Ahnentafel Indexing into Morton-Ordered Arrays, or Matrix Locality for Free

Abstract. Definitions for the uniform representation of d-dimensional matrices serially in Morton-order (or Z-order) support both their use with cartesian indices, and their divide-and-conquer manipulation as quaternary trees. In the latter case, d-dimensional arrays are accessed as 2d -ary trees. This data structure is important because, at once, it relaxes serious problems of locality and latency, and the tree helps schedule multiprocessing. It enables algorithms that avoid cache misses and page faults at all levels in hierarchical memory, independently of a specific runtime environment. This paper gathers the properties of Morton order and its mappings to other indexings, and outlines for compiler support of it. Statistics elsewhere show that the new ordering and block algorithms achieve high flop rates and, indirectly, parallelism without any low-level tuning. CCS Categories and subject descriptors: E.1 [Data Structures]: Arrays; D.3.2 [Programming Languages]: Language Classificati...

• Type: Conference
• Year: 2000
• Where: EUROPAR
• Authors: David S. Wise
• Keywords: Data Storage Representations, Data Structures, Distributed And Parallel Computing, EUROPAR 2000, Specific Runtime Environment