lib/prime_numbers.c

   1 #define pr_fmt(fmt) "prime numbers: " fmt "\n"
   2
   3 #include <linux/module.h>
   4 #include <linux/mutex.h>
   5 #include <linux/prime_numbers.h>
   6 #include <linux/slab.h>
   7
   8 #define bitmap_size(nbits) (BITS_TO_LONGS(nbits) * sizeof(unsigned long))
   9
  10 struct primes {
  11         struct rcu_head rcu;
  12         unsigned long last, sz;
  13         unsigned long primes[];
  14 };
  15
  16 #if BITS_PER_LONG == 64
  17 static const struct primes small_primes = {
  18         .last = 61,
  19         .sz = 64,
  20         .primes = {
  21                 BIT(2) |
  22                 BIT(3) |
  23                 BIT(5) |
  24                 BIT(7) |
  25                 BIT(11) |
  26                 BIT(13) |
  27                 BIT(17) |
  28                 BIT(19) |
  29                 BIT(23) |
  30                 BIT(29) |
  31                 BIT(31) |
  32                 BIT(37) |
  33                 BIT(41) |
  34                 BIT(43) |
  35                 BIT(47) |
  36                 BIT(53) |
  37                 BIT(59) |
  38                 BIT(61)
  39         }
  40 };
  41 #elif BITS_PER_LONG == 32
  42 static const struct primes small_primes = {
  43         .last = 31,
  44         .sz = 32,
  45         .primes = {
  46                 BIT(2) |
  47                 BIT(3) |
  48                 BIT(5) |
  49                 BIT(7) |
  50                 BIT(11) |
  51                 BIT(13) |
  52                 BIT(17) |
  53                 BIT(19) |
  54                 BIT(23) |
  55                 BIT(29) |
  56                 BIT(31)
  57         }
  58 };
  59 #else
  60 #error "unhandled BITS_PER_LONG"
  61 #endif
  62
  63 static DEFINE_MUTEX(lock);
  64 static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);
  65
  66 static unsigned long selftest_max;
  67
  68 static bool slow_is_prime_number(unsigned long x)
  69 {
  70         unsigned long y = int_sqrt(x);
  71
  72         while (y > 1) {
  73                 if ((x % y) == 0)
  74                         break;
  75                 y--;
  76         }
  77
  78         return y == 1;
  79 }
  80
  81 static unsigned long slow_next_prime_number(unsigned long x)
  82 {
  83         while (x < ULONG_MAX && !slow_is_prime_number(++x))
  84                 ;
  85
  86         return x;
  87 }
  88
  89 static unsigned long clear_multiples(unsigned long x,
  90                                      unsigned long *p,
  91                                      unsigned long start,
  92                                      unsigned long end)
  93 {
  94         unsigned long m;
  95
  96         m = 2 * x;
  97         if (m < start)
  98                 m = roundup(start, x);
  99
 100         while (m < end) {
 101                 __clear_bit(m, p);
 102                 m += x;
 103         }
 104
 105         return x;
 106 }
 107
 108 static bool expand_to_next_prime(unsigned long x)
 109 {
 110         const struct primes *p;
 111         struct primes *new;
 112         unsigned long sz, y;
 113
 114         /* Betrand's Postulate (or Chebyshev's theorem) states that if n > 3,
 115          * there is always at least one prime p between n and 2n - 2.
 116          * Equivalently, if n > 1, then there is always at least one prime p
 117          * such that n < p < 2n.
 118          *
 119          * http://mathworld.wolfram.com/BertrandsPostulate.html
 120          * https://en.wikipedia.org/wiki/Bertrand's_postulate
 121          */
 122         sz = 2 * x;
 123         if (sz < x)
 124                 return false;
 125
 126         sz = round_up(sz, BITS_PER_LONG);
 127         new = kmalloc(sizeof(*new) + bitmap_size(sz),
 128                       GFP_KERNEL | __GFP_NOWARN);
 129         if (!new)
 130                 return false;
 131
 132         mutex_lock(&lock);
 133         p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
 134         if (x < p->last) {
 135                 kfree(new);
 136                 goto unlock;
 137         }
 138
 139         /* Where memory permits, track the primes using the
 140          * Sieve of Eratosthenes. The sieve is to remove all multiples of known
 141          * primes from the set, what remains in the set is therefore prime.
 142          */
 143         bitmap_fill(new->primes, sz);
 144         bitmap_copy(new->primes, p->primes, p->sz);
 145         for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
 146                 new->last = clear_multiples(y, new->primes, p->sz, sz);
 147         new->sz = sz;
 148
 149         BUG_ON(new->last <= x);
 150
 151         rcu_assign_pointer(primes, new);
 152         if (p != &small_primes)
 153                 kfree_rcu((struct primes *)p, rcu);
 154
 155 unlock:
 156         mutex_unlock(&lock);
 157         return true;
 158 }
 159
 160 static void free_primes(void)
 161 {
 162         const struct primes *p;
 163
 164         mutex_lock(&lock);
 165         p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
 166         if (p != &small_primes) {
 167                 rcu_assign_pointer(primes, &small_primes);
 168                 kfree_rcu((struct primes *)p, rcu);
 169         }
 170         mutex_unlock(&lock);
 171 }
 172
 173 /**
 174  * next_prime_number - return the next prime number
 175  * @x: the starting point for searching to test
 176  *
 177  * A prime number is an integer greater than 1 that is only divisible by
 178  * itself and 1.  The set of prime numbers is computed using the Sieve of
 179  * Eratoshenes (on finding a prime, all multiples of that prime are removed
 180  * from the set) enabling a fast lookup of the next prime number larger than
 181  * @x. If the sieve fails (memory limitation), the search falls back to using
 182  * slow trial-divison, up to the value of ULONG_MAX (which is reported as the
 183  * final prime as a sentinel).
 184  *
 185  * Returns: the next prime number larger than @x
 186  */
 187 unsigned long next_prime_number(unsigned long x)
 188 {
 189         const struct primes *p;
 190
 191         rcu_read_lock();
 192         p = rcu_dereference(primes);
 193         while (x >= p->last) {
 194                 rcu_read_unlock();
 195
 196                 if (!expand_to_next_prime(x))
 197                         return slow_next_prime_number(x);
 198
 199                 rcu_read_lock();
 200                 p = rcu_dereference(primes);
 201         }
 202         x = find_next_bit(p->primes, p->last, x + 1);
 203         rcu_read_unlock();
 204
 205         return x;
 206 }
 207 EXPORT_SYMBOL(next_prime_number);
 208
 209 /**
 210  * is_prime_number - test whether the given number is prime
 211  * @x: the number to test
 212  *
 213  * A prime number is an integer greater than 1 that is only divisible by
 214  * itself and 1. Internally a cache of prime numbers is kept (to speed up
 215  * searching for sequential primes, see next_prime_number()), but if the number
 216  * falls outside of that cache, its primality is tested using trial-divison.
 217  *
 218  * Returns: true if @x is prime, false for composite numbers.
 219  */
 220 bool is_prime_number(unsigned long x)
 221 {
 222         const struct primes *p;
 223         bool result;
 224
 225         rcu_read_lock();
 226         p = rcu_dereference(primes);
 227         while (x >= p->sz) {
 228                 rcu_read_unlock();
 229
 230                 if (!expand_to_next_prime(x))
 231                         return slow_is_prime_number(x);
 232
 233                 rcu_read_lock();
 234                 p = rcu_dereference(primes);
 235         }
 236         result = test_bit(x, p->primes);
 237         rcu_read_unlock();
 238
 239         return result;
 240 }
 241 EXPORT_SYMBOL(is_prime_number);
 242
 243 static void dump_primes(void)
 244 {
 245         const struct primes *p;
 246         char *buf;
 247
 248         buf = kmalloc(PAGE_SIZE, GFP_KERNEL);
 249
 250         rcu_read_lock();
 251         p = rcu_dereference(primes);
 252
 253         if (buf)
 254                 bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
 255         pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s",
 256                 p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);
 257
 258         rcu_read_unlock();
 259
 260         kfree(buf);
 261 }
 262
 263 static int selftest(unsigned long max)
 264 {
 265         unsigned long x, last;
 266
 267         if (!max)
 268                 return 0;
 269
 270         for (last = 0, x = 2; x < max; x++) {
 271                 bool slow = slow_is_prime_number(x);
 272                 bool fast = is_prime_number(x);
 273
 274                 if (slow != fast) {
 275                         pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!",
 276                                x, slow ? "yes" : "no", fast ? "yes" : "no");
 277                         goto err;
 278                 }
 279
 280                 if (!slow)
 281                         continue;
 282
 283                 if (next_prime_number(last) != x) {
 284                         pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu",
 285                                last, x, next_prime_number(last));
 286                         goto err;
 287                 }
 288                 last = x;
 289         }
 290
 291         pr_info("selftest(%lu) passed, last prime was %lu", x, last);
 292         return 0;
 293
 294 err:
 295         dump_primes();
 296         return -EINVAL;
 297 }
 298
 299 static int __init primes_init(void)
 300 {
 301         return selftest(selftest_max);
 302 }
 303
 304 static void __exit primes_exit(void)
 305 {
 306         free_primes();
 307 }
 308
 309 module_init(primes_init);
 310 module_exit(primes_exit);
 311
 312 module_param_named(selftest, selftest_max, ulong, 0400);
 313
 314 MODULE_AUTHOR("Intel Corporation");
 315 MODULE_LICENSE("GPL");