Vector Pipeline Research Articles

Implementation of digital filtering algorithms using pipelined vector processors

The implementation of digital filtering algorithms using pipelined vector processors is investigated. Modeling of vector processors and vectorization methods are explained, and then the performances of several implementation methods are evaluated based on the model. Vector processor implementation of FIR filtering algorithms using the outer product method and the indirect convolution method is evaluated. Recursive and adaptive filtering algorithms, which lead to dependency problems in direct vector processor implementations, are implemented very efficiently using a newly developed vectorization method. The proposed method computes multiple output samples at a time, making the vector length independent of the filter order. Illustrative examples comparing theoretical results with Cray X-MP simulation results are included.

Design of a vector processor

This paper discusses the inherent parallelism limits on several applications for vector computers, the parallel capabilities of several architectures and two ways (traditional instruction control flow and data control flow) by which the capabilities can be used. Then a scheme for a pipelined vector processor of multi-processing units is presented. The basic system structure and its function on highly sparse vector processing are described. A vector cache system and a distributed main memory are also considered, which are intended to sustain extremely high access rates for the processor. A microprocessor based vector processor is constructed, which can simulate the high performance version of the processor.

On the possibility of attaining high productivity in the solution of problems of mathematical physics using vector pipeline digital computers

The analysis of algorithms for solving problems in mathematical physics when they are programmed on vector pipeline digital computers are considered. A technique is proposed which enables one to match an algorithm with the architecture of a machine and to obtain a highly efficient program. The analysis is carried out using the example of the difference scheme for the method of flows which is employed for the numerical solution of problems in the mechanics of continuous media. Estimates of the rates of processing the resulting translations from a high-level language and using the proposed technique are presented.

Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine

This paper examines common implementations of linear algebra algorithms, such as matrix-vector multiplication, matrix-matrix multiplication and the solution of linear equations. The different versions are examined for efficiency on a computer architecture which uses vector processing and has pipelined instruction execution. By using the advanced architectural features of such machines, one can usually achieve maximum performance, and tremendous improvements in terms of execution speed can be seen over conventional computers.

Vectorized procedural models for natural terrain

A ray-tracing procedural model is described, in which ocean waves and islands are rendered by different but related algorithms. The algorithms are based on analytic formulas involving arithmetic operations, trigonometric functions, and square roots, and are organized for a vectorizing compiler on a Cray 1, a “supercomputer” with a vector pipeline architecture. Height field methods are used, one vertical scan line at a time, to trace the direct rays to the ocean, where they are reflected. Approximate methods are then applied to find whether the reflected rays meet any other object on their way to the sky. The output, at eight bits per pixel, gives information for shading, e.g. the angle of the surface normal for rays meeting the islands, or the angle of elevation from the horizon for rays continuing unobstructed to the sky. The output is recorded on a magnetic tape for each frame in one cycle of the wave motion, and plotted offline on a Dicomed D-48 color film recorder. The eight bits per pixel are interpreted by a color translation table, which is gradually changed as the wave cycle is repeated to simulate the changing illumination during sunset.

Pipeline Architecture

Pipelined computer architecture has received considerable attention since the 1960s when the need for faster and more cost-effective systems became critical. The merit of pipelining is that it can help to match the speeds of various subsystems without duplicating the cost of the entire system involved. As technology evolves, faster and cheaper LSI circuits become available, and the future of pipelining, either in a simple or complex form, becomes more promising. This paper reviews the many theoretical considerations and problems behind pipelining, surveying and comparing various representative pipeline machines that operate in either sequential or vector pipeline mode, the practical solutions adopted, and the tradeoffs involved. The performance of a simple pipe, the physical speed limitation, and the control structures for penalty-incurring events are analyzed separately. The problems faced by the system designers are tackled, including buffering, busing structur, branching, and interrupt handling. Aspects of sequential and vector processing are studied. Fundamental advantages of vector processing are unveiled, and additional requirements (costs) are discussed to establish a criterion for the tradeoff between sequential and vector pipeline processing. Finally, two recent machines (the CRAY-1 and the Amdahl 470 V/6 systems) are presented to demonstrate how complex pipeline techniques can be used and how simple but advantageous pipeline concepts can be exploited.