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/*
Copyright (C) 2013, 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_powmod_ui_preinv(ulong a, ulong exp, ulong n, ulong ninv, ulong norm)
{
ulong x;
/* check normalisation */
FLINT_ASSERT((n & (UWORD(1) << (FLINT_BITS - 1))) != 0);
FLINT_ASSERT(a < n);
FLINT_ASSERT(n != 0);
if (exp == 0)
{
x = UWORD(1) << norm;
/* anything modulo 1 is 0 */
return x == n ? 0 : x;
}
if (a == 0)
return 0;
/* find first 1 in binary repn of exp */
while ((exp & 1) == 0)
{
a = n_mulmod_preinv(a, a, n, ninv, norm);
exp >>= 1;
}
x = a;
/* binary exponentiation */
while (exp >>= 1)
{
a = n_mulmod_preinv(a, a, n, ninv, norm);
if (exp & 1)
x = n_mulmod_preinv(x, a, n, ninv, norm);
}
return x;
}