Algorithms for arbitrary precision floating point arithmetic
نویسنده
چکیده
We present techniques which may be used to perform computations of very high accuracy using only straightforward oating point arithmetic operations of limited precision, and we prove the validity of these techniques under very general hypotheses satissed by most implementations of oating point arithmetic. To illustrate the application of these techniques, we present an algorithm which computes the intersection of a line and a line segment. The algorithm is guaranteed to correctly decide whether an intersection exists and, if so, to produce the coordinates of the intersection point accurate to full precision. Moreover, the algorithm is usually quite eecient; only in a few cases does guaranteed accuracy necessitate an expensive computation.
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