Near-optimal loop tiling by means of cache miss equations and genetic algorithms

The effectiveness of the memory hierarchy is critical for the performance of current processors. The performance of the memory hierarchy can be improved by means of program transformations such as loop tiling, which is a code transformation targeted to reduce capacity misses. This paper presents a novel systematic approach to perform near-optimal loop tiling based on an accurate data locality analysis (cache miss equations) and a powerful technique to search the solution space that is based on a genetic algorithm. The results show that this approach can remove practically all capacity misses for all considered benchmarks. The reduction of replacement misses results in a decrease of the miss ratio that can be as significant as a factor of 7 for the matrix multiply kernel.Peer ReviewedPostprint (published version

A comparison of cache hierarchies for SMT processors

In the multithread and multicore era, programs are forced to share part of the processor structures. On one hand, the state of the art in multithreading describes how efficiently manage and distribute inner resources such as reorder buffer or issue windows. On the other hand, there is a substantial body of works focused on outer resources, mainly on how to effectively share last level caches in multicores. Between these ends, first and second level caches have remained apart even if they are shared in most commercial multithreaded processors. This work analyzes multiprogrammed workloads as the worst-case scenario for cache sharing among threads. In order to obtain representative results, we present a sampling-based methodology that for multiple metrics such as STP, ANTT, IPC throughput, or fairness, reduces simulation time up to 4 orders of magnitude when running 8-thread workloads with an error lower than 3% and a confidence level of 97%. With the above mentioned methodology, we compare several state-of-the-art cache hierarchies, and observe that Light NUCA provides performance benefits in SMT processors regardless the organization of the last level cache. Most importantly, Light NUCA gains are consistent across the entire number of simulated threads, from one to eight.Peer ReviewedPostprint (author's final draft

Topology-aware optimization of big sparse matrices and matrix multiplications on main-memory systems

Since data sizes of analytical applications are continuously growing, many data scientists are switching from customized micro-solutions to scalable alternatives, such as statistical and scientific databases. However, many algorithms in data mining and science are expressed in terms of linear algebra, which is barely supported by major database vendors and big data solutions. On the other side, conventional linear algebra algorithms and legacy matrix representations are often not suitable for very large matrices. We propose a strategy for large matrix processing on modern multicore systems that is based on a novel, adaptive tile matrix representation (AT MATRIX). Our solution utilizes multiple techniques inspired from database technology, such as multidimensional data partitioning, cardinality estimation, indexing, dynamic rewrites, and many more in order to optimize the execution time. Based thereon we present a matrix multiplication operator ATMULT, which outperforms alternative approaches. The aim of our solution is to overcome the burden for data scientists of selecting appropriate algorithms and matrix storage representations. We evaluated AT MATRIX together with ATMULT on several real-world and synthetic random matrices

Data locality and parallelism optimization using a constraint-based approach

Cataloged from PDF version of article.Embedded applications are becoming increasingly complex and processing ever-increasing datasets. In the context of data-intensive embedded applications, there have been two complementary approaches to enhancing application behavior, namely, data locality optimizations and improving loop-level parallelism. Data locality needs to be enhanced to maximize the number of data accesses satisfied from the higher levels of the memory hierarchy. On the other hand, compiler-based code parallelization schemes require a fresh look for chip multiprocessors as interprocessor communication is much cheaper than off-chip memory accesses. Therefore, a compiler needs to minimize the number of off-chip memory accesses. This can be achieved by considering multiple loop nests simultaneously. Although compilers address these two problems, there is an inherent difficulty in optimizing both data locality and parallelism simultaneously. Therefore, an integrated approach that combines these two can generate much better results than each individual approach. Based on these observations, this paper proposes a constraint network (CN)-based formulation for data locality optimization and code parallelization. The paper also presents experimental evidence, demonstrating the success of the proposed approach, and compares our results with those obtained through previously proposed approaches. The experiments from our implementation indicate that the proposed approach is very effective in enhancing data locality and parallelization. © 2010 Elsevier Inc. All rights reserved

Exploiting Locality and Parallelism with Hierarchically Tiled Arrays

The importance of tiles or blocks in mathematics and thus computer science cannot be overstated. From a high level point of view, they are the natural way to express many algorithms, both in iterative and recursive forms. Tiles or sub-tiles are used as basic units in the algorithm description. From a low level point of view, tiling, either as the unit maintained by the algorithm, or as a class of data layouts, is one of the most effective ways to exploit locality, which is a must to achieve good performance in current computers given the growing gap between memory and processor speed. Finally, tiles and operations on them are also basic to express data distribution and parallelism. Despite the importance of this concept, which makes inevitable its widespread usage, most languages do not support it directly. Programmers have to understand and manage the low-level details along with the introduction of tiling. This gives place to bloated potentially error-prone programs in which opportunities for performance are lost. On the other hand, the disparity between the algorithm and the actual implementation enlarges. This thesis illustrates the power of Hierarchically Tiled Arrays (HTAs), a data type which enables the easy manipulation of tiles in object-oriented languages. The objective is to evolve this data type in order to make the representation of all classes for algorithms with a high degree of parallelism and/or locality as natural as possible. We show in the thesis a set of tile operations which leads to a natural and easy implementation of different algorithms in parallel and in sequential with higher clarity and smaller size. In particular, two new language constructs dynamic partitioning and overlapped tiling are discussed in detail. They are extensions of the HTA data type to improve its capabilities to express algorithms with a high abstraction and free programmers from programming tedious low-level tasks. To prove the claims, two popular languages, C++ and MATLAB are extended with our HTA data type. In addition, several important dense linear algebra kernels, stencil computation kernels, as well as some benchmarks in NAS benchmark suite were implemented. We show that the HTA codes needs less programming effort with a negligible effect on performance

Automatic creation of tile size selection models using neural networks

2010 Spring.Includes bibliographic references (pages 54-59).Covers not scanned.Print version deaccessioned 2022.Tiling is a widely used loop transformation for exposing/exploiting parallelism and data locality. Effective use of tiling requires selection and tuning of the tile sizes. This is usually achieved by hand-crafting tile size selection (TSS) models that characterize the performance of the tiled program as a function of tile sizes. The best tile sizes are selected by either directly using the TSS model or by using the TSS model together with an empirical search. Hand-crafting accurate TSS models is hard, and adapting them to different architecture/compiler, or even keeping them up-to-date with respect to the evolution of a single compiler is often just as hard. Instead of hand-crafting TSS models, can we automatically learn or create them? In this paper, we show that for a specific class of programs fairly accurate TSS models can be automatically created by using a combination of simple program features, synthetic kernels, and standard machine learning techniques. The automatic TSS model generation scheme can also be directly used for adapting the model and/or keeping it up-to-date. We evaluate our scheme on six different architecture-compiler combinations (chosen from three different architectures and four different compilers). The models learned by our method have consistently shown near-optimal performance (within 5% of the optimal on average) across the tested architecture-compiler combinations