1 /*
2 Copyright (C) 2008 Peter Shrimpton
3 Copyright (C) 2009 William Hart
4
5 This file is part of FLINT.
6
7 FLINT is free software: you can redistribute it and/or modify it under
8 the terms of the GNU Lesser General Public License (LGPL) as published
9 by the Free Software Foundation; either version 2.1 of the License, or
10 (at your option) any later version. See <https://www.gnu.org/licenses/>.
11 */
12
13 #include <gmp.h>
14 #include "flint.h"
15 #include "ulong_extras.h"
16
17 n_pair_t
lchain_precomp(mp_limb_t m,mp_limb_t a,mp_limb_t n,double npre)18 lchain_precomp(mp_limb_t m, mp_limb_t a, mp_limb_t n, double npre)
19 {
20 n_pair_t current = {0, 0}, old;
21 int length, i;
22 mp_limb_t power, xy, xx, yy;
23
24 old.x = UWORD(2);
25 old.y = a;
26
27 length = FLINT_BIT_COUNT(m);
28 power = (UWORD(1) << (length - 1));
29
30 for (i = 0; i < length; i++)
31 {
32 xy = n_submod(n_mulmod_precomp(old.x, old.y, n, npre), a, n);
33
34 if (m & power)
35 {
36 yy = n_submod(n_mulmod_precomp(old.y, old.y, n, npre), UWORD(2), n);
37 current.x = xy;
38 current.y = yy;
39 }
40 else
41 {
42 xx = n_submod(n_mulmod_precomp(old.x, old.x, n, npre), UWORD(2), n);
43 current.x = xx;
44 current.y = xy;
45 }
46
47 power >>= 1;
48 old = current;
49 }
50
51 return current;
52 }
53
54 n_pair_t
lchain2_preinv(mp_limb_t m,mp_limb_t a,mp_limb_t n,mp_limb_t ninv)55 lchain2_preinv(mp_limb_t m, mp_limb_t a, mp_limb_t n, mp_limb_t ninv)
56 {
57 n_pair_t current = {0, 0}, old;
58 int length, i;
59 mp_limb_t power, xy, xx, yy;
60
61 old.x = UWORD(2);
62 old.y = a;
63
64 length = FLINT_BIT_COUNT(m);
65 power = (UWORD(1) << (length - 1));
66
67 for (i = 0; i < length; i++)
68 {
69 xy = n_submod(n_mulmod2_preinv(old.x, old.y, n, ninv), a, n);
70
71 if (m & power)
72 {
73 yy = n_submod(n_mulmod2_preinv(old.y, old.y, n, ninv), UWORD(2), n);
74 current.x = xy;
75 current.y = yy;
76 }
77 else
78 {
79 xx = n_submod(n_mulmod2_preinv(old.x, old.x, n, ninv), UWORD(2), n);
80 current.x = xx;
81 current.y = xy;
82 }
83
84 power >>= 1;
85 old = current;
86 }
87
88 return current;
89 }
90
91 int
n_is_probabprime_lucas(mp_limb_t n)92 n_is_probabprime_lucas(mp_limb_t n)
93 {
94 int i, D, Q;
95 mp_limb_t A;
96 mp_limb_t left, right;
97 n_pair_t V;
98
99 D = 0;
100 Q = 0;
101
102 if (((n % 2) == 0) || (FLINT_ABS((mp_limb_signed_t) n) <= 2))
103 {
104 return (n == UWORD(2));
105 }
106
107 for (i = 0; i < 100; i++)
108 {
109 D = 5 + 2 * i;
110 if (n_gcd(D, n % D) != UWORD(1))
111 {
112 if (n == D)
113 continue;
114 else
115 return 0;
116 }
117 if (i % 2 == 1)
118 D = -D;
119 if (n_jacobi(D, n) == -1)
120 break;
121 }
122
123 if (i == 100)
124 {
125 return (n_is_square(n) ? -1 : 1);
126 }
127
128 Q = (1 - D) / 4;
129 if (Q < 0)
130 {
131 if (n < UWORD(52))
132 {
133 while (Q < 0)
134 Q += n;
135 A = n_submod(n_invmod(Q, n), UWORD(2), n);
136 }
137 else
138 A = n_submod(n_invmod(Q + n, n), UWORD(2), n);
139 }
140 else
141 {
142 if (n < UWORD(52))
143 {
144 while (Q >= n)
145 Q -= n;
146 A = n_submod(n_invmod(Q, n), UWORD(2), n);
147 }
148 else
149 A = n_submod(n_invmod(Q, n), UWORD(2), n);
150 }
151
152 if (FLINT_BIT_COUNT(n) <= FLINT_D_BITS)
153 {
154 double npre = n_precompute_inverse(n);
155 V = lchain_precomp(n + 1, A, n, npre);
156
157 left = n_mulmod_precomp(A, V.x, n, npre);
158 right = n_mulmod_precomp(2, V.y, n, npre);
159 }
160 else
161 {
162 mp_limb_t ninv = n_preinvert_limb(n);
163 V = lchain2_preinv(n + 1, A, n, ninv);
164
165 left = n_mulmod_precomp(A, V.x, n, ninv);
166 right = n_mulmod_precomp(2, V.y, n, ninv);
167 }
168
169 return (left == right);
170 }
171