Evaluating rational functions: infinite precision is finite cost and tractable on average
SIAM Journal on Computing
Subpolynomial complexity classes of real functions and real numbers
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Computability
On the continued fraction representation of computable real numbers
Theoretical Computer Science
An on-line arithmetic unit for bit-pipelined rational arithmetic
Journal of Parallel and Distributed Computing - Parallelism in Computer Arithmetic
Exact real computer arithmetic with continued fractions
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Optimizing programs over the constructive reals
PLDI '90 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation
An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic
IEEE Transactions on Computers
Algorithm 693: a FORTRAN package for floating-point multiple-precision arithmetic
ACM Transactions on Mathematical Software (TOMS)
Exact real arithmetic formulating real numbers as functions
Research topics in functional programming
Complexity theory of real functions
Complexity theory of real functions
Feasible real random access machines
Journal of Complexity
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
A Fortran Multiple-Precision Arithmetic Package
ACM Transactions on Mathematical Software (TOMS)
Computable analysis: an introduction
Computable analysis: an introduction
A Priori Worst Case Error Bounds for Floating-Point Computations
IEEE Transactions on Computers
Exact Real Arithmetic Systems: Results of Competition
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
The iRRAM: Exact Arithmetic in C++
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Theorem Proving with the Real Numbers
Theorem Proving with the Real Numbers
Exact Real Arithmetic Systems: Results of Competition
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Theoretical Computer Science - Real numbers and computers
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Algebraic Model of an Arithmetic Unit for TTE-Computable Normalized Rational Numbers
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Efficient exact arithmetic over constructive reals
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Exact exploration and hanging algorithms
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
The role of algebraic models and type-2 theory of effectivity in special purpose processor design
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Hi-index | 0.00 |
This paper provides a survey of practical systems for exact arithmetic. We describe some of the methods used in their implementation, and suggest reasons for the performance differences displayed by some of the competing systems at this years CCA Exact Arithmetic Competition.Because the practical aspects of the field of exact arithmetic are at an early stage, and many of the systems are prototypes, we have not discussed: portability, user-interfaces, and general usability. It is to be hoped that these aspects might be addressed by participants in any further competitions organised by the CCA committee.