/*=============================================================================

    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
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    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

******************************************************************************/

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    Quadratic sieve

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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.