Tiramisu: A Polyhedral Compiler for Expressing Fast and Portable Code

This paper introduces Tiramisu, a polyhedral framework designed to generate high performance code for multiple platforms including multicores, GPUs, and distributed machines. Tiramisu introduces a scheduling language with novel extensions to explicitly manage the complexities that arise when targeting these systems. The framework is designed for the areas of image processing, stencils, linear algebra and deep learning. Tiramisu has two main features: it relies on a flexible representation based on the polyhedral model and it has a rich scheduling language allowing fine-grained control of optimizations. Tiramisu uses a four-level intermediate representation that allows full separation between the algorithms, loop transformations, data layouts, and communication. This separation simplifies targeting multiple hardware architectures with the same algorithm. We evaluate Tiramisu by writing a set of image processing, deep learning, and linear algebra benchmarks and compare them with state-of-the-art compilers and hand-tuned libraries. We show that Tiramisu matches or outperforms existing compilers and libraries on different hardware architectures, including multicore CPUs, GPUs, and distributed machines.Comment: arXiv admin note: substantial text overlap with arXiv:1803.0041

Polly's Polyhedral Scheduling in the Presence of Reductions

The polyhedral model provides a powerful mathematical abstraction to enable effective optimization of loop nests with respect to a given optimization goal, e.g., exploiting parallelism. Unexploited reduction properties are a frequent reason for polyhedral optimizers to assume parallelism prohibiting dependences. To our knowledge, no polyhedral loop optimizer available in any production compiler provides support for reductions. In this paper, we show that leveraging the parallelism of reductions can lead to a significant performance increase. We give a precise, dependence based, definition of reductions and discuss ways to extend polyhedral optimization to exploit the associativity and commutativity of reduction computations. We have implemented a reduction-enabled scheduling approach in the Polly polyhedral optimizer and evaluate it on the standard Polybench 3.2 benchmark suite. We were able to detect and model all 52 arithmetic reductions and achieve speedups up to 2.21$\times$ on a quad core machine by exploiting the multidimensional reduction in the BiCG benchmark.Comment: Presented at the IMPACT15 worksho

Towards an Achievable Performance for the Loop Nests

Numerous code optimization techniques, including loop nest optimizations, have been developed over the last four decades. Loop optimization techniques transform loop nests to improve the performance of the code on a target architecture, including exposing parallelism. Finding and evaluating an optimal, semantic-preserving sequence of transformations is a complex problem. The sequence is guided using heuristics and/or analytical models and there is no way of knowing how close it gets to optimal performance or if there is any headroom for improvement. This paper makes two contributions. First, it uses a comparative analysis of loop optimizations/transformations across multiple compilers to determine how much headroom may exist for each compiler. And second, it presents an approach to characterize the loop nests based on their hardware performance counter values and a Machine Learning approach that predicts which compiler will generate the fastest code for a loop nest. The prediction is made for both auto-vectorized, serial compilation and for auto-parallelization. The results show that the headroom for state-of-the-art compilers ranges from 1.10x to 1.42x for the serial code and from 1.30x to 1.71x for the auto-parallelized code. These results are based on the Machine Learning predictions.Comment: Accepted at the 31st International Workshop on Languages and Compilers for Parallel Computing (LCPC 2018

Introducing Molly: Distributed Memory Parallelization with LLVM

Programming for distributed memory machines has always been a tedious task, but necessary because compilers have not been sufficiently able to optimize for such machines themselves. Molly is an extension to the LLVM compiler toolchain that is able to distribute and reorganize workload and data if the program is organized in statically determined loop control-flows. These are represented as polyhedral integer-point sets that allow program transformations applied on them. Memory distribution and layout can be declared by the programmer as needed and the necessary asynchronous MPI communication is generated automatically. The primary motivation is to run Lattice QCD simulations on IBM Blue Gene/Q supercomputers, but since the implementation is not yet completed, this paper shows the capabilities on Conway's Game of Life