1/* mpz_si_kronecker -- long+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_si_kronecker (long a, mpz_srcptr b)
37{
38  mp_srcptr  b_ptr;
39  mp_limb_t  b_low;
40  mp_size_t  b_size;
41  mp_size_t  b_abs_size;
42  mp_limb_t  a_limb, b_rem;
43  unsigned   twos;
44  int        result_bit1;
45
46#if GMP_NUMB_BITS < BITS_PER_ULONG
47  if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX)
48    {
49      mp_limb_t  alimbs[2];
50      mpz_t      az;
51      ALLOC(az) = numberof (alimbs);
52      PTR(az) = alimbs;
53      mpz_set_si (az, a);
54      return mpz_kronecker (az, b);
55    }
56#endif
57
58  b_size = SIZ (b);
59  if (b_size == 0)
60    return JACOBI_S0 (a);  /* (a/0) */
61
62  /* account for the effect of the sign of b, then ignore it */
63  result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size);
64
65  b_ptr = PTR(b);
66  b_low = b_ptr[0];
67  b_abs_size = ABS (b_size);
68
69  if ((b_low & 1) != 0)
70    {
71      /* b odd */
72
73      result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
74      a_limb = ABS_CAST(mp_limb_t, a);
75
76      if ((a_limb & 1) == 0)
77	{
78	  /* (0/b)=1 for b=+/-1, 0 otherwise */
79	  if (a_limb == 0)
80	    return (b_abs_size == 1 && b_low == 1);
81
82	  /* a even, b odd */
83	  count_trailing_zeros (twos, a_limb);
84	  a_limb >>= twos;
85	  /* (a*2^n/b) = (a/b) * twos(n,a) */
86	  result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low);
87	}
88    }
89  else
90    {
91      /* (even/even)=0, and (0/b)=0 for b!=+/-1 */
92      if ((a & 1) == 0)
93	return 0;
94
95      /* a odd, b even
96
97	 Establish shifted b_low with valid bit1 for ASGN and RECIP below.
98	 Zero limbs stripped are accounted for, but zero bits on b_low are
99	 not because they remain in {b_ptr,b_abs_size} for the
100	 JACOBI_MOD_OR_MODEXACT_1_ODD. */
101
102      JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
103      if ((b_low & 1) == 0)
104	{
105	  if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
106	    {
107	      /* need b_ptr[1] to get bit1 in b_low */
108	      if (b_abs_size == 1)
109		{
110		  /* (a/0x80000000) = (a/2)^(BPML-1) */
111		  if ((GMP_NUMB_BITS % 2) == 0)
112		    result_bit1 ^= JACOBI_TWO_U_BIT1 (a);
113		  return JACOBI_BIT1_TO_PN (result_bit1);
114		}
115
116	      /* b_abs_size > 1 */
117	      b_low = b_ptr[1] << 1;
118	    }
119	  else
120	    {
121	      count_trailing_zeros (twos, b_low);
122	      b_low >>= twos;
123	    }
124	}
125
126      result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low);
127      a_limb = (unsigned long) ABS(a);
128    }
129
130  if (a_limb == 1)
131    return JACOBI_BIT1_TO_PN (result_bit1);  /* (1/b)=1 */
132
133  /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */
134  JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb);
135  result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low);
136  return mpn_jacobi_base (b_rem, a_limb, result_bit1);
137}
138