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

A Novel Compiler Support for Automatic Parallelization on Multicore Systems

[Abstract] The widespread use of multicore processors is not a consequence of significant advances in parallel programming. In contrast, multicore processors arise due to the complexity of building power-efficient, high-clock-rate, single-core chips. Automatic parallelization of sequential applications is the ideal solution for making parallel programming as easy as writing programs for sequential computers. However, automatic parallelization remains a grand challenge due to its need for complex program analysis and the existence of unknowns during compilation. This paper proposes a new method for converting a sequential application into a parallel counterpart that can be executed on current multicore processors. It hinges on an intermediate representation based on the concept of domain-independent kernel (e.g., assignment, reduction, recurrence). Such kernel-centric view hides the complexity of the implementation details, enabling the construction of the parallel version even when the source code of the sequential application contains different syntactic variations of the computations (e.g., pointers, arrays, complex control flows). Experiments that evaluate the effectiveness and performance of our approach with respect to state-of-the-art compilers are also presented. The benchmark suite consists of synthetic codes that represent common domain-independent kernels, dense/sparse linear algebra and image processing routines, and full-scale applications from SPEC CPU2000.[Resumen] El uso generalizado de procesadores multinúcleo no es consecuencia de avances significativos en programación paralela. Por el contrario, los procesadores multinúcleo surgen debido a la complejidad de construir chips mononúcleo que sean eficiente energéticamente y tengan altas velocidades de reloj. La paralelización automática de aplicaciones secuenciales es la solución ideal para hacer la programación paralela tan fácil como escribir programas para ordenadores secuenciales. Sin embargo, la paralelización automática continua a ser un gran reto debido a su necesidad de complejos análisis del programa y la existencia de incógnitas durante la compilación. Este artículo propone un nuevo método para convertir una aplicación secuencial en su contrapartida paralela que pueda ser ejecutada en los procesadores multinúcleo actuales. Este método depende de una representación intermedia basada en el concepto de núcleos independientes del dominio (p. ej., asignación, reducción, recurrencia). Esta visión centrada en núcleos oculta la complejidad de los detalles de implementación, permitiendo la construcción de la versión paralela incluso cuando el código fuente de la aplicación secuencial contiene diferentes variantes de las computaciones (p. ej., punteros, arrays, flujos de control complejos). Se presentan experimentos que evalúan la efectividad y el rendimiento de nuestra aproximación con respecto al estado del arte. La serie programas de prueba consiste en códigos sintéticos que representan núcleos independientes del dominio comunes, rutinas de álgebra lineal densa/dispersa y de procesamiento de imagen, y aplicaciones completas del SPEC CPU2000.[Resumo] O uso xeralizado de procesadores multinúcleo non é consecuencia de avances significativos en programación paralela. Pola contra, os procesadores multinúcleo xurden debido á complexidade de construir chips mononúcleo que sexan eficientes enerxéticamente e teñan altas velocidades de reloxo. A paralelización automática de aplicacións secuenciais é a solución ideal para facer a programación paralela tan sinxela como escribir programas para ordenadores secuenciais. Sen embargo, a paralelización automática continua a ser un gran reto debido a súa necesidade de complexas análises do programa e a existencia de incógnitas durante a compilación. Este artigo propón un novo método para convertir unha aplicación secuencias na súa contrapartida paralela que poida ser executada nos procesadores multinúcleo actuais. Este método depende dunha representación intermedia baseada no concepto dos núcleos independentes do dominio (p. ex., asignación, reducción, recurrencia). Esta visión centrada en núcleos oculta a complexidade dos detalles de implementación, permitindo a construcción da versión paralela incluso cando o código fonte da aplicación secuencial contén diferentes variantes das computacións (p. ex., punteiros, arrays, fluxos de control complejo). Preséntanse experimentos que evalúan a efectividade e o rendemento da nosa aproximación con respecto ao estado da arte. A serie de programas de proba consiste en códigos sintéticos que representan núcleos independentes do dominio comunes, rutinas de álxebra lineal densa/dispersa e de procesamento de imaxe, e aplicacións completas do SPEC CPU2000.Ministerio de Economía y Competitividad; TIN2010-16735Ministerio de Educación y Cultura; AP2008-0101

XARK: an extensible framework for automatic recognition of computational kernels

This is a post-peer-review, pre-copyedit version of an article published in ACM Transactions on Programming Languages and Systems. The final authenticated version is available online at: http://dx.doi.org/10.1145/1391956.1391959[Abstract] The recognition of program constructs that are frequently used by software developers is a powerful mechanism for optimizing and parallelizing compilers to improve the performance of the object code. The development of techniques for automatic recognition of computational kernels such as inductions, reductions and array recurrences has been an intensive research area in the scope of compiler technology during the 90's. This article presents a new compiler framework that, unlike previous techniques that focus on specific and isolated kernels, recognizes a comprehensive collection of computational kernels that appear frequently in full-scale real applications. The XARK compiler operates on top of the Gated Single Assignment (GSA) form of a high-level intermediate representation (IR) of the source code. Recognition is carried out through a demand-driven analysis of this high-level IR at two different levels. First, the dependences between the statements that compose the strongly connected components (SCCs) of the data-dependence graph of the GSA form are analyzed. As a result of this intra-SCC analysis, the computational kernels corresponding to the execution of the statements of the SCCs are recognized. Second, the dependences between statements of different SCCs are examined in order to recognize more complex kernels that result from combining simpler kernels in the same code. Overall, the XARK compiler builds a hierarchical representation of the source code as kernels and dependence relationships between those kernels. This article describes in detail the collection of computational kernels recognized by the XARK compiler. Besides, the internals of the recognition algorithms are presented. The design of the algorithms enables to extend the recognition capabilities of XARK to cope with new kernels, and provides an advanced symbolic analysis framework to run other compiler techniques on demand. Finally, extensive experiments showing the effectiveness of XARK for a collection of benchmarks from different application domains are presented. In particular, the SparsKit-II library for the manipulation of sparse matrices, the Perfect benchmarks, the SPEC CPU2000 collection and the PLTMG package for solving elliptic partial differential equations are analyzed in detail.Ministeiro de Educación y Ciencia; TIN2004-07797-C02Ministeiro de Educación y Ciencia; TIN2007-67537-C03Xunta de Galicia; PGIDIT05PXIC10504PNXunta de Galicia; PGIDIT06PXIB105228P

Automatic matching of legacy code to heterogeneous APIs: An idiomatic approach

Heterogeneous accelerators often disappoint. They provide the prospect of great performance, but only deliver it when using vendor specific optimized libraries or domain specific languages. This requires considerable legacy code modifications, hindering the adoption of heterogeneous computing. This paper develops a novel approach to automatically detect opportunities for accelerator exploitation. We focus on calculations that are well supported by established APIs: sparse and dense linear algebra, stencil codes and generalized reductions and histograms. We call them idioms and use a custom constraint-based Idiom Description Language (IDL) to discover them within user code. Detected idioms are then mapped to BLAS libraries, cuSPARSE and clSPARSE and two DSLs: Halide and Lift. We implemented the approach in LLVM and evaluated it on the NAS and Parboil sequential C/C++ benchmarks, where we detect 60 idiom instances. In those cases where idioms are a significant part of the sequential execution time, we generate code that achieves 1.26× to over 20× speedup on integrated and external GPUs

Set-oriented data mining in relational databases

Data mining is an important real-life application for businesses. It is critical to find efficient ways of mining large data sets. In order to benefit from the experience with relational databases, a set-oriented approach to mining data is needed. In such an approach, the data mining operations are expressed in terms of relational or set-oriented operations. Query optimization technology can then be used for efficient processing.\ud \ud In this paper, we describe set-oriented algorithms for mining association rules. Such algorithms imply performing multiple joins and thus may appear to be inherently less efficient than special-purpose algorithms. We develop new algorithms that can be expressed as SQL queries, and discuss optimization of these algorithms. After analytical evaluation, an algorithm named SETM emerges as the algorithm of choice. Algorithm SETM uses only simple database primitives, viz., sorting and merge-scan join. Algorithm SETM is simple, fast, and stable over the range of parameter values. It is easily parallelized and we suggest several additional optimizations. The set-oriented nature of Algorithm SETM makes it possible to develop extensions easily and its performance makes it feasible to build interactive data mining tools for large databases