Date of Degree
PhD (Doctor of Philosophy)
First Committee Member
Second Committee Member
Third Committee Member
Fourth Committee Member
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.
Computable Reals, Exact Arithmetic, Floating Point Computation, Haskell, Lazy Programming
vii, 152 pages
Includes bibliographical references (pages 151-152).
Copyright © 2019 Ryan McCleeary
McCleeary, Ryan. "Lazy exact real arithmetic using floating point operations." PhD (Doctor of Philosophy) thesis, University of Iowa, 2019.