89 lines
2.5 KiB
C
89 lines
2.5 KiB
C
/*=============================================================================
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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) 2009, 2010 William Hart
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "ulong_extras.h"
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/*
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New method of Moller and Granlund
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see paper Improved Division by Invariant Integers (Torbjorn Granlund
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and Niels Moller) (preprint): (pp. 4)
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http://www.lysator.liu.se/~nisse/archive/draft-division-paper.pdf
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*/
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mp_limb_t
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n_lll_mod_preinv(mp_limb_t a_hi, mp_limb_t a_mi, mp_limb_t a_lo,
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mp_limb_t n, mp_limb_t ninv)
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{
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mp_limb_t q0, q1, r, norm;
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count_leading_zeros(norm, n);
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n <<= norm;
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/*
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we assume a_hi is already reduced
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first reduce a_hi, a_mi mod n
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*/
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{
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const mp_limb_t u1 = (a_hi << norm) + r_shift(a_mi, FLINT_BITS - norm);
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const mp_limb_t u0 = (a_mi << norm);
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umul_ppmm(q1, q0, ninv, u1);
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add_ssaaaa(q1, q0, q1, q0, u1, u0);
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r = (u0 - (q1 + 1) * n);
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if (r >= q0)
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r += n;
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if (r < n)
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a_mi = (r >> norm);
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else
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a_mi = ((r - n) >> norm);
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}
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/*
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now a_mid is reduced mod n
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so reduce a_mi, a_lo mod n
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*/
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{
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const mp_limb_t u1 = (a_mi << norm) + r_shift(a_lo, FLINT_BITS - norm);
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const mp_limb_t u0 = (a_lo << norm);
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umul_ppmm(q1, q0, ninv, u1);
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add_ssaaaa(q1, q0, q1, q0, u1, u0);
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r = (u0 - (q1 + 1) * n);
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if (r >= q0)
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r += n;
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if (r < n)
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return (r >> norm);
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else
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return ((r - n) >> norm);
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}
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}
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