Module Name: src
Committed By: christos
Date: Sat Feb 3 15:40:29 UTC 2018
Modified Files:
src/games/primes: primes.6 primes.c primes.h spsp.c
Log Message:
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
To generate a diff of this commit:
cvs rdiff -u -r1.5 -r1.6 src/games/primes/primes.6
cvs rdiff -u -r1.21 -r1.22 src/games/primes/primes.c
cvs rdiff -u -r1.6 -r1.7 src/games/primes/primes.h
cvs rdiff -u -r1.1 -r1.2 src/games/primes/spsp.c
Please note that diffs are not public domain; they are subject to the
copyright notices on the relevant files.
Modified files:
Index: src/games/primes/primes.6
diff -u src/games/primes/primes.6:1.5 src/games/primes/primes.6:1.6
--- src/games/primes/primes.6:1.5 Sat Oct 4 09:15:50 2014
+++ src/games/primes/primes.6 Sat Feb 3 10:40:29 2018
@@ -1,4 +1,4 @@
-.\" $NetBSD: primes.6,v 1.5 2014/10/04 13:15:50 wiz Exp $
+.\" $NetBSD: primes.6,v 1.6 2018/02/03 15:40:29 christos Exp $
.\"
.\" Copyright (c) 1989, 1993
.\" The Regents of the University of California. All rights reserved.
@@ -35,7 +35,7 @@
.\"
.\" By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
.\"
-.Dd February 3, 2008
+.Dd February 2, 2018
.Dt PRIMES 6
.Os
.Sh NAME
@@ -100,14 +100,7 @@ Originally by
.An Landon Curt Noll ,
extended to some 64-bit primes by
.An Colin Percival .
-.Sh CAVEATS
+.Sh BUGS
This
.Nm
program won't get you a world record.
-.Pp
-The program is not able to list primes between
-3825123056546413050 and 18446744073709551615 (2^64
-- 1) as it relies on strong pseudoprime tests after
-sieving, and it is yet unknown how many of those
-tests are needed to prove primality for integers
-larger than 3825123056546413050.
Index: src/games/primes/primes.c
diff -u src/games/primes/primes.c:1.21 src/games/primes/primes.c:1.22
--- src/games/primes/primes.c:1.21 Sat Oct 4 09:15:50 2014
+++ src/games/primes/primes.c Sat Feb 3 10:40:29 2018
@@ -1,4 +1,4 @@
-/* $NetBSD: primes.c,v 1.21 2014/10/04 13:15:50 wiz Exp $ */
+/* $NetBSD: primes.c,v 1.22 2018/02/03 15:40:29 christos Exp $ */
/*
* Copyright (c) 1989, 1993
@@ -42,7 +42,7 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 19
#if 0
static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95";
#else
-__RCSID("$NetBSD: primes.c,v 1.21 2014/10/04 13:15:50 wiz Exp $");
+__RCSID("$NetBSD: primes.c,v 1.22 2018/02/03 15:40:29 christos Exp $");
#endif
#endif /* not lint */
@@ -118,7 +118,7 @@ main(int argc, char *argv[])
argv += optind;
start = 0;
- stop = SPSPMAX;
+ stop = (uint64_t)(-1);
/*
* Convert low and high args. Strtoumax(3) sets errno to
@@ -145,9 +145,6 @@ main(int argc, char *argv[])
err(1, "%s", argv[1]);
if (*p != '\0')
errx(1, "%s: illegal numeric format.", argv[1]);
- if (stop > SPSPMAX)
- errx(1, "%s: stop value too large (>%" PRIu64 ").",
- argv[1], (uint64_t) SPSPMAX);
break;
case 1:
/* Start on the command line. */
Index: src/games/primes/primes.h
diff -u src/games/primes/primes.h:1.6 src/games/primes/primes.h:1.7
--- src/games/primes/primes.h:1.6 Thu Oct 2 17:36:37 2014
+++ src/games/primes/primes.h Sat Feb 3 10:40:29 2018
@@ -1,4 +1,4 @@
-/* $NetBSD: primes.h,v 1.6 2014/10/02 21:36:37 ast Exp $ */
+/* $NetBSD: primes.h,v 1.7 2018/02/03 15:40:29 christos Exp $ */
/*
* Copyright (c) 1989, 1993
@@ -69,6 +69,3 @@ extern const size_t pattern_size; /* len
/* Test for primality using strong pseudoprime tests. */
int isprime(uint64_t);
-
-/* Maximum value which the SPSP code can handle. */
-#define SPSPMAX 3825123056546413050ULL
Index: src/games/primes/spsp.c
diff -u src/games/primes/spsp.c:1.1 src/games/primes/spsp.c:1.2
--- src/games/primes/spsp.c:1.1 Thu Oct 2 17:36:37 2014
+++ src/games/primes/spsp.c Sat Feb 3 10:40:29 2018
@@ -1,4 +1,4 @@
-/* $NetBSD: spsp.c,v 1.1 2014/10/02 21:36:37 ast Exp $ */
+/* $NetBSD: spsp.c,v 1.2 2018/02/03 15:40:29 christos Exp $ */
/*-
* Copyright (c) 2014 Colin Percival
@@ -36,7 +36,7 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 19
#if 0
static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95";
#else
-__RCSID("$NetBSD: spsp.c,v 1.1 2014/10/02 21:36:37 ast Exp $");
+__RCSID("$NetBSD: spsp.c,v 1.2 2018/02/03 15:40:29 christos Exp $");
#endif
#endif /* not lint */
@@ -46,23 +46,33 @@ __RCSID("$NetBSD: spsp.c,v 1.1 2014/10/0
#include "primes.h"
-/* Return a * b % n, where 0 <= a, b < 2^63, 0 < n < 2^63. */
+/* Return a * b % n, where 0 <= n. */
static uint64_t
mulmod(uint64_t a, uint64_t b, uint64_t n)
{
uint64_t x = 0;
+ uint64_t an = a % n;
while (b != 0) {
- if (b & 1)
- x = (x + a) % n;
- a = (a + a) % n;
+ if (b & 1) {
+ x += an;
+ if ((x < an) || (x >= n))
+ x -= n;
+ }
+ if (an + an < an)
+ an = an + an - n;
+ else if (an + an >= n)
+ an = an + an - n;
+ else
+ an = an + an;
+
b >>= 1;
}
return (x);
}
-/* Return a^r % n, where 0 <= a < 2^63, 0 < n < 2^63. */
+/* Return a^r % n, where 0 < n. */
static uint64_t
powmod(uint64_t a, uint64_t r, uint64_t n)
{
@@ -186,10 +196,20 @@ isprime(uint64_t _n)
return (0);
if (n < 3825123056546413051)
return (1);
+ /*
+ * Value from:
+ * J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime
+ * bases, Math. Comp. 86(304):985-1003, 2017.
+ */
- /* We can't handle values larger than this. */
- assert(n <= SPSPMAX);
+ /* No SPSPs to bases 2..37 less than 318665857834031151167461. */
+ if (!spsp(n, 29))
+ return (0);
+ if (!spsp(n, 31))
+ return (0);
+ if (!spsp(n, 37))
+ return (0);
- /* UNREACHABLE */
- return (0);
+ /* All 64-bit values are less than 318665857834031151167461. */
+ return (1);
}
