RealLib: An efficient implementation of exact real arithmetic

This paper is an introduction to the RealLib package for exact real number computations. The library provides certified accuracy, but tries to achieve this at performance close to the performance of hardware floating point for problems that do not require higher precision. The paper gives the motivation and features of the design of the library and compares it with other packages for exact real arithmetic.

[1]  Oliver Aberth Precise Numerical Analysis with Disk , 1988 .

[2]  Tommy Färnqvist Number Theory Meets Cache Locality – Efficient Implementation of a Small Prime FFT for the GNU Multiple Precision Arithmetic Library , 2005 .

[3]  Oliver Aberth A precise numerical analysis program , 1974, CACM.

[4]  Branimir Lambov Complexity and Intensionality in a Type-1 Framework for Computable Analysis , 2005, CSL.

[5]  A. Grzegorczyk On the definitions of computable real continuous functions , 1957 .

[6]  Klaus Weihrauch,et al.  Computable Analysis: An Introduction , 2014, Texts in Theoretical Computer Science. An EATCS Series.

[7]  Xiaoye S. Li,et al.  Algorithms for quad-double precision floating point arithmetic , 2000, Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001.

[8]  Norbert Th. Müller,et al.  The iRRAM: Exact Arithmetic in C++ , 2000, CCA.

[9]  Abbas Edalat,et al.  A Domain-Theoretic Approach to Computability on the Real Line , 1999, Theor. Comput. Sci..

[10]  Keith Briggs,et al.  Implementing exact real arithmetic in python, C++ and C , 2006, Theor. Comput. Sci..

[11]  Kurt Mehlhorn,et al.  A Generalized and improved constructive separation bound for real algebraic expressions , 2000 .

[12]  Hans-Juergen Boehm,et al.  Optimizing programs over the constructive reals , 1990, PLDI '90.

[13]  Peter Hertling,et al.  Feasible Real Random Access Machines , 1998, J. Complex..

[14]  Marian Boykan Pour-El,et al.  Computability in analysis and physics , 1989, Perspectives in Mathematical Logic.

[15]  Oliver Aberth,et al.  Precise computation using range arithmetic, via C++ , 1992, TOMS.

[16]  Jens Blanck,et al.  Computability and complexity in analysis : 4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000 : selected papers , 2001 .

[17]  Ker-I Ko,et al.  Complexity Theory of Real Functions , 1991, Progress in Theoretical Computer Science.