This CORDIC explanation seems quite plausible. However, it seems like we probably don't want to use this algorithm, which means that we're not at this point able to get any kind of speedup for sincos(x) relative to sin(x), cos(x).
On Mon, Jul 28, 2014 at 10:13 AM, Stuart Brorson <[email protected]> wrote: > A bell rang in the back of my head as I was on my way to work this > morning. I was thinking about sincos again, and remembered something > about CORDIC algorithms from the distant past. These are add and > shift algorithms used to compute certain trig and other elementary > functions. They were very popular for scientific calculators back when > hand-held calculators were new since they are easily implementable in > hardware, and don't require floating point multiply. A couple of > references: > > http://en.wikipedia.org/wiki/CORDIC > http://ww1.microchip.com/downloads/en/AppNotes/01061A.pdf > > It appears that a common CORDIC computation will product sin & cos > together. I'll bet dollars to doughnuts (without actually knowing) > that the x87 assembly instruction mentioned below was doing a CORDIC > computation, and it made sense to return both sin & cos since > they were computed together. > > The paper by Jeannerod & JourdanLu refer to CORDIC methods, but is > apparently an extension, as far as I can tell. > > Stuart > > > > > On Mon, 28 Jul 2014, Simon Byrne wrote: > > I've often wondered this myself. As I understand it, the purpose of the >> sincos function was to call the FSINCOS assembly instruction for x87 FPU. >> On modern processors however, it is generally acknowledged that calling a >> well-written math library compiled to use SSE instructions is typically >> faster (and can be more accurate) than using x87 trig instructions. See >> this discussion: >> http://stackoverflow.com/questions/12485190/calling- >> fsincos-instruction-in-llvm-slower-than-calling-libc-sin-cos-functions >> >> Calling sincos using Isaiah's method seems to be about 9 times slower than >> calling the sin and cos separately: >> https://gist.github.com/734dcacde1f107397b3b.git >> though a lot of this seems to be due to the overhead in creating and >> destroying the arrays for return values. >> >> >> On Monday, 28 July 2014 13:34:53 UTC+1, Kevin Squire wrote: >> >>> >>> This paper seems relevant, though possibly only for 32-bit: >>> >>> >>> http://hal.archives-ouvertes.fr/docs/00/67/23/27/PDF/ >>> Jeannerod-JourdanLu.pdf >>> >>> Cheers, >>> Kevin >>> >>> On Monday, July 28, 2014, Stuart Brorson <[email protected] <javascript:>> >>> >>> wrote: >>> >>> On Sun, 27 Jul 2014, Viral Shah wrote: >>>> >>>> Is sincos a standard libm function? >>>> >>>>> >>>>> >>>> Out of curiosity I looked into sincos since I had never heard of it. >>>> A quick check shows there's no sincos in fdlibm >>>> (on netlib). However, a little Googling reveals an old Sun math >>>> library libsunmath seems to implement it. >>>> >>>> I did find a couple of libm variants which implemented sincos. >>>> However, they simply called sin & cos separately. As Stephan says >>>> upthread, no performance improvement. >>>> >>>> As far as I know, sin & cos are usually computed using mod to fold >>>> the input x down to the first quadrant, and then using a power series >>>> (needs only 6 or 8 terms IIRC) to compute the function. Perhaps >>>> libsunmath computed e.g. cos first, and then did sin = sqrt(1 - >>>> cos^2)? Taking the sqrt seems non-performant compared to evaluating a >>>> short power series, but maybe they had a reason? Another thought: sin >>>> and cos are reflections of each other (over the line x = pi/4) in the >>>> first quadrant. Perhaps there some other clever way to get sin from >>>> cos? I couldn't think if any in the short time I spent considering >>>> it. >>>> >>>> Stuart >>>> >>>> >>>> On Sun, 27 Jul 2014, Viral Shah wrote: >>>> >>>> Is sincos a standard libm function? >>>> >>>>> >>>>> Also, I wonder if creating the one entry array is too expensive, and if >>>>> we >>>>> should just call sin and cos separately. The vectorized version may be >>>>> able >>>>> to benefit from calling sincos directly. >>>>> >>>>> -viral >>>>> >>>>> On Monday, July 28, 2014 1:02:06 AM UTC+5:30, Isaiah wrote: >>>>> >>>>> >>>>>> It doesn't appear to be wrapped, but you can call it yourself like >>>>>> this: >>>>>> >>>>>> julia> sincos(x) = begin psin = Cdouble[0]; pcos = Cdouble[0]; >>>>>> ccall(:sincos, Void, (Cdouble, Ptr{Cdouble}, Ptr{Cdouble}), x, psin, >>>>>> pcos); >>>>>> (psin[1], pcos[1]); end >>>>>> sincos (generic function with 1 method) >>>>>> >>>>>> julia> sincos(pi) >>>>>> (1.2246467991473532e-16,-1.0) >>>>>> >>>>>> Feel free to open an issue or pull request if you think it should be >>>>>> exported - might have just been an oversight. >>>>>> >>>>>> >>>>>> On Sun, Jul 27, 2014 at 3:25 PM, Ken B <[email protected]> >>>>>> wrote: >>>>>> >>>>>> Hi, >>>>>> >>>>>>> >>>>>>> I want to calculated sine and cosine together of the same angle. I >>>>>>> saw >>>>>>> this function is implemented in openlibm, but is it available in >>>>>>> julia >>>>>>> and >>>>>>> how? >>>>>>> >>>>>>> >>>>>>> https://github.com/JuliaLang/openlibm/blob/ >>>>>>> 18f475de56ec7b478b9220a5f28eb9a23cb51d96/src/s_sincos.c >>>>>>> >>>>>>> Thanks! >>>>>>> Ken >>>>>>> >>>>>>> >>>>>>> >>>>>> >>>>>>
