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
10struct primes {
11 struct rcu_head rcu;
12 unsigned long last, sz;
13 unsigned long primes[];
14};
15
16#if BITS_PER_LONG == 64
17static 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
42static 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
63static DEFINE_MUTEX(lock);
64static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);
65
66static unsigned long selftest_max;
67
68static 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
81static 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
89static 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
108static 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
155unlock:
156 mutex_unlock(&lock);
157 return true;
158}
159
160static 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 */
187unsigned 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}
207EXPORT_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 */
220bool 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}
241EXPORT_SYMBOL(is_prime_number);
242
243static 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
263static 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
294err:
295 dump_primes();
296 return -EINVAL;
297}
298
299static int __init primes_init(void)
300{
301 return selftest(selftest_max);
302}
303
304static void __exit primes_exit(void)
305{
306 free_primes();
307}
308
309module_init(primes_init);
310module_exit(primes_exit);
311
312module_param_named(selftest, selftest_max, ulong, 0400);
313
314MODULE_AUTHOR("Intel Corporation");
315MODULE_LICENSE("GPL");
316