AERN-Real: datatypes and abstractions for approximating exact real numbers

[ bsd3, data, deprecated, library, math ] [ Propose Tags ]
Deprecated. in favor of aern2-mp, aern2-real
Versions 0.9.0, 0.9.1, 0.9.2, 0.9.3,, 0.9.4, 0.9.5, 0.9.6,, 0.9.7,,, 0.9.8, 0.9.9, 0.10.0,,, 2011.1, 2011.1.0.1
Dependencies base, binary (>=0.4), containers, haskell98 [details]
License BSD-3-Clause
Copyright (c) 2007-2008 Michal Konecny, Amin Farjudian, Jan Duracz
Author Michal Konecny
Maintainer Michal Konecny
Category Data, Math
Uploaded by MichalKonecny at Fri Jul 11 17:46:26 UTC 2008
Distributions NixOS:2011.1.0.1
Downloads 9832 total (93 in the last 30 days)
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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:

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.





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