AERN-Real: arbitrary precision interval arithmetic for approximating exact real numbers

[ bsd3, data, deprecated, library, math ] [ Propose Tags ]
Deprecated. in favor of aern2-mp, aern2-real

Datatypes and abstractions for approximating exact real numbers and a basic arithmetic over such approximations. The design is inspired to some degree by Mueller's iRRAM and Lambov's RealLib (both are C++ libraries for exact real arithmetic).

Abstractions are provided via 4 type classes:

• ERRealBase: abstracts floating point numbers

• ERApprox: abstracts neighbourhoods of real numbers

• ERIntApprox: abstracts neighbourhoods of real numbers that are known to be intervals

• ERApproxElementary: abstracts real number approximations that support elementary operations

For ERRealBase we give several implementations. The default is an arbitrary precision floating point type that uses Double for lower precisions and an Integer-based simulation for higher precisions. Rational numbers can be used as one of the alternatives. Augustsson's Data.Number.BigFloat can be easily wrapped as an instance of ERRealBase except that it uses a different method to control precision.

ERIntApprox is implemented via outwards-rounded arbitrary precision interval arithmetic. Any instance of ERRealBase can be used for the endpoints of the intervals.

ERApproxElementary is implemented generically for any implementation of ERIntApprox. This way some of the most common elementary operations are provided, notably: sqrt, exp, log, sin, cos, atan. These operations converge to an arbitrary precision and also work well over larger intervals without excessive wrapping.

There is also some support for generic Taylor series, interval Newton method and simple numerical integration.

Simple examples of usage can be found in tests/Demo.hs.

Versions [faq] 0.9.0, 0.9.1, 0.9.2, 0.9.3, 0.9.3.1, 0.9.4, 0.9.5, 0.9.6, 0.9.6.1, 0.9.7, 0.9.7.1, 0.9.7.2, 0.9.8, 0.9.9, 0.10.0, 0.10.0.1, 0.10.0.2, 2011.1, 2011.1.0.1 ChangeLog base, binary (>=0.4), containers [details] BSD-3-Clause (c) 2007-2008 Michal Konecny, Amin Farjudian, Jan Duracz Michal Konecny (Aston University) mik@konecny.aow.cz Data, Math by MichalKonecny at Thu Aug 7 10:18:21 UTC 2008 NixOS:2011.1.0.1 11101 total (286 in the last 30 days) (no votes yet) [estimated by rule of succession] λ λ λ Docs uploaded by userBuild status unknown

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