On Wednesday, 9 March 2016 14:57:14 UTC+1, Tanu Hari Dixit wrote: > > > 2)The optimizer can implement the following with individual switches: > > > i)unrolled pow(x, n) > > ii)fused add multiply for floating point calculations > > iii)intelligent guess about whether to use exp2 >
i, ii) any modern compiler makes this moot, it's simply a matter of supplying the correct flags (whether SymPy should know about these flags for respective compiler or not I don't know). iii) I know Anthony Scopatz does this, but on the hardware and compilers I've tested this on I've seen everything from ~15% faster to 50% slower execution. Again, we would have to teach SymPy about combinations of math library versions, compiler versions and hardware. > iv)horner > > v)horner with fused add multiply, maybe? > > vi)fast matrix exponentiation that takes in an AST > > vii)trignometric simplification > > viii)pre-computing constant expressions > > ix)using cse with 'basic' optimization. > > x)splitting very large expressions into number of Augmented Assignments > > xi)fractional power optimization (a=x**(1/2), b=x**(3/2) => a=x**(1/2), > b=x*a) > > xii)integer power optimization (a=x**8, b=x**10 => t1=x**2, t2=t1**2, > a=t2**2, b=a*t1 > I wonder if compilers do this already, I have not tried myself. xiii)Sub-product optimization (a=xyz, b=wyz => t1=yz, a=xt1, b=wt1) > > xiv)Sum multiple optimization (a =x-y, b=2y-2x => a=x-y, b=-2a) > > > The last four are taken from > http://www.jnaiam.org/new/uploads/files/16985fffb53018456cf3506db1c5e42b.pdf > <http://www.google.com/url?q=http%3A%2F%2Fwww.jnaiam.org%2Fnew%2Fuploads%2Ffiles%2F16985fffb53018456cf3506db1c5e42b.pdf&sa=D&sntz=1&usg=AFQjCNGVWjH-_xSZm7FrCwPL9qBOAubkUQ> > > which is a paper by Allan Wittkopf on code generation in Maple. > I would be inclined to think that a lot has happened to the optimizers in compilers since 2007, one would need to replicate some of the experiments on modern hardware/compilers. > > I understand that these optimizations need to be tested and might not > necessarily provide a speed up in all contexts. > > I would like to ask if you have any comments on how you think the > optimization pipeline should be (improvements on the naive model I drew on > Pinta) and according to you, which of the above optimizations are worth > being included ( after being tested ). > As you say, testing this will be crucial. SymPy would need access to some dedicated hardware and I suppose a benchmark suite for SymPy generated code would be almost a must? > > Thank you, > > Tanu Hari Dixit. > -- 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+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/979cd70b-82cd-4638-a1c2-7f55a87df452%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
