:>> wrote: > > Cool > > > > > > On Wed, Aug 27, 2014 at 8:07 PM, James Crist <cris...@umn.edu > <javascript:>> 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 <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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 <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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-EHZXbd5aFFNRy7gJ0hcydpAsG2qxv7Py65DQ9cA9VUUA%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 <javascript:>. > > > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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_S4XPxWOX2jr2zmda9VCRpWpzHMTGLkmHPQ%40mail.gmail.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 <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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/CAJ2L7mfL_xO%3DO-ZRMx-zfpZzJKJ-%2BUdTzSCz5jYf%2B%3DdovR%2B_7Q%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 <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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/CAP7f1AjcHrsopXjwK5uYdALeSrokxLMwA7xebTikHyhwL-%2BOVg%40mail.gmail.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 <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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/CAJ2L7me73iJmkWm%3D_LiyWrsuOCZm%2B4OZbqD%2BkwwScWWx23HVdg%40mail.gmail.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 <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > 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/CAP7f1Agdi_X-o0B%2B9mH2CGOSN-TyYGVwgZm4q8%3DYwxieBzZkzA%40mail.gmail.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. 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