Abstract The Genesis benchmark suite has been assembled to evaluate the performance of distributed‐memory MIMD systems. The problems selected all have a scientific origin (mostly from physics or theoretical chemistry), and range from synthetic code fragments designed to measure the basic hardware properties of the computer (especially communication and synchronisation overheads), through commonly used library subroutines, to full application codes. This is the second of a series of papers on the Genesis distributed‐memory benchmarks, which were developed under the European ESPRIT research program. Results are presented for the SUPRENUM and iPSC/860 computers when running the following benchmarks: COMMS1 (communications), TRANS1 (matrix transpose), FFT1 (fast Fourier transform) and QCD2 (conjugate gradient kernel). The theoretical predictions are compared with, or fitted to, the measured results, and then used to predict (with due caution) how the performance might scale for larger problems and more processors than were actually available during the benchmarking.

Abstract The paper enunciates the principle of computational similarity, whereby calculations with the same values for certain dimensionless ratios are said to be ‘computationally similar’ and as a consequence have the same optimum self‐speed‐up and optimum number of processors. Based on a three‐parameter description of the computer hardware, two dimensionless ratios, which are only a function of the problem size and the hardware parameters, completely determine the scaling. Contours of constant self‐speed‐up can be drawn on a two‐dimensional dimensionless universal scaling diagram (DUSD). This diagram is for a particular class of timing expressions that can be shown to represent approximately the performance of a corresponding class of computer programs or benchmarks, but it applies to all computers describable by the three hardware parameters and to all problem sizes. Thus the dimensionless ratios play a similar role in the study of computer performance, as do the Reynolds and other dimensionless numbers in fluid dynamics. This dimensional analysis of computer performance is illustrated by the case of the FFT1 benchmark from the Southampton ‘Genesis’ distributed‐memory benchmarks.

Abstract This is the first of a series of papers on the Genesis distributed‐memory benchmarks, which were developed under the European ESPRIT research program. The benchmarks provide a standard reference Fortran77 uniprocessor version, a distributed memory. MIMD version, and in some cases a Fortran90 version suitable for SIMD computers. The problems selected all have a scientific origin (mostly from physics or theoretical chemistry), and range from synthetic code fragments designed to measure the basic hardware properties of the computer (especially communication and synchronisation overheads), through commonly used library subroutines, to full application codes. This first paper defines the methodology to be used to analyse the benchmark results, and gives an example of a fully analysed application benchmark from General Relativity (GR1). First, suitable absolute performance metrics are carefully defined, then the performance analysis treats the execution time and absolute performance as functions of at least two variables, namely the problem size and the number of proecssors. The theoretical predictions are compared with, or fitted to, the measured results, and then used to predict (with due caution) how the performance might scale for larger problems and more processors than were actually available during the benchmarking. Benchmark measurements are given primarily for the German SUPRENUM computer, but also for the IBM 3083J, Convex C210 and a Parsys Supernode with 32 T800‐20 transputers.

algorithm is reported, and demonstrated in use for interpreting medical images. The SIMD machine acts as a "compute server " to a general-purpose AI environment, which provides and interactive user interface, or controls the server autonomously.

Algorithmic phase diagrams are a neat and compact representation of the results of comparing the execution time of several algorithms for the solution of the same problem. As an example we show the recent results of Gannon and Van Rosendale on the solution of multiple tridiagonal systems of equations in the form of such diagrams. The act of preparing these diagrams has revealed an unexpectedly complex relationship between the best algorithm and the number and size of the tridiagonal systems, which was not evident from the algebraic formulae in the original paper. Even so, for a particular computer, one diagram suffices to predict the best algorithm for all problems that are likely to be encountered-the prediction being read directly from the diagram without complex calculation.

A two-parameter description of any computer is given that characterizes the performance of serial, pipelined, and array-like architectures. The first parameter (r∞) is the traditional maximum performance in megaflops, and the new second parameter (n½) measures the apparent parallelism of the computer. For computers with a single instruction stream (unicomputers), the relative performance of two algorithms on the same computer depends only on n½ and the average vector length of the algorithm. The performance of a family of FACR direct methods for solving Poisson's equation is optimized on the basis of this characterization.

The demand for rapid procedures to solve Poisson's equation has led to the development of a direct method of solution involving Fourier analysis which can solve P0isson's equation in a square region covered by a 48 X 48 mesh in 0,9 seconds ca the IBM 7090.This compares favorably with the best iterative methods which would require about 10 seconds to solve the same problem.The method is applicable to rectangular regions with simple boundary conditions and the maximum observed error in the potential for several random charge distributions is 5 X i0 -r of the maximum potentiM change in the region. * Computation Center.Computation times given in this paper will be for this machine except where specified.95

The author believes that Algol 60 is not sufficiently powerful to serve as a computer language for the solution of scientific problems in industry, and that the language should be extended for this purpose without delay. This paper presents such an extension, which is written as additional wording to the Algol 60 report, and is primarily aimed at simplifying work on complex numbers and matrices. Special care has been taken to ensure that any Algol 60 program is also a legal program in ABS12 Algol.