pqc/external/flint-2.4.3/qsieve/doc/qsieve.txt
2014-05-24 23:16:06 +02:00

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/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 William Hart
******************************************************************************/
*******************************************************************************
Quadratic sieve
*******************************************************************************
mp_limb_t qsieve_ll_factor(mp_limb_t hi, mp_limb_t lo)
Given an integer \code{n = (hi, lo)} find a factor and return it.
If a tiny factor is encountered, this is returned very quickly.
Otherwise the quadratic sieve algorithm is employed. The algorithm
requires that $n$ not be prime and not be a perfect power. There is
also a limit to the size of $n$. During the algorithm $n$ will be
multiplied by a small multiplier $k$ (from 1 to 47). The product
$kn$ must fit in two limbs. If not the algorithm will silently
fail, returning 0. Otherwise a factor of $n$ which fits in a single
limb will be returned.