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Diffstat (limited to 'usr.bin/primes/spsp.c')
| -rw-r--r-- | usr.bin/primes/spsp.c | 181 |
1 files changed, 181 insertions, 0 deletions
diff --git a/usr.bin/primes/spsp.c b/usr.bin/primes/spsp.c new file mode 100644 index 0000000..f61acd6 --- /dev/null +++ b/usr.bin/primes/spsp.c @@ -0,0 +1,181 @@ +/*- + * Copyright (c) 2014 Colin Percival + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ +#include <sys/cdefs.h> +__FBSDID("$FreeBSD$"); + +#include <assert.h> +#include <stddef.h> +#include <stdint.h> + +#include "primes.h" + +/* Return a * b % n, where 0 <= a, b < 2^63, 0 < n < 2^63. */ +static uint64_t +mulmod(uint64_t a, uint64_t b, uint64_t n) +{ + uint64_t x = 0; + + while (b != 0) { + if (b & 1) + x = (x + a) % n; + a = (a + a) % n; + b >>= 1; + } + + return (x); +} + +/* Return a^r % n, where 0 <= a < 2^63, 0 < n < 2^63. */ +static uint64_t +powmod(uint64_t a, uint64_t r, uint64_t n) +{ + uint64_t x = 1; + + while (r != 0) { + if (r & 1) + x = mulmod(a, x, n); + a = mulmod(a, a, n); + r >>= 1; + } + + return (x); +} + +/* Return non-zero if n is a strong pseudoprime to base p. */ +static int +spsp(uint64_t n, uint64_t p) +{ + uint64_t x; + uint64_t r = n - 1; + int k = 0; + + /* Compute n - 1 = 2^k * r. */ + while ((r & 1) == 0) { + k++; + r >>= 1; + } + + /* Compute x = p^r mod n. If x = 1, n is a p-spsp. */ + x = powmod(p, r, n); + if (x == 1) + return (1); + + /* Compute x^(2^i) for 0 <= i < n. If any are -1, n is a p-spsp. */ + while (k > 0) { + if (x == n - 1) + return (1); + x = powmod(x, 2, n); + k--; + } + + /* Not a p-spsp. */ + return (0); +} + +/* Test for primality using strong pseudoprime tests. */ +int +isprime(ubig _n) +{ + uint64_t n = _n; + + /* + * Values from: + * C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr., + * The pseudoprimes to 25 * 10^9, Math. Comp. 35(151):1003-1026, 1980. + */ + + /* No SPSPs to base 2 less than 2047. */ + if (!spsp(n, 2)) + return (0); + if (n < 2047ULL) + return (1); + + /* No SPSPs to bases 2,3 less than 1373653. */ + if (!spsp(n, 3)) + return (0); + if (n < 1373653ULL) + return (1); + + /* No SPSPs to bases 2,3,5 less than 25326001. */ + if (!spsp(n, 5)) + return (0); + if (n < 25326001ULL) + return (1); + + /* No SPSPs to bases 2,3,5,7 less than 3215031751. */ + if (!spsp(n, 7)) + return (0); + if (n < 3215031751ULL) + return (1); + + /* + * Values from: + * G. Jaeschke, On strong pseudoprimes to several bases, + * Math. Comp. 61(204):915-926, 1993. + */ + + /* No SPSPs to bases 2,3,5,7,11 less than 2152302898747. */ + if (!spsp(n, 11)) + return (0); + if (n < 2152302898747ULL) + return (1); + + /* No SPSPs to bases 2,3,5,7,11,13 less than 3474749660383. */ + if (!spsp(n, 13)) + return (0); + if (n < 3474749660383ULL) + return (1); + + /* No SPSPs to bases 2,3,5,7,11,13,17 less than 341550071728321. */ + if (!spsp(n, 17)) + return (0); + if (n < 341550071728321ULL) + return (1); + + /* No SPSPs to bases 2,3,5,7,11,13,17,19 less than 341550071728321. */ + if (!spsp(n, 19)) + return (0); + if (n < 341550071728321ULL) + return (1); + + /* + * Value from: + * Y. Jiang and Y. Deng, Strong pseudoprimes to the first eight prime + * bases, Math. Comp. 83(290):2915-2924, 2014. + */ + + /* No SPSPs to bases 2..23 less than 3825123056546413051. */ + if (!spsp(n, 23)) + return (0); + if (n < 3825123056546413051) + return (1); + + /* We can't handle values larger than this. */ + assert(n <= SPSPMAX); + + /* UNREACHABLE */ + return (0); +} |
