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