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 December 10th, 2007, 01:43 AM #1 Newbie   Joined: Dec 2007 From: Egypt Posts: 1 Thanks: 0 Interval Arithmetic and Reliable Computing A Good Paper in Interval Arithmetic (or Range Arithmetic) and Reliable Computing: Title: [color=darkred]Interval Arithmetic, Accurate Self-Validating Arithmetic for Digital Computing[/color] Author: [color=darkred]Hend Dawood[/color] 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 report 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. Link: http://mihd.net/8uex3q
 December 10th, 2007, 06:14 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms I've always liked the idea of modular arithmetic, but in practice I hear that intervals often become too wide for practical use, since most rounding errors cancel (related to the idea that a random 1-D walk has an expected value of only k sqrt(n) after n steps). How do you addresss this -- just more bits of precision?

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