1/* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
2
3Copyright 1999-2002 Free Software Foundation, Inc.
4
5This file is part of the GNU MP Library.
6
7The GNU MP Library is free software; you can redistribute it and/or modify
8it 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
14or
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
20or both in parallel, as here.
21
22The GNU MP Library is distributed in the hope that it will be useful, but
23WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
24or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
25for more details.
26
27You should have received copies of the GNU General Public License and the
28GNU Lesser General Public License along with the GNU MP Library.  If not,
29see https://www.gnu.org/licenses/.  */
30
31#include "gmp-impl.h"
32#include "longlong.h"
33
34
35int
36mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
37{
38  mp_srcptr  b_ptr;
39  mp_limb_t  b_low;
40  int        b_abs_size;
41  mp_limb_t  b_rem;
42  int        twos;
43  int        result_bit1;
44
45  /* (a/-1)=1 when a>=0, so the sign of b is ignored */
46  b_abs_size = ABSIZ (b);
47
48  if (b_abs_size == 0)
49    return JACOBI_U0 (a);  /* (a/0) */
50
51  if (a > GMP_NUMB_MAX)
52    {
53      mp_limb_t  alimbs[2];
54      mpz_t      az;
55      ALLOC(az) = numberof (alimbs);
56      PTR(az) = alimbs;
57      mpz_set_ui (az, a);
58      return mpz_kronecker (az, b);
59    }
60
61  b_ptr = PTR(b);
62  b_low = b_ptr[0];
63  result_bit1 = 0;
64
65  if (! (b_low & 1))
66    {
67      /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
68      if (! (a & 1))
69	return 0;
70
71      /* a odd, b even
72
73	 Establish shifted b_low with valid bit1 for the RECIP below.  Zero
74	 limbs stripped are accounted for, but zero bits on b_low are not
75	 because they remain in {b_ptr,b_abs_size} for
76	 JACOBI_MOD_OR_MODEXACT_1_ODD. */
77
78      JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
79      if (! (b_low & 1))
80	{
81	  if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
82	    {
83	      /* need b_ptr[1] to get bit1 in b_low */
84	      if (b_abs_size == 1)
85		{
86		  /* (a/0x80...00) == (a/2)^(NUMB-1) */
87		  if ((GMP_NUMB_BITS % 2) == 0)
88		    {
89		      /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
90			 when GMP_NUMB_BITS is even, so it's still 0. */
91		      ASSERT (result_bit1 == 0);
92		      result_bit1 = JACOBI_TWO_U_BIT1 (a);
93		    }
94		  return JACOBI_BIT1_TO_PN (result_bit1);
95		}
96
97	      /* b_abs_size > 1 */
98	      b_low = b_ptr[1] << 1;
99	    }
100	  else
101	    {
102	      count_trailing_zeros (twos, b_low);
103	      b_low >>= twos;
104	    }
105	}
106    }
107  else
108    {
109      if (a == 0)        /* (0/b)=1 for b=+/-1, 0 otherwise */
110	return (b_abs_size == 1 && b_low == 1);
111
112      if (! (a & 1))
113	{
114	  /* a even, b odd */
115	  count_trailing_zeros (twos, a);
116	  a >>= twos;
117	  /* (a*2^n/b) = (a/b) * (2/a)^n */
118	  result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
119	}
120    }
121
122  if (a == 1)
123    return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
124
125  /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
126  JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
127  result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
128  return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
129}
130