344 lines
6.8 KiB
C
344 lines
6.8 KiB
C
/* Reference mpz functions.
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Copyright 1997, 1999-2002 Free Software Foundation, Inc.
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This file is part of the GNU MP Library test suite.
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The GNU MP Library test suite is free software; you can redistribute it
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and/or modify it under the terms of the GNU General Public License as
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published by the Free Software Foundation; either version 3 of the License,
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or (at your option) any later version.
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The GNU MP Library test suite is distributed in the hope that it will be
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useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
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Public License for more details.
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You should have received a copy of the GNU General Public License along with
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the GNU MP Library test suite. If not, see https://www.gnu.org/licenses/. */
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/* always do assertion checking */
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#define WANT_ASSERT 1
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#include <stdio.h>
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#include <stdlib.h> /* for free */
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#include "gmp-impl.h"
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#include "longlong.h"
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#include "tests.h"
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/* Change this to "#define TRACE(x) x" for some traces. */
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#define TRACE(x)
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/* FIXME: Shouldn't use plain mpz functions in a reference routine. */
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void
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refmpz_combit (mpz_ptr r, unsigned long bit)
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{
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if (mpz_tstbit (r, bit))
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mpz_clrbit (r, bit);
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else
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mpz_setbit (r, bit);
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}
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unsigned long
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refmpz_hamdist (mpz_srcptr x, mpz_srcptr y)
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{
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mp_size_t xsize, ysize, tsize;
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mp_ptr xp, yp;
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unsigned long ret;
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if ((SIZ(x) < 0 && SIZ(y) >= 0)
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|| (SIZ(y) < 0 && SIZ(x) >= 0))
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return ULONG_MAX;
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xsize = ABSIZ(x);
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ysize = ABSIZ(y);
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tsize = MAX (xsize, ysize);
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xp = refmpn_malloc_limbs (tsize);
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refmpn_zero (xp, tsize);
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refmpn_copy (xp, PTR(x), xsize);
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yp = refmpn_malloc_limbs (tsize);
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refmpn_zero (yp, tsize);
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refmpn_copy (yp, PTR(y), ysize);
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if (SIZ(x) < 0)
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refmpn_neg (xp, xp, tsize);
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if (SIZ(x) < 0)
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refmpn_neg (yp, yp, tsize);
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ret = refmpn_hamdist (xp, yp, tsize);
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free (xp);
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free (yp);
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return ret;
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}
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void
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refmpz_gcd (mpz_ptr g, mpz_srcptr a_orig, mpz_srcptr b_orig)
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{
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mp_bitcnt_t a_twos, b_twos, common_twos;
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mpz_t a;
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mpz_t b;
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mpz_init (a);
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mpz_init (b);
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mpz_abs (a, a_orig);
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mpz_abs (b, b_orig);
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if (mpz_sgn (a) == 0)
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{
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mpz_set (g, b);
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return;
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}
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if (mpz_sgn (b) == 0)
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{
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mpz_set (g, a);
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return;
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}
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a_twos = mpz_scan1 (a, 0);
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mpz_tdiv_q_2exp (a, a, a_twos);
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b_twos = mpz_scan1 (b, 0);
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mpz_tdiv_q_2exp (b, b, b_twos);
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common_twos = MIN(a_twos, b_twos);
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for (;;)
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{
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int c;
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mp_bitcnt_t twos;
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c = mpz_cmp (a, b);
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if (c == 0)
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break;
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if (c < 0)
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mpz_swap (a, b);
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mpz_sub (a, a, b);
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twos = mpz_scan1 (a, 0);
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mpz_tdiv_q_2exp (a, a, twos);
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}
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mpz_mul_2exp (g, a, common_twos);
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mpz_clear (a);
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mpz_clear (b);
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}
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/* (0/b), with mpz b; is 1 if b=+/-1, 0 otherwise */
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#define JACOBI_0Z(b) JACOBI_0LS (PTR(b)[0], SIZ(b))
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/* (a/b) effect due to sign of b: mpz/mpz */
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#define JACOBI_BSGN_ZZ_BIT1(a, b) JACOBI_BSGN_SS_BIT1 (SIZ(a), SIZ(b))
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/* (a/b) effect due to sign of a: mpz/unsigned-mpz, b odd;
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is (-1/b) if a<0, or +1 if a>=0 */
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#define JACOBI_ASGN_ZZU_BIT1(a, b) JACOBI_ASGN_SU_BIT1 (SIZ(a), PTR(b)[0])
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int
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refmpz_kronecker (mpz_srcptr a_orig, mpz_srcptr b_orig)
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{
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unsigned long twos;
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mpz_t a, b;
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int result_bit1 = 0;
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if (mpz_sgn (b_orig) == 0)
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return JACOBI_Z0 (a_orig); /* (a/0) */
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if (mpz_sgn (a_orig) == 0)
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return JACOBI_0Z (b_orig); /* (0/b) */
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if (mpz_even_p (a_orig) && mpz_even_p (b_orig))
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return 0;
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if (mpz_cmp_ui (b_orig, 1) == 0)
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return 1;
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mpz_init_set (a, a_orig);
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mpz_init_set (b, b_orig);
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if (mpz_sgn (b) < 0)
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{
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result_bit1 ^= JACOBI_BSGN_ZZ_BIT1 (a, b);
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mpz_neg (b, b);
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}
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if (mpz_even_p (b))
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{
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twos = mpz_scan1 (b, 0L);
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mpz_tdiv_q_2exp (b, b, twos);
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(a)[0]);
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}
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if (mpz_sgn (a) < 0)
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{
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result_bit1 ^= JACOBI_N1B_BIT1 (PTR(b)[0]);
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mpz_neg (a, a);
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}
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if (mpz_even_p (a))
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{
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twos = mpz_scan1 (a, 0L);
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mpz_tdiv_q_2exp (a, a, twos);
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(b)[0]);
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}
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for (;;)
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{
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ASSERT (mpz_odd_p (a));
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ASSERT (mpz_odd_p (b));
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ASSERT (mpz_sgn (a) > 0);
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ASSERT (mpz_sgn (b) > 0);
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TRACE (printf ("top\n");
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mpz_trace (" a", a);
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mpz_trace (" b", b));
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if (mpz_cmp (a, b) < 0)
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{
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TRACE (printf ("swap\n"));
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mpz_swap (a, b);
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result_bit1 ^= JACOBI_RECIP_UU_BIT1 (PTR(a)[0], PTR(b)[0]);
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}
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if (mpz_cmp_ui (b, 1) == 0)
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break;
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mpz_sub (a, a, b);
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TRACE (printf ("sub\n");
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mpz_trace (" a", a));
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if (mpz_sgn (a) == 0)
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goto zero;
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twos = mpz_scan1 (a, 0L);
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mpz_fdiv_q_2exp (a, a, twos);
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TRACE (printf ("twos %lu\n", twos);
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mpz_trace (" a", a));
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result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(b)[0]);
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}
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mpz_clear (a);
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mpz_clear (b);
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return JACOBI_BIT1_TO_PN (result_bit1);
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zero:
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mpz_clear (a);
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mpz_clear (b);
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return 0;
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}
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/* Same as mpz_kronecker, but ignoring factors of 2 on b */
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int
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refmpz_jacobi (mpz_srcptr a, mpz_srcptr b)
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{
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ASSERT_ALWAYS (mpz_sgn (b) > 0);
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ASSERT_ALWAYS (mpz_odd_p (b));
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return refmpz_kronecker (a, b);
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}
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/* Legendre symbol via powm. p must be an odd prime. */
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int
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refmpz_legendre (mpz_srcptr a, mpz_srcptr p)
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{
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int res;
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mpz_t r;
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mpz_t e;
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ASSERT_ALWAYS (mpz_sgn (p) > 0);
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ASSERT_ALWAYS (mpz_odd_p (p));
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mpz_init (r);
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mpz_init (e);
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mpz_fdiv_r (r, a, p);
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mpz_set (e, p);
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mpz_sub_ui (e, e, 1);
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mpz_fdiv_q_2exp (e, e, 1);
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mpz_powm (r, r, e, p);
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/* Normalize to a more or less symmetric range around zero */
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if (mpz_cmp (r, e) > 0)
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mpz_sub (r, r, p);
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ASSERT_ALWAYS (mpz_cmpabs_ui (r, 1) <= 0);
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res = mpz_sgn (r);
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mpz_clear (r);
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mpz_clear (e);
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return res;
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}
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int
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refmpz_kronecker_ui (mpz_srcptr a, unsigned long b)
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{
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mpz_t bz;
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int ret;
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mpz_init_set_ui (bz, b);
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ret = refmpz_kronecker (a, bz);
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mpz_clear (bz);
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return ret;
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}
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int
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refmpz_kronecker_si (mpz_srcptr a, long b)
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{
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mpz_t bz;
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int ret;
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mpz_init_set_si (bz, b);
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ret = refmpz_kronecker (a, bz);
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mpz_clear (bz);
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return ret;
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}
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int
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refmpz_ui_kronecker (unsigned long a, mpz_srcptr b)
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{
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mpz_t az;
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int ret;
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mpz_init_set_ui (az, a);
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ret = refmpz_kronecker (az, b);
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mpz_clear (az);
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return ret;
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}
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int
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refmpz_si_kronecker (long a, mpz_srcptr b)
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{
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mpz_t az;
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int ret;
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mpz_init_set_si (az, a);
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ret = refmpz_kronecker (az, b);
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mpz_clear (az);
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return ret;
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}
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void
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refmpz_pow_ui (mpz_ptr w, mpz_srcptr b, unsigned long e)
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{
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mpz_t s, t;
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unsigned long i;
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mpz_init_set_ui (t, 1L);
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mpz_init_set (s, b);
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if ((e & 1) != 0)
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mpz_mul (t, t, s);
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for (i = 2; i <= e; i <<= 1)
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{
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mpz_mul (s, s, s);
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if ((i & e) != 0)
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mpz_mul (t, t, s);
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}
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mpz_set (w, t);
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mpz_clear (s);
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mpz_clear (t);
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}
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