NDLI: Fast additions on masked integers

Content Provider	ACM Digital Library
Author	Adams, Michael D. Wise, David S.
Abstract	Suppose the bits of a computer word are partitioned into d disjoint sets, each of which is used to represent one of a d-tuple of cartesian indices into d-dimensional space. Then, regardless of the partition, simple group operations and comparisons can be implemented for each index on a conventional processor in a sequence of two or three register operations.These indexings allow any blocked algorithm from linear algebra to use some non-standard matrix orderings that increase locality and enhance their performance. The underlying implementations were designed for alternating bit postitions to index Morton-ordered matrices, but they apply, as well, to any bit partitioning. A hybrid ordering of the elements of a matrix becomes possible, therefore, with row-/column-major ordering within cache-sized blocks and Morton ordering of those blocks, themselves. So, one can enjoy the temporal locality of nested blocks, as well as compiler optimizations on row- or column-major ordering in base blocks.
Starting Page	39
Ending Page	45
Page Count	7
File Format	PDF
ISSN	03621340 15581160
DOI	10.1145/1149982.1149987
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	41
Issue Number	5
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quadtrees Dilated integers Morton order Index arithmetic Compilers
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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