Keck Foundation Computational Science Education Modules
Computable Performance Metrics

Kris Stewart, Professor, Computer Science Professor
San Diego State University

This url: ; Updated 04Feb2022 [Zip File (PKzip compatible) with three module files and their two zip files]

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Kris Stewart modules using Internet Archive (Wayback Machine) Computer Science Modules

Computer Science Modules
Computable Performance Metrics: Module 0b: Floating Point Precision MACHAR – Test for IEEE 754
Computable Performance Metrics: Module 0b: Supporting Documents I
Computable Performance Metrics: Module 0b: Supporting Documents II
Module Author: Kris Stewart
Author Contact:
Funded By: W.M. Keck Foundation
Module 0: Floating Point Precision covered the task to find “computable” ways to detect the actual manner in which a computer performed arithmetic, developed by W.J. Cody [1] in 1988. In that module, a minimal test was examined to compute a machine’s unit round-off, the value eps so that 1.0 + eps = 1.0. Considering the extent to which the FORTRAN subroutine MACHAR can compute the properties of a processor, some may wish to examine the full range of values computed. This can be used to test if the user’s computer platform actually follows the IEEE 754 Floating Point Standard [2].

Our goal was to provide linkages between the mathematical theory of error estimates for numerical approximation and actual, computable estimates of error that validates these theoretical results. An equally important property of numerical approximations is the amount of computational time that is needed to complete the calculation. We provide a sequence of three modules that start by clearly describing the fundamental property of calculations, their finite precision based on the size of the computer word used to storage the final, as well as intermediate, values. This focussed on the Machine Unit Round-off, presented in Module 0. To appreciation the evolution over time of the capabilities of calculations and to understand the importance of the IEEE Floating Point Standard, we provide the code to actually compute the values that characterize these hardware properties in a portable manner that can be used on a wide array of compute platforms from many different manufacturers in Module 1. We finish with the Module 2 treatment of solve the 2d diffusion equation with finite difference approximation and the double-precision and single-precision codes that succeed in verifying the Linear Work for solving the tridiagonal system and the Quadratic Accuracy of the finite difference approximation.

Computable Performance Metrics - Module 0 Floating Point Precision
word doc

Computable Performance Metrics - Module 1 Floating Point Precision MACHAR – Test for IEEE 754
word doc and zip file.

Computable Performance Metrics - Module 2 Computing Error and Work Estimators
word doc and Module2 - zip file

This work was supported by a grant from the Keck Foundation to Capital University, Columbus, Ohio.
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Thank you Ignatios Vakalis and Terry Lahm for your patience.