缓存和I/O高效的函数算法

G. Blelloch, R. Harper
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引用次数: 20

摘要

广泛研究的I/O和理想缓存模型被开发出来,以解释在内存层次结构的不同级别访问内存的成本的巨大差异。这两种模型都基于两级内存层次结构,其中固定大小的主内存(缓存)大小为M,无界的辅助内存组织在大小为b的块中。成本衡量完全基于主内存和辅助内存之间的块传输数量。所有其他操作都是免费的。在这些模型中分析了许多算法,实际上这些模型比标准RAM模型更准确地预测了算法的相对性能。然而,这些模型需要在非常低的级别上指定算法,这要求用户在内存中的数组中仔细布局他们的数据,并管理他们自己的内存分配。在本文中,我们提出了一个成本模型来分析用简单函数语言表示的算法的内存效率。我们展示了一些仅使用列表和树(没有数组)、不需要显式内存布局或内存管理的标准形式编写的算法在模型中是如何高效的。然后,我们描述了该语言的实现,并展示了将我们模型中的成本映射到理想缓存模型中的成本的可证明界限。这些约束意味着,基于列表和树而不特别关注内存布局细节的纯函数式程序可以与精心设计的命令式I/O高效算法一样渐进地高效。例如,我们描述了一个O(n_B logM/Bn_B)代价排序算法,它在理想的缓存和I/O模型中是最优的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cache and I/O efficent functional algorithms
The widely studied I/O and ideal-cache models were developed to account for the large difference in costs to access memory at different levels of the memory hierarchy. Both models are based on a two level memory hierarchy with a fixed size primary memory(cache) of size M, an unbounded secondary memory organized in blocks of size B. The cost measure is based purely on the number of block transfers between the primary and secondary memory. All other operations are free. Many algorithms have been analyzed in these models and indeed these models predict the relative performance of algorithms much more accurately than the standard RAM model. The models, however, require specifying algorithms at a very low level requiring the user to carefully lay out their data in arrays in memory and manage their own memory allocation. In this paper we present a cost model for analyzing the memory efficiency of algorithms expressed in a simple functional language. We show how some algorithms written in standard forms using just lists and trees (no arrays) and requiring no explicit memory layout or memory management are efficient in the model. We then describe an implementation of the language and show provable bounds for mapping the cost in our model to the cost in the ideal-cache model. These bound imply that purely functional programs based on lists and trees with no special attention to any details of memory layout can be as asymptotically as efficient as the carefully designed imperative I/O efficient algorithms. For example we describe an O(n_B logM/Bn_B)cost sorting algorithm, which is optimal in the ideal cache and I/O models.
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