Automatically Optimizing Tree Traversal Algorithms

Many domains in computer science, from data-mining to graphics to computational astrophysics, focus heavily on irregular applications. In contrast to regular applications, which operate over dense matrices and arrays, irregular programs manipulate and traverse complex data structures like trees and graphs. As irregular applications operate on ever larger datasets, their performance suffers from poor locality and parallelism. Programmers are burdened with the arduous task of manually tuning such applications for better performance. Generally applicable techniques to optimize irregular applications are highly desired, yet scarce. In this dissertation, we argue that, for an important subset of irregular programs which arises in many domains, namely, tree traversal algorithms like Barnes-Hut, nearest neighbor and ray tracing, there exist general techniques to enhance performance. We investigate two sources of performance improvement: locality enhancement and vectorization. Furthermore we demonstrate that these techniques can be automatically applied by an optimizing compiler, relieving programmers of manual, error-prone, application-specific effort. Achieving high performance in many applications requires achieving good locality of reference. We propose two novel transformations called point blocking and traversal splicing, inspired by the classic tiling loop transformation, and show that it can substantially enhance temporal locality in tree traversals. We then present a transformation framework called TreeSplicer, that automatically applies these transformations, and uses autotuning techniques to determine appropriate parameters for the transformations. For six benchmark algorithms, we show that a combination of point blocking and traversal splicing can deliver single-thread speedups of up to 8.71 (geometric mean: 2.48), just from better locality. Modern commodity processors support SIMD instructions, and using these instructions to process multiple traversals at once has the potential to provide substantial performance improvements. Unfortunately tree algorithms often feature highly diverging traversals which inhibit efficient SIMD utilization, to the point that other, less profitable sources of vectorization must be exploited instead. We propose a dynamic reordering of traversals based on previous behavior, based on the insight that traversals which have behaved similarly so far are likely to behave similarly in the future, and show that this reordering can dramatically improve the SIMD utilization of diverging traversals, close to ideal utilization. We present a transformation framework, SIMTree, which facilitates vectorization of tree algorithms, and demonstrate speedups of up to 6.59 (geometric mean: 2.78). Furthermore our techniques can effectively SIMDize algorithms that prior, manual vectorization attempts could not

Faster Ray Tracing through Hierarchy Cut Code

We propose a novel ray reordering technique to accelerate the ray tracing process by encoding and sorting rays prior to traversal. Instead of spatial coordinates, our method encodes rays according to the cuts of the hierarchical acceleration structure, which is called the hierarchy cut code. This approach can better adapt to the acceleration structure and obtain a more reliable encoding result. We also propose a compression scheme to decrease the sorting overhead by a shorter sorting key. In addition, based on the phenomenon of boundary drift, we theoretically explain the reason why existing reordering methods cannot achieve better performance by using longer sorting keys. The experiment demonstrates that our method can accelerate secondary ray tracing by up to 1.81 times, outperforming the existing methods. Such result proves the effectiveness of hierarchy cut code, and indicate that the reordering technique can achieve greater performance improvement, which worth further research

Optimizing the Performance of Streaming Numerical Kernels on the IBM Blue Gene/P PowerPC 450 Processor

Several emerging petascale architectures use energy-efficient processors with vectorized computational units and in-order thread processing. On these architectures the sustained performance of streaming numerical kernels, ubiquitous in the solution of partial differential equations, represents a challenge despite the regularity of memory access. Sophisticated optimization techniques are required to fully utilize the Central Processing Unit (CPU). We propose a new method for constructing streaming numerical kernels using a high-level assembly synthesis and optimization framework. We describe an implementation of this method in Python targeting the IBM Blue Gene/P supercomputer's PowerPC 450 core. This paper details the high-level design, construction, simulation, verification, and analysis of these kernels utilizing a subset of the CPU's instruction set. We demonstrate the effectiveness of our approach by implementing several three-dimensional stencil kernels over a variety of cached memory scenarios and analyzing the mechanically scheduled variants, including a 27-point stencil achieving a 1.7x speedup over the best previously published results

Matching non-uniformity for program optimizations on heterogeneous many-core systems

As computing enters an era of heterogeneity and massive parallelism, it exhibits a distinct feature: the deepening non-uniform relations among the computing elements in both hardware and software. Besides traditional non-uniform memory accesses, much deeper non-uniformity shows in a processor, runtime, and application, exemplified by the asymmetric cache sharing, memory coalescing, and thread divergences on multicore and many-core processors. Being oblivious to the non-uniformity, current applications fail to tap into the full potential of modern computing devices.;My research presents a systematic exploration into the emerging property. It examines the existence of such a property in modern computing, its influence on computing efficiency, and the challenges for establishing a non-uniformity--aware paradigm. I propose several techniques to translate the property into efficiency, including data reorganization to eliminate non-coalesced accesses, asynchronous data transformations for locality enhancement and a controllable scheduling for exploiting non-uniformity among thread blocks. The experiments show much promise of these techniques in maximizing computing throughput, especially for programs with complex data access patterns

Doctor of Philosophy in Computer Science

dissertationRay tracing is becoming more widely adopted in offline rendering systems due to its natural support for high quality lighting. Since quality is also a concern in most real time systems, we believe ray tracing would be a welcome change in the real time world, but is avoided due to insufficient performance. Since power consumption is one of the primary factors limiting the increase of processor performance, it must be addressed as a foremost concern in any future ray tracing system designs. This will require cooperating advances in both algorithms and architecture. In this dissertation I study ray tracing system designs from a data movement perspective, targeting the various memory resources that are the primary consumer of power on a modern processor. The result is high performance, low energy ray tracing architectures

木を用いた構造化並列プログラミング

High-level abstractions for parallel programming are still immature. Computations on complicated data structures such as pointer structures are considered as irregular algorithms. General graph structures, which irregular algorithms generally deal with, are difficult to divide and conquer. Because the divide-and-conquer paradigm is essential for load balancing in parallel algorithms and a key to parallel programming, general graphs are reasonably difficult. However, trees lead to divide-and-conquer computations by definition and are sufficiently general and powerful as a tool of programming. We therefore deal with abstractions of tree-based computations. Our study has started from Matsuzaki’s work on tree skeletons. We have improved the usability of tree skeletons by enriching their implementation aspect. Specifically, we have dealt with two issues. We first have implemented the loose coupling between skeletons and data structures and developed a flexible tree skeleton library. We secondly have implemented a parallelizer that transforms sequential recursive functions in C into parallel programs that use tree skeletons implicitly. This parallelizer hides the complicated API of tree skeletons and makes programmers to use tree skeletons with no burden. Unfortunately, the practicality of tree skeletons, however, has not been improved. On the basis of the observations from the practice of tree skeletons, we deal with two application domains: program analysis and neighborhood computation. In the domain of program analysis, compilers treat input programs as control-flow graphs (CFGs) and perform analysis on CFGs. Program analysis is therefore difficult to divide and conquer. To resolve this problem, we have developed divide-and-conquer methods for program analysis in a syntax-directed manner on the basis of Rosen’s high-level approach. Specifically, we have dealt with data-flow analysis based on Tarjan’s formalization and value-graph construction based on a functional formalization. In the domain of neighborhood computations, a primary issue is locality. A naive parallel neighborhood computation without locality enhancement causes a lot of cache misses. The divide-and-conquer paradigm is known to be useful also for locality enhancement. We therefore have applied algebraic formalizations and a tree-segmenting technique derived from tree skeletons to the locality enhancement of neighborhood computations.電気通信大学201