Vectorising code to take advantage of modern CPUs (AVX and SSE)
Updated 26th March 2015
I’ve been playing with AVX vectorisation on modern CPUs off and on for a while now and thought that I’d write up a little of what I’ve discovered. The basic idea of vectorisation is that each processor core in a modern CPU can operate on multiple values (i.e. a vector) simultaneously per instruction cycle.
Modern processors have 256bit wide vector units which means that each CORE can perform up to 16 double precision or 32 single precision floating point operations (FLOPS) per clock cycle. So, on a quad core CPU that’s typically found in a decent laptop you have 4 vector units (one per core) and could perform up to 64 double precision FLOPS per cycle. The Intel Xeon Phi accelerator unit has even wider vector units — 512bit!
This all sounds great but how does a programmer actually make use of this neat hardware trick? There are many routes:-
At the ‘close to the metal’ level you code for these vector units using instructions called AVX intrinsics. This is relatively difficult and leads to none-portable code if you are not careful.
- The Intel Intrinsics Guide – An interactive reference tool for Intel intrinsic instructions,
- Introduction to Intel Advanced Vector Extensions – includes some example C++ programs using AVX intinsics
- Benefits of Intel AVX for small matrices – More code examples along with speed comparisons.
Auto-vectorisation in compilers
Since working with intrinsics is such hard work, why not let the compiler take the strain? Many modern compilers can automatically vectorize your C, C++ or Fortran code including gcc, PGI and Intel. Sometimes all you need to do is add an extra switch at compile time and reap the speed benefits. In truth, vectorization isn’t always automatic and the programmer needs to give the compiler some assistance but it is a lot easier than hand-coding intrinsics.
- A Guide to Auto-vectorization with Intel C++ Compilers – Exactly what it says. In my experience, the intel compilers do auto-vectorisation better than other compilers.
- Auto-vectorisation in gcc 4.7 – A superb article showing how auto-vectorisation works in practice when using gcc 4.7. Lots of C code examples along with the emitted assembler and a good discussion of the hints you may need to give to the compiler to get maximum performance.
- Auto-vectorisation in gcc – The project page for auto-vectorisation in gcc
- Optimizing Application Performance on x64 Processor-based Systems with PGI Compilers and Tools – Includes discussion and example of auto-vectorisation using the PGI compiler
- Jim Radigan: Inside Auto-Vectorization, 1 of n – A video by a Microsoft engineer working on Visual Studio 2012. A superb introduction to what vectorisation is along with speed-up demonstrations and discussion on how the auto-vectoriser will work in Visual Studio 2012.
- Auto Vectorizer in Visual Studio 2012 – A series of blog articles about vectorization in Visual Studio 2012.
Intel SPMD Program Compiler (ispc)
There is a midway point between automagic vectorisation and having to use intrinsics. Intel have a free compiler called ispc (http://ispc.github.com/) that allows you to write compute kernels in a modified subset of C. These kernels are then compiled to make use of vectorised instruction sets. Programming using ispc feels a little like using OpenCL or CUDA. I figured out how to hook it up to MATLAB a few months ago and developed a version of the Square Root function that is almost twice as fast as MATLAB’s own version for sandy bridge i7 processors.
- http://ispc.github.com/ – The website for ispc
- http://ispc.github.com/perf.html – Some performance metrics. In some cases combining vectorisation and parallelisation can increase single precision throughput by more than a factor of 32 on a quad-core machine!
- ispc: A SPMD Compiler For High-Performance CPU Programming, Illinois-Intel Parallelism Center Distinguished Speaker Series (UIUC), March 15, 2012. (talk video–requires Windows Media Player.) This link was taken from Matt Pharr’s website (The author of ispc).
- Performance Essentials with OpenMP 4.0 Vectorization – A series of seven videos from Intel covering performance essentials using OpenMP 4.0 Vectorization with C/C++.
- Explicit Vector Programming with OpenMP 4.0 SIMD Extensions – A tutorial from HPC today.
Vendors of numerical libraries are steadily applying vectorisation techniques in order to maximise performance. If the execution speed of your application depends upon these library functions, you may get a significant speed boost simply by updating to the latest version of the library and recompiling with the relevant compiler flags.
- Yeppp! – A fast, vectorised math library (benchmarks here)
- NAG Library for Xeon Phi – A huge, commercial library for the Intel Xeon Phi Accelerator
- Intel AVX optimization in Intel Math Kernel Library (MKL) – See what’s been vectorised in version 10.3 of the MKL
- Intel Integrated Performance Primitives (IPP) Functions Optimized for AVX – The IPP library includes many basic algorithms used in image and signal processing
- SIMD Library for Evaluating Elementary Functions (SLEEF) – An open-source, vectorised library for the calculation of various mathematical functions. Someone has done benchmarks for it here.
- SIMD-oriented Fast Mersenne Twister (SFMT) – Uses vectorisation to implement a very fast random number generation.
CUDA for x86
Another route to vectorised code is to make use of the PGI Compiler’s support for x86 CUDA. What you do is take CUDA kernels written for NVIDIA GPUs and use the PGI Compiler to compile these kernels for x86 processors. The resulting executables take advantage of vectorisation. In essence, the vector units of the CPU are acting like CUDA cores–which they sort of are anyway!
The PGI compilers also have technology which they call PGI Unified binary which allows you to use NVIDIA GPUs when present or default to using multi-core x86 if no GPU is present.
- PGI CUDA-x86 – PGI’s main page for their CUDA on x86 technologies
OpenCL for x86 processors
Yet another route to vectorisation would be to use Intel’s OpenCL implementation which takes OpenCL kernels and compiles them down to take advantage of vector units (http://software.intel.com/en-us/blogs/2011/09/26/autovectorization-in-intel-opencl-sdk-15/). The AMD OpenCL implementation may also do this but I haven’t tried it and haven’t had chance to research it yet.
I’ve written a couple of blog posts that made use of this technology.
- Using Intel’s SPMD Compiler (ispc) with MATLAB on Linux
- Using the Portland PGI Compiler for MATLAB mex files in Windows
There is other stuff out there but the above covers everything that I have used so far. I’ll finish by saying that everyone interested in vectorisation should check out this website…It’s the bible!
Research Articles on SSE/AVX vectorisation
I found the following research articles useful/interesting. I’ll add to this list over time as I dig out other articles.