1 /* mpz_ui_kronecker -- ulong+mpz Kronecker/Jacobi symbol.
2
3 Copyright 1999, 2000, 2001, 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 the GNU Lesser General Public License as published by
9 the Free Software Foundation; either version 3 of the License, or (at your
10 option) any later version.
11
12 The GNU MP Library is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
15 License for more details.
16
17 You should have received a copy of the GNU Lesser General Public License
18 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
19
20 #include "gmp.h"
21 #include "gmp-impl.h"
22 #include "longlong.h"
23
24
25 int
mpz_ui_kronecker(unsigned long a,mpz_srcptr b)26 mpz_ui_kronecker (unsigned long a, mpz_srcptr b)
27 {
28 mp_srcptr b_ptr;
29 mp_limb_t b_low;
30 int b_abs_size;
31 mp_limb_t b_rem;
32 int twos;
33 int result_bit1;
34
35 /* (a/-1)=1 when a>=0, so the sign of b is ignored */
36 b_abs_size = ABSIZ (b);
37
38 if (b_abs_size == 0)
39 return JACOBI_U0 (a); /* (a/0) */
40
41 if (a > GMP_NUMB_MAX)
42 {
43 mp_limb_t alimbs[2];
44 mpz_t az;
45 ALLOC(az) = numberof (alimbs);
46 PTR(az) = alimbs;
47 mpz_set_ui (az, a);
48 return mpz_kronecker (az, b);
49 }
50
51 b_ptr = PTR(b);
52 b_low = b_ptr[0];
53 result_bit1 = 0;
54
55 if (! (b_low & 1))
56 {
57 /* (0/b)=0 for b!=+/-1; and (even/even)=0 */
58 if (! (a & 1))
59 return 0;
60
61 /* a odd, b even
62
63 Establish shifted b_low with valid bit1 for the RECIP below. Zero
64 limbs stripped are accounted for, but zero bits on b_low are not
65 because they remain in {b_ptr,b_abs_size} for
66 JACOBI_MOD_OR_MODEXACT_1_ODD. */
67
68 JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low);
69 if (! (b_low & 1))
70 {
71 if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT))
72 {
73 /* need b_ptr[1] to get bit1 in b_low */
74 if (b_abs_size == 1)
75 {
76 /* (a/0x80...00) == (a/2)^(NUMB-1) */
77 if ((GMP_NUMB_BITS % 2) == 0)
78 {
79 /* JACOBI_STRIP_LOW_ZEROS does nothing to result_bit1
80 when GMP_NUMB_BITS is even, so it's still 0. */
81 ASSERT (result_bit1 == 0);
82 result_bit1 = JACOBI_TWO_U_BIT1 (a);
83 }
84 return JACOBI_BIT1_TO_PN (result_bit1);
85 }
86
87 /* b_abs_size > 1 */
88 b_low = b_ptr[1] << 1;
89 }
90 else
91 {
92 count_trailing_zeros (twos, b_low);
93 b_low >>= twos;
94 }
95 }
96 }
97 else
98 {
99 if (a == 0) /* (0/b)=1 for b=+/-1, 0 otherwise */
100 return (b_abs_size == 1 && b_low == 1);
101
102 if (! (a & 1))
103 {
104 /* a even, b odd */
105 count_trailing_zeros (twos, a);
106 a >>= twos;
107 /* (a*2^n/b) = (a/b) * (2/a)^n */
108 result_bit1 = JACOBI_TWOS_U_BIT1 (twos, b_low);
109 }
110 }
111
112 if (a == 1)
113 return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */
114
115 /* (a/b*2^n) = (b*2^n mod a / a) * RECIP(a,b) */
116 JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a);
117 result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b_low);
118 return mpn_jacobi_base (b_rem, (mp_limb_t) a, result_bit1);
119 }
120