From: "Dr. Tobias Quathamer" 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 +#include + #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 /\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 /\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 + #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 /\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 #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 $"); #endif #endif /* not lint */ /* * primes - generate a table of primes between two values * - * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo - * - * chongo /\oo/\ + * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\ * * usage: - * primes [start [stop]] + * primes [-dh] [start [stop]] * * Print primes >= start and < stop. If stop is omitted, - * the value 4294967295 (2^32-1) is assumed. If start is + * the value SPSPMAX is assumed. If start is * omitted, start is read from standard input. + * -d: print difference to previous prime, e.g. 3 (1) + * -h: print primes in hexadecimal * * validation check: there are 664579 primes between 0 and 10^7 */ @@ -66,11 +66,12 @@ __RCSID("$NetBSD: primes.c,v 1.12 2004/01/27 20:30:30 jsm Exp $"); #include #include #include +#include #include #include -#include #include #include +#include #include #include "primes.h" @@ -80,49 +81,35 @@ __RCSID("$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 /\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 /* 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 +#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 +#include +#include + +#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); +}