I'm looking to calculate highly parallelized trig functions (in block of like 1024), and I'd like to take advantage of at least some of the parallelism that modern architectures have.
When I compile a block
for(int i=0; i<SIZE; i++) {
arr[i]=sin((float)i/1024);
}
GCC won't vectorize it, and says
not vectorized: relevant stmt not supported: D.3068_39 = __builtin_sinf (D.3069_38);
Which makes sense to me. However, I'm wondering if there's a library to do parallel trig computations.
With just a simple taylor series up the 11th order, GCC will vectorize all the loops, and I'm getting speeds over twice as fast as a naive sin loop (with bit-exact answers, or with 9th order series, only a single bit off for the last two out of 1600 values, for a >3x speedup). I'm sure someone has encountered a problem like this before, but when I google, I find no mentions of any libraries or the like.
A. Is there something existing already?
B. If not, advice for optimizing parallel trig functions?
EDIT: I found the following library called "SLEEF": http://shibatch.sourceforge.net/ which is described in this paper and uses SIMD instructions to calculate several elementary functions. It uses SSE and AVX specific code, but I don't think it will be hard to turn it into standard C loops.
Since you said you were using GCC it looks like there are some options:
- http://gruntthepeon.free.fr/ssemath/
- This uses SSE and SSE2 instructions to implement it.
- http://www.gamasutra.com/view/feature/4248/designing_fast_crossplatform_simd_.php
- This has an alternate implementation. Some of the comments are pretty good.
That said, I'd probably look into GPGPU for a solution. Maybe writing it in CUDA or OpenCL (If I remember correctly CUDA supports the sine function). Here are some libraries that look like they might make it easier.
- https://code.google.com/p/slmath/
- https://code.google.com/p/thrust/
Since you are looking to calculate harmonics here, I have some code that addressed a similar problem. It is vectorized already and faster than anything else I have found. As a side benefit, you get the cosine for free.
What platform are you using? Many libraries of this sort already exist:
- Intel's provides the Vector Math Library (VML) with icc.
- Apple provides the vForce library as part of the Accelerate framework.
- HP provides their own Vector Math Library for Itanium (and may other architectures, too).
- Sun provided libmvec with their compiler tools.
- ...
Instead of the taylor series, I would look at the algorithms fdlibm uses. They should get you as much precision with fewer steps.
My answer was to create my own library to do exactly this called vectrig: https://github.com/jeremysalwen/vectrig
