Am 28.07.2021 um 01:50 schrieb Sebastian Berg <sebastian@sipsolutions.net>:
Hi all,
there is a proposal to add some Intel specific fast math routine to NumPy:
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.... (Mainly the LA column) https://software.intel.com/content/www/us/en/develop/documentation/onemkl-vm...
Different implementation give different accuracy, but formulating some guidelines/expectation (or referencing them) would be useful guidance.
For basic
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