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Fixed Precision Patterns for the Formal Verification of Mathematical Constant Approximations

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Yves BertotAuthors Info & Claims

CPP '15: Proceedings of the 2015 Conference on Certified Programs and Proofs

Pages 147 - 155

https://doi.org/10.1145/2676724.2693172

Published: 13 January 2015 Publication History

Abstract

We describe two approaches for the computation of mathematical constant approximations inside interactive theorem provers. These two approaches share the same basis of fixed point computation and differ only in the way the proofs of correctness of the approximations are described. The first approach performs interval computations, while the second approach relies on bounding errors, for example with the help of derivatives. As an illustration, we show how to describe good approximations of the logarithm function and we compute -- to a precision of a million decimals inside the proof system, with a guarantee that all digits up to the millionth decimal are correct. All these experiments are performed with the Coq system, but most of the steps should apply to any interactive theorem prover.

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Cited By

Bertot YRideau LThéry L(2018)Distant Decimals of $$\pi $$źJournal of Automated Reasoning10.1007/s10817-017-9444-261:1-4(33-71)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1007/s10817-017-9444-2
Murphy CGray PStewart GShpeisman TGottschlich J(2017)Verified perceptron convergence theoremProceedings of the 1st ACM SIGPLAN International Workshop on Machine Learning and Programming Languages10.1145/3088525.3088673(43-50)Online publication date: 18-Jun-2017
https://dl.acm.org/doi/10.1145/3088525.3088673

Index Terms

Fixed Precision Patterns for the Formal Verification of Mathematical Constant Approximations
1. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Program specifications

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cover image ACM Conferences

CPP '15: Proceedings of the 2015 Conference on Certified Programs and Proofs

January 2015

192 pages

ISBN:9781450332965

DOI:10.1145/2676724

Program Chairs:
Xavier Leroy
Inria Paris-Rocquencourt, France
,
Alwen Tiu
Nanyang Technological University, Singapore

Copyright © 2015 ACM.

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Published: 13 January 2015

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POPL '15: The 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 13 - 14, 2015

Mumbai, India

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Overall Acceptance Rate 18 of 26 submissions, 69%

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Cited By

Bertot YRideau LThéry L(2018)Distant Decimals of $$\pi $$źJournal of Automated Reasoning10.1007/s10817-017-9444-261:1-4(33-71)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1007/s10817-017-9444-2
Murphy CGray PStewart GShpeisman TGottschlich J(2017)Verified perceptron convergence theoremProceedings of the 1st ACM SIGPLAN International Workshop on Machine Learning and Programming Languages10.1145/3088525.3088673(43-50)Online publication date: 18-Jun-2017
https://dl.acm.org/doi/10.1145/3088525.3088673

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