2 * Copyright (c) 2014 Colin Percival
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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.
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
26 #include <sys/cdefs.h>
27 __FBSDID("$FreeBSD$");
35 /* Return a * b % n, where 0 <= a, b < 2^63, 0 < n < 2^63. */
37 mulmod(uint64_t a, uint64_t b, uint64_t n)
51 /* Return a^r % n, where 0 <= a < 2^63, 0 < n < 2^63. */
53 powmod(uint64_t a, uint64_t r, uint64_t n)
67 /* Return non-zero if n is a strong pseudoprime to base p. */
69 spsp(uint64_t n, uint64_t p)
75 /* Compute n - 1 = 2^k * r. */
76 while ((r & 1) == 0) {
81 /* Compute x = p^r mod n. If x = 1, n is a p-spsp. */
86 /* Compute x^(2^i) for 0 <= i < n. If any are -1, n is a p-spsp. */
98 /* Test for primality using strong pseudoprime tests. */
106 * C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr.,
107 * The pseudoprimes to 25 * 10^9, Math. Comp. 35(151):1003-1026, 1980.
110 /* No SPSPs to base 2 less than 2047. */
116 /* No SPSPs to bases 2,3 less than 1373653. */
122 /* No SPSPs to bases 2,3,5 less than 25326001. */
128 /* No SPSPs to bases 2,3,5,7 less than 3215031751. */
131 if (n < 3215031751ULL)
136 * G. Jaeschke, On strong pseudoprimes to several bases,
137 * Math. Comp. 61(204):915-926, 1993.
140 /* No SPSPs to bases 2,3,5,7,11 less than 2152302898747. */
143 if (n < 2152302898747ULL)
146 /* No SPSPs to bases 2,3,5,7,11,13 less than 3474749660383. */
149 if (n < 3474749660383ULL)
152 /* No SPSPs to bases 2,3,5,7,11,13,17 less than 341550071728321. */
155 if (n < 341550071728321ULL)
158 /* No SPSPs to bases 2,3,5,7,11,13,17,19 less than 341550071728321. */
161 if (n < 341550071728321ULL)
166 * Y. Jiang and Y. Deng, Strong pseudoprimes to the first eight prime
167 * bases, Math. Comp. 83(290):2915-2924, 2014.
170 /* No SPSPs to bases 2..23 less than 3825123056546413051. */
173 if (n < 3825123056546413051)
176 /* We can't handle values larger than this. */
177 assert(n <= SPSPMAX);