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/*
Copyright (C) 2009, 2010, 2012, 2016 William Hart
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ulong_extras.h"
ulong
n_mulmod_preinv(ulong a, ulong b, ulong n, ulong ninv, ulong norm)
{
ulong q0, q1, r, p_hi, p_lo;
/* check normalisation */
FLINT_ASSERT((n & (UWORD(1) << (FLINT_BITS - 1))) != 0);
FLINT_ASSERT(a < n);
FLINT_ASSERT(b < n);
FLINT_ASSERT(n != 0);
/* renormalise product */
a >>= norm;
/* multiply */
umul_ppmm(p_hi, p_lo, a, b);
/* reduce mod n */
{
umul_ppmm(q1, q0, ninv, p_hi);
add_ssaaaa(q1, q0, q1, q0, p_hi, p_lo);
r = (p_lo - (q1 + 1) * n);
if (r > q0)
r += n;
return (r < n ? r : r - n);
}
}