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 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