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How to Read Floating Point Numbers Accurately (1990)
| Venue: | In PLDI 1990 [16 |
| Citations: | 29 - 0 self |
BibTeX
@INPROCEEDINGS{Clinger90howto,
author = {William D. Clinger},
title = {How to Read Floating Point Numbers Accurately},
booktitle = {In PLDI 1990 [16},
year = {1990},
pages = {92--101}
}
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Abstract
Consider the problem of converting decimal scientific notation for a number into the best binary floating point approximation to that number, for some fixed precision. This problem cannot be solved using arithmetic of any fixed precision. Hence the IEEE Standard for Binary Floating-Point Arithmetic does not require the result of such a conversion to be the best approximation. This paper presents an efficient algorithm that always finds the best approximation. The algorithm uses a few extra bits of precision to compute an IEEE-conforming approximation while testing an intermediate result to determine whether the approximation could be other than the best. If the approximation might not be the best, then the best approximation is determined by a few simple operations on multiple-precision integers, where the precision is determined by the input. When using 64 bits of precision to compute IEEE double precision results, the algorithm avoids higher-precision arithmetic over 99% of the time....
Keyphrases
point number fixed precision binary floating-point arithmetic efficient algorithm algorithm avoids higher-precision arithmetic ieee double precision result simple operation multiple-precision integer intermediate result decimal scientific notation problem cannot ieee standard ieee-conforming approximation point approximation extra bit
