DOI

10.17077/etd.128d-ci14

Document Type

Dissertation

Date of Degree

Summer 2019

Degree Name

PhD (Doctor of Philosophy)

Degree In

Computer Science

First Advisor

Stump, Aaron

First Committee Member

Jones, Douglas

Second Committee Member

Segre, Alberto

Third Committee Member

Tinelli, Cesare

Fourth Committee Member

Varadarajan, Kasturi

Abstract

Exact real arithmetic systems can specify any amount of precision on the output of the computations. They are used in a wide variety of applications when a high degree of precision is necessary. Some of these applications include: differential equation solvers, linear equation solvers, large scale mathematical models, and SMT solvers. This dissertation proposes a new exact real arithmetic system which uses lazy list of floating point numbers to represent the real numbers. It proposes algorithms for basic arithmetic computations on these structures and proves their correctness. This proposed system has the advantage of algorithms which can be supported by modern floating point hardware, while still being a lazy exact real arithmetic system.

Keywords

Computable Reals, Exact Arithmetic, Floating Point Computation, Haskell, Lazy Programming

Pages

vii, 152 pages

Bibliography

Includes bibliographical references (pages 151-152).

Copyright

Copyright © 2019 Ryan McCleeary

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