## Algorithms for Arbitrary Precision Floating Point Arithmetic (1991)

Venue: | Proceedings of the 10th Symposium on Computer Arithmetic |

Citations: | 71 - 1 self |

### BibTeX

@INPROCEEDINGS{Priest91algorithmsfor,

author = {Douglas M. Priest},

title = {Algorithms for Arbitrary Precision Floating Point Arithmetic},

booktitle = {Proceedings of the 10th Symposium on Computer Arithmetic},

year = {1991},

pages = {132--145},

publisher = {IEEE Computer Society Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present techniques which may be used to perform computations of very high accuracy using only straightforward floating point arithmetic operations of limited precision, and we prove the validity of these techniques under very general hypotheses satisfied by most implementations of floating 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 efficient; only in a few cases does guaranteed accuracy necessitate an expensive computation. 1. Introduction "How accurate is a computed result if each intermediate quantity is computed using floating point arithmetic of a given precision?" The casual reader of Wilkinson's famous treatise [21] and similar roundoff error analyses might...

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