Arbitrary accuracy with variable precision arithmetic
Proceedings of the International Symposium on interval mathematics on Interval mathematics 1985
The program dependence graph and its use in optimization
ACM Transactions on Programming Languages and Systems (TOPLAS)
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Constructive real interpretation of numerical programs
SIGPLAN '87 Papers of the Symposium on Interpreters and interpretive techniques
Automatic translation of FORTRAN programs to vector form
ACM Transactions on Programming Languages and Systems (TOPLAS)
Exact real computer arithmetic with continued fractions
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Integrating noninterfering versions of programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
A precise numerical analysis program
Communications of the ACM
Precise Numerical Analysis with Disk
Precise Numerical Analysis with Disk
Using PVS to validate the algorithms of an exact arithmetic
Theoretical Computer Science - Real numbers and computers
A Survey of Exact Arithmetic Implementations
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
RealLib: An efficient implementation of exact real arithmetic
Mathematical Structures in Computer Science
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The constructive reals provide programmers with a useful mechanism for prototyping numerical programs, and for experimenting with numerical algorithms. Unfortunately, the performance of current implementations is inadequate for some potential applications. In particular, these implementations tend to be space inefficient, in that they essentially require a complete computation history to be maintained.Some numerical analysts (cf. [3]) propose that the programmer instead be provided with variable precision interval arithmetic, and then be required to write code to restart a computation when the intervals become too inaccurate. Though this model is no doubt appropriate at times, it is not an adequate replacement for exact arithmetic. The correct transformation from a program operating on the constructive reals to a reasonable program using iterated interval arithmetic can be nontrivial and error prone. Here we present a technique based on program slicing to both automate this process and reduce the amount of reexecution. Thus the programmer is still free to use the simpler abstraction of exact real arithmetic, but we can provide a more efficient interval arithmetic based implementation. Some preliminary empirical results are presented.