blob: c9b3c29614aa766a81e1ba26da71c447ea8e12d4 [file] [log] [blame]
Chris Wilsoncf4a7202016-12-22 14:45:14 +00001#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), GFP_KERNEL);
128 if (!new)
129 return false;
130
131 mutex_lock(&lock);
132 p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
133 if (x < p->last) {
134 kfree(new);
135 goto unlock;
136 }
137
138 /* Where memory permits, track the primes using the
139 * Sieve of Eratosthenes. The sieve is to remove all multiples of known
140 * primes from the set, what remains in the set is therefore prime.
141 */
142 bitmap_fill(new->primes, sz);
143 bitmap_copy(new->primes, p->primes, p->sz);
144 for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
145 new->last = clear_multiples(y, new->primes, p->sz, sz);
146 new->sz = sz;
147
148 BUG_ON(new->last <= x);
149
150 rcu_assign_pointer(primes, new);
151 if (p != &small_primes)
152 kfree_rcu((struct primes *)p, rcu);
153
154unlock:
155 mutex_unlock(&lock);
156 return true;
157}
158
159static void free_primes(void)
160{
161 const struct primes *p;
162
163 mutex_lock(&lock);
164 p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
165 if (p != &small_primes) {
166 rcu_assign_pointer(primes, &small_primes);
167 kfree_rcu((struct primes *)p, rcu);
168 }
169 mutex_unlock(&lock);
170}
171
172/**
173 * next_prime_number - return the next prime number
174 * @x: the starting point for searching to test
175 *
176 * A prime number is an integer greater than 1 that is only divisible by
177 * itself and 1. The set of prime numbers is computed using the Sieve of
178 * Eratoshenes (on finding a prime, all multiples of that prime are removed
179 * from the set) enabling a fast lookup of the next prime number larger than
180 * @x. If the sieve fails (memory limitation), the search falls back to using
181 * slow trial-divison, up to the value of ULONG_MAX (which is reported as the
182 * final prime as a sentinel).
183 *
184 * Returns: the next prime number larger than @x
185 */
186unsigned long next_prime_number(unsigned long x)
187{
188 const struct primes *p;
189
190 rcu_read_lock();
191 p = rcu_dereference(primes);
192 while (x >= p->last) {
193 rcu_read_unlock();
194
195 if (!expand_to_next_prime(x))
196 return slow_next_prime_number(x);
197
198 rcu_read_lock();
199 p = rcu_dereference(primes);
200 }
201 x = find_next_bit(p->primes, p->last, x + 1);
202 rcu_read_unlock();
203
204 return x;
205}
206EXPORT_SYMBOL(next_prime_number);
207
208/**
209 * is_prime_number - test whether the given number is prime
210 * @x: the number to test
211 *
212 * A prime number is an integer greater than 1 that is only divisible by
213 * itself and 1. Internally a cache of prime numbers is kept (to speed up
214 * searching for sequential primes, see next_prime_number()), but if the number
215 * falls outside of that cache, its primality is tested using trial-divison.
216 *
217 * Returns: true if @x is prime, false for composite numbers.
218 */
219bool is_prime_number(unsigned long x)
220{
221 const struct primes *p;
222 bool result;
223
224 rcu_read_lock();
225 p = rcu_dereference(primes);
226 while (x >= p->sz) {
227 rcu_read_unlock();
228
229 if (!expand_to_next_prime(x))
230 return slow_is_prime_number(x);
231
232 rcu_read_lock();
233 p = rcu_dereference(primes);
234 }
235 result = test_bit(x, p->primes);
236 rcu_read_unlock();
237
238 return result;
239}
240EXPORT_SYMBOL(is_prime_number);
241
242static void dump_primes(void)
243{
244 const struct primes *p;
245 char *buf;
246
247 buf = kmalloc(PAGE_SIZE, GFP_KERNEL);
248
249 rcu_read_lock();
250 p = rcu_dereference(primes);
251
252 if (buf)
253 bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
254 pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s",
255 p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);
256
257 rcu_read_unlock();
258
259 kfree(buf);
260}
261
262static int selftest(unsigned long max)
263{
264 unsigned long x, last;
265
266 if (!max)
267 return 0;
268
269 for (last = 0, x = 2; x < max; x++) {
270 bool slow = slow_is_prime_number(x);
271 bool fast = is_prime_number(x);
272
273 if (slow != fast) {
274 pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!",
275 x, slow ? "yes" : "no", fast ? "yes" : "no");
276 goto err;
277 }
278
279 if (!slow)
280 continue;
281
282 if (next_prime_number(last) != x) {
283 pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu",
284 last, x, next_prime_number(last));
285 goto err;
286 }
287 last = x;
288 }
289
290 pr_info("selftest(%lu) passed, last prime was %lu", x, last);
291 return 0;
292
293err:
294 dump_primes();
295 return -EINVAL;
296}
297
298static int __init primes_init(void)
299{
300 return selftest(selftest_max);
301}
302
303static void __exit primes_exit(void)
304{
305 free_primes();
306}
307
308module_init(primes_init);
309module_exit(primes_exit);
310
311module_param_named(selftest, selftest_max, ulong, 0400);
312
313MODULE_AUTHOR("Intel Corporation");
314MODULE_LICENSE("GPL");