Different type of FastSin

[GlebKonstPub]

Different fastSin implementation, without LUT.

Here is couple illustrations. Green is error with linear interpolation on LUT with 512 entries. Red line is error with this implementation. Both are scaled by 2048 for visibility.

This method has much smaller assembly size, since it doesn't require table preparation. Also it is considerably more performant:

• up to 5.5 times on SSE2
• up to 2 times on AVX2

PolySin here is the new implementation.

Both basically without actual vectorization, just by virtue of pure and simple computation without retrieving stuff from memory.

Basically it generates triangle wave with sine shaper afterwards. Sine shapers idea is a simple 7-th degree polynomial. Idea of exact polynomial construction was taken from NI Reaktor Core library and recalculated with better precision.

[GlebKonstPub]

IMHO, this version is precise enough. However, if necessary, it can be improved dramatically by the cost of couple more multiply/accumulate instructions. Approximately 1 mul/acc per order of magnitude of error.

[GlebKonstPub]

Just for fun I tried benchmarking this on x87 FPU. Results are stading. Same with 32-bit x86. Actually this target shows biggest difference in performance. I can assume that this is somehow connected with x86 calling convention. Double results are stored on ST(0), so this means they should be pushed from MMX registers into memory and than loaded into FPU stack. PolySin just interact with memory less.

[GlebKonstPub]

I recompiled benchmark with /fp:fast. I understand that original FastSin was there mostly there to avoid calls to std, but I hope this further demonstrates that PolySin does not only have a smaller footprint, but also is so optimized that even default strict fp precision doesn't affect it in any detectable way.