1 /* 2 * Copyright (c) 1989 The Regents of the University of California. 3 * All rights reserved. 4 * 5 * This code is derived from software contributed to Berkeley by 6 * Landon Curt Noll. 7 * 8 * Redistribution and use in source and binary forms are permitted 9 * provided that the above copyright notice and this paragraph are 10 * duplicated in all such forms and that any documentation, 11 * advertising materials, and other materials related to such 12 * distribution and use acknowledge that the software was developed 13 * by the University of California, Berkeley. The name of the 14 * University may not be used to endorse or promote products derived 15 * from this software without specific prior written permission. 16 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR 17 * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED 18 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. 19 */ 20 21 #ifndef lint 22 char copyright[] = 23 "@(#) Copyright (c) 1989 The Regents of the University of California.\n\ 24 All rights reserved.\n"; 25 #endif /* not lint */ 26 27 #ifndef lint 28 static char sccsid[] = "@(#)primes.c 5.2 (Berkeley) 02/01/90"; 29 #endif /* not lint */ 30 31 /* 32 * primes - generate a table of primes between two values 33 * 34 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 35 * 36 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 37 * 38 * usage: 39 * primes [start [stop]] 40 * 41 * Print primes >= start and <= stop. If stop is omitted, 42 * the value 4294967295 (2^32-1) is assumed. If start is 43 * omitted, start is read from standard input. 44 * 45 * Prints "ouch" if start or stop is > 4294967295 (2^32-1) 46 * or if a non-numeric is read on stdin. 47 * 48 * Validation check: there are 664579 primes between 0 and 10^7 49 */ 50 51 #include <stdio.h> 52 #include <math.h> 53 #include <memory.h> 54 #include <ctype.h> 55 #include "primes.h" 56 57 /* 58 * Eratosthenes sieve table 59 * 60 * We only sieve the odd numbers. The base of our sieve windows are always 61 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 62 * sieve, table[i] == 1 if and only iff 2*i-1 is prime. 63 * 64 * We make TABSIZE large to reduce the overhead of inner loop setup. 65 */ 66 char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 67 68 /* 69 * prime[i] is the (i-1)th prime. 70 * 71 * We are able to sieve 2^32-1 because this byte table yields all primes 72 * up to 65537 and 65537^2 > 2^32-1. 73 */ 74 extern ubig prime[]; 75 extern ubig *pr_limit; /* largest prime in the prime array */ 76 77 /* 78 * To avoid excessive sieves for small factors, we use the table below to 79 * setup our sieve blocks. Each element represents a odd number starting 80 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13. 81 */ 82 extern char pattern[]; 83 extern int pattern_size; /* length of pattern array */ 84 85 #define MAX_LINE 255 /* max line allowed on stdin */ 86 87 char *read_num_buf(); /* read a number buffer */ 88 void primes(); /* print the primes in range */ 89 char *program; /* our name */ 90 91 main(argc, argv) 92 int argc; /* arg count */ 93 char *argv[]; /* args */ 94 { 95 char buf[MAX_LINE+1]; /* input buffer */ 96 char *ret; /* return result */ 97 ubig start; /* where to start generating */ 98 ubig stop; /* don't generate at or above this value */ 99 100 /* 101 * parse args 102 */ 103 program = argv[0]; 104 start = 0; 105 stop = BIG; 106 if (argc == 3) { 107 /* convert low and high args */ 108 if (read_num_buf(NULL, argv[1]) == NULL) { 109 fprintf(stderr, "%s: ouch\n", program); 110 exit(1); 111 } 112 if (read_num_buf(NULL, argv[2]) == NULL) { 113 fprintf(stderr, "%s: ouch\n", program); 114 exit(1); 115 } 116 if (sscanf(argv[1], "%ld", &start) != 1) { 117 fprintf(stderr, "%s: ouch\n", program); 118 exit(1); 119 } 120 if (sscanf(argv[2], "%ld", &stop) != 1) { 121 fprintf(stderr, "%s: ouch\n", program); 122 exit(1); 123 } 124 125 } else if (argc == 2) { 126 /* convert low arg */ 127 if (read_num_buf(NULL, argv[1]) == NULL) { 128 fprintf(stderr, "%s: ouch\n", program); 129 exit(1); 130 } 131 if (sscanf(argv[1], "%ld", &start) != 1) { 132 fprintf(stderr, "%s: ouch\n", program); 133 exit(1); 134 } 135 136 } else { 137 /* read input until we get a good line */ 138 if (read_num_buf(stdin, buf) != NULL) { 139 140 /* convert the buffer */ 141 if (sscanf(buf, "%ld", &start) != 1) { 142 fprintf(stderr, "%s: ouch\n", program); 143 exit(1); 144 } 145 } else { 146 exit(0); 147 } 148 } 149 if (start > stop) { 150 fprintf(stderr, "%s: ouch\n", program); 151 exit(1); 152 } 153 primes(start, stop); 154 exit(0); 155 } 156 157 /* 158 * read_num_buf - read a number buffer from a stream 159 * 160 * Read a number on a line of the form: 161 * 162 * ^[ \t]*\(+?[0-9][0-9]\)*.*$ 163 * 164 * where ? is a 1-or-0 operator and the number is within \( \). 165 * 166 * If does not match the above pattern, it is ignored and a new 167 * line is read. If the number is too large or small, we will 168 * print ouch and read a new line. 169 * 170 * We have to be very careful on how we check the magnitude of the 171 * input. We can not use numeric checks because of the need to 172 * check values against maximum numeric values. 173 * 174 * This routine will return a line containing a ascii number between 175 * 0 and BIG, or it will return NULL. 176 * 177 * If the stream is NULL then buf will be processed as if were 178 * a single line stream. 179 * 180 * returns: 181 * char * pointer to leading digit or + 182 * NULL EOF or error 183 */ 184 char * 185 read_num_buf(input, buf) 186 FILE *input; /* input stream or NULL */ 187 char *buf; /* input buffer */ 188 { 189 static char limit[MAX_LINE+1]; /* ascii value of BIG */ 190 static int limit_len; /* digit count of limit */ 191 int len; /* digits in input (excluding +/-) */ 192 char *s; /* line start marker */ 193 char *d; /* first digit, skip +/- */ 194 char *p; /* scan pointer */ 195 char *z; /* zero scan pointer */ 196 197 /* form the ascii value of SEMIBIG if needed */ 198 if (!isascii(limit[0]) || !isdigit(limit[0])) { 199 sprintf(limit, "%ld", SEMIBIG); 200 limit_len = strlen(limit); 201 } 202 203 /* 204 * the search for a good line 205 */ 206 if (input != NULL && fgets(buf, MAX_LINE, input) == NULL) { 207 /* error or EOF */ 208 return NULL; 209 } 210 do { 211 212 /* ignore leading whitespace */ 213 for (s=buf; *s && s < buf+MAX_LINE; ++s) { 214 if (!isascii(*s) || !isspace(*s)) { 215 break; 216 } 217 } 218 219 /* object if - */ 220 if (*s == '-') { 221 fprintf(stderr, "%s: ouch\n", program); 222 continue; 223 } 224 225 /* skip over any leading + */ 226 if (*s == '+') { 227 d = s+1; 228 } else { 229 d = s; 230 } 231 232 /* note leading zeros */ 233 for (z=d; *z && z < buf+MAX_LINE; ++z) { 234 if (*z != '0') { 235 break; 236 } 237 } 238 239 /* scan for the first non-digit/non-plus/non-minus */ 240 for (p=d; *p && p < buf+MAX_LINE; ++p) { 241 if (!isascii(*p) || !isdigit(*p)) { 242 break; 243 } 244 } 245 246 /* ignore empty lines */ 247 if (p == d) { 248 continue; 249 } 250 *p = '\0'; 251 252 /* object if too many digits */ 253 len = strlen(z); 254 len = (len<=0) ? 1 : len; 255 /* accept if digit count is below limit */ 256 if (len < limit_len) { 257 /* we have good input */ 258 return s; 259 260 /* reject very large numbers */ 261 } else if (len > limit_len) { 262 fprintf(stderr, "%s: ouch\n", program); 263 continue; 264 265 /* carefully check against near limit numbers */ 266 } else if (strcmp(z, limit) > 0) { 267 fprintf(stderr, "%s: ouch\n", program); 268 continue; 269 } 270 /* number is near limit, but is under it */ 271 return s; 272 } while (input != NULL && fgets(buf, MAX_LINE, input) != NULL); 273 274 /* error or EOF */ 275 return NULL; 276 } 277 278 /* 279 * primes - sieve and print primes from start up to and but not including stop 280 */ 281 void 282 primes(start, stop) 283 ubig start; /* where to start generating */ 284 ubig stop; /* don't generate at or above this value */ 285 { 286 register char *q; /* sieve spot */ 287 register ubig factor; /* index and factor */ 288 register char *tab_lim; /* the limit to sieve on the table */ 289 register ubig *p; /* prime table pointer */ 290 register ubig fact_lim; /* highest prime for current block */ 291 292 /* 293 * A number of systems can not convert double values 294 * into unsigned longs when the values are larger than 295 * the largest signed value. Thus we take case when 296 * the double is larger than the value SEMIBIG. *sigh* 297 */ 298 if (start < 3) { 299 start = (ubig)2; 300 } 301 if (stop < 3) { 302 stop = (ubig)2; 303 } 304 if (stop <= start) { 305 return; 306 } 307 308 /* 309 * be sure that the values are odd, or 2 310 */ 311 if (start != 2 && (start&0x1) == 0) { 312 ++start; 313 } 314 if (stop != 2 && (stop&0x1) == 0) { 315 ++stop; 316 } 317 318 /* 319 * quick list of primes <= pr_limit 320 */ 321 if (start <= *pr_limit) { 322 /* skip primes up to the start value */ 323 for (p = &prime[0], factor = prime[0]; 324 factor < stop && p <= pr_limit; 325 factor = *(++p)) { 326 if (factor >= start) { 327 printf("%u\n", factor); 328 } 329 } 330 /* return early if we are done */ 331 if (p <= pr_limit) { 332 return; 333 } 334 start = *pr_limit+2; 335 } 336 337 /* 338 * we shall sieve a bytemap window, note primes and move the window 339 * upward until we pass the stop point 340 */ 341 while (start < stop) { 342 /* 343 * factor out 3, 5, 7, 11 and 13 344 */ 345 /* initial pattern copy */ 346 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 347 memcpy(table, &pattern[factor], pattern_size-factor); 348 /* main block pattern copies */ 349 for (fact_lim=pattern_size-factor; 350 fact_lim+pattern_size<=TABSIZE; 351 fact_lim+=pattern_size) { 352 memcpy(&table[fact_lim], pattern, pattern_size); 353 } 354 /* final block pattern copy */ 355 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 356 357 /* 358 * sieve for primes 17 and higher 359 */ 360 /* note highest useful factor and sieve spot */ 361 if (stop-start > TABSIZE+TABSIZE) { 362 tab_lim = &table[TABSIZE]; /* sieve it all */ 363 fact_lim = (int)sqrt( 364 (double)(start)+TABSIZE+TABSIZE+1.0); 365 } else { 366 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 367 fact_lim = (int)sqrt((double)(stop)+1.0); 368 } 369 /* sieve for factors >= 17 */ 370 factor = 17; /* 17 is first prime to use */ 371 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 372 do { 373 /* determine the factor's initial sieve point */ 374 q = (char *)(start%factor); /* temp storage for mod */ 375 if ((int)q & 0x1) { 376 q = &table[(factor-(int)q)/2]; 377 } else { 378 q = &table[q ? factor-((int)q/2) : 0]; 379 } 380 /* sive for our current factor */ 381 for ( ; q < tab_lim; q += factor) { 382 *q = '\0'; /* sieve out a spot */ 383 } 384 } while ((factor=(ubig)(*(p++))) <= fact_lim); 385 386 /* 387 * print generated primes 388 */ 389 for (q = table; q < tab_lim; ++q, start+=2) { 390 if (*q) { 391 printf("%u\n", start); 392 } 393 } 394 } 395 } 396