Parallel Execution of Three-Dimensional Vector Operations
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概要
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This paper discusses a mechanism for parallel execution of an expression composed of three-dimensional vectors and/or 3 x 3 matrices from the set theory viewpoint. First, we compose the set of all three-dimensional constant vectors and all 3 x 3 constant matrices, where constant means real number, and define basic operations on the set. Then, we compose an extended set G by introducing a three-dimensional vector variable, and discuss the basic properties of G. We also introduce a differential operator, and show that the result of differentiation of an expression in G is also in G. Next, we show a parallel execution mechanism for basic operations on G. Since the highest utilization rate is obtained when three operation units are used, we show a detailed parallel execution mechanism consisting of three operation units. Defining operation parallelism, or simply parallelism, by the ratio of the number of operation steps executed by the sequential execution mechanism to that of the parallel execution mechanism, we show that the basic operations on the set G can be carried out with a parallelism of three. We also show that the major operations used in the linear algebra are composed of a combination of the basic operations. These operations include intrinsically sequential operations such as the sum of vector elements. Only such operations decrease the parallelism. Otherwise, an expression in G can be processed with a parallelism of three.
- 一般社団法人情報処理学会の論文
- 1992-03-15