> > I agree that it's a good idea. I guess a single header which is included > is easiest to start with? > Should the functions be implemented in C? or C and Fortran? Or C++ even? > Are there any other functions except pow that needs special implementation? >
As we're generating C compatible code, they should be in C. There is no need for a Fortran variant; Fortan already handles Pow(double, int) in an efficient way. I can't think of any other functions that should be implemented currently. Adding to the already created header sounds fine, although it may be unexpected. Right now I'm kind of leaning to the creation and inclusion of a separate header-only library that includes SymPy's specially defined functions. Can you point me to some examples from your experience when > -ffast-math may result in loss of precision? I use it all the time in > all my production codes. So I would like to learn more about the > pitfalls. > Personally, I've never had an issue arise from using it, but a number of people more knowledgable than myself have warned against it. -ffast-math is just an easy way of setting a number of compiler flags that may result in more optimized math operations. Most of these result in code that is functional, and does what is intended, but no longer follows the IEEE floating point standard exactly. As the GCC manual says <https://gcc.gnu.org/onlinedocs/gcc-3.4.4/gcc/Optimize-Options.html>: This option should never be turned on by any -O option since it can result > in incorrect output for programs which depend on an exact implementation of > IEEE or ISO rules/specifications for math functions. Looking through the flags that -ffast-math sets <https://gcc.gnu.org/wiki/FloatingPointMath>, it seems that -funsafe-math-operations is the big one that may cause issues. This allows a larger set of transformations on the computations to be used, which may result in changes to summation error, over/underflow behavior, and differences in rounding behavior from the code *as written*. For many things these may not matter, but for some they may. - Jim On Wednesday, September 3, 2014 10:49:03 AM UTC-5, Ondřej Čertík wrote: > > Hi James, > > > On Mon, Sep 1, 2014 at 2:37 PM, James Crist <cris...@umn.edu <javascript:>> > wrote: > >> > >> 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. > > > Can you point me to some examples from your experience when > -ffast-math may result in loss of precision? I use it all the time in > all my production codes. So I would like to learn more about the > pitfalls. > > Ondrej > > > > > > > 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 > <javascript:>> 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, 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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