* mpz/kronzu.c, mpz/kronzs.c, mpz/kronuz.c, mpz/kronsz.c: Use

	mpn_modexact_1_odd and new JACOBI macros, various rearrangements in
	support of this.

3 files changed, 135 insertions, 110 deletions

diff --git a/mpz/kronsz.c b/mpz/kronsz.c
index cf58a6d60..892ed2763 100644
--- a/mpz/kronsz.c
+++ b/mpz/kronsz.c
@@ -1,4 +1,4 @@
-/* mpz_si_kronecker -- Kronecker/Jacobi symbol. */
+/* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol. */
 
 /*
 Copyright 1999, 2000, 2001 Free Software Foundation, Inc.
@@ -26,95 +26,89 @@ MA 02111-1307, USA.
 #include "longlong.h"
 
 
+/* This implementation depends on BITS_PER_MP_LIMB being even, so that
+   (a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how
+   many low zero limbs are stripped.  */
+#if BITS_PER_MP_LIMB % 2 != 0
+Error, error, unsupported BITS_PER_MP_LIMB
+#endif
+
+
 int
 mpz_si_kronecker (long a, mpz_srcptr b)
 {
-  int        b_abs_size;
-  mp_srcptr  b_ptr;
-  mp_limb_t  b_low;
+  mp_srcptr  b_ptr = PTR(b);
+  mp_limb_t  b_low = b_ptr[0];
+  int        b_size = SIZ (b);
+  int        b_abs_size = ABS (b_size);
+  mp_limb_t  b_rem;
   int        twos;
   int        result_bit1;
 
-  b_abs_size = ABSIZ (b);
   if (b_abs_size == 0)
     return JACOBI_S0 (a);  /* (a/0) */
 
-  b_ptr = PTR(b);
-  b_low = b_ptr[0];
-
-  /* (0/b) = 1 if b=+/-1, 0 otherwise */
-  if (a == 0)
-    return (b_abs_size == 1) & (b_low == 1);
+  /* account for the effect of the sign of b, then ignore it */
+  result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);
 
-  /* account for the effect of the sign of b, so can then ignore it */
-  result_bit1 = JACOBI_BSGN_SZ_BIT1 (a, b);
-
-  if ((b_low & 1) == 0)
+  if (! (b_low & 1))
     {
-      /* b even */
-
-      if ((a & 1) == 0)
-        return 0;  /* (a/b)=0 if both a,b even */
+      /* (even/even)=0, and (0/b)=0 for b!=+/-1 */
+      if (! (a & 1))
+        return 0;
 
-      /* Require MP_BITS_PER_LIMB even, so that (a/2)^MP_BITS_PER_LIMB = 1,
-         and so that therefore there's no need to account for how many zero
-         limbs are stripped.  */
-      ASSERT ((BITS_PER_MP_LIMB & 1) == 0);
+      /* a odd, b even */
 
-      MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size);
-      b_low = b_ptr[0];
-
-      if ((b_low & 1) == 0)
+      /* establish shifted b_low for use with reciprocity below */
+      MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size, b_low);
+      if (! (b_low & 1))
         {
-          /* odd a, even b */
-
-          mp_limb_t  b_shl_bit1;
-
-          count_trailing_zeros (twos, b_low);
-
-          /* b_shl_bit1 is b>>twos, but with only bit 1 guaranteed */
-          if (twos == BITS_PER_MP_LIMB-1)
-            b_shl_bit1 = (b_abs_size == 1) ? 0 : (b_ptr[1] << 1);
+          if (b_low == MP_LIMB_T_HIGHBIT)
+            {
+              if (b_abs_size == 1)
+                {
+                  /* (a/0x80000000) = (a/2)^(BPML-1) */
+                  result_bit1 ^= JACOBI_TWOS_U_BIT1 (BITS_PER_MP_LIMB-1, a);
+                  return JACOBI_BIT1_TO_PN (result_bit1);
+                }
+      
+              /* b_abs_size > 1 */
+              b_low = b_ptr[1] << 1;
+            }
           else
-            b_shl_bit1 = (b_low >> twos);
-
-          result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_shl_bit1);
-          a = ABS(a);
+            {
+              count_trailing_zeros (twos, b_low);
+              b_low >>= twos;
+            }
+        }
+    }
+  else
+    {
+      /* b odd */
 
-          if (a == 1)
-            return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
+      /* (0/b)=1 for b=+/-1, 0 otherwise */
+      if (a == 0)
+        return (b_abs_size == 1 && b_low == 1);
 
-          /* twos (a/2), reciprocity to (b/a), and (b/a) = (b mod a / b) */
-          return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size,
-                                                    twos, a),
-                                  a,
-                                  result_bit1
-                                  ^ JACOBI_TWOS_U_BIT1 (twos, a)
-                                  ^ JACOBI_RECIP_UU_BIT1 (a, b_shl_bit1));
+      if (! (a & 1))
+        {
+          /* a even, b odd */
+          count_trailing_zeros (twos, a);
+          a >>= twos;
+          /* (a*2^n/b) = (a/b) * twos(n,a) */
+          result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
         }
     }
 
-  /* b odd */
-
   result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
   a = ABS(a);
 
-  /* (a/1) = 1 for any a */
-  if (b_abs_size == 1 && b_low == 1)
-    return JACOBI_BIT1_TO_PN (result_bit1);
-
-  /* Note a is cast to unsigned because 0x80..00 doesn't fit in a signed. */
-  if ((a & 1) == 0)
-    {
-      count_trailing_zeros (twos, a);
-      a = ((unsigned long) a) >> twos;
-      result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
-    }
-
   if (a == 1)
     return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
 
-  /* reciprocity to (b/a), and (b/a) == (b mod a / a) */
-  return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a), a,
-                          result_bit1 ^ JACOBI_RECIP_UU_BIT1 (a, b_low));
+  /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */
+  JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size,
+                                (unsigned long) a);
+  result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
+  return mpn_jacobi_base (b_rem, (mp_limb_t) (unsigned long) a, result_bit1);
 }
diff --git a/mpz/kronzs.c b/mpz/kronzs.c
index 6bd7ef441..6089cd0c8 100644
--- a/mpz/kronzs.c
+++ b/mpz/kronzs.c
@@ -1,4 +1,4 @@
-/* mpz_kronecker_si -- Kronecker/Jacobi symbol. */
+/* mpz_kronecker_si -- mpz+long Kronecker/Jacobi symbol. */
 
 /*
 Copyright 1999, 2000, 2001 Free Software Foundation, Inc.
@@ -26,43 +26,59 @@ MA 02111-1307, USA.
 #include "longlong.h"
 
 
-/* This function is expected to be often used with b odd, so there's a test
-   for this before invoking count_trailing_zeros().
+/* This implementation depends on BITS_PER_MP_LIMB being even, so that
+   (a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how
+   many low zero limbs are stripped.  */
+#if BITS_PER_MP_LIMB % 2 != 0
+Error, error, unsupported BITS_PER_MP_LIMB
+#endif
 
-   After the absolute value of b is established it's treated as an unsigned
+
+/* After the absolute value of b is established it's treated as an unsigned
    long, because 0x80..00 doesn't fit in a signed long. */
 
 int
 mpz_kronecker_si (mpz_srcptr a, long b)
 {
-  int  result_bit1;
-  int  twos;
+  mp_srcptr  a_ptr = PTR(a);
+  int        a_size = SIZ(a);
+  mp_limb_t  a_rem;
+  int        result_bit1;
+
+  if (b & 1)
+    {
+      result_bit1 = JACOBI_BSGN_SS_BIT1 (a_size, b);
+    }
+  else
+    {
+      mp_limb_t  a_low = a_ptr[0];
+      int        twos;
+
+      if (b == 0)
+        return JACOBI_LS0 (a_low, a_size);   /* (a/0) */
+
+      if (! (a_low & 1))
+        return 0;  /* (even/even)=0 */
 
-  if (b == 0)
-    return JACOBI_Z0 (a);
+      /* (a/2)=(2/a) for a odd */
+      count_trailing_zeros (twos, b);  
+      b >>= twos;
+      result_bit1 = (JACOBI_TWOS_U_BIT1 (twos, a_low)
+                     ^ JACOBI_BSGN_SS_BIT1 (a_size, b));
+    }
 
-  result_bit1 = JACOBI_BSGN_ZS_BIT1(a, b);
   b = ABS (b);
 
   if (b == 1)
-    return JACOBI_BIT1_TO_PN (result_bit1);  /* (a/1) = 1 for any a */
+    return JACOBI_BIT1_TO_PN (result_bit1);  /* (a/1)=1 for any a */
 
-  if (b & 1) 
-    return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, result_bit1);
-      
-  /* result 0 if both a,b even */
-  if (mpz_even_p (a))
-    return 0;
+  result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a_size, b);
+  a_size = ABS(a_size);
 
-  /* (a/2)=(2/a) when a odd */
-  count_trailing_zeros (twos, b);
-  result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, PTR(a)[0]);
-
-  b = ((unsigned long) b) >> twos;
-  if (b == 1)
-    return JACOBI_BIT1_TO_PN (result_bit1);
-  else
-    return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, result_bit1);
+  /* (a/b) = (a mod b / b) */
+  JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size,
+                                (unsigned long) b);
+  return mpn_jacobi_base (a_rem, (mp_limb_t) (unsigned long) b, result_bit1);
 }
 
 
diff --git a/mpz/kronzu.c b/mpz/kronzu.c
index b6681fec8..11e552f91 100644
--- a/mpz/kronzu.c
+++ b/mpz/kronzu.c
@@ -1,4 +1,4 @@
-/* mpz_kronecker_ui -- Kronecker/Jacobi symbol. */
+/* mpz_kronecker_ui -- mpz+ulong Kronecker/Jacobi symbol. */
 
 /*
 Copyright 1999, 2000, 2001 Free Software Foundation, Inc.
@@ -26,35 +26,50 @@ MA 02111-1307, USA.
 #include "longlong.h"
 
 
-/* This function is expected to be often used with b an odd prime, so the
-   code for odd b is nice and short. */
+/* This implementation depends on BITS_PER_MP_LIMB being even, so that
+   (a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how
+   many low zero limbs are stripped.  */
+#if BITS_PER_MP_LIMB % 2 != 0
+Error, error, unsupported BITS_PER_MP_LIMB
+#endif
+
 
 int
 mpz_kronecker_ui (mpz_srcptr a, unsigned long b)
 {
-  int  twos;
+  mp_srcptr  a_ptr = PTR(a);
+  int        a_size = SIZ(a);
+  mp_limb_t  a_rem;
+  int        result_bit1;
 
   if (b & 1)
     {
-      if (b != 1)
-        return mpn_jacobi_base (mpz_fdiv_ui (a, b), b, 0);
-      else
-        return 1;  /* (a/1)=1 for any a */
+      result_bit1 = JACOBI_ASGN_SU_BIT1 (a_size, b);
     }
+  else
+    {
+      mp_limb_t  a_low = a_ptr[0];
+      int        twos;
 
-  if (b == 0)
-    return JACOBI_Z0 (a);
+      if (b == 0)
+        return JACOBI_LS0 (a_low, a_size);   /* (a/0) */
 
-  /* (a/2)=0 if a even */
-  if (mpz_even_p (a))
-    return 0;
+      if (! (a_low & 1))
+        return 0;  /* (even/even)=0 */
+
+      /* (a/2)=(2/a) for a odd */
+      count_trailing_zeros (twos, b);  
+      b >>= twos;
+      result_bit1 = (JACOBI_TWOS_U_BIT1 (twos, a_low)
+                     ^ JACOBI_ASGN_SU_BIT1 (a_size, b));
+    }
 
-  /* (a/2)=(2/a) when a odd */
-  count_trailing_zeros (twos, b);  
-  b >>= twos;
   if (b == 1)
-    return JACOBI_TWOS_U (twos, PTR(a)[0]);
+    return JACOBI_BIT1_TO_PN (result_bit1);  /* (a/1)=1 for any a */
+
+  a_size = ABS(a_size);
 
-  return mpn_jacobi_base (mpz_fdiv_ui (a, b), b,
-                          JACOBI_TWOS_U_BIT1(twos, PTR(a)[0]));
+  /* (a/b) = (a mod b / b) */
+  JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b);
+  return mpn_jacobi_base (a_rem, (mp_limb_t) b, result_bit1);
 }