+++ /dev/null
-/* mpz_legendre (op1, op2).
- Contributed by Bennet Yee (bsy) at Carnegie-Mellon University
-
-Copyright (C) 1992, 1996 Free Software Foundation, Inc.
-
-This file is part of the GNU MP Library.
-
-The GNU MP Library is free software; you can redistribute it and/or modify
-it under the terms of the GNU Lesser General Public License as published by
-the Free Software Foundation; either version 2.1 of the License, or (at your
-option) any later version.
-
-The GNU MP Library 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 Lesser General Public
-License for more details.
-
-You should have received a copy of the GNU Lesser General Public License
-along with the GNU MP Library; see the file COPYING.LIB. If not, write to
-the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
-MA 02111-1307, USA. */
-
-#include "gmp.h"
-
-#if defined (DEBUG)
-#include <stdio.h>
-#endif
-
-/* Precondition: both p and q are positive */
-
-int
-#if __STDC__
-mpz_legendre (mpz_srcptr pi, mpz_srcptr qi)
-#else
-mpz_legendre (pi, qi)
-mpz_srcptr pi, qi;
-#endif
-{
- mpz_t p, q, qdiv2;
-#ifdef Q_MINUS_1
- mpz_t q_minus_1;
-#endif
- mpz_ptr mtmp;
- register mpz_ptr pptr, qptr;
- register int retval = 1;
- register unsigned long int s;
-
- pptr = p;
- mpz_init_set (pptr, pi);
- qptr = q;
- mpz_init_set (qptr, qi);
-
-#ifdef Q_MINUS_1
- mpz_init (q_minus_1);
-#endif
- mpz_init (qdiv2);
-
-tail_recurse2:
-#ifdef DEBUG
- printf ("tail_recurse2: p=");
- mpz_out_str (stdout, 10, pptr);
- printf ("\nq=");
- mpz_out_str (stdout, 10, qptr);
- putchar ('\n');
-#endif
- s = mpz_scan1 (qptr, 0);
- if (s) mpz_tdiv_q_2exp (qptr, qptr, s); /* J(a,2) = 1 */
-#ifdef DEBUG
- printf ("2 factor decomposition: p=");
- mpz_out_str (stdout, 10, pptr);
- printf ("\nq=");
- mpz_out_str (stdout, 10, qptr);
- putchar ('\n');
-#endif
- /* postcondition q odd */
- if (!mpz_cmp_ui (qptr, 1L)) /* J(a,1) = 1 */
- goto done;
- mpz_mod (pptr, pptr, qptr); /* J(a,q) = J(b,q) when a == b mod q */
-#ifdef DEBUG
- printf ("mod out by q: p=");
- mpz_out_str (stdout, 10, pptr);
- printf ("\nq=");
- mpz_out_str (stdout, 10, qptr);
- putchar ('\n');
-#endif
- /* quick calculation to get approximate size first */
- /* precondition: p < q */
- if ((mpz_sizeinbase (pptr, 2) + 1 >= mpz_sizeinbase (qptr,2))
- && (mpz_tdiv_q_2exp (qdiv2, qptr, 1L), mpz_cmp (pptr, qdiv2) > 0))
- {
- /* p > q/2 */
- mpz_sub (pptr, qptr, pptr);
- /* J(-1,q) = (-1)^((q-1)/2), q odd */
- if (mpz_get_ui (qptr) & 2)
- retval = -retval;
- }
- /* p < q/2 */
-#ifdef Q_MINUS_1
- mpz_sub_ui (q_minus_q, qptr, 1L);
-#endif
-tail_recurse: /* we use tail_recurse only if q has not changed */
-#ifdef DEBUG
- printf ("tail_recurse1: p=");
- mpz_out_str (stdout, 10, pptr);
- printf ("\nq=");
- mpz_out_str (stdout, 10, qptr);
- putchar ('\n');
-#endif
- /*
- * J(0,q) = 0
- * this occurs only if gcd(p,q) != 1 which is never true for
- * Legendre function.
- */
- if (!mpz_cmp_ui (pptr, 0L))
- {
- retval = 0;
- goto done;
- }
-
- if (!mpz_cmp_ui (pptr, 1L))
- {
- /* J(1,q) = 1 */
- /* retval *= 1; */
- goto done;
- }
-#ifdef Q_MINUS_1
- if (!mpz_cmp (pptr, q_minus_1))
- {
- /* J(-1,q) = (-1)^((q-1)/2) */
- if (mpz_get_ui (qptr) & 2)
- retval = -retval;
- /* else retval *= 1; */
- goto done;
- }
-#endif
- /*
- * we do not handle J(xy,q) except for x==2
- * since we do not want to factor
- */
- if ((s = mpz_scan1 (pptr, 0)) != 0)
- {
- /*
- * J(2,q) = (-1)^((q^2-1)/8)
- *
- * Note that q odd guarantees that q^2-1 is divisible by 8:
- * Let a: q=2a+1. q^2 = 4a^2+4a+1, (q^2-1)/8 = a(a+1)/2, qed
- *
- * Now, note that this means that the low two bits of _a_
- * (or the low bits of q shifted over by 1 determines
- * the factor).
- */
- mpz_tdiv_q_2exp (pptr, pptr, s);
-
- /* even powers of 2 gives J(2,q)^{2n} = 1 */
- if (s & 1)
- {
- s = mpz_get_ui (qptr) >> 1;
- s = s * (s + 1);
- if (s & 2)
- retval = -retval;
- }
- goto tail_recurse;
- }
- /*
- * we know p is odd since we have cast out 2s
- * precondition that q is odd guarantees both odd.
- *
- * quadratic reciprocity
- * J(p,q) = (-1)^((p-1)(q-1)/4) * J(q,p)
- */
- if ((s = mpz_scan1 (pptr, 1)) <= 2 && (s + mpz_scan1 (qptr, 1)) <= 2)
- retval = -retval;
-
- mtmp = pptr; pptr = qptr; qptr = mtmp;
- goto tail_recurse2;
-done:
- mpz_clear (p);
- mpz_clear (q);
- mpz_clear (qdiv2);
-#ifdef Q_MINUS_1
- mpz_clear (q_minus_1);
-#endif
- return retval;
-}
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