Computer Science – Logic in Computer Science
Scientific paper
2011-05-13
Proceedings of CICM11, vol 6824, Springer LNAI, 90-106, 2011
Computer Science
Logic in Computer Science
Proceedings of CICM11, Springer LNAI, 2011
Scientific paper
10.1007/978-3-642-22673-1_7
Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. We provide an implementation of the exact real numbers in the Coq proof assistant. This improves on the earlier Coq-implementation by O'Connor in two ways: we use dyadic rationals built from the machine integers and we optimize computation of power series by using approximate division. Moreover, we use type classes for clean mathematical interfaces. This appears to be the first time that type classes are used in heavy computation. We obtain over a 100 times speed up of the basic operations and indications for improving the Coq system.
Krebbers Robbert
Spitters Bas
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