I strongly agree with you Gregor: * Best precision should remain the default. I lost months in finding the compiler option (in ICC) which switched to LA mode and broke all my calculations. * I wonder how those SVML behaves on non-intel plateform ? Sleef provides the same approach but it works also on Power and ARM platforms (and is designed to be extended...).
Cheers, Jerome On Wed, 28 Jul 2021 12:13:44 +0200 Gregor Thalhammer <gregor.thalham...@gmail.com> wrote: > > Am 28.07.2021 um 01:50 schrieb Sebastian Berg <sebast...@sipsolutions.net>: > > > > Hi all, > > > > there is a proposal to add some Intel specific fast math routine to > > NumPy: > > > > https://github.com/numpy/numpy/pull/19478 > > Many years ago I wrote a package > https://github.com/geggo/uvml > that makes the VML, a fast implementation of transcendetal math functions, > available for numpy. Don’t know if it still compiles. > It uses Intel VML, designed for processing arrays, not the SVML intrinsics. > By this it is less machine dependent (optimized implementations are selected > automatically depending on the availability of, e.g., SSE, AVX, or AVX512), > just link to a library. It compiles as an external module, can be activated > at runtime. > > Different precision models can be selected at runtime (globally). I thinks > Intel advocates to use the LA (low accuracy) mode as a good compromise > between performance and accuracy. Different people have strongly diverging > opinions about what to expect. > > The speedups possibly gained by these approaches often vaporize in > non-benchmark applications, as for those functions performance is often > limited by memory bandwidth, unless all your data stays in CPU cache. By > default I would go for high accuracy mode, with option to switch to low > accuracy if one urgently needs the better performance. But then one should > use different approaches for speeding up numpy. > > Gregor > > > > > > part of numerical algorithms is that there is always a speed vs. > > precision trade-off, giving a more precise result is slower. > > > > So there is a question what the general precision expectation should be > > in NumPy. And how much is it acceptable to diverge in the > > precision/speed trade-off depending on CPU/system? > > > > I doubt we can formulate very clear rules here, but any input on what > > precision you would expect or trade-offs seem acceptable would be > > appreciated! > > > > > > Some more details > > ----------------- > > > > This is mainly interesting e.g. for functions like logarithms, > > trigonometric functions, or cubic roots. > > > > Some basic functions (multiplication, addition) are correct as per IEEE > > standard and give the best possible result, but these are typically > > only correct within very small numerical errors. > > > > This is typically measured as "ULP": > > > > https://en.wikipedia.org/wiki/Unit_in_the_last_place > > > > where 0.5 ULP would be the best possible result. > > > > > > Merging the PR may mean relaxing the current precision slightly in some > > places. In general Intel advertises 4 ULP of precision (although the > > actual precision for most functions seems better). > > > > > > Here are two tables, one from glibc and one for the Intel functions: > > > > https://www.gnu.org/software/libc/manual/html_node/Errors-in-Math-Functions.html > > (Mainly the LA column) > > https://software.intel.com/content/www/us/en/develop/documentation/onemkl-vmperfdata/top/real-functions/measured-accuracy-of-all-real-vm-functions.html > > > > > > Different implementation give different accuracy, but formulating some > > guidelines/expectation (or referencing them) would be useful guidance. > > > > For basic > > > > _______________________________________________ > > NumPy-Discussion mailing list > > NumPy-Discussion@python.org > > https://mail.python.org/mailman/listinfo/numpy-discussion > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@python.org > https://mail.python.org/mailman/listinfo/numpy-discussion -- Jérôme Kieffer tel +33 476 882 445 _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@python.org https://mail.python.org/mailman/listinfo/numpy-discussion
