PR/52976: Eitan Adler: handle larger primes
Using results from
J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime
bases, Math. Comp. 86(304):985-1003, 2017.
teach primes(6) to enumerate primes up to 2^64 - 1. Until Sorenson
and Webster's paper, we did not know how many strong speudoprime tests
were required when testing alleged primes between 3825123056546413051
and 2^64 - 1.
Adapted from: FreeBSD
This commit is contained in:
christos
parent
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@ -1,4 +1,4 @@
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.\" $NetBSD: primes.6,v 1.5 2014/10/04 13:15:50 wiz Exp $
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.\" $NetBSD: primes.6,v 1.6 2018/02/03 15:40:29 christos Exp $
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.\"
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.\" Copyright (c) 1989, 1993
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.\" The Regents of the University of California. All rights reserved.
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@ -35,7 +35,7 @@
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.\"
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.\" By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
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.\"
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.Dd February 3, 2008
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.Dd February 2, 2018
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.Dt PRIMES 6
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.Os
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.Sh NAME
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@ -100,14 +100,7 @@ Originally by
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.An Landon Curt Noll ,
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extended to some 64-bit primes by
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.An Colin Percival .
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.Sh CAVEATS
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.Sh BUGS
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This
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.Nm
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program won't get you a world record.
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.Pp
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The program is not able to list primes between
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3825123056546413050 and 18446744073709551615 (2^64
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- 1) as it relies on strong pseudoprime tests after
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sieving, and it is yet unknown how many of those
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tests are needed to prove primality for integers
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larger than 3825123056546413050.
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@ -1,4 +1,4 @@
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/* $NetBSD: primes.c,v 1.21 2014/10/04 13:15:50 wiz Exp $ */
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/* $NetBSD: primes.c,v 1.22 2018/02/03 15:40:29 christos Exp $ */
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/*
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* Copyright (c) 1989, 1993
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@ -42,7 +42,7 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
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#if 0
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static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95";
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#else
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__RCSID("$NetBSD: primes.c,v 1.21 2014/10/04 13:15:50 wiz Exp $");
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__RCSID("$NetBSD: primes.c,v 1.22 2018/02/03 15:40:29 christos Exp $");
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#endif
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#endif /* not lint */
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@ -118,7 +118,7 @@ main(int argc, char *argv[])
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argv += optind;
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start = 0;
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stop = SPSPMAX;
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stop = (uint64_t)(-1);
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/*
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* Convert low and high args. Strtoumax(3) sets errno to
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@ -145,9 +145,6 @@ main(int argc, char *argv[])
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err(1, "%s", argv[1]);
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if (*p != '\0')
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errx(1, "%s: illegal numeric format.", argv[1]);
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if (stop > SPSPMAX)
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errx(1, "%s: stop value too large (>%" PRIu64 ").",
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argv[1], (uint64_t) SPSPMAX);
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break;
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case 1:
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/* Start on the command line. */
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@ -1,4 +1,4 @@
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/* $NetBSD: primes.h,v 1.6 2014/10/02 21:36:37 ast Exp $ */
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/* $NetBSD: primes.h,v 1.7 2018/02/03 15:40:29 christos Exp $ */
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/*
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* Copyright (c) 1989, 1993
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@ -69,6 +69,3 @@ extern const size_t pattern_size; /* length of pattern array */
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/* Test for primality using strong pseudoprime tests. */
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int isprime(uint64_t);
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/* Maximum value which the SPSP code can handle. */
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#define SPSPMAX 3825123056546413050ULL
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@ -1,4 +1,4 @@
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/* $NetBSD: spsp.c,v 1.1 2014/10/02 21:36:37 ast Exp $ */
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/* $NetBSD: spsp.c,v 1.2 2018/02/03 15:40:29 christos Exp $ */
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/*-
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* Copyright (c) 2014 Colin Percival
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@ -36,7 +36,7 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
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#if 0
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static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95";
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#else
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__RCSID("$NetBSD: spsp.c,v 1.1 2014/10/02 21:36:37 ast Exp $");
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__RCSID("$NetBSD: spsp.c,v 1.2 2018/02/03 15:40:29 christos Exp $");
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#endif
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#endif /* not lint */
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@ -46,23 +46,33 @@ __RCSID("$NetBSD: spsp.c,v 1.1 2014/10/02 21:36:37 ast Exp $");
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#include "primes.h"
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/* Return a * b % n, where 0 <= a, b < 2^63, 0 < n < 2^63. */
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/* Return a * b % n, where 0 <= n. */
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static uint64_t
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mulmod(uint64_t a, uint64_t b, uint64_t n)
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{
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uint64_t x = 0;
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uint64_t an = a % n;
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while (b != 0) {
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if (b & 1)
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x = (x + a) % n;
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a = (a + a) % n;
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if (b & 1) {
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x += an;
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if ((x < an) || (x >= n))
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x -= n;
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}
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if (an + an < an)
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an = an + an - n;
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else if (an + an >= n)
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an = an + an - n;
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else
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an = an + an;
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b >>= 1;
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}
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return (x);
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}
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/* Return a^r % n, where 0 <= a < 2^63, 0 < n < 2^63. */
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/* Return a^r % n, where 0 < n. */
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static uint64_t
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powmod(uint64_t a, uint64_t r, uint64_t n)
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{
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@ -186,10 +196,20 @@ isprime(uint64_t _n)
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return (0);
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if (n < 3825123056546413051)
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return (1);
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/*
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* Value from:
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* J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime
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* bases, Math. Comp. 86(304):985-1003, 2017.
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*/
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/* We can't handle values larger than this. */
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assert(n <= SPSPMAX);
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/* No SPSPs to bases 2..37 less than 318665857834031151167461. */
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if (!spsp(n, 29))
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return (0);
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if (!spsp(n, 31))
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return (0);
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if (!spsp(n, 37))
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return (0);
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/* UNREACHABLE */
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return (0);
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/* All 64-bit values are less than 318665857834031151167461. */
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return (1);
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}
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