Appendix: Number Theory Tools for Floating-Point Arithmetic

Abstract

Continued fractions make it possible to build very good (indeed, the best possible, in a sense that will be made explicit by Theorems 49 and 50) rational approximations to real numbers. As such, they naturally appear in many problems of number theory, discrete mathematics, and computer science. Since floating-point numbers are rational approximations to real numbers, it is not surprising that continued fractions play a role in some areas of floating-point arithmetic.