Sensitivities for guiding refinement in arbitrary-precision arithmetic
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1192966915-MIT.pdf
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450.19 KB
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Adobe PDF
Checksum (MD5)
c0228f6c43dc63cc1130acd6be2d3bb1
Author(s)
Michel, Jesse(Jesse M.)
Advisor(s)
Michael Carbin.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
Programmers often develop and analyze numerical algorithms assuming that they operate on real numbers, but implementations generally use floating-point approximations. Arbitrary precision arithmetic enables developers to write programs that operate over reals: given an output error bound, the program will produce a result within that bound. A key drawback of arbitrary-precision arithmetic is its speed. Fast implementations of arbitrary-precision arithmetic use interval arithmetic (which provides a lower and upper bound for all variables and expressions in a computation) computed at successively higher precisions until the result is within the error bound. Current approaches refine computations at precisions that increase uniformly across the computation rather than changing precisions per-variable or per-operator. This thesis proposes a novel definition and implementation of derivatives through interval code that I use to create a sensitivity analysis. I present and analyze the critical path algorithm, which uses sensitivities to guide precision refinements in the computation. Finally, I evaluate this approach empirically on sample programs and demonstrate its effectiveness..
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 59-61).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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