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/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2009 William Hart
Copyright (C) 2011 Sebastian Pancratz
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
mp_limb_t n_sqrtmod(mp_limb_t a, mp_limb_t p)
{
slong i, r, m;
mp_limb_t p1, k, b, g, bpow, gpow, res;
mp_limb_t pinv;
if (a <= 1)
{
return a;
}
pinv = n_preinvert_limb(p);
if (n_jacobi_unsigned(a, p) == -1)
return 0;
if ((p & UWORD(3)) == 3)
{
return n_powmod2_ui_preinv(a, (p + 1) / 4, p, pinv);
}
r = 0;
p1 = p - 1;
do {
p1 >>= UWORD(1);
r++;
} while ((p1 & UWORD(1)) == 0);
b = n_powmod2_ui_preinv(a, p1, p, pinv);
for (k = 2; ; k++)
{
if (n_jacobi_unsigned(k, p) == -1) break;
}
g = n_powmod2_ui_preinv(k, p1, p, pinv);
res = n_powmod2_ui_preinv(a, (p1 + 1) / 2, p, pinv);
while (b != 1)
{
bpow = b;
m = 0;
do
{
bpow = n_mulmod2_preinv(bpow, bpow, p, pinv);
m++;
} while (m < r && bpow != 1);
gpow = g;
for (i = 1; i < r - m; i++)
{
gpow = n_mulmod2_preinv(gpow, gpow, p, pinv);
}
res = n_mulmod2_preinv(res, gpow, p, pinv);
g = n_mulmod2_preinv(gpow, gpow, p, pinv);
b = n_mulmod2_preinv(b, g, p, pinv);
r = m;
}
return res;
}
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