X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/mp-jacobi.c?ds=sidebyside

diff --git a/mp-jacobi.c b/mp-jacobi.c
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-/* -*-c-*-
- *
- * $Id$
- *
- * Compute Jacobi symbol
- *
- * (c) 1999 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb 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.
- *
- * Catacomb 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 Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "mp.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @mp_jacobi@ --- *
- *
- * Arguments:	@mp *a@ = an integer
- *		@mp *n@ = another integer
- *
- * Returns:	@-1@, @0@ or @1@ -- the Jacobi symbol %$J(a, n)$%.
- *
- * Use:		Computes the Kronecker symbol %$\jacobi{a}{n}$%.  If @n@ is
- *		prime, this is the Legendre symbol and is equal to 1 if and
- *		only if @a@ is a quadratic residue mod @n@.  The result is
- *		zero if and only if @a@ and @n@ have a common factor greater
- *		than one.
- *
- *		If @n@ is composite, then this computes the Kronecker symbol
- *
- *		  %$\jacobi{a}{n}=\jacobi{a}{u}\prod_i\jacobi{a}{p_i}^{e_i}$%
- *
- *		where %$n = u p_0^{e_0} \ldots p_{n-1}^{e_{n-1}}$% is the
- *		prime factorization of %$n$%.  The missing bits are:
- *
- *		  * %$\jacobi{a}{1} = 1$%;
- *		  * %$\jacobi{a}{-1} = 1$% if @a@ is negative, or 1 if
- *		    positive;
- *		  * %$\jacobi{a}{0} = 0$%;
- *	          * %$\jacobi{a}{2}$ is 0 if @a@ is even, 1 if @a@ is
- *		    congruent to 1 or 7 (mod 8), or %$-1$% otherwise.
- *
- *		If %$n$% is positive and odd, then this is the Jacobi
- *		symbol.  (The Kronecker symbol is a consistant domain
- *		extension; the Jacobi symbol was implemented first, and the
- *		name stuck.)
- */
-
-int mp_jacobi(mp *a, mp *n)
-{
-  int s = 1;
-  size_t p2;
-
-  /* --- Handle zero specially --- *
-   *
-   * I can't find any specific statement for what to do when %$n = 0$%; PARI
-   * opts to set %$\jacobi{\pm1}{0} = \pm 1$% and %$\jacobi{a}{0} = 0$% for
-   * other %$a$%.
-   */
-
-  if (MP_ZEROP(n)) {
-    if (MP_EQ(a, MP_ONE)) return (+1);
-    else if (MP_EQ(a, MP_MONE)) return (-1);
-    else return (0);
-  }
-
-  /* --- Deal with powers of two --- *
-   *
-   * This implicitly takes a copy of %$n$%.  Copy %$a$% at the same time to
-   * make cleanup easier.
-   */
-
-  MP_COPY(a);
-  n = mp_odd(MP_NEW, n, &p2);
-  if (p2) {
-    if (MP_EVENP(a)) {
-      s = 0;
-      goto done;
-    } else if ((p2 & 1) && ((a->v[0] & 7) == 3 || (a->v[0] & 7) == 5))
-      s = -s;
-  }
-
-  /* --- Deal with negative %$n$% --- */
-
-  if (MP_NEGP(n)) {
-    n = mp_neg(n, n);
-    if (MP_NEGP(a))
-      s = -s;
-  }
-
-  /* --- Check for unit %$n$% --- */
-
-  if (MP_EQ(n, MP_ONE))
-    goto done;
-
-  /* --- Reduce %$a$% modulo %$n$% --- */
-
-  if (MP_NEGP(a) || MP_CMP(a, >=, n))
-    mp_div(0, &a, a, n);
-
-  /* --- Main recursive mess, flattened out into something nice --- */
-
-  for (;;) {
-    mpw nn;
-    size_t e;
-
-    /* --- Some simple special cases --- */
-
-    MP_SHRINK(a);
-    if (MP_ZEROP(a)) {
-      s = 0;
-      goto done;
-    }
-
-    /* --- Main case with powers of two --- */
-
-    a = mp_odd(a, a, &e);
-    nn = n->v[0] & 7;
-    if ((e & 1) && (nn == 3 || nn == 5))
-      s = -s;
-    if (MP_LEN(a) == 1 && a->v[0] == 1)
-      goto done;
-    if ((nn & 3) == 3 && (a->v[0] & 3) == 3)
-      s = -s;
-
-    /* --- Reduce and swap --- */
-
-    mp_div(0, &n, n, a);
-    { mp *t = n; n = a; a = t; }
-  }
-
-  /* --- Wrap everything up --- */
-
-done:
-  MP_DROP(a);
-  MP_DROP(n);
-  return (s);
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-#include <mLib/testrig.h>
-
-static int verify(dstr *v)
-{
-  mp *a = *(mp **)v[0].buf;
-  mp *n = *(mp **)v[1].buf;
-  int s = *(int *)v[2].buf;
-  int j = mp_jacobi(a, n);
-  int ok = 1;
-
-  if (s != j) {
-    fputs("\n*** fail", stderr);
-    fputs("a = ", stderr); mp_writefile(a, stderr, 10); fputc('\n', stderr);
-    fputs("n = ", stderr); mp_writefile(n, stderr, 10); fputc('\n', stderr);
-    fprintf(stderr, "s = %i\n", s);
-    fprintf(stderr, "j = %i\n", j);
-    ok = 0;
-  }
-
-  mp_drop(a);
-  mp_drop(n);
-  assert(mparena_count(MPARENA_GLOBAL) == 0);
-  return (ok);
-}
-
-static test_chunk tests[] = {
-  { "jacobi", verify, { &type_mp, &type_mp, &type_int, 0 } },
-  { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
-  sub_init();
-  test_run(argc, argv, tests, SRCDIR "/tests/mp");
-  return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/