Book Title:
Interval Arithmetic, Accurate Self-validating Arithmetic for Digital Computing
Author: Hend Dawood
Abstract:
Interval arithmetic (range arithmetic) is a broad field in which rigorous mathematics is associated with scientific computing. It is an arithmetic defined on sets of intervals rather than sets of real numbers. The connection between computing and mathematics provided by intervals makes it possible to solve problems that can’t be efficiently solved using traditional floating point arithmetic. Today, the interval methods are becoming rapidly popular as a perspective weapon against round-off errors. A number of researchers worldwide produced a voluminous literature on the subject. This book introduces the theoretical aspects of interval arithmetic, as well as some of its computational and scientific applications. Also, we introduce the hardware implementations of a 4-by-4 bit multiplier and an interval squaring circuit.
Keywords:
Interval Arithmetic, Range Arithmetic, Reliable Computing, Round-off Errors, Self-validating Arithmetic, 4-by-4 Multiplier, Interval Squaring Circuit.