michalkonecny/aern2

A Haskell library for Approximating Exact Real Numbers (AERN) based on interval computation. (aern2 is a rewrite of aern.)

AERN2

A set of Haskell packages for approximating exact real numbers and other validated numerical computation.

• A quick start
• Libraries
• Other components
• Significant dependencies
• Other references

A quick start

• Installation guide
• Examples in aern2-real README

Libraries

• aern2-mp: Multiple-precision interval arithmetic (fairly complete)

• aern2-real: Cauchy real numbers (fairly complete)

• aern2-fun: Generic operations for real functions

• aern2-fun-univariate: Continuous real functions of one variable and their polynomial enclosures (currently broken, working version on branch fnreps2020)

Other components

• aern2-erc: A prototype implementation of the language ERC (Exact Real Computation) as defined in Park, Sewon, et al. "Foundation of Computer (Algebra) ANALYSIS Systems: Semantics, Logic, Programming, Verification." arXiv e-prints (2016): arXiv-1608.

• aern2-fnreps: Benchmarks evaluating various representations of univariate continuous real functions (currently broken, working version on branch fnreps2020)

Significant dependencies

• collect-errors: Type wrapper CN for gracefully propagating numerical errors through expressions

• mixed-types-num: Bottom-up-typed numerical expressions

• cdar-mBound: Exact real arithmetic built on floating-point-like intervals based on Haskell Integers. AERN2 currently uses the types Dyadic and Approx.

Other references

• haskell-reals-comparison: Benchmark(s) comparing the performance of Haskell libraries for exact real computation (work in progress)