contrib/gmp/mpz/kronsz.c

   1 /* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol.
   2
   3 Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
   4
   5 This file is part of the GNU MP Library.
   6
   7 The GNU MP Library is free software; you can redistribute it and/or modify
   8 it under the terms of the GNU Lesser General Public License as published by
   9 the Free Software Foundation; either version 3 of the License, or (at your
  10 option) any later version.
  11
  12 The GNU MP Library is distributed in the hope that it will be useful, but
  13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  14 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  15 License for more details.
  16
  17 You should have received a copy of the GNU Lesser General Public License
  18 along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
  19
  20 #include "gmp.h"
  21 #include "gmp-impl.h"
  22 #include "longlong.h"
  23
  24
  25 int
  26 mpz_si_kronecker (long a, mpz_srcptr b)
  27 {
  28   mp_srcptr  b_ptr;
  29   mp_limb_t  b_low;
  30   mp_size_t  b_size;
  31   mp_size_t  b_abs_size;
  32   mp_limb_t  a_limb, b_rem;
  33   unsigned   twos;
  34   int        result_bit1;
  35
  36 #if GMP_NUMB_BITS < BITS_PER_ULONG
  37   if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX)
  38     {
  39       mp_limb_t  alimbs[2];
  40       mpz_t      az;
  41       ALLOC(az) = numberof (alimbs);
  42       PTR(az) = alimbs;
  43       mpz_set_si (az, a);
  44       return mpz_kronecker (az, b);
  45     }
  46 #endif
  47
  48   b_size = SIZ (b);
  49   if (b_size == 0)
  50     return JACOBI_S0 (a);  /* (a/0) */
  51
  52   /* account for the effect of the sign of b, then ignore it */
  53   result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);
  54
  55   b_ptr = PTR(b);
  56   b_low = b_ptr[0];
  57   b_abs_size = ABS (b_size);
  58
  59   if ((b_low & 1) != 0)
  60     {
  61       /* b odd */
  62
  63       result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
  64       a_limb = (unsigned long) ABS(a);
  65
  66       if ((a_limb & 1) == 0)
  67         {
  68           /* (0/b)=1 for b=+/-1, 0 otherwise */
  69           if (a_limb == 0)
  70             return (b_abs_size == 1 && b_low == 1);
  71
  72           /* a even, b odd */
  73           count_trailing_zeros (twos, a_limb);
  74           a_limb >>= twos;
  75           /* (a*2^n/b) = (a/b) * twos(n,a) */
  76           result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
  77         }
  78     }
  79   else
  80     {
  81       /* (even/even)=0, and (0/b)=0 for b!=+/-1 */
  82       if ((a & 1) == 0)
  83         return 0;
  84
  85       /* a odd, b even
  86
  87          Establish shifted b_low with valid bit1 for ASGN and RECIP below.
  88          Zero limbs stripped are accounted for, but zero bits on b_low are
  89          not because they remain in {b_ptr,b_abs_size} for the
  90          JACOBI_MOD_OR_MODEXACT_1_ODD. */
  91
  92       JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
  93       if ((b_low & 1) == 0)
  94         {
  95           if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
  96             {
  97               /* need b_ptr[1] to get bit1 in b_low */
  98               if (b_abs_size == 1)
  99                 {
 100                   /* (a/0x80000000) = (a/2)^(BPML-1) */
 101                   if ((GMP_NUMB_BITS % 2) == 0)
 102                     result_bit1 ^= JACOBI_TWO_U_BIT1 (a);
 103                   return JACOBI_BIT1_TO_PN (result_bit1);
 104                 }
 105
 106               /* b_abs_size > 1 */
 107               b_low = b_ptr[1] << 1;
 108             }
 109           else
 110             {
 111               count_trailing_zeros (twos, b_low);
 112               b_low >>= twos;
 113             }
 114         }
 115
 116       result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
 117       a_limb = (unsigned long) ABS(a);
 118     }
 119
 120   if (a_limb == 1)
 121     return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
 122
 123   /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */
 124   JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb);
 125   result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low);
 126   return mpn_jacobi_base (b_rem, a_limb, result_bit1);
 127 }