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Development of SLI Arithmetic

D.W. Lozier and F.W.J. Olver, ACMD
A. Mink, High Performance Systems & Services Division
M.A. Anuta, Cray Research, Inc
N. Schabanel, École Normale Supérieure de Lyon, France
P.R. Turner, Mathematics Department, US Naval Academy

The SLI computer arithmetic system eliminates some of the deficiencies of floating-point arithmetic as exemplified by the IEEE Standard 754-1985. These are related to over/underflow and the related IEEE infinity and NaN conventions, and also to the inadequacy of conventional absolute/relative error analysis. It is well known in the software engineering community that programming that is resistant to failure from over/underflow is costly and tedious to achieve, and that the devices provided by the IEEE standard to deal with over/underflow are not universally available or effective. Similarly, ambiguity exists as to when absolute or relative error is appropriate for the mathematical assessment of rounding and truncation errors in a computational process. Because SLI arithmetic is immune to over/underflow, and because its associated error analysis is in terms of a generalized error measure that smoothly connects absolute, relative, and higher-order errors, the proposed new arithmetic has the potential to revolutionize numerical scientific computing.

A major accomplishment has been the development of parallel algorithms for basic linear algebra operations (sometimes called the BLAs). A paper on this work by Anuta, Lozier, Schabanel and Turner will be presented in Workshop 10, Computer Arithmetic, at the Euro-Par'96 Conference in Lyon in August, 1996. In essence, the work shows that fundamental vector and scalar processes have essentially the same computational complexity in SLI arithmetic, regardless of the vector length. These algorithms were developed in part to demonstrate how SLI arithmetic can take advantage of parallel processing at the level of a VLSI chip. They also suggest that SLI algorithms may be particularly effective in numerical linear algebra which is basic in many scientific computing algorithms.

A new initiative by Drs. Lozier and Mink is a proposal to implement SLI arithmetic operations and SLI BLAs on a prototype VLSI chip, attach the chip to a suitable computer with appropriate operating software, and use the resulting computing capability to demonstrate the effectiveness of the new arithmetic on typical scientific computing applications. An informal survey of nongovernmental mathematicians, computer scientists, and others who are very familiar with scientific computing elicited commentary supporting the proposed project. This initiative, if approved, would be of great interest to all who are interested in computer arithmetic research.

next up previous
Next: Measurement of Fortran Up: Testing and Evaluation Previous: Software Test System

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