CSR: SMALL: Design Validation Methods for Reliable and Efficient Floating-Point

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Floating-point arithmetic enables computers to smoothly andefficiently handle widely varying magnitudes such as the diameter ofan atom or that of a star, and fit these measures within computerwords that come in standard widths. Unfortunately,when calculations are performed on floating numbers, round-off errorsare introduced, often causing real-world disasters, such as errantmissile launches. While employing large computer word widths canminimize these errors, it also slows down computations, increasestheir memory, and energy needs. This project could have a broad impactby providing much needed debug support for scientific programmers to develop more reliable floating point programs.This project develops novel ways to estimate round-off errors, thushelping programmers arrive at efficient floating-point computer codes.Special emphasis is placed on handling tricky cases such as squaringnumbers and taking their trigonometric values where prior research hadnot sufficiently advanced. By developing powerful and automated toolsfor precision estimation, it allows programmers to tune their codesand pick word widths parsimoniously while not losing accuracy. The investigators use these tools to develop pedagogical material and bestpractices based on hands-on experience that helps inform students whotypically are not taught the pitfalls of floating-point arithmetic.