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-impl.h"
32 #include "longlong.h"
33
34
35 int
36 mpz_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 }