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Lazy Arithmetic
September 1997 (vol. 46 no. 9)
pp. 961-975

Abstract—Finite-precision leads to many problems in geometric methods from CAD or Computational Geometry. Until now, using exact rational arithmetic was a simple, yet much too slow, solution to be of any practical use in real-scale applications. A recent optimization—the lazy rational arithmetic [5]—seems promising: It defers exact computations until they become either unnecessary (in most cases) or unavoidable; in such a context, only indispensable computations are performed exactly, that is, those without which any given decision cannot be reached safely using only floating-point arithmetic. This paper takes stock of the lazy arithmetic paradigm: principles, functionalities and limits, speed, possible variants and extensions, difficulties, problems solved or left unresolved.

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Index Terms:
Computational geometry, hash coding, interval arithmetic, robustness, exact rational arithmetic, lazy arithmetic, inconsistencies.
Citation:
Dominique Michelucci, Jean-Michel Moreau, "Lazy Arithmetic," IEEE Transactions on Computers, vol. 46, no. 9, pp. 961-975, Sept. 1997, doi:10.1109/12.620478
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