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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) 2012 Fredrik Johansson
******************************************************************************/
#include "flint.h"
#include "nmod_poly.h"
static __inline__
int _nmod_poly_sqrt_2(mp_ptr s, mp_srcptr p, slong len)
{
slong i;
for (i = 1; i < len; i += 2)
if (p[i] != 0)
return 0;
for (i = 0; i < len; i += 2)
s[i / 2] = p[i];
return 1;
}
int
_nmod_poly_sqrt(mp_ptr s, mp_srcptr p, slong len, nmod_t mod)
{
slong slen;
int result;
mp_ptr t;
mp_limb_t c, d;
if (len % 2 == 0)
return len == 0;
if (mod.n == 2)
return _nmod_poly_sqrt_2(s, p, len);
/* valuation must be even, and then can be reduced to 0 */
while (p[0] == 0)
{
if (p[1] != 0)
return 0;
s[0] = 0;
p += 2;
len -= 2;
s++;
}
c = d = p[0];
if (c != 1)
{
c = n_sqrtmod(c, mod.n);
if (c == 0)
return 0;
}
if (len == 1)
{
s[0] = c;
return 1;
}
slen = len / 2 + 1;
t = _nmod_vec_init(len);
if (c == 1)
_nmod_poly_sqrt_series(s, p, slen, mod);
else
{
_nmod_vec_scalar_mul_nmod(t, p, slen, n_invmod(d, mod.n), mod);
_nmod_poly_sqrt_series(s, t, slen, mod);
}
if (c != 1)
_nmod_vec_scalar_mul_nmod(s, s, slen, c, mod);
_nmod_poly_mulhigh(t, s, slen, s, slen, slen, mod);
result = _nmod_vec_equal(t + slen, p + slen, len - slen);
_nmod_vec_clear(t);
return result;
}
int
nmod_poly_sqrt(nmod_poly_t b, const nmod_poly_t a)
{
slong blen, len = a->length;
int result;
if (len % 2 == 0)
{
nmod_poly_zero(b);
return len == 0;
}
if (b == a)
{
nmod_poly_t tmp;
nmod_poly_init_preinv(tmp, a->mod.n, a->mod.ninv);
result = nmod_poly_sqrt(tmp, a);
nmod_poly_swap(b, tmp);
nmod_poly_clear(tmp);
return result;
}
blen = len / 2 + 1;
nmod_poly_fit_length(b, blen);
b->length = blen;
result = _nmod_poly_sqrt(b->coeffs, a->coeffs, len, a->mod);
if (!result)
b->length = 0;
return result;
}
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