Constructive real interpretation of numerical programs
SIGPLAN '87 Papers of the Symposium on Interpreters and interpretive techniques
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
Lazy computation with exact real numbers
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Contractivity of linear fractional transformations
Theoretical Computer Science
The continuum as a final coalgebra
Theoretical Computer Science
Real number computation through gray code embedding
Theoretical Computer Science
Some Characterizations of Functions Computable in On-Line Arithmetic
IEEE Transactions on Computers
Equality in computer algebra and beyond
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Numerical Integration with Exact Real Arithmetic
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Static Analyses of the Precision of Floating-Point Operations
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
On Termination of Logic Programs with Floating Point Computations
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
Computing a Required Absolute Precision from a Stream of Linear Fractional Transformations
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Real functions incrementally computable by finite automata
Theoretical Computer Science - Mathematical foundations of programming semantics
Termination of Floating-Point Computations
Journal of Automated Reasoning
Theoretical Computer Science - Real numbers and computers
Implementing exact real arithmetic in python, C++ and C
Theoretical Computer Science - Real numbers and computers
Metamorphisms: Streaming representation-changers
Science of Computer Programming
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Exact arithmetic on the Stern-Brocot tree
Journal of Discrete Algorithms
Useful computations need useful numbers
ACM Communications in Computer Algebra
Efficient exact arithmetic over constructive reals
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Coinductive correctness of homographic and quadratic algorithms for exact real numbers
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Finite state transducers for modular möbius number systems
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
| Hi-index | 14.99 |
A representation of the computable real numbers by continued fractions is introduced. This representation deals with the subtle points of undecidable comparison and integer division, as well as representing the infinite 1/0 and undefined 0/0 numbers. Two general algorithms for performing arithmetic operations are introduced. The algebraic algorithm, which computes sums and products of continued fractions as a special case, basically operates in a positional manner, producing one term of output for each term of input. The transcendental algorithm uses a general formula of Gauss to compute the continued fractions of exponentials, logarithms, trigonometric functions, and a wide class of special functions. A prototype system has been implemented in LeLisp and the performance of these algorithms is promising.