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Conference Papers Year : 2002

Motivations for an arbitrary precision interval arithmetic and the mpfi library

Abstract

MPFI is a library implementing interval arithmetic with arbitrary accuracy. It can be freely downloaded (including source code and documentation). It is written in C and is based on the MPFR library for arbitrary precision floating-point arithmetic, which is in turn built upon the GMP library. MPFR has been chosen because it provides outward rounding, even for the elementary functions, which is mandatory to implement interval arithmetic. An important issue in interval computation is "computing in the large", {\it i.e.} getting tight enclosures for the range of a function over a large interval. However, this issue has no well established answer, and one common way to circumvent the problem consists in bisecting the input interval again and again, until the evaluation of the function upon each sub-part is tight enough. For some problems, such as roots approximations or optimization of a "very flat" function, splitting beyond the limits of usual (single or double) floating-point capacities reveals necessary in order to reach the required accuracy on the function evaluation.

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Other [cs.OH]
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Dates and versions

inria-00100985 , version 1 (26-09-2006)

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  • HAL Id : inria-00100985 , version 1

Cite

Nathalie Revol, Fabrice Rouillier. Motivations for an arbitrary precision interval arithmetic and the mpfi library. SIAM Workshop on Validated Computing 2002, 2002, Toronto, Canada. pp.155-161. ⟨inria-00100985⟩
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