174 lines
3.9 KiB
C
174 lines
3.9 KiB
C
/*=============================================================================
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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) 2009 William Hart
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Copyright (C) 2011 Sebastian Pancratz
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******************************************************************************/
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#include <gmp.h>
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#include "flint.h"
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#include "fmpz.h"
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#include "ulong_extras.h"
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/*
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Assumes that p is an odd prime, and that 0 <= a < p.
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Returns 1 if a is a quadratic residue and 0 otherwise.
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Does not support aliasing.
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*/
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static int _fmpz_sqrtmod(mpz_t rop, const mpz_t a, const mpz_t p)
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{
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slong i, r, m;
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mpz_t p1, k, exp, b, g, bpow, gpow;
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if (mpz_jacobi(a, p) == -1)
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return 0;
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if (flint_mpz_congruent_ui_p(p, 3, 4))
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{
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mpz_init(exp);
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flint_mpz_add_ui(exp, p, 1);
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mpz_tdiv_q_2exp(exp, exp, 2);
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mpz_powm(rop, a, exp, p);
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mpz_clear(exp);
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return 1;
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}
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mpz_init(p1);
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mpz_init(k);
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mpz_init(exp);
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mpz_init(b);
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mpz_init(g);
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mpz_init(bpow);
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mpz_init(gpow);
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r = 0;
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flint_mpz_sub_ui(p1, p, 1);
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do {
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mpz_tdiv_q_2exp(p1, p1, 1);
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r++;
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} while (mpz_even_p(p1));
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mpz_powm(b, a, p1, p);
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for (flint_mpz_set_ui(k, 2); ; flint_mpz_add_ui(k, k, 1))
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{
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if (mpz_jacobi(k, p) == -1) break;
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}
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mpz_powm(g, k, p1, p);
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flint_mpz_add_ui(exp, p1, 1);
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mpz_tdiv_q_2exp(exp, exp, 1);
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mpz_powm(rop, a, exp, p);
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while (flint_mpz_cmp_ui(b, 1))
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{
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mpz_set(bpow, b);
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m = 0;
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do
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{
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mpz_mul(bpow, bpow, bpow);
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mpz_mod(bpow, bpow, p);
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m++;
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} while (m < r && flint_mpz_cmp_ui(bpow, 1));
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mpz_set(gpow, g);
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for (i = 1; i < r - m; i++)
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{
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mpz_mul(gpow, gpow, gpow);
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mpz_mod(gpow, gpow, p);
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}
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mpz_mul(rop, rop, gpow);
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mpz_mod(rop, rop, p);
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mpz_mul(g, gpow, gpow);
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mpz_mod(g, g, p);
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mpz_mul(b, b, g);
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mpz_mod(b, b, p);
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r = m;
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}
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mpz_clear(p1);
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mpz_clear(k);
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mpz_clear(exp);
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mpz_clear(b);
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mpz_clear(g);
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mpz_clear(bpow);
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mpz_clear(gpow);
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return mpz_sgn(rop) ? 1 : 0;
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}
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int fmpz_sqrtmod(fmpz_t b, const fmpz_t a, const fmpz_t p)
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{
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if (b == a || b == p)
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{
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int ans;
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fmpz_t t;
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fmpz_init(t);
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ans = fmpz_sqrtmod(t, a, p);
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fmpz_swap(b, t);
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fmpz_clear(t);
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return ans;
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}
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fmpz_mod(b, a, p);
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if (fmpz_cmp_ui(b, 1) <= 0)
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{
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return 1;
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}
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if (!COEFF_IS_MPZ(*p)) /* p, and b are small */
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{
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mp_limb_t ans;
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ans = n_sqrtmod(*b, *p);
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if (ans)
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fmpz_set_ui(b, ans);
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return ans != 0;
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}
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else /* p is large */
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{
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int ans;
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mpz_t t;
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__mpz_struct *bptr;
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bptr = _fmpz_promote_val(b);
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mpz_init(t);
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ans = _fmpz_sqrtmod(t, bptr, COEFF_TO_PTR(*p));
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mpz_swap(bptr, t);
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mpz_clear(t);
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_fmpz_demote_val(b);
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return ans;
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}
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}
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