GPUs have been used to accelerate many regular applications and, more recently, irregular applications in which the control flow and memory access patterns are data-dependent and statically unpredictable. This paper defines two measures of irregularity called control-flow irregularity and memory-access irregularity, and investigates, using performance-counter measurements, how irregular GPU kernels differ from regular kernels with respect to these measures. For a suite of 13 benchmarks, we find that (i) irregularity at the warp level varies widely, (ii) control-flow irregularity and memory-access irregularity are largely independent of each other, and (iii) most kernels, including regular ones, exhibit some irregularity. A program's irregularity can change between different inputs, systems, and arithmetic precision but generally stays in a specific region of the irregularity space. Whereas some highly tuned implementations of irregular algorithms exhibit little irregularity, trading off extra irregularity for better locality or less work can improve overall performance.
Abstract-Irregular algorithms are algorithms with complex main data structures such as directed and undirected graphs, trees, etc. A useful abstraction for many irregular algorithms is its operator formulation in which the algorithm is viewed as the iterated application of an operator to certain nodes, called active nodes, in the graph. Each operator application, called an activity, usually touches only a small part of the overall graph, so nonoverlapping activities can be performed in parallel. In topologydriven implementations, all nodes are assumed to be active so the operator is applied everywhere in the graph even if there is no work to do at some nodes. In contrast, in data-driven implementations the operator is applied only to nodes at which there might be work to do. Multicore implementations of irregular algorithms are usually data-driven because current multicores only support small numbers of threads and work-efficiency is important. Conversely, many irregular GPU implementations use a topology-driven approach because work inefficiency can be counterbalanced by the large number of GPU threads.In this paper, we study data-driven and topology-driven implementations of six important graph algorithms on GPUs. Our goal is to understand the tradeoffs between these implementations and how to optimize them. We find that data-driven versions are generally faster and scale better despite the cost of maintaining a worklist. However, topology-driven versions can be superior when certain algorithmic properties are exploited to optimize the implementation. These results led us to devise hybrid approaches that combine the two techniques and outperform both of them.
There is growing interest in using GPUs to accelerate graph algorithms such as breadth-first search, computing page-ranks, and finding shortest paths. However, these algorithms do not modify the graph structure, so their implementation is relatively easy compared to general graph algorithms like mesh generation and refinement, which morph the underlying graph in non-trivial ways by adding and removing nodes and edges. We know relatively little about how to implement morph algorithms efficiently on GPUs. In this paper, we present and study four morph algorithms: (i) a computational geometry algorithm called Delaunay Mesh Refinement (DMR), (ii) an approximate SAT solver called Survey Propagation (SP), (iii) a compiler analysis called Points-To Analysis (PTA), and (iv) Boruvka's Minimum Spanning Tree algorithm (MST). Each of these algorithms modifies the graph data structure in different ways and thus poses interesting challenges. We overcome these challenges using algorithmic and GPU-specific optimizations. We propose efficient techniques to perform concurrent subgraph addition, subgraph deletion, conflict detection and several optimizations to improve the scalability of morph algorithms. For an input mesh with 10 million triangles, our DMR code achieves an 80x speedup over the highly optimized serial Triangle program and a 2.3x speedup over a multicore implementation running with 48 threads. Our SP code is 3x faster than a multicore implementation with 48 threads on an input with 1 million literals. The PTA implementation is able to analyze six SPEC 2000 benchmark programs in just 74 milliseconds, achieving a geometric mean speedup of 9.3x over a 48-thread multicore version. Our MST code is slower than a multicore version with 48 threads for sparse graphs but significantly faster for denser graphs. This work provides several insights into how other morph algorithms can be efficiently implemented on GPUs.
Abstract. Memory models for shared-memory concurrent programming languages typically guarantee sequential consistency (SC) semantics for datarace-free (DRF) programs, while providing very weak or no guarantees for non-DRF programs. In effect programmers are expected to write only DRF programs, which are then executed with SC semantics. With this in mind, we propose a novel scalable solution for dataflow analysis of concurrent programs, which is proved to be sound for DRF programs with SC semantics. We use the synchronization structure of the program to propagate dataflow information among threads without requiring to consider all interleavings explicitly. Given a dataflow analysis that is sound for sequential programs and meets certain criteria, our technique automatically converts it to an analysis for concurrent programs.
Abstract. Context-sensitive points-to analysis is critical for several program optimizations. However, as the number of contexts grows exponentially, storage requirements for the analysis increase tremendously for large programs, making the analysis non-scalable. We propose a scalable flow-insensitive context-sensitive inclusion-based points-to analysis that uses a specially designed multi-dimensional bloom filter to store the points-to information. Two key observations motivate our proposal: (i) points-to information (between pointer-object and between pointerpointer) is sparse, and (ii) moving from an exact to an approximate representation of points-to information only leads to reduced precision without affecting correctness of the (may-points-to) analysis. By using an approximate representation a multi-dimensional bloom filter can significantly reduce the memory requirements with a probabilistic bound on loss in precision. Experimental evaluation on SPEC 2000 benchmarks and two large open source programs reveals that with an average storage requirement of 4MB, our approach achieves almost the same precision (98.6%) as the exact implementation. By increasing the average memory to 27MB, it achieves precision upto 99.7% for these benchmarks. Using Mod/Ref analysis as the client, we find that the client analysis is not affected that often even when there is some loss of precision in the points-to representation. We find that the NoModRef percentage is within 2% of the exact analysis while requiring 4MB (maximum 15MB) memory and less than 4 minutes on average for the points-to analysis. Another major advantage of our technique is that it allows to trade off precision for memory usage of the analysis.
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