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We start with a mathematical definition of a real interval as a closed, connected set of reals. Interval arithmetic operations (addition, subtraction, multiplication, and division) are likewise defined mathematically and we provide algorithms for computing these operations assuming exact real arithmetic. Next, we define interval arithmetic operations on… (More)

- Timothy J Hickey, Qun Ju
- 1997

We present and analyze several implementations of the interval arithmetic narrowing function for multiplication. Starting from the Cleary algorithm for narrowing multiplication we describe two optimizations which produce code that is 10-15 times faster on the average. Finally, we propose a few simple RISC instructions which would allow eecient execution of… (More)

- Timothy Hickey, Qun Ju
- 1996

In this paper we present an algorithm for narrowing the constraint y = e x. The algorithm has been designed to be fast by using only IEEE multiplication. The main diiculty is to design algorithms which soundly, rapidly, and precisely compute upper and lower bounds on e x and ln(y). We prove that our algorithms are correct and produce upper and lower bounds… (More)

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