> > I prefer either to pass -ffast-math flag (setting compiler flags is > already an issue since we need > to indicate optimization level, right?) or write a specialized callback to > be inlined (tuned to an Intel i7): >
I'm not a fan of using the -ffast-math flag. It does other things that may result in a loss of precision, and not all users may want to use it. Handling compiler options should definitely be added to the codewrappers though, but should be a separate issue. I do like the specialized function idea, as it can easily be done using our current framework. Instead of linking to pow in math.h by default for integer exponents, we can use a specialized integer exponent function that is printed by the codeprinter (separate header file? In the header file? In the .c file? Not sure the best spot). This way the user can override our default as they normally would, and requires no additional kwargs. If pow is overridden by the user, it will not be included in the code printout. Easy, simple, and requires no user facing changes. Thoughts? On Sat, Aug 30, 2014 at 3:04 PM, Björn Dahlgren <bjo...@gmail.com> wrote: > Cool! Great work! > > > On Friday, 29 August 2014 22:48:23 UTC+2, James Crist wrote: >> >> If I understand correctly, there is no cost in representing pow(x, n) as >> x*x*x*x... for any positive integer n, as long as it's done correctly. >> > > Compilation will be slower for large n. > > >> C compilers don't like to change how you write out calculations unless >> they're asked too. So x*x*x*x will not generate the same machine code as >> (x*x)*(x*x). The second case is preferable, as it will result in y = x*x, >> sol = y*y, rather than sol = x*x*x*x. This removes the need for one >> computation. Also, the second way apparently results in better precision >> for the end result (not sure why). >> >> I am all for writing all positive integer powers as multiplication, >> provided we can get the parenthesis convention correct. So x**4 -> >> (x*x)*(x*x), or x**11 -> x*((x*x)*(x*x)*x)*((x*x)*(x*x)*x), etc... If >> others are supportive of this, I'll submit a PR. >> > > I prefer either to pass -ffast-math flag (setting compiler flags is > already an issue since we need > to indicate optimization level, right?) or write a specialized callback to > be inlined (tuned to an Intel i7): > https://github.com/bjodah/cinterpol/blob/master/cInterpol/power.c > > and tell sympy to generate code using it: > https://github.com/sympy/sympy/pull/7517 > > > >> >> On Fri, Aug 29, 2014 at 2:00 PM, Aaron Meurer <asme...@gmail.com> wrote: >> >>> 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 <moore...@gmail.com> 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 <moore...@gmail.com> >>> 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 <moore...@gmail.com> >>> wrote: >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> Jason >>> >>> moorepants.info >>> >>> +01 530-601-9791 >>> >>> >>> >>> >>> >>> On Fri, Aug 29, 2014 at 2:38 AM, James Crist <cris...@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, 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