1  /* mpz_kronecker_si -- mpz+long 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-impl.h"
      32  #include "longlong.h"
      33  
      34  
      35  /* After the absolute value of b is established it's treated as an unsigned
      36     long, because 0x80..00 doesn't fit in a signed long. */
      37  
      38  int
      39  mpz_kronecker_si (mpz_srcptr a, long b)
      40  {
      41    mp_srcptr  a_ptr;
      42    mp_size_t  a_size;
      43    mp_limb_t  a_rem, b_limb;
      44    int        result_bit1;
      45  
      46    a_size = SIZ(a);
      47    if (a_size == 0)
      48      return JACOBI_0S (b);
      49  
      50  #if GMP_NUMB_BITS < BITS_PER_ULONG
      51    if (b > GMP_NUMB_MAX || b < -GMP_NUMB_MAX)
      52      {
      53        mp_limb_t  blimbs[2];
      54        mpz_t      bz;
      55        ALLOC(bz) = numberof (blimbs);
      56        PTR(bz) = blimbs;
      57        mpz_set_si (bz, b);
      58        return mpz_kronecker (a, bz);
      59      }
      60  #endif
      61  
      62    result_bit1 = JACOBI_BSGN_SS_BIT1 (a_size, b);
      63    b_limb = ABS_CAST (unsigned long, b);
      64    a_ptr = PTR(a);
      65  
      66    if ((b_limb & 1) == 0)
      67      {
      68        mp_limb_t  a_low = a_ptr[0];
      69        int        twos;
      70  
      71        if (b_limb == 0)
      72  	return JACOBI_LS0 (a_low, a_size);   /* (a/0) */
      73  
      74        if (! (a_low & 1))
      75  	return 0;  /* (even/even)=0 */
      76  
      77        /* (a/2)=(2/a) for a odd */
      78        count_trailing_zeros (twos, b_limb);
      79        b_limb >>= twos;
      80        result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, a_low);
      81      }
      82  
      83    if (b_limb == 1)
      84      return JACOBI_BIT1_TO_PN (result_bit1);  /* (a/1)=1 for any a */
      85  
      86    result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a_size, b_limb);
      87    a_size = ABS(a_size);
      88  
      89    /* (a/b) = (a mod b / b) */
      90    JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, a_rem, a_ptr, a_size, b_limb);
      91    return mpn_jacobi_base (a_rem, b_limb, result_bit1);
      92  }