135 lines
3.5 KiB
C
135 lines
3.5 KiB
C
/*=============================================================================
|
|
|
|
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 <gmp.h>
|
|
#include "flint.h"
|
|
#include "fmpz.h"
|
|
#include "fmpz_poly.h"
|
|
|
|
int
|
|
_fmpz_poly_sqrt_classical(fmpz * res, const fmpz * poly, slong len)
|
|
{
|
|
slong i, m;
|
|
int result;
|
|
|
|
/* the degree must be even */
|
|
if (len % 2 == 0)
|
|
return 0;
|
|
|
|
/* valuation must be even, and then can be reduced to 0 */
|
|
while (fmpz_is_zero(poly))
|
|
{
|
|
if (!fmpz_is_zero(poly + 1))
|
|
return 0;
|
|
|
|
fmpz_zero(res);
|
|
poly += 2;
|
|
len -= 2;
|
|
res++;
|
|
}
|
|
|
|
/* check whether a square root exists modulo 2 */
|
|
for (i = 1; i < len; i += 2)
|
|
if (!fmpz_is_even(poly + i))
|
|
return 0;
|
|
|
|
/* check endpoints */
|
|
if (!fmpz_is_square(poly) || (len > 1 && !fmpz_is_square(poly + len - 1)))
|
|
return 0;
|
|
|
|
/* square root of leading coefficient */
|
|
m = (len + 1) / 2;
|
|
fmpz_sqrt(res + m - 1, poly + len - 1);
|
|
result = 1;
|
|
|
|
/* do slong divison style 'square root with remainder' from top to bottom */
|
|
if (len > 1)
|
|
{
|
|
fmpz_t t, u;
|
|
fmpz * r;
|
|
|
|
fmpz_init(t);
|
|
fmpz_init(u);
|
|
r = _fmpz_vec_init(len);
|
|
_fmpz_vec_set(r, poly, len);
|
|
fmpz_mul_ui(u, res + m - 1, 2);
|
|
|
|
for (i = 1; i < m; i++)
|
|
{
|
|
fmpz_fdiv_qr(res + m - i - 1, t, r + len - i - 1, u);
|
|
if (!fmpz_is_zero(t))
|
|
{
|
|
result = 0;
|
|
break;
|
|
}
|
|
|
|
fmpz_mul_si(t, res + m - i - 1, -2);
|
|
_fmpz_vec_scalar_addmul_fmpz(r + len - 2*i, res + m - i, i - 1, t);
|
|
fmpz_submul(r + len - 2*i - 1, res + m - i - 1, res + m - i - 1);
|
|
}
|
|
|
|
for (i = m; i < len && result; i++)
|
|
if (!fmpz_is_zero(r + len - 1 - i))
|
|
result = 0;
|
|
|
|
_fmpz_vec_clear(r, len);
|
|
fmpz_clear(t);
|
|
fmpz_clear(u);
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
int
|
|
fmpz_poly_sqrt_classical(fmpz_poly_t b, const fmpz_poly_t a)
|
|
{
|
|
slong blen, len = a->length;
|
|
int result;
|
|
|
|
if (len % 2 == 0)
|
|
{
|
|
fmpz_poly_zero(b);
|
|
return len == 0;
|
|
}
|
|
|
|
if (b == a)
|
|
{
|
|
fmpz_poly_t tmp;
|
|
fmpz_poly_init(tmp);
|
|
result = fmpz_poly_sqrt_classical(tmp, a);
|
|
fmpz_poly_swap(b, tmp);
|
|
fmpz_poly_clear(tmp);
|
|
return result;
|
|
}
|
|
|
|
blen = len / 2 + 1;
|
|
fmpz_poly_fit_length(b, blen);
|
|
_fmpz_poly_set_length(b, blen);
|
|
result = _fmpz_poly_sqrt_classical(b->coeffs, a->coeffs, len);
|
|
if (!result)
|
|
_fmpz_poly_set_length(b, 0);
|
|
return result;
|
|
}
|