基于SIMD机器的优化数据传输的并行循环分割

本文提出一个基于分布式局存的ＳＩＭＤ机器的循环分割理论体系以优化运算中所需要的数据传输。该体系使用矩阵表示迭代空间、数据空间和数组存取式。我们引入数据传输概念，并建立一个简单有效的数据传输模型来评估数据在全局内存和局部内存之间的传输开销。最后，对于给定的循环嵌套，我们给出一个循环分割算法以获得优化循环块，使得循环嵌套中所需要的数据传输开销最小，并且大大减少了数据传输和计算的同步开销。实验结果证明了     

A Computation+Communication Load Balanced Loop Partitioning Method for Distributed Memory Systems

Due to a significant communication overhead of sending and receiving data, the loop partitioning approaches on distributed memory systems must guarantee not just the computation load balance but computation+communication load balance. The previous approaches in loop partitioning have achieved a communication-free, computation load balanced iteration space partitioning solution for a limited subset of DOALL loops. But a large category of DOALL loops inevitably result in communication and the trade-offs between computation and communication must be carefully analyzed for these loops in order to balance out the combined computation time and communication overheads. In this work, we describe a partitioning approach based on the above motivation for the general cases of DOALL loops. Our goal is to achieve a computation+communication load balanced partitioning through static data and iteration space distribution. Our approach first performs partitioning of iteration and data spaces of a loop nest by analyzing communication and parallelism; it then performs architecture-dependent analysis to adjust the granularity of partitions, load balance each partition with respect to total computation+communication, and then performs mapping of partitions onto the available number of processors. This multiphase partitioning method works as follows. First, the code partitioning phase analyzes the references in the body of the DOALL loop nest and determines a set of directions for reducing a larger degree of communication by trading a lesser degree of parallelism. The partitioning is carried out in the iteration space of the loop by cyclically following a set of direction vectors such that the data references are maximally localized and reused, eliminating a larger communication volume than parallelism. We then perform data space partitioning based on a new larger partition owns rule to minimize the communication overhead for a compute intensive partition by localizing its references relatively more than a smaller noncompute intensive partition. A partition interaction graph is then constructed which is used by the architecture-dependent analysis phase to merge the partitions to achieve granularity adjustment, computation+communication load balance, and mapping on the actual number of available processors. Relevant theory and algorithms are developed along with a performance evaluation on the Cray T3D.     

On the parallel execution time of tiled loops

Many computationally-intensive programs, such as those for differential equations, spatial interpolation, and dynamic programming, spend a large portion of their execution time in multiply-nested loops that have a regular stencil of data dependences. Tiling is a well-known compiler optimization that improves performance on such loops, particularly for computers with a multilevel hierarchy of parallelism and memory. Most previous work on tiling is limited in at least one of the following ways: they only handle nested loops of depth two, orthogonal tiling, or rectangular tiles. In our work, we tile loop nests of arbitrary depth using polyhedral tiles. We derive a prediction formula for the execution time of such tiled loops, which can be used by a compiler to automatically determine the tiling parameters that minimizes the execution time. We also explain the notion of rise, a measure of the relationship between the shape of the tiles and the shape of the iteration space generated by the loop nest. The rise is a powerful tool in predicting the execution time of a tiled loop. It allows us to reason about how the tiling affects the length of the longest path of dependent tiles, which is a measure of the execution time of a tiling. We use a model of the tiled iteration space that allows us to determine the length of the longest path of dependent tiles using linear programming. Using the rise, we derive a simple formula for the length of the longest path of dependent tiles in rectilinear iteration spaces, a subclass of the convex iteration spaces, and show how to choose the optimal tile shape.     

Compile-time techniques for data distribution in distributed memorymachines

A solution to the problem of partitioning data for distributed memory machines is discussed. The solution uses a matrix notation to describe array accesses in fully parallel loops, which allows the derivation of sufficient conditions for communication-free partitioning (decomposition) of arrays. A series of examples that illustrate the effectiveness of the technique for linear references, the use of loop transformations in deriving the necessary data decompositions, and a formulation that aids in deriving heuristics for minimizing a communication when communication-free partitions are not feasible are presented     

COMPILE TIME PARTITIONING OF NESTED LOOP ITERATION SPACES WITH NON-UNIFORM DEPENDENCES*

In this paper we address the problem of partitioning nested loops with non-uniform (irregular) dependence vectors. Parallelizing and partitioning of nested loops requires efficient inter-iteration dependence analysis. Although many methods exist for nested loop partitioning, most of these perform poorly when parallelizing nested loops with irregular dependences. Unlike the case of nested loops with uniform dependences these will have a complicated dependence pattern which forms a non-uniform dependence vector set. We apply the results of classical convex theory and principles of linear programming to iteration spaces and show the correspondence between minimum dependence distance computation and iteration space tiling. Cross-iteration dependences are analyzed by forming an Integer Dependence Convex Hull (IDCH). Every integer point in this IDCH corresponds to a dependence vector in the iteration space of the nested loops. A simple way to compute minimum dependence distances from the dependence distance vectors of the extreme points of the IDCH is presented. Using these minimum dependence distances the iteration space can be tiled. Iterations within a tile can be executed in parallel and the different tiles can then be executed with proper synchronization. We demonstrate that our technique gives much better speedup and extracts more parallelism than the existing techniques.     

Compiler analysis for cache coherence: interprocedural array data-flow analysis and its impact on cache performance

In this paper, we present compiler algorithms for detecting references to stale data in shared-memory multiprocessors. The algorithm consists of two key analysis techniques, state reference detection and locality preserving analysis. While the stale reference detection finds the memory reference patterns that may violate cache coherence, the locality preserving analysis minimizes the number of such stale references by analyzing both temporal and spatial reuses. By computing the regions referenced by arrays inside loops, we extend the previous scalar algorithms for more precise analysis. We develop a full interprocedural array data-flow algorithm, which performs both bottom-up side-effect analysis and top-down context analysis on the procedure call graph to further exploit locality across procedure boundaries. The interprocedural algorithm eliminates cache invalidations at procedure boundaries, which were assumed in the previous compiler algorithms. We have fully implemented the algorithm in the Polaris parallelizing compiler. Using execution-driven simulations on Perfect Club benchmarks, we demonstrate how unnecessary cache misses can be eliminated by the automatic stale reference detection. The algorithm can be used to implement cache coherence in the shared-memory multiprocessors that do not have hardware directories, such as Cray T3D.     

嵌套循环到多处理机的映射

给出了将具有变相关的嵌套循环映射到具有分布式存储的多处理机上的两种方法.通过相关向量的分解或由相关向量导入方向向量,可将具有变相关的嵌套循环分解成若干互相没有相关关系的独立部分.由于它们可以被独立地执行,从而可以被映射到各个处理机上并行处理.     

Essential Misses and Data Traffic in Coherence Protocols

In this paper, we introduce a classification of misses and of components of the data traffic in shared-memory multiprocessors based on interprocessor communication. We consider protocols with invalidations, updates, and prefetches in systems with infinite and finite caches. We identify the set of essential misses and the essential traffic, i.e., the smallest set of misses and the smallest amount of traffic necessary for correct execution. The rest of the misses and of the data traffic is nonessential and could be ignored without affecting the correctness of program execution. To illustrate the classification of misses and traffic, we apply it to a set of parallel scientific programs and observe the overhead created by different hardware mechanisms when block sizes and cache sizes are varied.     

Compiler Support for Array Distribution on NUMA Shared Memory Multiprocessors

Management of program data to improve data locality and reduce false sharing is critical for scaling performance on NUMA shared memory multiprocessors. We use HPF-like data decomposition directives to partition and place arrays in data-parallel applications on Hector, a shared-memory NUMA multiprocessor. We describe a compiler system for automating the partitioning and placement of arrays. The compiler exploits Hectors shared memory architecture to efficiently implement distributed arrays. Experimental results from a prototype implementation demonstrate the effectiveness of these techniques. They also demonstrate the magnitude of the performance improvement attainable when our compiler-based data management schemes are used instead of operating system data management policies; performance improves by up to a factor of 5.     

Communication-free data allocation techniques for parallelizingcompilers on multicomputers

In distributed memory multicomputers, local memory accesses are much faster than those involving interprocessor communication. For the sake of reducing or even eliminating the interprocessor communication, the array elements in programs must be carefully distributed to local memory of processors for parallel execution. We devote our efforts to the techniques of allocating array elements of nested loops onto multicomputers in a communication-free fashion for parallelizing compilers. We first analyze the pattern of references among all arrays referenced by a nested loop, and then partition the iteration space into blocks without interblock communication. The arrays can be partitioned under the communication-free criteria with nonduplicate or duplicate data. Finally, a heuristic method for mapping the partitioned array elements and iterations onto the fixed-size multicomputers under the consideration of load balancing is proposed. Based on these methods, the nested loops can execute without any communication overhead on the distributed memory multicomputers. Moreover, the performance of the strategies with nonduplicate and duplicate data for matrix multiplication is studied     

A linear algebra framework for automatic determination of optimaldata layouts

This paper presents a data layout optimization technique for sequential and parallel programs based on the theory of hyperplanes from linear algebra. Given a program, our framework automatically determines suitable memory layouts that can be expressed by hyperplanes for each array that is referenced. We discuss the cases where data transformations are preferable to loop transformations and show that under certain conditions a loop nest can be optimized for perfect spatial locality by using data transformations. We argue that data transformations can also optimize spatial locality for some arrays without distorting temporal/spatial locality exhibited by others. We divide the problem of optimizing data layout into two independent subproblems: 1) determining optimal static data layouts, and 2) determining data transformation matrices to implement the optimal layouts. By postponing the determination of the transformation matrix to the last stage, our method can be adapted to compilers with different default layouts. We then present an algorithm that considers optimizing parallelism and spatial locality simultaneously. Our results on eight programs on two distributed shared-memory multiprocessors, the Convex Exemplar SPP-2000 and the SGI Origin 2000, show that the layout optimizations are effective in optimizing spatial locality and parallelism     

面向SIMD机器的全局自动数据分割

提出了一种面向ＳＩＭＤ机器的全局数据自动分割算法,该算法能处理多个非紧嵌折循环嵌套,并且数组下标存取为循环变量的线性式,首先通过数据与迭代映射抽象了计算中的通信方式,然事提出识别规则模式通信模式的形式比条件,接着建立包含对准信息和相应通信开销的数据迭代图,并在数据迭代图的基础上提出了一个启发式算法来计算较优的数据分布和迭代分布,以优化处理单元之间的通信开销,通过发析多个循环嵌套所涉及的多个数组映和     

An Application-Driven Study of Multicast Communication for Write Invalidation

In distributed shared-memory (DSM) multiprocessors, a write operation requires multiple messages to invalidate the nodes which share and cache the memory block to being written. The consequent write stall time impedes the performance of such systems. An effective means of achieving efficient invalidation is to employ multicast messages to reach the sharing nodes. This study evaluates two multicast-based invalidation schemes, dual-path and pruning, by performing application-driven simulation. The experimental settings used herein find that multicasts improve invalidation traffic for four of the six evaluated real applications. The remaining two applications are computationally intensive, and multicast-based invalidation is less effective. However, since multicasts encourage bursty communication, our results indicate that they help relieve network congestion during these periods. Dual-path performs slightly better than pruning, because it is less sensitive to routing delay in the routers. Our results further demonstrate that cache size is an important design parameter for multicast-based invalidation, and is highly effective for DSM multiprocessors with larger caches.     

Exploiting wavefront parallelism on large-scale shared-memorymultiprocessors

Wavefront parallelism, in which parallelism is limited to hyperplanes in an iteration space, can arise when compilers apply tiling to loop nests to enhance locality. Previous approaches for scheduling wavefront parallelism focused on maximizing parallelism; balancing workloads, and reducing synchronization. In this paper, we show that on large-scale shared-memory multiprocessors, locality is a crucial factor. We make the distinction between intratile and intertile locality and show that as the number of processors grows, intertile locality becomes more important. We consider and experimentally evaluate existing strategies for scheduling wavefront parallelism. We show that dynamic self-scheduling can be efficiently used on a small number of processors, but performs poorly at large scale because it does not enhance intertile locality. By contrast, static scheduling strategies enhance intertile locality for small tiles, maintaining parallelism and resulting in better performance at large scale. Results from a Convex SPP1000 multiprocessor demonstrate the importance of taking intertile locality into account. Static scheduling outperforms dynamic self-scheduling by a factor of up to 2.3 on 30 processors     

On supernode transformation with minimized total running time

With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses how to find an optimal supernode size and optimal supernode relative side lengths of a supernode transformation (also known as tiling). We identify three parameters of supernode transformation: supernode size, relative side lengths, and cutting hyperplane directions. For algorithms with perfectly nested loops and uniform dependencies, for sufficiently large supernodes and number of processors, and for the case where multiple supernodes are mapped to a single processor, we give an order n polynomial whose real positive roots include the optimal supernode size. For two special cases, 1) two-dimensional algorithm problems and 2) n-dimensional algorithm problems, where the communication cost is dominated by the startup penalty and, therefore, can be approximated by a constant, we give a closed form expression for the optimal supernode size, which is independent of the supernode relative side lengths and cutting hyperplanes. For the case where the algorithm iteration index space and the supernodes are hyperrectangular, we give closed form expressions for the optimal supernode relative side lengths. Our experiment shows a good match of the closed form expressions with experimental data     

Statement-Level Communication-Free Partitioning Techniques for Parallelizing Compilers

This paper addresses the problem of communication-free partition of iteration spaces and data spaces along hyperplanes. To finding more possible communication-free hyperplane partitions, we treat statements within a loop body as separate schedulable units. Instead of using the information about data dependence distance or direction vectors, our technique explicitly formulates array references as transformations from statement-iteration spaces to data spaces. Based on these transformations, the necessary and sufficient conditions for communication-free partition along hyperplanes to be feasible have been proposed. This approach can be applied to all programs with an imperfectly nested loop or sequences of imperfectly nested loops, whose array references are affine functions of outer loop indices or loop invariant variables. The proposed approach is more practical than existing methods in finding the data and computation distribution patterns that can cause the processor to execute fully-parallel on multicomputers without any interprocessor communication.     

Tuning Compiler Optimizations for Simultaneous Multithreading

Simultaneous Multithreading (SMT) is a processor architectural technique that promises to significantly improve the utilization and performance of modern wide-issue superscalar processors. An SM T processor is capable of issuing multiple instructions from multiple threads to a processor's functional units each cycle. Unlike shared-memory multiprocessors, SMT provides and benefits from fine-grained sharing of processor and memory system resources; unlike current uniprocessors, SMT exposes and benefits from inter-thread instruction-level parallelism when hiding long-latency operations. Compiler optimizations are often driven by specific assumptions about the underlying architecture and implementation of the target machine, particularly for parallel processors. For example, when targeting shared-memory multiprocessors, parallel programs are compiled to minimize sharing, in order to decrease high-cost inter-processor communication. Therefore, optimizations that are appropriate for these conventional machines may be inappropriate for SMT, which can benefit from finegrained resource sharing within the processor. This paper reexamines several compiler optimizations in the context of simultaneous multithreading. We revisit three optimizations in this light: loop-iteration scheduling, software speculative execution, and loop tiling. Our results show that all three optimizations should be applied differently in the context of SMT architectures: threads should be parallelized with a cyclic, rather than a blocked algorithm; non-loop programs should not be software speculated, and compilers no longer need to be concerned about precisely sizing tiles to match cache sizes. By following these new guidelines, compilers can generate code that improves the performance of programs executing on SMT machines.     

Using processor affinity in loop scheduling on shared-memorymultiprocessors

Loops are the single largest source of parallelism in many applications. One way to exploit this parallelism is to execute loop iterations in parallel on different processors. Previous approaches to loop scheduling attempted to achieve the minimum completion time by distributing the workload as evenly as possible while minimizing the number of synchronization operations required. The authors consider a third dimension to the problem of loop scheduling on shared-memory multiprocessors: communication overhead caused by accesses to nonlocal data. They show that traditional algorithms for loop scheduling, which ignore the location of data when assigning iterations to processors, incur a significant performance penalty on modern shared-memory multiprocessors. They propose a new loop scheduling algorithm that attempts to simultaneously balance the workload, minimize synchronization, and co-locate loop iterations with the necessary data. They compare the performance of this new algorithm to other known algorithms by using five representative kernel programs on a Silicon Graphics multiprocessor workstation, a BBN Butterfly, a Sequent Symmetry, and a KSR-1, and show that the new algorithm offers substantial performance improvements, up to a factor of 4 in some cases. The authors conclude that loop scheduling algorithms for shared-memory multiprocessors cannot afford to ignore the location of data, particularly in light of the increasing disparity between processor and memory speeds     

Global Optimization for Mapping Parallel Image Processing Tasks on Distributed Memory Machines

Many parallel algorithms and library routines for computer vision and image processing (CVIP) tasks on distributed-memory multiprocessors are available. The typical image distribution may use column, row, and block based mapping. Integrating a set of library routines for a CVIP application requires a global optimization to determine the data mapping of individual tasks by considering inter-task communication. The main difficulty in deriving the optimal image data distribution for each task is that CVIP task computation may involve loops, and the number of processors available and the size of the input image may vary at the run time. In this paper, a CVIP application is modeled using a task chain with imperfectly nested loops, specified by conventional visual languages such asKhorosandExplorer. A mapping algorithm is proposed that optimizes the average run-time performance for CVIP applications with nested loops by considering the data redistribution overheads and possible run-time parameter variations. A taxonomy of CVIP operations is provided and used for further reducing the complexity of the algorithm. Experimental results on both low-level image processing and high-level computer vision applications are presented to validate this approach.     

A Loop Transformation Algorithm for Communication Overlapping

Overlapping communication with computation is a well-known approach to improving performance. Previous research has focused on optimizations performed by the programmer. This paper presents a compiler algorithm that automatically determines the appropriate loop indices of a given nested loop and applies loop interchange and tiling in order to overlap communication with computation. The algorithm avoids generating redundant communication by providing a framework for combining information on data dependence, communication, and reuse. It also describes a method of generating messages to exchange data between processors for tiled loops on distributed memory machines. The algorithm has been implemented in our High Performance Fortran (HPF) compiler, and experimental results have shown its effectiveness on distributed memory machines, such as the RISC System/6000 Scalable POWERparallel System. This paper also discusses the architectural problems of efficient optimization.