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Published Articles >> Table of Contents >> Abstract
18th IEEE Symposium on Computer Arithmetic (ARITH '07)
pp. 133-140
Worst Cases of a Periodic Function for Large Arguments
Guillaume Hanrot, INRIA/LORIA, France
Vincent Lefevre, INRIA/LIP, France
Damien Stehle, CNRS/LIP, France
Paul Zimmermann, INRIA/LORIA, France
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DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2007.37
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| Abstract |
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One considers the problem of finding hard to round cases
of a periodic function for large floating-point inputs, more
precisely when the function cannot be efficiently approximated
by a polynomial. This is one of the last few issues
that prevents from guaranteeing an efficient computation of
correctly rounded transcendentals for the whole IEEE-754
double precision format. The first non-naive algorithm for
that problem is presented, with a heuristic complexity of
O(20.676p) for a precision of p bits. The efficiency of the
algorithm is shown on the largest IEEE-754 double precision
binade for the sine function, and some corresponding
bad cases are given. We can hope that all the worst cases
of the trigonometric functions in their whole domain will be
found within a few years, a task that was considered out of
reach until now.
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 Additional Information
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Citation:
Guillaume Hanrot, Vincent Lefevre, Damien Stehle, Paul Zimmermann,
"Worst Cases of a Periodic Function for Large Arguments,"
arith,
pp. 133-140,
18th IEEE Symposium on Computer Arithmetic (ARITH '07),
2007
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