Real Analysis

• Corky: Mantissa, Exponent Performance
  • Exact Real Arithmetic: A Case Study in High Order Programming: 1986
  • Exact Real Arithmetic: Formulating Real Numbers as Functions: 1993
  • Constructive Reals Calculator by Hans-J. Boehm at SGI: 1999
• Jean Vuillemin: Continued Fractions
  • Exact_Real_Computer_Arithmetic_with_Continued_Fractions: 1988
• Walerie_Menissier_Morain: B-adic Stream
  • Arbitrary_precision_real_arithmetic_design_and_algorithms: 1995
• Abbas Edalat & Peter John Potts Linear Fractional Transformation
  • Semantics of Exact Real Arithmetic: 1997
  • Exact_Real_Computer_Arithmetic: 1997
  • A_New_Representation_for_Exact_Real_Numbers: 1998
• Reinhold Heckmann Linear Fractional Transformation
  • Contractivity_of_linear_fractional_transformations: 1998
  • The_apprearance_of_Big_integers_in_exact_real_arithmetic_based_on_linear_fractional_transformations: 1998
• Dave Plume Signed Binary Digit & Dyadic Rational
  • A Calculator for Exact Real Number Computation: 1998 (pdf version)
• Alex K. Simpson: Functional Operations
  • Lazy_Functional_Algorithms_for_Exact_Real_Functionls: 1998
• Pietro Di Gianantonio
  • Lazy Algorithms for Exact Real Arithmetic: 2004
• Branimir Lambov
  • Implementing Efficient Exact Real Arithmetic: 2005
• Russell Connor: Coq
  • Few Digits: 2008
• RealLib C++
  • Branimir Lambov RealLib_An_Efficient_Implementation_of_Exact_Real_Arithmetic: 2006
• iRRAM C++
  • Norbert Th Muller The_iRRAM_Exact_Arithmetic_in_C: 2001
• Keith Briggs XRC C
• GMP: GNU Multiple Precision Arithmetic, BigNum^?
• Colin Percival
  • Rapid Multiplication Modulo the Sum and Difference of Highly Composite Numbers: 2002
  • Error Bounds on Complex Floating-point Multiplication: 2007
• John Robert Harrison
  • Theorem Proving with the Real Numbers
• Arash Hariri and Arash Reyhani-Masoleh
  • Bit-Serial and Bit-Parallel Montgomery Multiplication and Squaring over GF(2^m)