I think we should print pow using repeated multiplication. People might not know about --ffast-math, not realize that we are using pow and that it is needed, or not want other optimizations that it provides.
Is there a reason to put a limit on the power (5 was suggested here, 10 on the pull request)? Aaron Meurer On Fri, Aug 29, 2014 at 9:38 AM, Jason Moore <[email protected]> wrote: > Sorry, it wasn't merged. He found that the --fast-math flag in the complier > takes care of this. > > > Jason > moorepants.info > +01 530-601-9791 > > > On Fri, Aug 29, 2014 at 10:37 AM, Jason Moore <[email protected]> wrote: >> >> Here is some work on the pow issue: >> https://github.com/sympy/sympy/pull/7519 >> >> Looks like it was merged so the ccode printer should print x*x*x... for >> less that 10 x's. >> >> >> Jason >> moorepants.info >> +01 530-601-9791 >> >> >> On Fri, Aug 29, 2014 at 7:33 AM, Jason Moore <[email protected]> wrote: >>> >>> >>> >>> >>> Jason >>> moorepants.info >>> +01 530-601-9791 >>> >>> >>> On Fri, Aug 29, 2014 at 2:38 AM, James Crist <[email protected]> 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 <[email protected]> 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 <[email protected]> >>>>> > 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 <[email protected]> >>>>> > 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 <[email protected]> >>>>> > 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 <[email protected]> >>>>> > 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 <[email protected]> >>>>> > wrote: >>>>> > Cool >>>>> > >>>>> > >>>>> > On Wed, Aug 27, 2014 at 8:07 PM, James Crist <[email protected]> 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 [email protected]. >>>>> > To post to this group, send email to [email protected]. >>>>> > 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 [email protected]. >>>>> > To post to this group, send email to [email protected]. >>>>> > 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 >>>>> > [email protected]. >>>>> > >>>>> > To post to this group, send email to [email protected]. >>>>> > 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 [email protected]. >>>>> > To post to this group, send email to [email protected]. >>>>> > 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 >>>>> > [email protected]. >>>>> > To post to this group, send email to [email protected]. >>>>> > 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 [email protected]. >>>>> > To post to this group, send email to [email protected]. >>>>> > 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 [email protected]. >>>>> > To post to this group, send email to [email protected]. >>>>> > 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. >>>> To unsubscribe from this group and stop receiving emails from it, send 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