Programming Discipline on Vector Computers: “Vectors” as a Data-Type and Vector Algorithms

Abstract

Vector machines perform well on vectors. The purpose of this paper is not primarily to explain how and why. If we do so, to some extent, it is only so far as necessary to find a functional characterization of this class of machines. Two concepts seem basic in this respect: extension and regular representation. “Extension”, defined below, is a functor by which a scalar arithmetic operation is extended to vectors. “Regularity” means that vectors should be stored at memory locations in arithmetic progression. “Vector operations” are, first the vector extensions of scalar ones, next all operations compatible with the regularity constraint. All of this is explained and justified at full length in the first part of this paper, with many references to the CRAY-1, so this part may be read as a presentation of vector computers, especially the CRAY. But the real point is to define an abstract model of vector computers, rich enough to take their special characteristics into account, yet simple enough not to obfuscate the essential ideas behind vector algorithms.