Scalable parallel processor array for Jacobi-type matrix computations

Abstract This paper addresses the problem of designing a family of potential processor arrays for the execution of the so-called Jacobi algorithms. It extends the more familiar problem of designing a single fixed-size processor array for a particular program and its is parametrised with respect to size in two ways. Firstly, the program is no longer a particular one but is a member from a set of related programs. Secondly, the processor array itself is now also parametrised with respect to its dimension and size. There are thus three parameters involved, one to identify the program, one to select the program's size and one for the possible dimensions/sizes of the array implementation. The approach proposed in this paper is to use the design model and methods which have been used so far for the ‘one array for one program’ design problem and provide — instead of a processor array — a parameter controlled generic processor and a program to generate the control for the execution of a selected program on a specific array of such processors. This allows a user to compose an array out of a number of these generic processors and generate the necessary control signals actually executing the selected program. The control signals propagate down the array and instruct each processor how to process the incoming data. The control is hierarchical in the sense that a processor decodes and processes the incoming control signals so as to fix internal behaviour. The more processors are used, the less sequential the execution of the program will be. The generic processor uses Cordic arithmetic for its processing part and in addition to this it consists of a communication part and an internal memory bank. Communication between processors is a-synchronous while the internal timing is clocked.

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