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)
Optimizing programs over the constructive reals
PLDI '90 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation
Cache behavior of combinator graph reduction
ACM Transactions on Programming Languages and Systems (TOPLAS)
HOPL-II The second ACM SIGPLAN conference on History of programming languages
A Survey of Exact Arithmetic Implementations
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Real PCF extended with integration
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Computational Economics
History of programming languages---II
Certified Computer Algebra on Top of an Interactive Theorem Prover
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Lazy Algorithms for Exact Real Arithmetic
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.00 |
We introduce a representation of the computable real numbers by continued fractions. This deals with the subtle points of undecidable comparison an 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, as well as a wide class of special functions. A prototype system has been implemented in LeLisp, and the performance of these algorithms is promising.