Jun 01, 2016

Enabling Polyhedral Optimizations in Julia

Over the the next few months I will be working on an exciting project as one of this year's Google Summer of Code students. My work will aim at making available the power of polyhedral optimizations to the programming language Julia (I also cordially invite you to have a look at my project proposal for an overview of my planned activities). When a Julia program is executed its source code will be translated, at run-time, to native machine code via the LLVM compiler framework. Fortunately, with Polly there already exists a polyhedral optimizer that can be used for LLVM-based compilers - so theoretically I will "just" have to integrate Polly into Julia's compiler tool-chain. As often, however, it's the technical details that make this practically challenging. Now, GSoC already started last week, the very first steps have been taken and I therefore would like to give a little insight on my initial activities.

First steps towards Polly

In LLVM, the basic means to organize functionality is a pass - a component that fulfills a certain (ideally coherent) responsibility within the whole compilation process. It is then possible to decide quite freely which of LLVM's functionality to use by instructing it to include only particular passes. The same holds true for Julia - when it initializes LLVM it chooses a certain set of passes that it wants to leverage when compiling programs to machine code. Also Polly is essentially a collection of such passes that provides all the necessary analyses and transformations which together make up a polyhedral optimizer.

LLVM makes it relatively easy to configure it's pass infrastructure, therefore also making it possible to add Polly's passes to Julia's pass-pipeline in a relatively non-intrusive manner. The required changes can be viewed at my according pull request that has already been merged into Julia's official github repository. Furthermore, this pull request adds the possibility for Julia programmers to explicitly run Polly's optimizations for particular functions - therefore a new macro @polly was introduced, to annotate those functions for which Polly should be run.

How to use the new features

This functionality is still at an early stage and using it requires a few preparative steps. First of all it is necessary to download and build LLVM and Polly from source (for example as described here). Furthermore, also the development version of Julia has to be downloaded from its github repository and Julia's build process has to be configured in order to build against the previously compiled version of LLVM/Polly. Therefore a Make.user file has to be created that has to be located where Julia will be built, containing the following lines (where YOUR_LLVM_BUILD_DIR has to point to the previously compiled LLVM build):


It will then be possible to annotate functions in your Julia programs, to optimize them via Polly:

@polly function foo()

What's next

One of the next goals is to ease this build process by removing the necessity to manually build LLVM/Polly. Instead, it should be possible to automatically retrieve and build Polly when building Julia. In addition to that, to give you an idea of what I will be doing for the rest of the summer then, let's have a look at the following code sample below. It multiplies the square matrices A and B, writing the result to C.

@polly function matmul(A,B,C)
    m,n = size(A)
    @inbounds for i=1:n, j=1:n, k=1:n
        C[i,j] += A[i,k] * B[k,j]

Provided the input data you use is not too small, Polly will cause this function to run significantly faster. However, you might notice the @inbounds macro in front of the for loop. Usually, Julia strives to emit bounds-checks array accesses. With this macro, however, it will skip these checks and assume that these accesses will be safe. Normally you should only use this macro for code regions for which you can be sure that there will not happen any out-of-bounds accesses. Even though we cannot guarantee all accesses to be safe there's a particular reason for the presence of the macro - at its current state Polly will not be able to optimize the code that Julia generates when bound-checks are enabled. This means removing @inbounds here also removes the ability to optimize this function.

Furthermore, you might also ask yourself why we restricted ourselves to square matrices. So let's at least remove this restriction to allow the multiplication of non-square matrices as well:

@polly function matmul(A,B,C)
    m,n = size(A)
    n,o = size(B)
    @inbounds for i=1:m, j=1:o, k=1:n
        C[i,j] += A[i,k] * B[k,j]

Unfortunately, also this change will cause Julia to emit code that can not be optimized by Polly.

So as these examples suggest, my work will not end here. In order to leverage the full power of Polly from within Julia it will be necessary to identify the reasons that prevent Polly from optimizing programs like the above ones. Then, of course, it will be necessary to either adapt Julia's LLVM code generator to emit code that is amenable to Polly or to directly adapt Polly's analysis and transformation passes and to improve their applicability.

Either way, I'm looking forward to letting you know about any prospective findings.


Special thanks go to Karthik Senthil who provided a first patch that experimentally integrated Polly into an earlier version of Julia which built the basis for my first changes and helped me to find my way into Julia's internals.