1 // SPDX-License-Identifier: GPL-2.0-only
2 #define pr_fmt(fmt) "prime numbers: " fmt
3
4 #include <linux/module.h>
5 #include <linux/mutex.h>
6 #include <linux/prime_numbers.h>
7 #include <linux/slab.h>
8
9 #define bitmap_size(nbits) (BITS_TO_LONGS(nbits) * sizeof(unsigned long))
10
11 struct primes {
12 struct rcu_head rcu;
13 unsigned long last, sz;
14 unsigned long primes[];
15 };
16
17 #if BITS_PER_LONG == 64
18 static const struct primes small_primes = {
19 .last = 61,
20 .sz = 64,
21 .primes = {
22 BIT(2) |
23 BIT(3) |
24 BIT(5) |
25 BIT(7) |
26 BIT(11) |
27 BIT(13) |
28 BIT(17) |
29 BIT(19) |
30 BIT(23) |
31 BIT(29) |
32 BIT(31) |
33 BIT(37) |
34 BIT(41) |
35 BIT(43) |
36 BIT(47) |
37 BIT(53) |
38 BIT(59) |
39 BIT(61)
40 }
41 };
42 #elif BITS_PER_LONG == 32
43 static const struct primes small_primes = {
44 .last = 31,
45 .sz = 32,
46 .primes = {
47 BIT(2) |
48 BIT(3) |
49 BIT(5) |
50 BIT(7) |
51 BIT(11) |
52 BIT(13) |
53 BIT(17) |
54 BIT(19) |
55 BIT(23) |
56 BIT(29) |
57 BIT(31)
58 }
59 };
60 #else
61 #error "unhandled BITS_PER_LONG"
62 #endif
63
64 static DEFINE_MUTEX(lock);
65 static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);
66
67 static unsigned long selftest_max;
68
slow_is_prime_number(unsigned long x)69 static bool slow_is_prime_number(unsigned long x)
70 {
71 unsigned long y = int_sqrt(x);
72
73 while (y > 1) {
74 if ((x % y) == 0)
75 break;
76 y--;
77 }
78
79 return y == 1;
80 }
81
slow_next_prime_number(unsigned long x)82 static unsigned long slow_next_prime_number(unsigned long x)
83 {
84 while (x < ULONG_MAX && !slow_is_prime_number(++x))
85 ;
86
87 return x;
88 }
89
clear_multiples(unsigned long x,unsigned long * p,unsigned long start,unsigned long end)90 static unsigned long clear_multiples(unsigned long x,
91 unsigned long *p,
92 unsigned long start,
93 unsigned long end)
94 {
95 unsigned long m;
96
97 m = 2 * x;
98 if (m < start)
99 m = roundup(start, x);
100
101 while (m < end) {
102 __clear_bit(m, p);
103 m += x;
104 }
105
106 return x;
107 }
108
expand_to_next_prime(unsigned long x)109 static bool expand_to_next_prime(unsigned long x)
110 {
111 const struct primes *p;
112 struct primes *new;
113 unsigned long sz, y;
114
115 /* Betrand's Postulate (or Chebyshev's theorem) states that if n > 3,
116 * there is always at least one prime p between n and 2n - 2.
117 * Equivalently, if n > 1, then there is always at least one prime p
118 * such that n < p < 2n.
119 *
120 * http://mathworld.wolfram.com/BertrandsPostulate.html
121 * https://en.wikipedia.org/wiki/Bertrand's_postulate
122 */
123 sz = 2 * x;
124 if (sz < x)
125 return false;
126
127 sz = round_up(sz, BITS_PER_LONG);
128 new = kmalloc(sizeof(*new) + bitmap_size(sz),
129 GFP_KERNEL | __GFP_NOWARN);
130 if (!new)
131 return false;
132
133 mutex_lock(&lock);
134 p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
135 if (x < p->last) {
136 kfree(new);
137 goto unlock;
138 }
139
140 /* Where memory permits, track the primes using the
141 * Sieve of Eratosthenes. The sieve is to remove all multiples of known
142 * primes from the set, what remains in the set is therefore prime.
143 */
144 bitmap_fill(new->primes, sz);
145 bitmap_copy(new->primes, p->primes, p->sz);
146 for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
147 new->last = clear_multiples(y, new->primes, p->sz, sz);
148 new->sz = sz;
149
150 BUG_ON(new->last <= x);
151
152 rcu_assign_pointer(primes, new);
153 if (p != &small_primes)
154 kfree_rcu((struct primes *)p, rcu);
155
156 unlock:
157 mutex_unlock(&lock);
158 return true;
159 }
160
free_primes(void)161 static void free_primes(void)
162 {
163 const struct primes *p;
164
165 mutex_lock(&lock);
166 p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
167 if (p != &small_primes) {
168 rcu_assign_pointer(primes, &small_primes);
169 kfree_rcu((struct primes *)p, rcu);
170 }
171 mutex_unlock(&lock);
172 }
173
174 /**
175 * next_prime_number - return the next prime number
176 * @x: the starting point for searching to test
177 *
178 * A prime number is an integer greater than 1 that is only divisible by
179 * itself and 1. The set of prime numbers is computed using the Sieve of
180 * Eratoshenes (on finding a prime, all multiples of that prime are removed
181 * from the set) enabling a fast lookup of the next prime number larger than
182 * @x. If the sieve fails (memory limitation), the search falls back to using
183 * slow trial-divison, up to the value of ULONG_MAX (which is reported as the
184 * final prime as a sentinel).
185 *
186 * Returns: the next prime number larger than @x
187 */
next_prime_number(unsigned long x)188 unsigned long next_prime_number(unsigned long x)
189 {
190 const struct primes *p;
191
192 rcu_read_lock();
193 p = rcu_dereference(primes);
194 while (x >= p->last) {
195 rcu_read_unlock();
196
197 if (!expand_to_next_prime(x))
198 return slow_next_prime_number(x);
199
200 rcu_read_lock();
201 p = rcu_dereference(primes);
202 }
203 x = find_next_bit(p->primes, p->last, x + 1);
204 rcu_read_unlock();
205
206 return x;
207 }
208 EXPORT_SYMBOL(next_prime_number);
209
210 /**
211 * is_prime_number - test whether the given number is prime
212 * @x: the number to test
213 *
214 * A prime number is an integer greater than 1 that is only divisible by
215 * itself and 1. Internally a cache of prime numbers is kept (to speed up
216 * searching for sequential primes, see next_prime_number()), but if the number
217 * falls outside of that cache, its primality is tested using trial-divison.
218 *
219 * Returns: true if @x is prime, false for composite numbers.
220 */
is_prime_number(unsigned long x)221 bool is_prime_number(unsigned long x)
222 {
223 const struct primes *p;
224 bool result;
225
226 rcu_read_lock();
227 p = rcu_dereference(primes);
228 while (x >= p->sz) {
229 rcu_read_unlock();
230
231 if (!expand_to_next_prime(x))
232 return slow_is_prime_number(x);
233
234 rcu_read_lock();
235 p = rcu_dereference(primes);
236 }
237 result = test_bit(x, p->primes);
238 rcu_read_unlock();
239
240 return result;
241 }
242 EXPORT_SYMBOL(is_prime_number);
243
dump_primes(void)244 static void dump_primes(void)
245 {
246 const struct primes *p;
247 char *buf;
248
249 buf = kmalloc(PAGE_SIZE, GFP_KERNEL);
250
251 rcu_read_lock();
252 p = rcu_dereference(primes);
253
254 if (buf)
255 bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
256 pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s\n",
257 p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);
258
259 rcu_read_unlock();
260
261 kfree(buf);
262 }
263
selftest(unsigned long max)264 static int selftest(unsigned long max)
265 {
266 unsigned long x, last;
267
268 if (!max)
269 return 0;
270
271 for (last = 0, x = 2; x < max; x++) {
272 bool slow = slow_is_prime_number(x);
273 bool fast = is_prime_number(x);
274
275 if (slow != fast) {
276 pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!\n",
277 x, slow ? "yes" : "no", fast ? "yes" : "no");
278 goto err;
279 }
280
281 if (!slow)
282 continue;
283
284 if (next_prime_number(last) != x) {
285 pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu\n",
286 last, x, next_prime_number(last));
287 goto err;
288 }
289 last = x;
290 }
291
292 pr_info("%s(%lu) passed, last prime was %lu\n", __func__, x, last);
293 return 0;
294
295 err:
296 dump_primes();
297 return -EINVAL;
298 }
299
primes_init(void)300 static int __init primes_init(void)
301 {
302 return selftest(selftest_max);
303 }
304
primes_exit(void)305 static void __exit primes_exit(void)
306 {
307 free_primes();
308 }
309
310 module_init(primes_init);
311 module_exit(primes_exit);
312
313 module_param_named(selftest, selftest_max, ulong, 0400);
314
315 MODULE_AUTHOR("Intel Corporation");
316 MODULE_LICENSE("GPL");
317