From 2eb43769534644ef8af78e6a1fa70c755d41200b Mon Sep 17 00:00:00 2001 From: ast Date: Thu, 2 Oct 2014 21:36:37 +0000 Subject: 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 --- factor/factor.6 | 17 ++--- factor/factor.c | 16 ++--- primes/Makefile | 4 +- primes/pattern.c | 13 ++-- primes/pr_tbl.c | 16 ++--- primes/primes.6 | 42 ++++++++---- primes/primes.c | 129 +++++++++++++++++------------------- primes/primes.h | 36 ++++++++-- primes/spsp.c | 195 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 9 files changed, 344 insertions(+), 124 deletions(-) create mode 100644 primes/spsp.c diff --git a/factor/factor.6 b/factor/factor.6 index 32029eca..c36fcb1f 100644 --- a/factor/factor.6 +++ b/factor/factor.6 @@ -1,4 +1,4 @@ -.\" $NetBSD: factor.6,v 1.12 2010/05/15 21:22:39 joerg Exp $ +.\" $NetBSD: factor.6,v 1.13 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 /\oo/\ +.\" By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\ .\" .Dd May 15, 2010 .Dt FACTOR 6 @@ -88,10 +86,7 @@ is compiled without OpenSSL it is limited to the maximum value of .Vt unsigned long . .Sh DIAGNOSTICS Out of range or invalid input results in -an appropriate error message -being written to standard error. -.\".Sh BUGS -.\".Nm -.\"cannot handle the -.\".Dq 10 most wanted -.\"factor list. +an appropriate error message to standard error. +.Sh AUTHORS +Originally by +.An Landon Curt Noll . diff --git a/factor/factor.c b/factor/factor.c index f2ff2e4b..0af41a14 100644 --- a/factor/factor.c +++ b/factor/factor.c @@ -1,4 +1,4 @@ -/* $NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $ */ +/* $NetBSD: factor.c,v 1.27 2014/10/02 21:36:37 ast Exp $ */ /* * Copyright (c) 1989, 1993 @@ -42,16 +42,14 @@ __COPYRIGHT("@(#) Copyright (c) 1989, 1993\ #if 0 static char sccsid[] = "@(#)factor.c 8.4 (Berkeley) 5/4/95"; #else -__RCSID("$NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $"); +__RCSID("$NetBSD: factor.c,v 1.27 2014/10/02 21:36:37 ast Exp $"); #endif #endif /* not lint */ /* * factor - factor a number into primes * - * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo - * - * chongo /\oo/\ + * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\ * * usage: * factor [number] ... @@ -72,6 +70,7 @@ __RCSID("$NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $"); #include #include #include +#include #ifdef HAVE_OPENSSL #include @@ -93,8 +92,7 @@ static int BN_dec2bn(BIGNUM **a, const char *str); * 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 */ + #if 0 /* debugging: limit table use to stress the "pollard" code */ #define pr_limit &prime[0] #endif @@ -198,7 +196,7 @@ main(int argc, char *argv[]) static void pr_fact(BIGNUM *val) { - const ubig *fact; /* The factor found. */ + const uint64_t *fact; /* The factor found. */ /* Firewall - catch 0 and 1. */ if (BN_is_zero(val) || BN_is_one(val)) @@ -239,7 +237,7 @@ pr_fact(BIGNUM *val) /* Divide factor out until none are left. */ do { - printf(" %lu", *fact); + printf(" %" PRIu64, *fact); BN_div_word(val, (BN_ULONG)*fact); } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 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 +#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 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 /\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 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 /\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 $"); #endif #endif /* not lint */ /* * primes - generate a table of primes between two values * - * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo - * - * chongo /\oo/\ + * By Landon Curt Noll, http://www.isthe.com/chongo/index.html /\oo/\ * * usage: - * primes [start [stop]] + * primes [-d] [-h] [start [stop]] * * Print primes >= start and < stop. If stop is omitted, - * the value 4294967295 (2^32-1) is assumed. If start is + * the value SPSPMAX is assumed. If start is * omitted, start is read from standard input. + * -h: print primes in hexadecimal + * -d: print difference to previous prime, e.g. 3 (1) * * validation check: there are 664579 primes between 0 and 10^7 */ @@ -66,11 +66,12 @@ __RCSID("$NetBSD: primes.c,v 1.19 2011/08/30 02:58:04 jakllsch Exp $"); #include #include #include +#include #include #include -#include #include #include +#include #include #include "primes.h" @@ -80,48 +81,35 @@ __RCSID("$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 /\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); + +/* 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 +#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 +#include +#include + +#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); +} -- cgit v1.2.3-56-ge451