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Diff for /OpenXM_contrib/gmp/mpz/Attic/kronuz.c between version 1.1.1.1 and 1.1.1.2

version 1.1.1.1, 2000/09/09 14:12:54 version 1.1.1.2, 2003/08/25 16:06:33
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 /* mpz_ui_kronecker -- Kronecker/Jacobi symbol. */  /* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
   
 /*  Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
 Copyright (C) 1999, 2000 Free Software Foundation, Inc.  
   
 This file is part of the GNU MP Library.  This file is part of the GNU MP Library.
   
Line 18  License for more details.
Line 17  License for more details.
 You should have received a copy of the GNU Lesser General Public License  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  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,  the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 MA 02111-1307, USA.  MA 02111-1307, USA. */
 */  
   
 #include "gmp.h"  #include "gmp.h"
 #include "gmp-impl.h"  #include "gmp-impl.h"
 #include "longlong.h"  #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  int
 #if __STDC__  
 mpz_ui_kronecker (unsigned long a, mpz_srcptr b)  mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
 #else  
 mpz_ui_kronecker (a, b)  
      unsigned long a;  
      mpz_srcptr    b;  
 #endif  
 {  {
   int        b_abs_size;    mp_srcptr  b_ptr = PTR(b);
   mp_srcptr  b_ptr;    mp_limb_t  b_low = b_ptr[0];
   mp_limb_t  b_low;    mp_size_t  b_abs_size = ABSIZ (b);
     mp_limb_t  b_rem;
   int        twos;    int        twos;
   int        result_bit1;    int        result_bit1 = 0;
   
   /* (a/0) */  
   b_abs_size = ABSIZ (b);  
   if (b_abs_size == 0)  
     return JACOBI_U0 (a);  
   
   /* (a/-1)=1 when a>=0, so the sign of b is ignored */    /* (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    if (b_abs_size == 0)
      (1/b)=1, for any b */      return JACOBI_U0 (a);  /* (a/0) */
   if (a <= 1)  
     return (a == 1) | ((b_abs_size == 1) & (b_low == 1));  
   
   if (b_low & 1)    if (a > GMP_NUMB_MAX)
     {      {
       /* (a/1) = 1 for any a */        mp_limb_t  alimbs[2];
       if (b_abs_size == 1 && b_low == 1)        mpz_t      az;
         return 1;        ALLOC(az) = numberof (alimbs);
         PTR(az) = alimbs;
       count_trailing_zeros (twos, a);        mpz_set_ui (az, a);
       a >>= twos;        return mpz_kronecker (az, b);
       if (a == 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 (! (b_low & 1))
   if ((a & 1) == 0)      {
     return 0;        /* (0/b)=0 for b!=+/-1; (even/even)=0 */
         if (! (a & 1))
           return 0;
   
   /* Require MP_BITS_PER_LIMB even, so (a/2)^MP_BITS_PER_LIMB = 1, and so we        /* a odd, b even */
      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);        /* establish shifted b_low for use with reciprocity below */
   b_low = b_ptr[0];        MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size, b_low);
         if (! (b_low & 1))
           {
             if (b_low == GMP_NUMB_HIGHBIT)
               {
                 if (b_abs_size == 1)   /* (a/0x80000000) == (a/2)^(BPML-1) */
                   return JACOBI_TWOS_U (GMP_NUMB_BITS-1, a);
   
   if (b_low & 1)                /* b_abs_size > 1 */
     /* reciprocity to (b/a); (b/a) == (b mod a / a) */                b_low = b_ptr[1] << 1;
     return mpn_jacobi_base (mpn_mod_1 (b_ptr, b_abs_size, a),              }
                             a,            else
                             JACOBI_RECIP_UU_BIT1 (b_low, a));              {
                 count_trailing_zeros (twos, b_low);
   count_trailing_zeros (twos, b_low);                b_low >>= twos;
               }
   /* reciprocity to get (b/a) */          }
   if (twos == BITS_PER_MP_LIMB-1)      }
     else
     {      {
       if (b_abs_size == 1)        if (a == 0)        /* (0/b)=1 for b=+/-1, 0 otherwise */
           return (b_abs_size == 1 && b_low == 1);
   
         if (! (a & 1))
         {          {
           /* b==0x800...00, one limb high bit only, so (a/2)^(BPML-1) */            /* a even, b odd */
           return JACOBI_TWOS_U (BITS_PER_MP_LIMB-1, a);            count_trailing_zeros (twos, a);
             a >>= twos;
             /* (a*2^n/b) = (a/b) * (2/a)^n */
             result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
         }          }
   
       /* 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) */    if (a == 1)
   return mpn_jacobi_base (mpn_mod_1_rshift (b_ptr, b_abs_size, twos, a),      return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
                           a,  
                           JACOBI_TWOS_U_BIT1 (twos, a) ^ result_bit1);    /* (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, a);
     result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
     return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
 }  }
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