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
