Reorganisation of the source tree

[ghc-hetmet.git] / rts / gmp / mpz / legendre.c

diff --git a/rts/gmp/mpz/legendre.c b/rts/gmp/mpz/legendre.c
new file mode 100644 (file)
index 0000000..ab665f7
--- /dev/null
+++ b/rts/gmp/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 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;
+}