> > I just did that. Here are the types: > > real-matrix* : (Array Real) (Array Real) -> (Array Real) > > flonum-matrix* : (Array Flonum) (Array Flonum) -> (Array Flonum) > > flmatrix* : FlArray FlArray -> FlArray > > Results so far, measured in DrRacket with debugging off: > > Function Size Time > ----------------------------------------- > matrix* 100x100 340ms > real-matrix* 100x100 40ms > flonum-matrix* 100x100 10ms > flmatrix* 100x100 6ms > > matrix* 1000x1000 418000ms > real-matrix* 1000x1000 76000ms > flonum-matrix* 1000x1000 7000ms > flmatrix* 1000x1000 4900ms > > The only difference between `real-matrix*' and `flonum-matrix*' is that the > former uses `+' and `*' and the latter uses `fl+' and `fl*'. But if I can > inline `real-matrix*', TR's optimizer will change the former to the latter, > making `flonum-matrix*' unnecessary. (FWIW, this would be the largest speedup > TR's optimizer will have ever shown me.) > > It looks like the biggest speedup comes from doing only flonum ops in the > inner loop sum, which keeps all the intermediate flonums unboxed (i.e. not > heap-allocated or later garbage-collected). > > Right now, `flmatrix*' is implemented a bit stupidly, so I could speed it up > further. I won't yet, because I haven't settled on a type for matrices of > unboxed flonums. The type has to work with LAPACK if it's installed, which > `FlArray' doesn't do because its data layout is row-major and LAPACK expects > column-major. > > I'll change `matrix*' to look like `real-matrix*'. It won't give the very > best performance, but it's a 60x speedup for 1000x1000 matrices. >
These results look very promising, esp. if , as you mentioned, in the end the real-matrix* will automatically reach the flonum-matrix* performance for Flonums and the flmatrix* automatically switches to a LAPACK based variant, when available. For the latter it would be great if one could even change the used library to, e.g., redirect to a installation of the highly efficient MKL library from Intel. Looking forward to benchmark it against Numpy and Mathematica (which is MKL based) again! Berthold ____________________ Racket Users list: http://lists.racket-lang.org/users
