source/libs/gmp/gmp-src/mpz/kronsz.c

   1 /* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol.
   2
   3 Copyright 1999-2002 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 either:
   9
  10   * the GNU Lesser General Public License as published by the Free
  11     Software Foundation; either version 3 of the License, or (at your
  12     option) any later version.
  13
  14 or
  15
  16   * the GNU General Public License as published by the Free Software
  17     Foundation; either version 2 of the License, or (at your option) any
  18     later version.
  19
  20 or both in parallel, as here.
  21
  22 The GNU MP Library is distributed in the hope that it will be useful, but
  23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  24 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  25 for more details.
  26
  27 You should have received copies of the GNU General Public License and the
  28 GNU Lesser General Public License along with the GNU MP Library.  If not,
  29 see https://www.gnu.org/licenses/.  */
  30
  31 #include "gmp.h"
  32 #include "gmp-impl.h"
  33 #include "longlong.h"
  34
  35
  36 int
  37 mpz_si_kronecker (long a, mpz_srcptr b)
  38 {
  39   mp_srcptr  b_ptr;
  40   mp_limb_t  b_low;
  41   mp_size_t  b_size;
  42   mp_size_t  b_abs_size;
  43   mp_limb_t  a_limb, b_rem;
  44   unsigned   twos;
  45   int        result_bit1;
  46
  47 #if GMP_NUMB_BITS < BITS_PER_ULONG
  48   if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX)
  49     {
  50       mp_limb_t  alimbs[2];
  51       mpz_t      az;
  52       ALLOC(az) = numberof (alimbs);
  53       PTR(az) = alimbs;
  54       mpz_set_si (az, a);
  55       return mpz_kronecker (az, b);
  56     }
  57 #endif
  58
  59   b_size = SIZ (b);
  60   if (b_size == 0)
  61     return JACOBI_S0 (a);  /* (a/0) */
  62
  63   /* account for the effect of the sign of b, then ignore it */
  64   result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);
  65
  66   b_ptr = PTR(b);
  67   b_low = b_ptr[0];
  68   b_abs_size = ABS (b_size);
  69
  70   if ((b_low & 1) != 0)
  71     {
  72       /* b odd */
  73
  74       result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
  75       a_limb = (unsigned long) ABS(a);
  76
  77       if ((a_limb & 1) == 0)
  78         {
  79           /* (0/b)=1 for b=+/-1, 0 otherwise */
  80           if (a_limb == 0)
  81             return (b_abs_size == 1 && b_low == 1);
  82
  83           /* a even, b odd */
  84           count_trailing_zeros (twos, a_limb);
  85           a_limb >>= twos;
  86           /* (a*2^n/b) = (a/b) * twos(n,a) */
  87           result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
  88         }
  89     }
  90   else
  91     {
  92       /* (even/even)=0, and (0/b)=0 for b!=+/-1 */
  93       if ((a & 1) == 0)
  94         return 0;
  95
  96       /* a odd, b even
  97
  98          Establish shifted b_low with valid bit1 for ASGN and RECIP below.
  99          Zero limbs stripped are accounted for, but zero bits on b_low are
 100          not because they remain in {b_ptr,b_abs_size} for the
 101          JACOBI_MOD_OR_MODEXACT_1_ODD. */
 102
 103       JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
 104       if ((b_low & 1) == 0)
 105         {
 106           if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
 107             {
 108               /* need b_ptr[1] to get bit1 in b_low */
 109               if (b_abs_size == 1)
 110                 {
 111                   /* (a/0x80000000) = (a/2)^(BPML-1) */
 112                   if ((GMP_NUMB_BITS % 2) == 0)
 113                     result_bit1 ^= JACOBI_TWO_U_BIT1 (a);
 114                   return JACOBI_BIT1_TO_PN (result_bit1);
 115                 }
 116
 117               /* b_abs_size > 1 */
 118               b_low = b_ptr[1] << 1;
 119             }
 120           else
 121             {
 122               count_trailing_zeros (twos, b_low);
 123               b_low >>= twos;
 124             }
 125         }
 126
 127       result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
 128       a_limb = (unsigned long) ABS(a);
 129     }
 130
 131   if (a_limb == 1)
 132     return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
 133
 134   /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */
 135   JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb);
 136   result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low);
 137   return mpn_jacobi_base (b_rem, a_limb, result_bit1);
 138 }