137 lines
3.1 KiB
C
137 lines
3.1 KiB
C
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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#include "flint.h"
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#include "nmod_poly.h"
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static __inline__
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int _nmod_poly_sqrt_2(mp_ptr s, mp_srcptr p, slong len)
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{
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slong i;
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for (i = 1; i < len; i += 2)
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if (p[i] != 0)
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return 0;
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for (i = 0; i < len; i += 2)
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s[i / 2] = p[i];
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return 1;
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}
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int
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_nmod_poly_sqrt(mp_ptr s, mp_srcptr p, slong len, nmod_t mod)
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{
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slong slen;
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int result;
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mp_ptr t;
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mp_limb_t c, d;
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if (len % 2 == 0)
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return len == 0;
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if (mod.n == 2)
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return _nmod_poly_sqrt_2(s, p, len);
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/* valuation must be even, and then can be reduced to 0 */
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while (p[0] == 0)
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{
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if (p[1] != 0)
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return 0;
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s[0] = 0;
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p += 2;
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len -= 2;
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s++;
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}
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c = d = p[0];
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if (c != 1)
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{
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c = n_sqrtmod(c, mod.n);
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if (c == 0)
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return 0;
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}
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if (len == 1)
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{
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s[0] = c;
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return 1;
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}
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slen = len / 2 + 1;
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t = _nmod_vec_init(len);
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if (c == 1)
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_nmod_poly_sqrt_series(s, p, slen, mod);
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else
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{
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_nmod_vec_scalar_mul_nmod(t, p, slen, n_invmod(d, mod.n), mod);
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_nmod_poly_sqrt_series(s, t, slen, mod);
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}
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if (c != 1)
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_nmod_vec_scalar_mul_nmod(s, s, slen, c, mod);
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_nmod_poly_mulhigh(t, s, slen, s, slen, slen, mod);
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result = _nmod_vec_equal(t + slen, p + slen, len - slen);
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_nmod_vec_clear(t);
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return result;
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}
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int
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nmod_poly_sqrt(nmod_poly_t b, const nmod_poly_t a)
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{
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slong blen, len = a->length;
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int result;
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if (len % 2 == 0)
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{
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nmod_poly_zero(b);
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return len == 0;
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}
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if (b == a)
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{
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nmod_poly_t tmp;
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nmod_poly_init_preinv(tmp, a->mod.n, a->mod.ninv);
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result = nmod_poly_sqrt(tmp, a);
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nmod_poly_swap(b, tmp);
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nmod_poly_clear(tmp);
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return result;
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}
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blen = len / 2 + 1;
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nmod_poly_fit_length(b, blen);
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b->length = blen;
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result = _nmod_poly_sqrt(b->coeffs, a->coeffs, len, a->mod);
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if (!result)
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b->length = 0;
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return result;
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}
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