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Diffstat (limited to 'contrib/libgmp/mpz/legendre.c')
| -rw-r--r-- | contrib/libgmp/mpz/legendre.c | 184 |
1 files changed, 184 insertions, 0 deletions
diff --git a/contrib/libgmp/mpz/legendre.c b/contrib/libgmp/mpz/legendre.c new file mode 100644 index 0000000..4de16a6 --- /dev/null +++ b/contrib/libgmp/mpz/legendre.c @@ -0,0 +1,184 @@ +/* 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 Library General Public License as published by +the Free Software Foundation; either version 2 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 Library General Public +License for more details. + +You should have received a copy of the GNU Library 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; +} |
