References
**********
Books
=====
* Henri Cohen, "A Course in Computational Algebraic Number Theory",
Graduate Texts in Mathematics number 138, Springer-Verlag, 1993.
`http://www.math.u-bordeaux.fr/~cohen'
* Donald E. Knuth, "The Art of Computer Programming", volume 2,
"Seminumerical Algorithms", 3rd edition, Addison-Wesley, 1998.
`http://www-cs-faculty.stanford.edu/~knuth/taocp.html'
* John D. Lipson, "Elements of Algebra and Algebraic Computing", The
Benjamin Cummings Publishing Company Inc, 1981.
* Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone,
"Handbook of Applied Cryptography",
`http://www.cacr.math.uwaterloo.ca/hac/'
* Richard M. Stallman, "Using and Porting GCC", Free Software
Foundation, 1999, available online
`http://www.gnu.org/software/gcc/onlinedocs/', and in the GCC
package `ftp://ftp.gnu.org/gnu/gcc/'
Papers
======
* Christoph Burnikel and Joachim Ziegler, "Fast Recursive Division",
Max-Planck-Institut fuer Informatik Research Report
MPI-I-98-1-022, `http://www.mpi-sb.mpg.de/~ziegler/TechRep.ps.gz'
* Torbjorn Granlund and Peter L. Montgomery, "Division by Invariant
Integers using Multiplication", in Proceedings of the SIGPLAN
PLDI'94 Conference, June 1994. Also available
`ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psa4.gz' (and .psl.gz).
* Peter L. Montgomery, "Modular Multiplication Without Trial
Division", in Mathematics of Computation, volume 44, number 170,
April 1985.
* Tudor Jebelean, "An algorithm for exact division", Journal of
Symbolic Computation, volume 15, 1993, pp. 169-180. Research
report version available
`ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-35.ps.gz'
* Tudor Jebelean, "Exact Division with Karatsuba Complexity -
Extended Abstract", RISC-Linz technical report 96-31,
`ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-31.ps.gz'
* Tudor Jebelean, "Practical Integer Division with Karatsuba
Complexity", ISSAC 97, pp. 339-341. Technical report available
`ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-29.ps.gz'
* Tudor Jebelean, "A Generalization of the Binary GCD Algorithm",
ISSAC 93, pp. 111-116. Technical report version available
`ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-01.ps.gz'
* Tudor Jebelean, "A Double-Digit Lehmer-Euclid Algorithm for
Finding the GCD of Long Integers", Journal of Symbolic
Computation, volume 19, 1995, pp. 145-157. Technical report
version also available
`ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz'
* Werner Krandick and Tudor Jebelean, "Bidirectional Exact Integer
Division", Journal of Symbolic Computation, volume 21, 1996, pp.
441-455. Early technical report version also available
`ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-50.ps.gz'
* R. Moenck and A. Borodin, "Fast Modular Transforms via Division",
Proceedings of the 13th Annual IEEE Symposium on Switching and
Automata Theory, October 1972, pp. 90-96. Reprinted as "Fast
Modular Transforms", Journal of Computer and System Sciences,
volume 8, number 3, June 1974, pp. 366-386.
* Arnold Scho"nhage and Volker Strassen, "Schnelle Multiplikation
grosser Zahlen", Computing 7, 1971, pp. 281-292.
* Kenneth Weber, "The accelerated integer GCD algorithm", ACM
Transactions on Mathematical Software, volume 21, number 1, March
1995, pp. 111-122.
* Paul Zimmermann, "Karatsuba Square Root", INRIA Research Report
3805, November 1999, `http://www.inria.fr/RRRT/RR-3805.html'
* Paul Zimmermann, "A Proof of GMP Fast Division and Square Root
Implementations",
`http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz'
* Dan Zuras, "On Squaring and Multiplying Large Integers", ARITH-11:
IEEE Symposium on Computer Arithmetic, 1993, pp. 260 to 271.
Reprinted as "More on Multiplying and Squaring Large Integers",
IEEE Transactions on Computers, volume 43, number 8, August 1994,
pp. 899-908.