Index: head/usr.bin/primes/primes.c =================================================================== --- head/usr.bin/primes/primes.c (revision 319560) +++ head/usr.bin/primes/primes.c (revision 319561) @@ -1,333 +1,331 @@ /* * Copyright (c) 1989, 1993 * The Regents of the University of California. All rights reserved. * * This code is derived from software contributed to Berkeley by * Landon Curt Noll. * * 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. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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. */ #ifndef lint static const char copyright[] = "@(#) Copyright (c) 1989, 1993\n\ The Regents of the University of California. All rights reserved.\n"; #endif /* not lint */ #ifndef lint #if 0 static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95"; #endif static const char rcsid[] = "$FreeBSD$"; #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/\ * * usage: * primes [-h] [start [stop]] * * Print primes >= start and < stop. If stop is omitted, * the value 4294967295 (2^32-1) is assumed. If start is * omitted, start is read from standard input. * * validation check: there are 664579 primes between 0 and 10^7 */ #include #include #include #include #include #include #include #include #include #include #include #include #include "primes.h" /* * Eratosthenes sieve table * * 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 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 */ static int hflag; static void primes(ubig, ubig); static ubig read_num_buf(void); static void usage(void); int main(int argc, char *argv[]) { ubig start; /* where to start generating */ ubig stop; /* don't generate at or above this value */ int ch; char *p; /* Cache NLS data, for strerror, for err(3), before cap_enter. */ (void)catopen("libc", NL_CAT_LOCALE); if (cap_enter() < 0 && errno != ENOSYS) err(1, "cap_enter"); while ((ch = getopt(argc, argv, "h")) != -1) switch (ch) { case 'h': hflag++; break; case '?': default: usage(); } argc -= optind; argv += optind; start = 0; - stop = SPSPMAX; + stop = (uint64_t)(-1); /* * 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. */ switch (argc) { case 2: /* Start and stop supplied on the command line. */ if (argv[0][0] == '-' || argv[1][0] == '-') errx(1, "negative numbers aren't permitted."); errno = 0; 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 = 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.", argv[1]); break; case 1: /* Start on the command line. */ if (argv[0][0] == '-') errx(1, "negative numbers aren't permitted."); errno = 0; start = strtoumax(argv[0], &p, 0); if (errno) err(1, "%s", argv[0]); if (*p != '\0') errx(1, "%s: illegal numeric format.", argv[0]); break; case 0: start = read_num_buf(); break; default: usage(); } if (start > stop) errx(1, "start value must be less than stop value."); primes(start, stop); return (0); } /* * read_num_buf -- * This routine returns a number n, where 0 <= n && n <= BIG. */ static ubig read_num_buf(void) { ubig val; char *p, buf[LINE_MAX]; /* > max number of digits. */ for (;;) { if (fgets(buf, sizeof(buf), stdin) == NULL) { if (ferror(stdin)) err(1, "stdin"); exit(0); } for (p = buf; isblank(*p); ++p); if (*p == '\n' || *p == '\0') continue; if (*p == '-') errx(1, "negative numbers aren't permitted."); errno = 0; val = strtoumax(buf, &p, 0); if (errno) err(1, "%s", buf); if (*p != '\n') errx(1, "%s: illegal numeric format.", buf); return (val); } } /* * primes - sieve and print primes from start up to and but not including stop */ static void primes(ubig start, ubig stop) { char *q; /* sieve spot */ ubig 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 */ /* * 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. */ if (start < 3) { start = (ubig)2; } if (stop < 3) { stop = (ubig)2; } if (stop <= start) { return; } /* * be sure that the values are odd, or 2 */ if (start != 2 && (start&0x1) == 0) { ++start; } if (stop != 2 && (stop&0x1) == 0) { ++stop; } /* * quick list of primes <= pr_limit */ if (start <= *pr_limit) { /* skip primes up to the start value */ for (p = &prime[0], factor = prime[0]; factor < stop && p <= pr_limit; factor = *(++p)) { if (factor >= start) { printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor); } } /* return early if we are done */ if (p <= pr_limit) { return; } start = *pr_limit+2; } /* * we shall sieve a bytemap window, note primes and move the window * upward until we pass the stop point */ while (start < stop) { /* * factor out 3, 5, 7, 11 and 13 */ /* initial pattern copy */ factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ memcpy(table, &pattern[factor], pattern_size-factor); /* main block pattern copies */ for (fact_lim=pattern_size-factor; fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { memcpy(&table[fact_lim], pattern, pattern_size); } /* final block pattern copy */ memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); /* * sieve for primes 17 and higher */ /* note highest useful factor and sieve spot */ if (stop-start > TABSIZE+TABSIZE) { tab_lim = &table[TABSIZE]; /* sieve it all */ fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE); } else { tab_lim = &table[(stop-start)/2]; /* partial sieve */ fact_lim = sqrt(stop+1.0); } /* sieve for factors >= 17 */ factor = 17; /* 17 is first prime to use */ p = &prime[7]; /* 19 is next prime, pi(19)=7 */ do { /* determine the factor's initial sieve point */ mod = start%factor; if (mod & 0x1) { q = &table[(factor-mod)/2]; } else { q = &table[mod ? factor-(mod/2) : 0]; } /* sive for our current factor */ for ( ; q < tab_lim; q += factor) { *q = '\0'; /* sieve out a spot */ } factor = *p++; } while (factor <= fact_lim); /* * print generated primes */ for (q = table; q < tab_lim; ++q, start+=2) { if (*q) { if (start > SIEVEMAX) { if (!isprime(start)) continue; } printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start); } } } } static void usage(void) { fprintf(stderr, "usage: primes [-h] [start [stop]]\n"); exit(1); } Index: head/usr.bin/primes/primes.h =================================================================== --- head/usr.bin/primes/primes.h (revision 319560) +++ head/usr.bin/primes/primes.h (revision 319561) @@ -1,77 +1,74 @@ /* * Copyright (c) 1989, 1993 * The Regents of the University of California. All rights reserved. * * This code is derived from software contributed to Berkeley by * Landon Curt Noll. * * 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. * 3. Neither the name of the University nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS 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 REGENTS 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. * * @(#)primes.h 8.2 (Berkeley) 3/1/94 * $FreeBSD$ */ /* * primes - generate a table of primes between two values * * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo * * chongo /\oo/\ */ #include /* ubig is the type that holds a large unsigned value */ typedef uint64_t ubig; /* must be >=32 bit unsigned value */ #define BIG ULONG_MAX /* largest value will sieve */ /* 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 ubig prime[]; extern const ubig *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(ubig); - -/* Maximum value which the SPSP code can handle. */ -#define SPSPMAX 3825123056546413050ULL Index: head/usr.bin/primes/spsp.c =================================================================== --- head/usr.bin/primes/spsp.c (revision 319560) +++ head/usr.bin/primes/spsp.c (revision 319561) @@ -1,181 +1,201 @@ /*- * 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 __FBSDID("$FreeBSD$"); #include #include #include #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) { 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(ubig _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); + /* + * Value from: + * J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime + * bases, Math. Comp. 86(304):985-1003, 2017. + */ - /* UNREACHABLE */ - return (0); + /* 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); }