Autotuning multigrid with PetaBricks

Algorithmic choice is essential in any problem domain to realizing optimal computational performance. Multigrid is a prime example: not only is it possible to make choices at the highest grid resolution, but a program can switch techniques as the problem is recursively attacked on coarser grid levels to take advantage of algorithms with different scaling behaviors. Additionally, users with different convergence criteria must experiment with parameters to yield a tuned algorithm that meets their accuracy requirements. Even after a tuned algorithm has been found, users often have to start all over when migrating from one machine to another. We present an algorithm and autotuning methodology that address these issues in a near-optimal and efficient manner. The freedom of independently tuning both the algorithm and the number of iterations at each recursion level results in an exponential search space of tuned algorithms that have different accuracies and performances. To search this space efficiently, our autotuner utilizes a novel dynamic programming method to build efficient tuned algorithms from the bottom up. The results are customized multigrid algorithms that invest targeted computational power to yield the accuracy required by the user. The techniques we describe allow the user to automatically generate tuned multigrid cycles of different shapes targeted to the user's specific combination of problem, hardware, and accuracy requirements. These cycle shapes dictate the order in which grid coarsening and grid refinement are interleaved with both iterative methods, such as Jacobi or Successive Over-Relaxation, as well as direct methods, which tend to have superior performance for small problem sizes. The need to make choices between all of these methods brings the issue of variable accuracy to the forefront. Not only must the autotuning framework compare different possible multigrid cycle shapes against each other, but it also needs the ability to compare tuned cycles against both direct and (non-multigrid) iterative methods. We address this problem by using an accuracy metric for measuring the effectiveness of tuned cycle shapes and making comparisons over all algorithmic types based on this common yardstick. In our results, we find that the flexibility to trade performance versus accuracy at all levels of recursive computation enables us to achieve excellent performance on a variety of platforms compared to algorithmically static implementations of multigrid. Our implementation uses PetaBricks, an implicitly parallel programming language where algorithmic choices are exposed in the language. The PetaBricks compiler uses these choices to analyze, autotune, and verify the PetaBricks program. These language features, most notably the autotuner, were key in enabling our implementation to be clear, correct, and fast.National Science Foundation (U.S.) (Award CCF-0832997)GigaScale Systems Research Cente

Language and Compiler Support for Auto-Tuning Variable-Accuracy Algorithms

Approximating ideal program outputs is a common technique for solving computationally difficult problems, for adhering to processing or timing constraints, and for performance optimization in situations where perfect precision is not necessary. To this end, programmers often use approximation algorithms, iterative methods, data resampling, and other heuristics. However, programming such variable accuracy algorithms presents difficult challenges since the optimal algorithms and parameters may change with different accuracy requirements and usage environments. This problem is further compounded when multiple variable accuracy algorithms are nested together due to the complex way that accuracy requirements can propagate across algorithms and because of the size of the set of allowable compositions. As a result, programmers often deal with this issue in an ad-hoc manner that can sometimes violate sound programming practices such as maintaining library abstractions. In this paper, we propose language extensions that expose trade-offs between time and accuracy to the compiler. The compiler performs fully automatic compile-time and installtime autotuning and analyses in order to construct optimized algorithms to achieve any given target accuracy. We present novel compiler techniques and a structured genetic tuning algorithm to search the space of candidate algorithms and accuracies in the presence of recursion and sub-calls to other variable accuracy code. These techniques benefit both the library writer, by providing an easy way to describe and search the parameter and algorithmic choice space, and the library user, by allowing high level specification of accuracy requirements which are then met automatically without the need for the user to understand any algorithm-specific parameters. Additionally, we present a new suite of benchmarks, written in our language, to examine the efficacy of our techniques. Our experimental results show that by relaxing accuracy requirements , we can easily obtain performance improvements ranging from 1.1× to orders of magnitude of speedup

OpenTuner: An Extensible Framework for Program Autotuning

Program autotuning has been shown to achieve better or more portable performance in a number of domains. However, autotuners themselves are rarely portable between projects, for a number of reasons: using a domain-informed search space representation is critical to achieving good results; search spaces can be intractably large and require advanced machine learning techniques; and the landscape of search spaces can vary greatly between different problems, sometimes requiring domain specific search techniques to explore efficiently. This paper introduces OpenTuner, a new open source framework for building domain-specific multi-objective program autotuners. OpenTuner supports fully-customizable configuration representations, an extensible technique representation to allow for domain-specific techniques, and an easy to use interface for communicating with the program to be autotuned. A key capability inside OpenTuner is the use of ensembles of disparate search techniques simultaneously; techniques that perform well will dynamically be allocated a larger proportion of tests. We demonstrate the efficacy and generality of OpenTuner by building autotuners for 6 distinct projects and 14 total benchmarks, showing speedups over prior techniques of these projects of up to 2.8x with little programmer effort.This work is partially supported by DOE award DE-SC0005288 and DOD DARPA award HR0011-10-9-0009. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231

Language and compiler for algorithmic choice

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 55-60).It is often impossible to obtain a one-size-fits-all solution for high performance algorithms when considering different choices for data distributions, parallelism, transformations, and blocking. The best solution to these choices is often tightly coupled to different architectures, problem sizes, data, and available system resources. In some cases, completely different algorithms may provide the best performance. Current compiler and programming language techniques are able to change some of these parameters, but today there is no simple way for the programmer to express or the compiler to choose different algorithms to handle different parts of the data. Existing solutions normally can handle only coarse-grained, library level selections or hand coded cutoffs between base cases and recursive cases. We present PetaBricks, a new implicitly parallel language and compiler where having multiple implementations of multiple algorithms to solve a problem is the natural way of programming. We make algorithmic choice a first class construct of the language. Choices are provided in a way that also allows our compiler to tune at a finer granularity. The PetaBricks compiler autotunes programs by making both fine-grained as well as algorithmic choices. Choices also include different automatic parallelization techniques, data distributions, algorithmic parameters, transformations, and blocking.by Jason Ansel.S.M

Machine Learning in Compiler Optimization

In the last decade, machine learning based compilation has moved from an an obscure research niche to a mainstream activity. In this article, we describe the relationship between machine learning and compiler optimisation and introduce the main concepts of features, models, training and deployment. We then provide a comprehensive survey and provide a road map for the wide variety of different research areas. We conclude with a discussion on open issues in the area and potential research directions. This paper provides both an accessible introduction to the fast moving area of machine learning based compilation and a detailed bibliography of its main achievements

High-performance computing with PetaBricks and Julia

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 163-170).We present two recent parallel programming languages, PetaBricks and Julia, and demonstrate how we can use these two languages to re-examine classic numerical algorithms in new approaches for high-performance computing. PetaBricks is an implicitly parallel language that allows programmers to naturally express algorithmic choice explicitly at the language level. The PetaBricks compiler and autotuner is not only able to compose a complex program using fine-grained algorithmic choices but also find the right choice for many other parameters including data distribution, parallelization and blocking. We re-examine classic numerical algorithms with PetaBricks, and show that the PetaBricks autotuner produces nontrivial optimal algorithms that are difficult to reproduce otherwise. We also introduce the notion of variable accuracy algorithms, in which accuracy measures and requirements are supplied by the programmer and incorporated by the PetaBricks compiler and autotuner in the search of optimal algorithms. We demonstrate the accuracy/performance trade-offs by benchmark problems, and show how nontrivial algorithmic choice can change with different user accuracy requirements. Julia is a new high-level programming language that aims at achieving performance comparable to traditional compiled languages, while remaining easy to program and offering flexible parallelism without extensive effort. We describe a problem in large-scale terrain data analysis which motivates the use of Julia. We perform classical filtering techniques to study the terrain profiles and propose a measure based on Singular Value Decomposition (SVD) to quantify terrain surface roughness. We then give a brief tutorial of Julia and present results of our serial blocked SVD algorithm implementation in Julia. We also describe the parallel implementation of our SVD algorithm and discuss how flexible parallelism can be further explored using Julia.by Yee Lok Wong.Ph.D

Automatische Codegenerierung für Massiv Parallele Applikationen in der Numerischen Strömungsmechanik

Solving partial differential equations (PDEs) is a fundamental challenge in many application domains in industry and academia alike. With increasingly large problems, efficient and highly scalable implementations become more and more crucial. Today, facing this challenge is more difficult than ever due to the increasingly heterogeneous hardware landscape. One promising approach is developing domain‐specific languages (DSLs) for a set of applications. Using code generation techniques then allows targeting a range of hardware platforms while concurrently applying domain‐specific optimizations in an automated fashion. The present work aims to further the state of the art in this field. As domain, we choose PDE solvers and, in particular, those from the group of geometric multigrid methods. To avoid having a focus too broad, we restrict ourselves to methods working on structured and patch‐structured grids. We face the challenge of handling a domain as complex as ours, while providing different abstractions for diverse user groups, by splitting our external DSL ExaSlang into multiple layers, each specifying different aspects of the final application. Layer 1 is designed to resemble LaTeX and allows inputting continuous equations and functions. Their discretization is expressed on layer 2. It is complemented by algorithmic components which can be implemented in a Matlab‐like syntax on layer 3. All information provided to this point is summarized on layer 4, enriched with particulars about data structures and the employed parallelization. Additionally, we support automated progression between the different layers. All ExaSlang input is processed by our jointly developed Scala code generation framework to ultimately emit C++ code. We particularly focus on how to generate applications parallelized with, e.g., MPI and OpenMP that are able to run on workstations and large‐scale cluster alike. We showcase the applicability of our approach by implementing simple test problems, like Poisson’s equation, as well as relevant applications from the field of computational fluid dynamics (CFD). In particular, we implement scalable solvers for the Stokes, Navier‐Stokes and shallow water equations (SWE) discretized using finite differences (FD) and finite volumes (FV). For the case of Navier‐Stokes, we also extend our implementation towards non‐uniform grids, thereby enabling static mesh refinement, and advanced effects such as the simulated fluid being non‐Newtonian and non‐isothermal

Evolutionary algorithms for compiler-enabled program autotuning

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 116-122).PetaBricks [4, 21, 7, 3, 5] is an implicitly parallel programming language which, through the process of autotuning, can automatically optimize programs for fast QoS-aware execution on any hardware. In this thesis we develop and evaluate two PetaBricks autotuners: INCREA and SiblingRivalry. INCREA, based on a novel bottom-up evolutionary algorithm, optimizes programs offline at compile time. SiblingRivalry improves on INCREA by optimizing online during a program's execution, dynamically adapting to changes in hardware and the operating system. Continuous adaptation is achieved through racing, where half of available resources are devoted to always-on learning. We evaluate INCREA and SiblingRivalry on a large number of real-world benchmarks, and show that our autotuners can significantly speed up PetaBricks programs with respect to many non-tuned and mis-tuned baselines. Our results indicate the need for a continuous learning loop that can optimize efficiently by exploiting online knowledge of a program's performance. The results leave open the question of how to solve the online optimization problem on all cores, i.e. without racing.by Maciej Pacula.M.Eng

GPU Array Access Auto-Tuning

GPUs have been used for years in compute intensive applications. Their massive parallel processing capabilities can speedup calculations significantly. However, to leverage this speedup it is necessary to rethink and develop new algorithms that allow parallel processing. These algorithms are only one piece to achieve high performance. Nearly as important as suitable algorithms is the actual implementation and the usage of special hardware features such as intra-warp communication, shared memory, caches, and memory access patterns. Optimizing these factors is usually a time consuming task that requires deep understanding of the algorithms and the underlying hardware. Unlike CPUs, the internal structure of GPUs has changed significantly and will likely change even more over the years. Therefore it does not suffice to optimize the code once during the development, but it has to be optimized for each new GPU generation that is released. To efficiently (re-)optimize code towards the underlying hardware, auto-tuning tools have been developed that perform these optimizations automatically, taking this burden from the programmer. In particular, NVIDIA -- the leading manufacturer for GPUs today -- applied significant changes to the memory hierarchy over the last four hardware generations. This makes the memory hierarchy an attractive objective for an auto-tuner. In this thesis we introduce the MATOG auto-tuner that automatically optimizes array access for NVIDIA CUDA applications. In order to achieve these optimizations, MATOG has to analyze the application to determine optimal parameter values. The analysis relies on empirical profiling combined with a prediction method and a data post-processing step. This allows to find nearly optimal parameter values in a minimal amount of time. Further, MATOG is able to automatically detect varying application workloads and can apply different optimization parameter settings at runtime. To show MATOG's capabilities, we evaluated it on a variety of different applications, ranging from simple algorithms up to complex applications on the last four hardware generations, with a total of 14 GPUs. MATOG is able to achieve equal or even better performance than hand-optimized code. Further, it is able to provide performance portability across different GPU types (low-, mid-, high-end and HPC) and generations. In some cases it is able to exceed the performance of hand-crafted code that has been specifically optimized for the tested GPU by dynamically changing data layouts throughout the execution