* mpz/kronuz.c: New file.

1 files changed, 116 insertions, 0 deletions

diff --git a/mpz/kronuz.c b/mpz/kronuz.c
new file mode 100644
index 000000000..4ef8c3c02
--- /dev/null
+++ b/mpz/kronuz.c
@@ -0,0 +1,116 @@
+/* mpz_kronecker_ui_zi -- Kronecker/Jacobi symbol. */
+
+/*
+Copyright (C) 1999, 2000 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"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+
+int
+#if __STDC__
+mpz_kronecker_ui_zi (unsigned long a, mpz_srcptr b)
+#else
+mpz_kronecker_ui_zi (a, b)
+     unsigned long a;
+     mpz_srcptr    b;
+#endif
+{
+  int        b_abs_size;
+  mp_srcptr  b_ptr;
+  mp_limb_t  b_low;
+  int        twos;
+  int        result_bit1;
+
+  /* unsigned long must fit in mp_limb_t */
+  ASSERT (sizeof (mp_limb_t) >= sizeof (unsigned long));
+
+  /* (a/0) */
+  if ((b_abs_size = ABSIZ (b)) == 0)
+    return JACOBI_U0 (a);
+
+  /* (a/-1)=1 when a>=0, so the sign of b is ignored */
+  b_ptr = PTR(b);
+  b_low = b_ptr[0];
+
+  /* (0/1)=1; (0/-1)=1; (0/b)=0 for b!=+/-1
+     (1/b)=1, for any b */
+  if (a <= 1)
+    return (a == 1) | ((b_abs_size == 1) & (b_low == 1));
+
+  if (b_low & 1)
+    {
+      /* (a/1) = 1 for any a */
+      if (b_abs_size == 1 && b_low == 1)
+        return 1;
+
+      count_trailing_zeros (twos, a);
+      if ((a >>= twos) == 1)
+        return JACOBI_TWOS_U (twos, b_low);  /* powers of (2/b) only */
+
+      /* powers of (2/b); reciprocity to (b/a); (b/a) == (b mod a / a) */
+      return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
+                              a,
+                              JACOBI_TWOS_U_BIT1 (twos, b_low)
+                              ^ JACOBI_RECIP_UU_BIT1 (b_low, a));
+    }
+
+  /* b is even; (a/2)=0 if a is even */
+  if ((a & 1) == 0)
+    return 0;
+
+  /* Require MP_BITS_PER_LIMB even, so (a/2)^MP_BITS_PER_LIMB = 1, and so we
+     don't have to pay attention to how many trailing zero limbs are
+     stripped.  */
+  ASSERT ((BITS_PER_MP_LIMB & 1) == 0);
+
+  MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size);
+  b_low = b_ptr[0];
+
+  if (b_low & 1)
+    /* reciprocity to (b/a); (b/a) == (b mod a / a) */
+    return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),
+                            a,
+                            JACOBI_RECIP_UU_BIT1 (b_low, a));
+
+  count_trailing_zeros (twos, b_low);
+
+  /* reciprocity to get (b/a) */
+  if (twos == BITS_PER_MP_LIMB-1)
+    {
+      if (b_abs_size == 1)
+        {
+          /* b==0x800...00, one limb high bit only, so (a/2)^(BPML-1) */
+          return JACOBI_TWOS_U (BITS_PER_MP_LIMB-1, a);
+        }
+
+      /* b_abs_size > 1 */
+      result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_ptr[1] << 1);
+    }
+  else
+    result_bit1 = JACOBI_RECIP_UU_BIT1 (a, b_low >> twos);
+
+  /* powers of (a/2); reciprocity to (b/a); (b/a) == (b mod a / a) */
+  return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size, twos, a),
+                          a,
+                          JACOBI_TWOS_U_BIT1 (twos, a) ^ result_bit1);
+}