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# Floating-point numbers

Version 0.6.2

29/08/2014

MPFR- and CXSC-based library for GAP

Laurent Bartholdi
Email: laurent dot bartholdi at gmail dot com
Homepage: http://www.uni-math.gwdg.de/laurent/

Address:
Mathematisches Institut
Bunsenstraße 3-5
D-37073 Göttingen
Germany

### Abstract

This document describes the package Float, which implements in GAP arbitrary-precision floating-point numbers.

The computer algebra system GAP is available at http://gap-system.org.

This documentation for Float is available at http://laurentbartholdi.github.com/float/manual.pdf in PDF format, and may be accessed online at http://laurentbartholdi.github.com/float/.

The latest release of the package may be downloaded as http://www.uni-math.gwdg.de/laurent/archive/float-0.6.2.tar.gz (tar, gzipped). The latest repository version (possibly unstable) may be downloaded as https://github.com/laurentbartholdi/float/tarball/master (tar, gzipped), https://github.com/laurentbartholdi/float.git (git repository), or explored at https://github.com/laurentbartholdi/float/tree/master/.

For comments or questions on Float please contact the author.

### Copyright

© 2011-2014 by Laurent Bartholdi

### Acknowledgements

Part of this work is supported by the "Swiss National Fund for Scientific Research (SNF)", the "German National Science Foundation (DFG)", and the Courant Research Centre "Higher Order Structures" of the University of Göttingen.

### Contents

1 Licensing
2 Float package
2.1 A sample run
3 Polynomials
3.1 The Floats pseudo-field
3.2 Roots of polynomials
3.3 Finding integer relations
3.3-1 PSLQ
3.4 LLL lattice reduction
4 Implemented packages
4.1 MPFR
4.1-1 IsMPFRFloat
4.2 MPFI
4.2-1 IsMPFIFloat
4.3 MPC
4.3-1 IsMPCFloat
4.4 CXSC
4.4-1 IsCXSCReal
4.5 FPLLL
4.5-1 FPLLLReducedBasis
4.5-2 FPLLLShortestVector
References
Index
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