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Contents
Introduction to
EXACT NUMERICAL COMPUTATION
Notes for a tutorial at ISSAC 2000
Martín Escardó
School of Computer Science
St Andrews University
http://www.dcs.st-and.ac.uk/~mhe/
Contents
Introduction
Overview
Floating-point computation
Example--the logistic map
Exact numerical computation
First attempt
Second attempt
Towards a third attempt
Third attempt
Towards a fourth attempt
Fourth attempt
Last attempt
Other approaches
Operational and denotational semantics
Operational semantics
Denotational semantics
Example
Computational adequacy
Examples
The space of decimal expansions
Computational inadequacy of decimal notation
The denotation map
Realizers
Alternative notations
Signed-digit notation
Computability
Canonical forms
Numerical order in signed-digit notation
Order normalization
Inequality tests in real number computation
Functional approaches
Turing-complete real number data types
Partial real numbers and Turing-completeness
Real PCF
Operational semantics of Real PCF
Turing-completeness of Real PCF
Bibliography
About this document ...
Martin Escardo
2000-10-02
