1 /*-
2 * Copyright (c) 2014 Colin Percival
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26 #include <sys/cdefs.h>
27 #include <stddef.h>
28 #include <stdint.h>
29
30 #include "primes.h"
31
32 /* Return a * b % n, where 0 < n. */
33 static uint64_t
mulmod(uint64_t a,uint64_t b,uint64_t n)34 mulmod(uint64_t a, uint64_t b, uint64_t n)
35 {
36 uint64_t x = 0;
37 uint64_t an = a % n;
38
39 while (b != 0) {
40 if (b & 1) {
41 x += an;
42 if ((x < an) || (x >= n))
43 x -= n;
44 }
45 if (an + an < an)
46 an = an + an - n;
47 else if (an + an >= n)
48 an = an + an - n;
49 else
50 an = an + an;
51 b >>= 1;
52 }
53
54 return (x);
55 }
56
57 /* Return a^r % n, where 0 < n. */
58 static uint64_t
powmod(uint64_t a,uint64_t r,uint64_t n)59 powmod(uint64_t a, uint64_t r, uint64_t n)
60 {
61 uint64_t x = 1;
62
63 while (r != 0) {
64 if (r & 1)
65 x = mulmod(a, x, n);
66 a = mulmod(a, a, n);
67 r >>= 1;
68 }
69
70 return (x);
71 }
72
73 /* Return non-zero if n is a strong pseudoprime to base p. */
74 static int
spsp(uint64_t n,uint64_t p)75 spsp(uint64_t n, uint64_t p)
76 {
77 uint64_t x;
78 uint64_t r = n - 1;
79 int k = 0;
80
81 /* Compute n - 1 = 2^k * r. */
82 while ((r & 1) == 0) {
83 k++;
84 r >>= 1;
85 }
86
87 /* Compute x = p^r mod n. If x = 1, n is a p-spsp. */
88 x = powmod(p, r, n);
89 if (x == 1)
90 return (1);
91
92 /* Compute x^(2^i) for 0 <= i < n. If any are -1, n is a p-spsp. */
93 while (k > 0) {
94 if (x == n - 1)
95 return (1);
96 x = powmod(x, 2, n);
97 k--;
98 }
99
100 /* Not a p-spsp. */
101 return (0);
102 }
103
104 /* Test for primality using strong pseudoprime tests. */
105 int
isprime(ubig _n)106 isprime(ubig _n)
107 {
108 uint64_t n = _n;
109
110 /*
111 * Values from:
112 * C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr.,
113 * The pseudoprimes to 25 * 10^9, Math. Comp. 35(151):1003-1026, 1980.
114 */
115
116 /* No SPSPs to base 2 less than 2047. */
117 if (!spsp(n, 2))
118 return (0);
119 if (n < 2047ULL)
120 return (1);
121
122 /* No SPSPs to bases 2,3 less than 1373653. */
123 if (!spsp(n, 3))
124 return (0);
125 if (n < 1373653ULL)
126 return (1);
127
128 /* No SPSPs to bases 2,3,5 less than 25326001. */
129 if (!spsp(n, 5))
130 return (0);
131 if (n < 25326001ULL)
132 return (1);
133
134 /* No SPSPs to bases 2,3,5,7 less than 3215031751. */
135 if (!spsp(n, 7))
136 return (0);
137 if (n < 3215031751ULL)
138 return (1);
139
140 /*
141 * Values from:
142 * G. Jaeschke, On strong pseudoprimes to several bases,
143 * Math. Comp. 61(204):915-926, 1993.
144 */
145
146 /* No SPSPs to bases 2,3,5,7,11 less than 2152302898747. */
147 if (!spsp(n, 11))
148 return (0);
149 if (n < 2152302898747ULL)
150 return (1);
151
152 /* No SPSPs to bases 2,3,5,7,11,13 less than 3474749660383. */
153 if (!spsp(n, 13))
154 return (0);
155 if (n < 3474749660383ULL)
156 return (1);
157
158 /* No SPSPs to bases 2,3,5,7,11,13,17 less than 341550071728321. */
159 if (!spsp(n, 17))
160 return (0);
161 if (n < 341550071728321ULL)
162 return (1);
163
164 /* No SPSPs to bases 2,3,5,7,11,13,17,19 less than 341550071728321. */
165 if (!spsp(n, 19))
166 return (0);
167 if (n < 341550071728321ULL)
168 return (1);
169
170 /*
171 * Value from:
172 * Y. Jiang and Y. Deng, Strong pseudoprimes to the first eight prime
173 * bases, Math. Comp. 83(290):2915-2924, 2014.
174 */
175
176 /* No SPSPs to bases 2..23 less than 3825123056546413051. */
177 if (!spsp(n, 23))
178 return (0);
179 if (n < 3825123056546413051)
180 return (1);
181
182 /*
183 * Value from:
184 * J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime
185 * bases, Math. Comp. 86(304):985-1003, 2017.
186 */
187
188 /* No SPSPs to bases 2..37 less than 318665857834031151167461. */
189 if (!spsp(n, 29))
190 return (0);
191 if (!spsp(n, 31))
192 return (0);
193 if (!spsp(n, 37))
194 return (0);
195
196 /* All 64-bit values are less than 318665857834031151167461. */
197 return (1);
198 }
199