summaryrefslogtreecommitdiff
path: root/games/primes/primes.c
blob: 860d9a2304924944ecfb89e47995ab277c0a4a13 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
/*	$OpenBSD: primes.c,v 1.17 2015/10/24 17:34:16 mmcc Exp $	*/
/*	$NetBSD: primes.c,v 1.5 1995/04/24 12:24:47 cgd Exp $	*/

/*
 * 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 - 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/\
 *
 * usage:
 *	primes [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 <sys/types.h>
#include <ctype.h>
#include <err.h>
#include <errno.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>

#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 iff 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 */

/*
 * 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 */

void	primes(ubig, ubig);
ubig	read_num_buf(void);
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;

	while ((ch = getopt(argc, argv, "")) != -1) {
		switch (ch) {
		case '?':
		default:
			usage();
		}
	}
	argc -= optind;
	argv += optind;

	start = 0;
	stop = BIG;

	/*
	 * Convert low and high args.  Strtoul(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 = strtoul(argv[0], &p, 10);
		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);
		if (errno)
			err(1, "%s", argv[1]);
		if (*p != '\0')
			errx(1, "%s: illegal numeric format.", argv[1]);
		break;
	case 1:
		/* Start on the command line. */
		if (argv[0][0] == '-')
			errx(1, "negative numbers aren't permitted.");

		errno = 0;
		start = strtoul(argv[0], &p, 10);
		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);
	exit(0);
}

/*
 * read_num_buf --
 *	This routine returns a number n, where 0 <= n && n <= BIG.
 */
ubig
read_num_buf(void)
{
	ubig val;
	char *p, buf[100];		/* > max number of digits. */

	for (;;) {
		if (fgets(buf, sizeof(buf), stdin) == NULL) {
			if (ferror(stdin))
				err(1, "stdin");
			exit(0);
		}
		buf[strcspn(buf, "\n")] = '\0';
		for (p = buf; isblank((unsigned char)*p); ++p)
			;
		if (*p == '\0')
			continue;
		if (*p == '-')
			errx(1, "negative numbers aren't permitted.");
		errno = 0;
		val = strtoul(buf, &p, 10);
		if (errno)
			err(1, "%s", buf);
		for (; isblank((unsigned char)*p); ++p)
			;
		if (*p != '\0')
			errx(1, "%s: illegal numeric format.", buf);
		return (val);
	}
}

/*
 * 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)
{
	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;

	/*
	 * 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("%lu\n", (unsigned long) 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 = (int)sqrt(
					(double)(start)+TABSIZE+TABSIZE+1.0);
		} else {
			tab_lim = &table[(stop-start)/2]; /* partial sieve */
			fact_lim = (int)sqrt((double)(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];
			/* sieve for our current factor */
			for ( ; q < tab_lim; q += factor) {
				*q = '\0'; /* sieve out a spot */
			}
		} while ((factor=(ubig)(*(p++))) <= fact_lim);

		/*
		 * print generated primes
		 */
		for (q = table; q < tab_lim; ++q, start+=2) {
			if (*q) {
				printf("%lu\n", (unsigned long) start);
			}
		}
	}
}

void
usage(void)
{
	(void)fprintf(stderr, "usage: primes [start [stop]]\n");
	exit(1);
}