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Re: Fast & accurate sine / cosine pairs

Thanks for all the responses. Thought I'd write a follow up in case anyone else was interested or searching for something similar...

My description was slightly wrong, the sample rate was 9,765.625 as opposed to 2,500,000. This means that the angle input to the sine / cosine calculation can be as large as ~3,500,000. For values at this magnitude, single precision floating point becomes pretty useless: the inputs to the sine / cosine algorithm were inaccurate, not the algorithm itself.

To get round this I use extra precision for the angle calculation and the initial range reduction step of the sine / cosine algorithm before doing the rest of it with Altivec as before.



I initially tried to use "double-float" arithmetic (using two Altivec single precision values to emulate a double precision value) using the "double-double" algorithm from the QD library:
http://crd.lbl.gov/~dhbailey/mpdist/
However, in practice this method (particularly the rounding / range reduction step) does not offer much parallelism and causes a large number of instruction stalls.

Simply implementing the angle calculation and rounding step in scalar double precision seems to get much better performance (particularly with 2 FPUs on the G5). The only caveat is converting the double precision values to single precision and then storing them to memory before they can be loaded into the Altivec unit.



r i c k
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