The complexity of multiple-precision arithmetic

Abstract

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.

An old (1976) paper with a postscript (1999) describing more recent developments. 30 pages. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub032.html. Typos corrected in v2

Cited by in corpus (7)

• The Borwein brothers, Pi and the AGM
• Arithmetic Branching Programs with Memory
• NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions
• Efficient implementation of elementary functions in the medium-precision range
• Improvements to the deformation method for counting points on smooth projective hypersurfaces
• Fast evaluation of some p-adic transcendental functions
• Rapid computation of special values of Dirichlet $L$-functions