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

   1 /* mpz_ui_kronecker -- ulong+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_ui_kronecker (unsigned long a, mpz_srcptr b)
  38 {
  39   mp_srcptr  b_ptr;
  40   mp_limb_t  b_low;
  41   int        b_abs_size;
  42   mp_limb_t  b_rem;
  43   int        twos;
  44   int        result_bit1;
  45
  46   /* (a/-1)=1 when a>=0, so the sign of b is ignored */
  47   b_abs_size = ABSIZ (b);
  48
  49   if (b_abs_size == 0)
  50     return JACOBI_U0 (a);  /* (a/0) */
  51
  52   if (a > GMP_NUMB_MAX)
  53     {
  54       mp_limb_t  alimbs[2];
  55       mpz_t      az;
  56       ALLOC(az) = numberof (alimbs);
  57       PTR(az) = alimbs;
  58       mpz_set_ui (az, a);
  59       return mpz_kronecker (az, b);
  60     }
  61
  62   b_ptr = PTR(b);
  63   b_low = b_ptr[0];
  64   result_bit1 = 0;
  65
  66   if (! (b_low & 1))
  67     {
  68       /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
  69       if (! (a & 1))
  70         return 0;
  71
  72       /* a odd, b even
  73
  74          Establish shifted b_low with valid bit1 for the RECIP below.  Zero
  75          limbs stripped are accounted for, but zero bits on b_low are not
  76          because they remain in {b_ptr,b_abs_size} for
  77          JACOBI_MOD_OR_MODEXACT_1_ODD. */
  78
  79       JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
  80       if (! (b_low & 1))
  81         {
  82           if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
  83             {
  84               /* need b_ptr[1] to get bit1 in b_low */
  85               if (b_abs_size == 1)
  86                 {
  87                   /* (a/0x80...00) == (a/2)^(NUMB-1) */
  88                   if ((GMP_NUMB_BITS % 2) == 0)
  89                     {
  90                       /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
  91                          when GMP_NUMB_BITS is even, so it's still 0. */
  92                       ASSERT (result_bit1 == 0);
  93                       result_bit1 = JACOBI_TWO_U_BIT1 (a);
  94                     }
  95                   return JACOBI_BIT1_TO_PN (result_bit1);
  96                 }
  97
  98               /* b_abs_size > 1 */
  99               b_low = b_ptr[1] << 1;
 100             }
 101           else
 102             {
 103               count_trailing_zeros (twos, b_low);
 104               b_low >>= twos;
 105             }
 106         }
 107     }
 108   else
 109     {
 110       if (a == 0)        /* (0/b)=1 for b=+/-1, 0 otherwise */
 111         return (b_abs_size == 1 && b_low == 1);
 112
 113       if (! (a & 1))
 114         {
 115           /* a even, b odd */
 116           count_trailing_zeros (twos, a);
 117           a >>= twos;
 118           /* (a*2^n/b) = (a/b) * (2/a)^n */
 119           result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
 120         }
 121     }
 122
 123   if (a == 1)
 124     return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
 125
 126   /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
 127   JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
 128   result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
 129   return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
 130 }