The layout of multi-dimensional data can have a significant impact on the efficacy of hardware caches and, by extension, the performance of applications. Common multi-dimensional layouts include the canonical row-major and column-major layouts as well as the Morton curve layout. In this paper, we describe how the Morton layout can be generalized to a very large family of multi-dimensional data layouts with widely varying performance characteristics. We posit that this design space can be efficiently explored using a combinatorial evolutionary methodology based on genetic algorithms. To this end, we propose a chromosomal representation for such layouts as well as a methodology for estimating the fitness of array layouts using cache simulation. We show that our fitness function correlates to kernel running time in real hardware, and that our evolutionary strategy allows us to find candidates with favorable simulated cache properties in four out of the eight real-world applications under consideration in a small number of generations. Finally, we demonstrate that the array layouts found using our evolutionary method perform well not only in simulated environments but that they can effect significant performance gains---up to a factor ten in extreme cases---in real hardware.

We present a novel benchmark suite for implementations of vector fields in high-performance computing environments to aid developers in quantifying and ranking their performance. We decompose the design space of such benchmarks into access patterns and storage backends, the latter of which can be further decomposed into components with different functional and non-functional properties. Through compile-time meta-programming, we generate a large number of benchmarks with minimal effort and ensure the extensibility of our suite. Our empirical analysis, based on real-world applications in high-energy physics, demonstrates the feasibility of our approach on CPU and GPU platforms, and highlights that our suite is able to evaluate performance-critical design choices. Finally, we propose that our work towards composing vector fields from elementary components is not only useful for the purposes of benchmarking, but that it naturally gives rise to a novel library for implementing such fields in domain applications.

When designing algorithms for single-instruction multiple-thread (SIMT) devices such as general purpose graphics processing units (GPGPUs), thread imbalance is an important performance consideration. Thread imbalance can emerge in iterative applications where workloads are of variable length, because threads processing larger amounts of work will cause threads with less work to idle. This form of thread imbalance influences the design space of algorithms-particularly in terms of processing granularity-but we lack models to quantify its impact on application performance. In this paper, we present a statistical model for quantifying the performance loss due to thread imbalance for iterative SIMT applications with stochastic, variable-length workloads. Our model is designed to operate with minimal knowledge of the implementation details of the algorithm, relying solely on an understanding of the probability distribution of the lengths of the workloads. We validate our model against a synthetic benchmark based on a Monte Carlo simulation of matrix exponentiation, and show that our model achieves nearly perfect accuracy. Compared to empirical data extracted from real hardware, our model maintains a high degree of accuracy, predicting mean performance loss within a margin of 2%.