summaryrefslogtreecommitdiff
path: root/lib/prime_numbers.c
blob: 550eec457c2edb45ba21fa6d5a40dd13663ddf0b (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
#define pr_fmt(fmt) "prime numbers: " fmt "\n"

#include <linux/module.h>
#include <linux/mutex.h>
#include <linux/prime_numbers.h>
#include <linux/slab.h>

#define bitmap_size(nbits) (BITS_TO_LONGS(nbits) * sizeof(unsigned long))

struct primes {
	struct rcu_head rcu;
	unsigned long last, sz;
	unsigned long primes[];
};

#if BITS_PER_LONG == 64
static const struct primes small_primes = {
	.last = 61,
	.sz = 64,
	.primes = {
		BIT(2) |
		BIT(3) |
		BIT(5) |
		BIT(7) |
		BIT(11) |
		BIT(13) |
		BIT(17) |
		BIT(19) |
		BIT(23) |
		BIT(29) |
		BIT(31) |
		BIT(37) |
		BIT(41) |
		BIT(43) |
		BIT(47) |
		BIT(53) |
		BIT(59) |
		BIT(61)
	}
};
#elif BITS_PER_LONG == 32
static const struct primes small_primes = {
	.last = 31,
	.sz = 32,
	.primes = {
		BIT(2) |
		BIT(3) |
		BIT(5) |
		BIT(7) |
		BIT(11) |
		BIT(13) |
		BIT(17) |
		BIT(19) |
		BIT(23) |
		BIT(29) |
		BIT(31)
	}
};
#else
#error "unhandled BITS_PER_LONG"
#endif

static DEFINE_MUTEX(lock);
static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);

static unsigned long selftest_max;

static bool slow_is_prime_number(unsigned long x)
{
	unsigned long y = int_sqrt(x);

	while (y > 1) {
		if ((x % y) == 0)
			break;
		y--;
	}

	return y == 1;
}

static unsigned long slow_next_prime_number(unsigned long x)
{
	while (x < ULONG_MAX && !slow_is_prime_number(++x))
		;

	return x;
}

static unsigned long clear_multiples(unsigned long x,
				     unsigned long *p,
				     unsigned long start,
				     unsigned long end)
{
	unsigned long m;

	m = 2 * x;
	if (m < start)
		m = roundup(start, x);

	while (m < end) {
		__clear_bit(m, p);
		m += x;
	}

	return x;
}

static bool expand_to_next_prime(unsigned long x)
{
	const struct primes *p;
	struct primes *new;
	unsigned long sz, y;

	/* Betrand's Postulate (or Chebyshev's theorem) states that if n > 3,
	 * there is always at least one prime p between n and 2n - 2.
	 * Equivalently, if n > 1, then there is always at least one prime p
	 * such that n < p < 2n.
	 *
	 * http://mathworld.wolfram.com/BertrandsPostulate.html
	 * https://en.wikipedia.org/wiki/Bertrand's_postulate
	 */
	sz = 2 * x;
	if (sz < x)
		return false;

	sz = round_up(sz, BITS_PER_LONG);
	new = kmalloc(sizeof(*new) + bitmap_size(sz),
		      GFP_KERNEL | __GFP_NOWARN);
	if (!new)
		return false;

	mutex_lock(&lock);
	p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
	if (x < p->last) {
		kfree(new);
		goto unlock;
	}

	/* Where memory permits, track the primes using the
	 * Sieve of Eratosthenes. The sieve is to remove all multiples of known
	 * primes from the set, what remains in the set is therefore prime.
	 */
	bitmap_fill(new->primes, sz);
	bitmap_copy(new->primes, p->primes, p->sz);
	for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
		new->last = clear_multiples(y, new->primes, p->sz, sz);
	new->sz = sz;

	BUG_ON(new->last <= x);

	rcu_assign_pointer(primes, new);
	if (p != &small_primes)
		kfree_rcu((struct primes *)p, rcu);

unlock:
	mutex_unlock(&lock);
	return true;
}

static void free_primes(void)
{
	const struct primes *p;

	mutex_lock(&lock);
	p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
	if (p != &small_primes) {
		rcu_assign_pointer(primes, &small_primes);
		kfree_rcu((struct primes *)p, rcu);
	}
	mutex_unlock(&lock);
}

/**
 * next_prime_number - return the next prime number
 * @x: the starting point for searching to test
 *
 * A prime number is an integer greater than 1 that is only divisible by
 * itself and 1.  The set of prime numbers is computed using the Sieve of
 * Eratoshenes (on finding a prime, all multiples of that prime are removed
 * from the set) enabling a fast lookup of the next prime number larger than
 * @x. If the sieve fails (memory limitation), the search falls back to using
 * slow trial-divison, up to the value of ULONG_MAX (which is reported as the
 * final prime as a sentinel).
 *
 * Returns: the next prime number larger than @x
 */
unsigned long next_prime_number(unsigned long x)
{
	const struct primes *p;

	rcu_read_lock();
	p = rcu_dereference(primes);
	while (x >= p->last) {
		rcu_read_unlock();

		if (!expand_to_next_prime(x))
			return slow_next_prime_number(x);

		rcu_read_lock();
		p = rcu_dereference(primes);
	}
	x = find_next_bit(p->primes, p->last, x + 1);
	rcu_read_unlock();

	return x;
}
EXPORT_SYMBOL(next_prime_number);

/**
 * is_prime_number - test whether the given number is prime
 * @x: the number to test
 *
 * A prime number is an integer greater than 1 that is only divisible by
 * itself and 1. Internally a cache of prime numbers is kept (to speed up
 * searching for sequential primes, see next_prime_number()), but if the number
 * falls outside of that cache, its primality is tested using trial-divison.
 *
 * Returns: true if @x is prime, false for composite numbers.
 */
bool is_prime_number(unsigned long x)
{
	const struct primes *p;
	bool result;

	rcu_read_lock();
	p = rcu_dereference(primes);
	while (x >= p->sz) {
		rcu_read_unlock();

		if (!expand_to_next_prime(x))
			return slow_is_prime_number(x);

		rcu_read_lock();
		p = rcu_dereference(primes);
	}
	result = test_bit(x, p->primes);
	rcu_read_unlock();

	return result;
}
EXPORT_SYMBOL(is_prime_number);

static void dump_primes(void)
{
	const struct primes *p;
	char *buf;

	buf = kmalloc(PAGE_SIZE, GFP_KERNEL);

	rcu_read_lock();
	p = rcu_dereference(primes);

	if (buf)
		bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
	pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s",
		p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);

	rcu_read_unlock();

	kfree(buf);
}

static int selftest(unsigned long max)
{
	unsigned long x, last;

	if (!max)
		return 0;

	for (last = 0, x = 2; x < max; x++) {
		bool slow = slow_is_prime_number(x);
		bool fast = is_prime_number(x);

		if (slow != fast) {
			pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!",
			       x, slow ? "yes" : "no", fast ? "yes" : "no");
			goto err;
		}

		if (!slow)
			continue;

		if (next_prime_number(last) != x) {
			pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu",
			       last, x, next_prime_number(last));
			goto err;
		}
		last = x;
	}

	pr_info("selftest(%lu) passed, last prime was %lu", x, last);
	return 0;

err:
	dump_primes();
	return -EINVAL;
}

static int __init primes_init(void)
{
	return selftest(selftest_max);
}

static void __exit primes_exit(void)
{
	free_primes();
}

module_init(primes_init);
module_exit(primes_exit);

module_param_named(selftest, selftest_max, ulong, 0400);

MODULE_AUTHOR("Intel Corporation");
MODULE_LICENSE("GPL");