Imported and adapted from FreeBSD svn r272166 and r272207; this fixes

false positives for products of primes larger than 2^16. For example,
before this commit:

  $ /usr/games/primes 4295360521 4295360522
  4295360521
but
  $ /usr/games/factor 4295360521
  4295360521: 65539 65539

or
  $ /usr/games/primes 3825123056546413049 3825123056546413050
  3825123056546413049
yet
  $ /usr/games/factor 3825123056546413049
  3825123056546413049: 165479 23115459100831

or
  $ /usr/games/primes 18446744073709551577
  18446744073709551577
although
  $ /usr/games/factor 18446744073709551577
  18446744073709551577: 139646831 132095686967

Incidentally, the above examples show the smallest and largest cases that
were erroneously stated as prime in the range 2^32 .. 3825123056546413049
.. 2^64; the primes(6) program now stops at 3825123056546413050 as
primality tests on larger integers would be by brute force factorization.

In addition, special to the NetBSD version:
. for -d option, skip first difference when start is >65537 as it is incorrect
. corrected usage to mention both the existing -d as well as the new -h option

For original FreeBSD commit message by Colin Percival, see:
http://svnweb.freebsd.org/base?view=revision&revision=272166

7 files changed, 331 insertions, 104 deletions

diff --git a/primes/Makefile b/primes/Makefile
index 42350418..8ed845cd 100644
--- a/primes/Makefile
+++ b/primes/Makefile
@@ -1,8 +1,8 @@
-#	$NetBSD: Makefile,v 1.7 2004/02/08 13:16:25 jsm Exp $
+#	$NetBSD: Makefile,v 1.8 2014/10/02 21:36:37 ast Exp $
 #	@(#)Makefile	8.1 (Berkeley) 5/31/93
 
 PROG=		primes
-SRCS=		pattern.c pr_tbl.c primes.c
+SRCS=		pattern.c pr_tbl.c primes.c spsp.c
 MAN=		primes.6
 DPADD=		${LIBM}
 LDADD=		-lm
diff --git a/primes/pattern.c b/primes/pattern.c
index 11960567..52784a5a 100644
--- a/primes/pattern.c
+++ b/primes/pattern.c
@@ -1,4 +1,4 @@
-/*	$NetBSD: pattern.c,v 1.6 2003/08/07 09:37:33 agc Exp $	*/
+/*	$NetBSD: pattern.c,v 1.7 2014/10/02 21:36:37 ast Exp $	*/
 
 /*
  * Copyright (c) 1989, 1993
@@ -32,21 +32,20 @@
  * SUCH DAMAGE.
  */
 
-#include <sys/cdefs.h>
+#include <sys/types.h>
+
 #ifndef lint
 #if 0
 static char sccsid[] = "@(#)pattern.c	8.1 (Berkeley) 5/31/93";
 #else
-__RCSID("$NetBSD: pattern.c,v 1.6 2003/08/07 09:37:33 agc Exp $");
+__RCSID("$NetBSD: pattern.c,v 1.7 2014/10/02 21:36:37 ast Exp $");
 #endif
 #endif /* not lint */
 
 /*
  * pattern - the Eratosthenes sieve on odd numbers for 3,5,7,11 and 13
  *
- * By: Landon Curt Noll                             chongo@toad.com
- *
- *   chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+ * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
  *
  * To avoid excessive sieves for small factors, we use the table below to 
  * setup our sieve blocks.  Each element represents a odd number starting 
@@ -440,4 +439,4 @@ const char pattern[] = {
 0,0,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,
 0,0,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1
 };
-const int pattern_size = (sizeof(pattern)/sizeof(pattern[0]));
+const size_t pattern_size = (sizeof(pattern)/sizeof(pattern[0]));
diff --git a/primes/pr_tbl.c b/primes/pr_tbl.c
index d45204a0..5e2f8134 100644
--- a/primes/pr_tbl.c
+++ b/primes/pr_tbl.c
@@ -1,4 +1,4 @@
-/*	$NetBSD: pr_tbl.c,v 1.7 2003/08/07 09:37:33 agc Exp $	*/
+/*	$NetBSD: pr_tbl.c,v 1.8 2014/10/02 21:36:37 ast Exp $	*/
 
 /*
  * Copyright (c) 1989, 1993
@@ -37,24 +37,24 @@
 #if 0
 static char sccsid[] = "@(#)pr_tbl.c	8.1 (Berkeley) 5/31/93";
 #else
-__RCSID("$NetBSD: pr_tbl.c,v 1.7 2003/08/07 09:37:33 agc Exp $");
+__RCSID("$NetBSD: pr_tbl.c,v 1.8 2014/10/02 21:36:37 ast Exp $");
 #endif
 #endif /* not lint */
 
 /*
  * prime - prime table
  *
- * By: Landon Curt Noll   chongo@toad.com,   ...!{sun,tolsoft}!hoptoad!chongo
+ * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
  *
- *   chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
- *
- * We are able to sieve 2^32-1 because this table has primes up to 65537 
+ * We are able to sieve 2^32-1 because this table has primes up to 65537
  * and 65537^2 > 2^32-1.
  */
 
+#include <stddef.h>
+
 #include "primes.h"
 
-const ubig prime[] = {
+const uint64_t prime[] = {
 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,
 107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,
 211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,
@@ -546,4 +546,4 @@ const ubig prime[] = {
 };
 
 /* pr_limit - largest prime in the prime table */
-const ubig *pr_limit = &prime[(sizeof(prime)/sizeof(prime[0]))-1];
+const uint64_t *const pr_limit = &prime[(sizeof(prime)/sizeof(prime[0]))-1];
diff --git a/primes/primes.6 b/primes/primes.6
index 9499398f..6928fe66 100644
--- a/primes/primes.6
+++ b/primes/primes.6
@@ -1,4 +1,4 @@
-.\"	$NetBSD: primes.6,v 1.3 2008/02/03 03:29:17 wiz Exp $
+.\"	$NetBSD: primes.6,v 1.4 2014/10/02 21:36:37 ast Exp $
 .\"
 .\" Copyright (c) 1989, 1993
 .\"	The Regents of the University of California.  All rights reserved.
@@ -33,9 +33,7 @@
 .\"	@(#)factor.6	8.1 (Berkeley) 5/31/93
 .\"
 .\"
-.\" By: Landon Curt Noll   chongo@toad.com,   ...!{sun,tolsoft}!hoptoad!chongo
-.\"
-.\"   chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+.\" By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
 .\"
 .Dd February 3, 2008
 .Dt PRIMES 6
@@ -46,6 +44,7 @@
 .Sh SYNOPSIS
 .Nm primes
 .Op Fl d
+.Op Fl h
 .Op Ar start Op Ar stop
 .Sh DESCRIPTION
 The
@@ -61,18 +60,18 @@ value must be at least 0 and not greater than
 .Ar stop .
 The
 .Ar stop
-value must not be greater than 4294967295.
+value must not be greater than 3825123056546413050.
 The default value of
 .Ar stop
-is 4294967295.
+is 3825123056546413050.
 .Pp
 When the
 .Nm
 utility is invoked with no arguments,
 .Ar start
-is read from standard input.
+is read from standard input and
 .Ar stop
-is taken to be 4294967295.
+is taken to be 3825123056546413050.
 The
 .Ar start
 value may be preceded by a single
@@ -81,15 +80,34 @@ The
 .Ar start
 value is terminated by a non-digit character (such as a newline).
 The input line must not be longer than 255 characters.
+.Pp
 When given the
 .Fl d
 argument,
 .Nm
 prints the difference between the current and the previous prime.
+.Pp
+When given the
+.Fl h
+argument,
+.Nm
+prints the prime numbers in hexadecimal.
 .Sh DIAGNOSTICS
 Out of range or invalid input results in
-an appropriate error message
-being written to standard error.
-.Sh BUGS
+an appropriate error message to standard error.
+.Sh AUTHORS
+Originally by
+.An Landon Curt Noll ,
+extended to some 64-bit primes by
+.An Colin Percival .
+.Sh CAVEATS
+This
 .Nm
-won't get you a world record.
+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.
diff --git a/primes/primes.c b/primes/primes.c
index 5952bbf6..15bdeadc 100644
--- a/primes/primes.c
+++ b/primes/primes.c
@@ -1,4 +1,4 @@
-/*	$NetBSD: primes.c,v 1.19 2011/08/30 02:58:04 jakllsch Exp $	*/
+/*	$NetBSD: primes.c,v 1.20 2014/10/02 21:36:37 ast Exp $	*/
 
 /*
  * Copyright (c) 1989, 1993
@@ -42,23 +42,23 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
 #if 0
 static char sccsid[] = "@(#)primes.c	8.5 (Berkeley) 5/10/95";
 #else
-__RCSID("$NetBSD: primes.c,v 1.19 2011/08/30 02:58:04 jakllsch Exp $");
+__RCSID("$NetBSD: primes.c,v 1.20 2014/10/02 21:36:37 ast Exp $");
 #endif
 #endif /* not lint */
 
 /*
  * primes - generate a table of primes between two values
  *
- * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
- *
- * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+ * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
  *
  * usage:
- *	primes [start [stop]]
+ *	primes [-d] [-h] [start [stop]]
  *
  *	Print primes >= start and < stop.  If stop is omitted,
- *	the value 4294967295 (2^32-1) is assumed.  If start is
+ *	the value SPSPMAX is assumed.  If start is
  *	omitted, start is read from standard input.
+ *		-h: print primes in hexadecimal
+ *		-d: print difference to previous prime, e.g. 3 (1)
  *
  * validation check: there are 664579 primes between 0 and 10^7
  */
@@ -66,11 +66,12 @@ __RCSID("$NetBSD: primes.c,v 1.19 2011/08/30 02:58:04 jakllsch Exp $");
 #include <ctype.h>
 #include <err.h>
 #include <errno.h>
+#include <inttypes.h>
 #include <limits.h>
 #include <math.h>
-#include <memory.h>
 #include <stdio.h>
 #include <stdlib.h>
+#include <string.h>
 #include <unistd.h>
 
 #include "primes.h"
@@ -80,48 +81,35 @@ __RCSID("$NetBSD: primes.c,v 1.19 2011/08/30 02:58:04 jakllsch Exp $");
  *
  * We only sieve the odd numbers.  The base of our sieve windows are always
  * odd.  If the base of table is 1, table[i] represents 2*i-1.  After the
- * sieve, table[i] == 1 if and only iff 2*i-1 is prime.
+ * sieve, table[i] == 1 if and only if 2*i-1 is prime.
  *
  * We make TABSIZE large to reduce the overhead of inner loop setup.
  */
 static char table[TABSIZE];	 /* Eratosthenes sieve of odd numbers */
 
-/*
- * prime[i] is the (i-1)th prime.
- *
- * We are able to sieve 2^32-1 because this byte table yields all primes 
- * up to 65537 and 65537^2 > 2^32-1.
- */
-extern const ubig prime[];
-extern const ubig *pr_limit;		/* largest prime in the prime array */
-
-/*
- * To avoid excessive sieves for small factors, we use the table below to 
- * setup our sieve blocks.  Each element represents a odd number starting 
- * with 1.  All non-zero elements are factors of 3, 5, 7, 11 and 13.
- */
-extern const char pattern[];
-extern const int pattern_size;	/* length of pattern array */
+static int dflag, hflag;
 
-static int dflag;
-
-static void primes(ubig, ubig);
-static ubig read_num_buf(void);
+static void primes(uint64_t, uint64_t);
+static uint64_t read_num_buf(void);
 static void usage(void) __dead;
 
+
 int
 main(int argc, char *argv[])
 {
-	ubig start;		/* where to start generating */
-	ubig stop;		/* don't generate at or above this value */
+	uint64_t start;		/* where to start generating */
+	uint64_t stop;		/* don't generate at or above this value */
 	int ch;
 	char *p;
 
-	while ((ch = getopt(argc, argv, "d")) != -1)
+	while ((ch = getopt(argc, argv, "dh")) != -1)
 		switch (ch) {
 		case 'd':
 			dflag++;
 			break;
+		case 'h':
+			hflag++;
+			break;
 		case '?':
 		default:
 			usage();
@@ -130,10 +118,10 @@ main(int argc, char *argv[])
 	argv += optind;
 
 	start = 0;
-	stop = BIG;
+	stop = SPSPMAX;
 
 	/*
-	 * Convert low and high args.  Strtoul(3) sets errno to
+	 * Convert low and high args.  Strtoumax(3) sets errno to
 	 * ERANGE if the number is too large, but, if there's
 	 * a leading minus sign it returns the negation of the
 	 * result of the conversion, which we'd rather disallow.
@@ -145,18 +133,21 @@ main(int argc, char *argv[])
 			errx(1, "negative numbers aren't permitted.");
 
 		errno = 0;
-		start = strtoul(argv[0], &p, 10);
+		start = strtoumax(argv[0], &p, 0);
 		if (errno)
 			err(1, "%s", argv[0]);
 		if (*p != '\0')
 			errx(1, "%s: illegal numeric format.", argv[0]);
 
 		errno = 0;
-		stop = strtoul(argv[1], &p, 10);
+		stop = strtoumax(argv[1], &p, 0);
 		if (errno)
 			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. */
@@ -164,7 +155,7 @@ main(int argc, char *argv[])
 			errx(1, "negative numbers aren't permitted.");
 
 		errno = 0;
-		start = strtoul(argv[0], &p, 10);
+		start = strtoumax(argv[0], &p, 0);
 		if (errno)
 			err(1, "%s", argv[0]);
 		if (*p != '\0')
@@ -180,18 +171,18 @@ main(int argc, char *argv[])
 	if (start > stop)
 		errx(1, "start value must be less than stop value.");
 	primes(start, stop);
-	exit(0);
+	return (0);
 }
 
 /*
  * read_num_buf --
- *	This routine returns a number n, where 0 <= n && n <= BIG.
+ *	This routine returns a number n, where 0 <= n && n <= ULONG_MAX.
  */
-ubig
+static uint64_t
 read_num_buf(void)
 {
-	ubig val;
-	char *p, buf[100];		/* > max number of digits. */
+	uint64_t val;
+	char *p, buf[LINE_MAX];		/* > max number of digits. */
 
 	for (;;) {
 		if (fgets(buf, sizeof(buf), stdin) == NULL) {
@@ -205,7 +196,7 @@ read_num_buf(void)
 		if (*p == '-')
 			errx(1, "negative numbers aren't permitted.");
 		errno = 0;
-		val = strtoul(buf, &p, 10);
+		val = strtoumax(buf, &p, 0);
 		if (errno)
 			err(1, "%s", buf);
 		if (*p != '\n')
@@ -216,31 +207,28 @@ read_num_buf(void)
 
 /*
  * primes - sieve and print primes from start up to and but not including stop
- *
- *	start	where to start generating
- *	stop	don't generate at or above this value
  */
-void
-primes(ubig start, ubig stop)
+static void
+primes(uint64_t start, uint64_t stop)
 {
 	char *q;		/* sieve spot */
-	ubig factor;		/* index and factor */
+	uint64_t factor;	/* index and factor */
 	char *tab_lim;		/* the limit to sieve on the table */
-	const ubig *p;		/* prime table pointer */
-	ubig fact_lim;		/* highest prime for current block */
-	ubig mod;		/* temp storage for mod */
-	ubig prev = 0;
+	const uint64_t *p;	/* prime table pointer */
+	uint64_t fact_lim;	/* highest prime for current block */
+	uint64_t mod;		/* temp storage for mod */
+	uint64_t prev = 0;
 
 	/*
 	 * A number of systems can not convert double values into unsigned
 	 * longs when the values are larger than the largest signed value.
-	 * We don't have this problem, so we can go all the way to BIG.
+	 * We don't have this problem, so we can go all the way to ULONG_MAX.
 	 */
 	if (start < 3) {
-		start = (ubig)2;
+		start = 2;
 	}
 	if (stop < 3) {
-		stop = (ubig)2;
+		stop = 2;
 	}
 	if (stop <= start) {
 		return;
@@ -264,10 +252,9 @@ primes(ubig start, ubig stop)
 		for (p = &prime[0], factor = prime[0];
 		    factor < stop && p <= pr_limit; factor = *(++p)) {
 			if (factor >= start) {
-				printf("%lu", (unsigned long) factor);
+				printf(hflag ? "%" PRIx64 : "%" PRIu64, factor);
 				if (dflag) {
-					printf(" (%lu)",
-					    (unsigned long) factor - prev);
+					printf(" (%" PRIu64 ")", factor - prev);
 				}
 				putchar('\n');
 			}
@@ -305,10 +292,10 @@ primes(ubig start, ubig stop)
 		/* note highest useful factor and sieve spot */
 		if (stop-start > TABSIZE+TABSIZE) {
 			tab_lim = &table[TABSIZE]; /* sieve it all */
-			fact_lim = sqrt((double)(start)+TABSIZE+TABSIZE+1.0);
+			fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE);
 		} else {
 			tab_lim = &table[(stop-start)/2]; /* partial sieve */
-			fact_lim = sqrt((double)(stop)+1.0);
+			fact_lim = sqrt(stop+1.0);
 		}
 		/* sieve for factors >= 17 */
 		factor = 17;	/* 17 is first prime to use */
@@ -325,28 +312,32 @@ primes(ubig start, ubig stop)
 			for ( ; q < tab_lim; q += factor) {
 				*q = '\0'; /* sieve out a spot */
 			}
-		} while ((factor=(ubig)(*(p++))) <= fact_lim);
+			factor = *p++;
+		} while (factor <= fact_lim);
 
 		/*
 		 * print generated primes
 		 */
 		for (q = table; q < tab_lim; ++q, start+=2) {
 			if (*q) {
-				printf("%lu", (unsigned long) start);
-				if (dflag) {
-					printf(" (%lu)",
-					    (unsigned long) start - prev);
-					prev = start;
+				if (start > SIEVEMAX) {
+					if (!isprime(start))
+						continue;
+				}
+				printf(hflag ? "%" PRIx64 : "%" PRIu64, start);
+				if (dflag && (prev || (start <= *pr_limit))) {
+					printf(" (%" PRIu64 ")", start - prev);
 				}
 				putchar('\n');
+				prev = start;
 			}
 		}
 	}
 }
 
-void
+static void
 usage(void)
 {
-	(void)fprintf(stderr, "usage: primes [-d] [start [stop]]\n");
+	(void)fprintf(stderr, "usage: primes [-d] [-h] [start [stop]]\n");
 	exit(1);
 }
diff --git a/primes/primes.h b/primes/primes.h
index a032c9b4..20da4ef6 100644
--- a/primes/primes.h
+++ b/primes/primes.h
@@ -1,4 +1,4 @@
-/*	$NetBSD: primes.h,v 1.5 2003/08/07 09:37:34 agc Exp $	*/
+/*	$NetBSD: primes.h,v 1.6 2014/10/02 21:36:37 ast Exp $	*/
 
 /*
  * Copyright (c) 1989, 1993
@@ -37,14 +37,38 @@
 /*
  * primes - generate a table of primes between two values
  *
- * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
+ * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
  *
- * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
  */
 
-/* ubig is the type that holds a large unsigned value */
-typedef unsigned long ubig;		/* must be >=32 bit unsigned value */
-#define	BIG		ULONG_MAX	/* largest value will sieve */
+#include <stdint.h>
 
 /* bytes in sieve table (must be > 3*5*7*11) */
 #define	TABSIZE		256*1024
+
+/*
+ * prime[i] is the (i-1)th prime.
+ *
+ * We are able to sieve 2^32-1 because this byte table yields all primes
+ * up to 65537 and 65537^2 > 2^32-1.
+ */
+
+extern const uint64_t prime[];		/* must be >=32 bit unsigned values */
+extern const uint64_t *const pr_limit;	/* largest prime in the prime array */
+
+/* Maximum size sieving alone can handle. */
+#define	SIEVEMAX 4295098368ULL
+
+/*
+ * To avoid excessive sieves for small factors, we use the table below to
+ * setup our sieve blocks.  Each element represents an odd number starting
+ * with 1.  All non-zero elements are factors of 3, 5, 7, 11 and 13.
+ */
+extern const char pattern[];
+extern const size_t pattern_size;	/* length of pattern array */
+
+/* Test for primality using strong pseudoprime tests. */
+int isprime(uint64_t);
+
+/* Maximum value which the SPSP code can handle. */
+#define	SPSPMAX 3825123056546413050ULL
diff --git a/primes/spsp.c b/primes/spsp.c
new file mode 100644
index 00000000..7d1b0841
--- /dev/null
+++ b/primes/spsp.c
@@ -0,0 +1,195 @@
+/*	$NetBSD: spsp.c,v 1.1 2014/10/02 21:36:37 ast Exp $	*/
+
+/*-
+ * 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>
+#ifndef lint
+__COPYRIGHT("@(#) Copyright (c) 1989, 1993\
+ The Regents of the University of California.  All rights reserved.");
+#endif /* not lint */
+
+#ifndef lint
+#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 $");
+#endif
+#endif /* not lint */
+
+#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(uint64_t _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);
+}