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207 lines
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4 years ago
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<!-- This manual describes how to install and use the GNU multiple precision
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arithmetic library, version 6.1.0.
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Copyright 1991, 1993-2015 Free Software Foundation, Inc.
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Permission is granted to copy, distribute and/or modify this document under
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the terms of the GNU Free Documentation License, Version 1.3 or any later
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version published by the Free Software Foundation; with no Invariant Sections,
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with the Front-Cover Texts being "A GNU Manual", and with the Back-Cover
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Texts being "You have freedom to copy and modify this GNU Manual, like GNU
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software". A copy of the license is included in
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GNU Free Documentation License. -->
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<!-- Created by GNU Texinfo 6.4, http://www.gnu.org/software/texinfo/ -->
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<head>
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<title>References (GNU MP 6.1.0)</title>
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<meta name="description" content="How to install and use the GNU multiple precision arithmetic library, version 6.1.0.">
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<meta name="keywords" content="References (GNU MP 6.1.0)">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="index.html#Top" rel="up" title="Top">
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<link href="GNU-Free-Documentation-License.html#GNU-Free-Documentation-License" rel="next" title="GNU Free Documentation License">
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<body lang="en">
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<a name="References"></a>
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<div class="header">
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<p>
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Next: <a href="GNU-Free-Documentation-License.html#GNU-Free-Documentation-License" accesskey="n" rel="next">GNU Free Documentation License</a>, Previous: <a href="Contributors.html#Contributors" accesskey="p" rel="prev">Contributors</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="References-1"></a>
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<h2 class="appendix">Appendix B References</h2>
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<a name="index-References"></a>
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<a name="Books"></a>
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<h3 class="section">B.1 Books</h3>
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<ul>
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<li> Jonathan M. Borwein and Peter B. Borwein, “Pi and the AGM: A Study in
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Analytic Number Theory and Computational Complexity”, Wiley, 1998.
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</li><li> Richard Crandall and Carl Pomerance, “Prime Numbers: A Computational
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Perspective”, 2nd edition, Springer-Verlag, 2005.
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<a href="http://www.math.dartmouth.edu/~carlp/">http://www.math.dartmouth.edu/~carlp/</a>
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</li><li> Henri Cohen, “A Course in Computational Algebraic Number Theory”, Graduate
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Texts in Mathematics number 138, Springer-Verlag, 1993.
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<a href="http://www.math.u-bordeaux.fr/~cohen/">http://www.math.u-bordeaux.fr/~cohen/</a>
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</li><li> Donald E. Knuth, “The Art of Computer Programming”, volume 2,
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“Seminumerical Algorithms”, 3rd edition, Addison-Wesley, 1998.
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<a href="http://www-cs-faculty.stanford.edu/~knuth/taocp.html">http://www-cs-faculty.stanford.edu/~knuth/taocp.html</a>
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</li><li> John D. Lipson, “Elements of Algebra and Algebraic Computing”,
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The Benjamin Cummings Publishing Company Inc, 1981.
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</li><li> Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, “Handbook of
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Applied Cryptography”, <a href="http://www.cacr.math.uwaterloo.ca/hac/">http://www.cacr.math.uwaterloo.ca/hac/</a>
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</li><li> Richard M. Stallman and the GCC Developer Community, “Using the GNU Compiler
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Collection”, Free Software Foundation, 2008, available online
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<a href="https://gcc.gnu.org/onlinedocs/">https://gcc.gnu.org/onlinedocs/</a>, and in the GCC package
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<a href="https://ftp.gnu.org/gnu/gcc/">https://ftp.gnu.org/gnu/gcc/</a>
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</li></ul>
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<a name="Papers"></a>
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<h3 class="section">B.2 Papers</h3>
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<ul>
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<li> Yves Bertot, Nicolas Magaud and Paul Zimmermann, “A Proof of GMP Square
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Root”, Journal of Automated Reasoning, volume 29, 2002, pp. 225-252. Also
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available online as INRIA Research Report 4475, June 2002,
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<a href="http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf">http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf</a>
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</li><li> Christoph Burnikel and Joachim Ziegler, “Fast Recursive Division”,
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Max-Planck-Institut fuer Informatik Research Report MPI-I-98-1-022,
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<a href="http://data.mpi-sb.mpg.de/internet/reports.nsf/NumberView/1998-1-022">http://data.mpi-sb.mpg.de/internet/reports.nsf/NumberView/1998-1-022</a>
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</li><li> Torbjörn Granlund and Peter L. Montgomery, “Division by Invariant Integers
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using Multiplication”, in Proceedings of the SIGPLAN PLDI’94 Conference, June
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1994. Also available <a href="https://gmplib.org/~tege/divcnst-pldi94.pdf">https://gmplib.org/~tege/divcnst-pldi94.pdf</a>.
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</li><li> Niels Möller and Torbjörn Granlund, “Improved division by invariant
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integers”, IEEE Transactions on Computers, 11 June 2010.
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<a href="https://gmplib.org/~tege/division-paper.pdf">https://gmplib.org/~tege/division-paper.pdf</a>
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</li><li> Torbjörn Granlund and Niels Möller, “Division of integers large and
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small”, to appear.
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</li><li> Tudor Jebelean,
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“An algorithm for exact division”,
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Journal of Symbolic Computation,
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volume 15, 1993, pp. 169-180.
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Research report version available
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<a href="ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-35.ps.gz">ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-35.ps.gz</a>
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</li><li> Tudor Jebelean, “Exact Division with Karatsuba Complexity - Extended
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Abstract”, RISC-Linz technical report 96-31,
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<a href="ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-31.ps.gz">ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-31.ps.gz</a>
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</li><li> Tudor Jebelean, “Practical Integer Division with Karatsuba Complexity”,
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ISSAC 97, pp. 339-341. Technical report available
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<a href="ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-29.ps.gz">ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-29.ps.gz</a>
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</li><li> Tudor Jebelean, “A Generalization of the Binary GCD Algorithm”, ISSAC 93,
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pp. 111-116. Technical report version available
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<a href="ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-01.ps.gz">ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-01.ps.gz</a>
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</li><li> Tudor Jebelean, “A Double-Digit Lehmer-Euclid Algorithm for Finding the GCD
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of Long Integers”, Journal of Symbolic Computation, volume 19, 1995,
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pp. 145-157. Technical report version also available
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<a href="ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz">ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz</a>
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</li><li> Werner Krandick and Tudor Jebelean, “Bidirectional Exact Integer Division”,
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Journal of Symbolic Computation, volume 21, 1996, pp. 441-455. Early
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technical report version also available
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<a href="ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-50.ps.gz">ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-50.ps.gz</a>
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</li><li> Makoto Matsumoto and Takuji Nishimura, “Mersenne Twister: A 623-dimensionally
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equidistributed uniform pseudorandom number generator”, ACM Transactions on
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Modelling and Computer Simulation, volume 8, January 1998, pp. 3-30.
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Available online
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<a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.ps.gz">http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.ps.gz</a> (or .pdf)
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</li><li> R. Moenck and A. Borodin, “Fast Modular Transforms via Division”,
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Proceedings of the 13th Annual IEEE Symposium on Switching and Automata
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Theory, October 1972, pp. 90-96. Reprinted as “Fast Modular Transforms”,
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Journal of Computer and System Sciences, volume 8, number 3, June 1974,
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pp. 366-386.
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</li><li> Niels Möller, “On Schönhage’s algorithm and subquadratic integer GCD
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computation”, in Mathematics of Computation, volume 77, January 2008, pp.
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589-607.
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</li><li> Peter L. Montgomery, “Modular Multiplication Without Trial Division”, in
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Mathematics of Computation, volume 44, number 170, April 1985.
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</li><li> Arnold Schönhage and Volker Strassen, “Schnelle Multiplikation grosser
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Zahlen”, Computing 7, 1971, pp. 281-292.
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</li><li> Kenneth Weber, “The accelerated integer GCD algorithm”,
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ACM Transactions on Mathematical Software,
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volume 21, number 1, March 1995, pp. 111-122.
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</li><li> Paul Zimmermann, “Karatsuba Square Root”, INRIA Research Report 3805,
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November 1999, <a href="http://hal.inria.fr/inria-00072854/PDF/RR-3805.pdf">http://hal.inria.fr/inria-00072854/PDF/RR-3805.pdf</a>
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</li><li> Paul Zimmermann, “A Proof of GMP Fast Division and Square Root
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Implementations”,
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<a href="http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz">http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz</a>
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</li><li> Dan Zuras, “On Squaring and Multiplying Large Integers”, ARITH-11: IEEE
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Symposium on Computer Arithmetic, 1993, pp. 260 to 271. Reprinted as “More
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on Multiplying and Squaring Large Integers”, IEEE Transactions on Computers,
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volume 43, number 8, August 1994, pp. 899-908.
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</li></ul>
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<hr>
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<div class="header">
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<p>
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Next: <a href="GNU-Free-Documentation-License.html#GNU-Free-Documentation-License" accesskey="n" rel="next">GNU Free Documentation License</a>, Previous: <a href="Contributors.html#Contributors" accesskey="p" rel="prev">Contributors</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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