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slackware-current/source/y/bsd-games/patches/0015-primes-Update-to-NetBSD-CVS-2018-02-03.patch
Patrick J Volkerding 66b0761fe7 Sun Feb 17 23:44:53 UTC 2019 
ap/cups-filters-1.22.1-x86_64-1.txz:  Upgraded.
y/bsd-games-2.17-x86_64-1.txz:  Upgraded.
2019-02-18 08:59:47 +01:00

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From: "Dr. Tobias Quathamer" <toddy@debian.org>
Date: Thu, 26 Apr 2018 15:42:07 +0200
Subject: primes: Update to NetBSD CVS, 2018-02-03
---
exec.objs | 2 +-
primes/Makefile.bsd | 4 +-
primes/pattern.c | 13 ++--
primes/pr_tbl.c | 16 ++--
primes/primes.6 | 41 +++++++---
primes/primes.c | 148 ++++++++++++++++++------------------
primes/primes.h | 33 ++++++--
primes/spsp.c | 215 ++++++++++++++++++++++++++++++++++++++++++++++++++++
8 files changed, 362 insertions(+), 110 deletions(-)
create mode 100644 primes/spsp.c
diff --git a/exec.objs b/exec.objs
index f081d60..3c184cc 100644
--- a/exec.objs
+++ b/exec.objs
@@ -100,7 +100,7 @@ phantasia/setup phantglobs.o setup.o
pig pig.o
pom pom.o
ppt ppt.o
-primes pattern.o pr_tbl.o primes.o
+primes pattern.o pr_tbl.o primes.o spsp.o
quiz quiz.o rxp.o lib/fgetln.o
rain rain.o lib/getprogname.o
random random.o
diff --git a/primes/Makefile.bsd b/primes/Makefile.bsd
index 4235041..8ed845c 100644
--- a/primes/Makefile.bsd
+++ b/primes/Makefile.bsd
@@ -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 1196056..52784a5 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 d45204a..5e2f813 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 14d5101..aa000ef 100644
--- a/primes/primes.6
+++ b/primes/primes.6
@@ -1,4 +1,4 @@
-.\" $NetBSD: primes.6,v 1.2 2004/02/09 23:25:47 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.
@@ -33,11 +33,9 @@
.\" @(#)factor.6 8.1 (Berkeley) 5/31/93
.\"
.\"
-.\" 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/\
-.\"
-.Dd February 8, 2004
+.Dd February 2, 2018
.Dt PRIMES 6
.Os
.Sh NAME
@@ -45,6 +43,7 @@
.Nd generate primes
.Sh SYNOPSIS
.Nm primes
+.Op Fl dh
.Op Ar start Op Ar stop
.Sh DESCRIPTION
The
@@ -60,18 +59,18 @@ 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
@@ -80,10 +79,28 @@ 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.
+an appropriate error message to standard error.
+.Sh AUTHORS
+.An -nosplit
+Originally by
+.An Landon Curt Noll ,
+extended to some 64-bit primes by
+.An Colin Percival .
.Sh BUGS
+This
.Nm
-won't get you a world record.
+program won't get you a world record.
diff --git a/primes/primes.c b/primes/primes.c
index 2d93594..a022aa9 100644
--- a/primes/primes.c
+++ b/primes/primes.c
@@ -1,4 +1,4 @@
-/* $NetBSD: primes.c,v 1.12 2004/01/27 20:30:30 jsm Exp $ */
+/* $NetBSD: primes.c,v 1.22 2018/02/03 15:40:29 christos Exp $ */
/*
* Copyright (c) 1989, 1993
@@ -34,31 +34,31 @@
#include <sys/cdefs.h>
#ifndef lint
-__COPYRIGHT("@(#) Copyright (c) 1989, 1993\n\
- The Regents of the University of California. All rights reserved.\n");
+__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: primes.c,v 1.12 2004/01/27 20:30:30 jsm Exp $");
+__RCSID("$NetBSD: primes.c,v 1.22 2018/02/03 15:40:29 christos Exp $");
#endif
#endif /* not lint */
/*
* primes - generate a table of primes between two values
*
- * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
- *
- * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+ * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\
*
* usage:
- * primes [start [stop]]
+ * primes [-dh] [start [stop]]
*
* Print primes >= start and < stop. If stop is omitted,
- * the value 4294967295 (2^32-1) is assumed. If start is
+ * the value SPSPMAX is assumed. If start is
* omitted, start is read from standard input.
+ * -d: print difference to previous prime, e.g. 3 (1)
+ * -h: print primes in hexadecimal
*
* validation check: there are 664579 primes between 0 and 10^7
*/
@@ -66,11 +66,12 @@ __RCSID("$NetBSD: primes.c,v 1.12 2004/01/27 20:30:30 jsm Exp $");
#include <ctype.h>
#include <err.h>
#include <errno.h>
+#include <inttypes.h>
#include <limits.h>
#include <math.h>
-#include <memory.h>
#include <stdio.h>
#include <stdlib.h>
+#include <string.h>
#include <unistd.h>
#include "primes.h"
@@ -80,49 +81,35 @@ __RCSID("$NetBSD: primes.c,v 1.12 2004/01/27 20:30:30 jsm 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.
*/
-char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */
+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 */
+static int dflag, hflag;
-/*
- * 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 void primes(uint64_t, uint64_t);
+static uint64_t read_num_buf(void);
+static void usage(void) __dead;
-int main(int, char *[]);
-void primes(ubig, ubig);
-ubig read_num_buf(void);
-void usage(void) __attribute__((__noreturn__));
int
-main(argc, argv)
- int argc;
- char *argv[];
+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;
- /* Revoke setgid privileges */
- setregid(getgid(), getgid());
-
- while ((ch = getopt(argc, argv, "")) != -1)
+ while ((ch = getopt(argc, argv, "dh")) != -1)
switch (ch) {
+ case 'd':
+ dflag++;
+ break;
+ case 'h':
+ hflag++;
+ break;
case '?':
default:
usage();
@@ -131,10 +118,10 @@ main(argc, argv)
argv += optind;
start = 0;
- stop = BIG;
+ stop = (uint64_t)(-1);
/*
- * 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.
@@ -146,14 +133,14 @@ main(argc, 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')
@@ -165,7 +152,7 @@ main(argc, 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')
@@ -181,18 +168,18 @@ main(argc, 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
-read_num_buf()
+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) {
@@ -200,13 +187,13 @@ read_num_buf()
err(1, "stdin");
exit(0);
}
- for (p = buf; isblank(*p); ++p);
+ for (p = buf; isblank((unsigned char)*p); ++p);
if (*p == '\n' || *p == '\0')
continue;
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')
@@ -218,28 +205,27 @@ read_num_buf()
/*
* primes - sieve and print primes from start up to and but not including stop
*/
-void
-primes(start, stop)
- ubig start; /* where to start generating */
- ubig stop; /* don't generate at or above this value */
+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 */
+ 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;
@@ -263,8 +249,13 @@ primes(start, stop)
for (p = &prime[0], factor = prime[0];
factor < stop && p <= pr_limit; factor = *(++p)) {
if (factor >= start) {
- printf("%lu\n", (unsigned long) factor);
+ printf(hflag ? "%" PRIx64 : "%" PRIu64, factor);
+ if (dflag) {
+ printf(" (%" PRIu64 ")", factor - prev);
+ }
+ putchar('\n');
}
+ prev = factor;
}
/* return early if we are done */
if (p <= pr_limit) {
@@ -298,11 +289,10 @@ primes(start, stop)
/* note highest useful factor and sieve spot */
if (stop-start > TABSIZE+TABSIZE) {
tab_lim = &table[TABSIZE]; /* sieve it all */
- fact_lim = (int)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 = (int)sqrt((double)(stop)+1.0);
+ fact_lim = sqrt(stop+1.0);
}
/* sieve for factors >= 17 */
factor = 17; /* 17 is first prime to use */
@@ -315,26 +305,36 @@ primes(start, stop)
} else {
q = &table[mod ? factor-(mod/2) : 0];
}
- /* sive for our current factor */
+ /* sieve for our current factor */
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\n", (unsigned long) 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
-usage()
+static void
+usage(void)
{
- (void)fprintf(stderr, "usage: primes [start [stop]]\n");
+ (void)fprintf(stderr, "usage: primes [-dh] [start [stop]]\n");
exit(1);
}
diff --git a/primes/primes.h b/primes/primes.h
index a032c9b..2c00446 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 1.7 2018/02/03 15:40:29 christos Exp $ */
/*
* Copyright (c) 1989, 1993
@@ -37,14 +37,35 @@
/*
* 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);
diff --git a/primes/spsp.c b/primes/spsp.c
new file mode 100644
index 0000000..998751c
--- /dev/null
+++ b/primes/spsp.c
@@ -0,0 +1,215 @@
+/* $NetBSD: spsp.c,v 1.2 2018/02/03 15:40:29 christos 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 1.2 2018/02/03 15:40:29 christos Exp $");
+#endif
+#endif /* not lint */
+
+#include <assert.h>
+#include <stddef.h>
+#include <stdint.h>
+
+#include "primes.h"
+
+/* 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 += 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 < n. */
+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);
+ /*
+ * Value from:
+ * J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime
+ * bases, Math. Comp. 86(304):985-1003, 2017.
+ */
+
+ /* 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);
+
+ /* All 64-bit values are less than 318665857834031151167461. */
+ return (1);
+}
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