The complexity of multiple-precision arithmetic

Details The complexity of multiple-precision arithmetic The complexity of multiple-precision arithmetic

2010-04-21

arxiv.org/abs/1004.3608v1

The Complexity of Computational Problem Solving (edited by R. S. Anderssen and R. P. Brent), University of Queensland Press, B

Computer Science

Computational Complexity

An old (1976) paper with a postscript (1999) describing more recent developments. 30 pages. For further details, see http://

Scientific paper

In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision required increases as the computation proceeds. We give upper and lower bounds on the number of single-precision operations required to perform various multiple-precision operations, and deduce some interesting consequences concerning the relative efficiencies of methods for solving nonlinear equations using variable-length multiple-precision arithmetic. A postscript describes more recent developments.

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