Interval arithmetic: From principles to implementation

@article{Hickey2001IntervalAF,
  title={Interval arithmetic: From principles to implementation},
  author={Timothy J. Hickey and Qun Ju and M. H. van Emden},
  journal={J. ACM},
  year={2001},
  volume={48},
  pages={1038-1068}
}
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 intervals with IEEE 754 floating point endpoints to be sound and optimal approximations of the real interval operations and we show that the… CONTINUE READING
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