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/*
Copyright (C) 2009, 2010, 2015 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"
/*
Method of Niels Moller and Torbjorn Granlund, see "Improved Division by
Invariant Integers: (Algorithm 4)
https://gmplib.org/~tege/division-paper.pdf
*/
#define r_shift(in, c) (((c) == FLINT_BITS) ? WORD(0) : ((in) >> (c)))
ulong
n_ll_mod_preinv(ulong a_hi, ulong a_lo, ulong n, ulong ninv)
{
ulong q0, q1, r, norm;
FLINT_ASSERT(n != 0);
norm = flint_clz(n);
/* reduce a_hi modulo n */
if (a_hi >= n)
{
const ulong u1 = r_shift(a_hi, FLINT_BITS - norm);
const ulong u0 = (a_hi << norm);
n <<= norm;
umul_ppmm(q1, q0, ninv, u1);
add_ssaaaa(q1, q0, q1, q0, u1, u0);
a_hi = (u0 - (q1 + 1) * n);
if (a_hi > q0)
a_hi += n;
if (a_hi >= n)
a_hi -= n;
}
else
{
n <<= norm;
a_hi <<= norm;
}
/* now reduce the rest of the way */
{
const ulong u1 = a_hi + r_shift(a_lo, FLINT_BITS - norm);
const ulong u0 = (a_lo << norm);
umul_ppmm(q1, q0, ninv, u1);
add_ssaaaa(q1, q0, q1, q0, u1, u0);
r = (u0 - (q1 + 1) * n);
if (r > q0)
r += n;
return (r < n) ? (r >> norm) : ((r - n) >> norm);
}
}