xref: /openbmc/linux/lib/math/prime_numbers.c (revision 2c64e9cb0b6b858901e9a386860d7d929d1cbaeb)
1*2c64e9cbSAndy Shevchenko #define pr_fmt(fmt) "prime numbers: " fmt "\n"
2*2c64e9cbSAndy Shevchenko 
3*2c64e9cbSAndy Shevchenko #include <linux/module.h>
4*2c64e9cbSAndy Shevchenko #include <linux/mutex.h>
5*2c64e9cbSAndy Shevchenko #include <linux/prime_numbers.h>
6*2c64e9cbSAndy Shevchenko #include <linux/slab.h>
7*2c64e9cbSAndy Shevchenko 
8*2c64e9cbSAndy Shevchenko #define bitmap_size(nbits) (BITS_TO_LONGS(nbits) * sizeof(unsigned long))
9*2c64e9cbSAndy Shevchenko 
10*2c64e9cbSAndy Shevchenko struct primes {
11*2c64e9cbSAndy Shevchenko 	struct rcu_head rcu;
12*2c64e9cbSAndy Shevchenko 	unsigned long last, sz;
13*2c64e9cbSAndy Shevchenko 	unsigned long primes[];
14*2c64e9cbSAndy Shevchenko };
15*2c64e9cbSAndy Shevchenko 
16*2c64e9cbSAndy Shevchenko #if BITS_PER_LONG == 64
17*2c64e9cbSAndy Shevchenko static const struct primes small_primes = {
18*2c64e9cbSAndy Shevchenko 	.last = 61,
19*2c64e9cbSAndy Shevchenko 	.sz = 64,
20*2c64e9cbSAndy Shevchenko 	.primes = {
21*2c64e9cbSAndy Shevchenko 		BIT(2) |
22*2c64e9cbSAndy Shevchenko 		BIT(3) |
23*2c64e9cbSAndy Shevchenko 		BIT(5) |
24*2c64e9cbSAndy Shevchenko 		BIT(7) |
25*2c64e9cbSAndy Shevchenko 		BIT(11) |
26*2c64e9cbSAndy Shevchenko 		BIT(13) |
27*2c64e9cbSAndy Shevchenko 		BIT(17) |
28*2c64e9cbSAndy Shevchenko 		BIT(19) |
29*2c64e9cbSAndy Shevchenko 		BIT(23) |
30*2c64e9cbSAndy Shevchenko 		BIT(29) |
31*2c64e9cbSAndy Shevchenko 		BIT(31) |
32*2c64e9cbSAndy Shevchenko 		BIT(37) |
33*2c64e9cbSAndy Shevchenko 		BIT(41) |
34*2c64e9cbSAndy Shevchenko 		BIT(43) |
35*2c64e9cbSAndy Shevchenko 		BIT(47) |
36*2c64e9cbSAndy Shevchenko 		BIT(53) |
37*2c64e9cbSAndy Shevchenko 		BIT(59) |
38*2c64e9cbSAndy Shevchenko 		BIT(61)
39*2c64e9cbSAndy Shevchenko 	}
40*2c64e9cbSAndy Shevchenko };
41*2c64e9cbSAndy Shevchenko #elif BITS_PER_LONG == 32
42*2c64e9cbSAndy Shevchenko static const struct primes small_primes = {
43*2c64e9cbSAndy Shevchenko 	.last = 31,
44*2c64e9cbSAndy Shevchenko 	.sz = 32,
45*2c64e9cbSAndy Shevchenko 	.primes = {
46*2c64e9cbSAndy Shevchenko 		BIT(2) |
47*2c64e9cbSAndy Shevchenko 		BIT(3) |
48*2c64e9cbSAndy Shevchenko 		BIT(5) |
49*2c64e9cbSAndy Shevchenko 		BIT(7) |
50*2c64e9cbSAndy Shevchenko 		BIT(11) |
51*2c64e9cbSAndy Shevchenko 		BIT(13) |
52*2c64e9cbSAndy Shevchenko 		BIT(17) |
53*2c64e9cbSAndy Shevchenko 		BIT(19) |
54*2c64e9cbSAndy Shevchenko 		BIT(23) |
55*2c64e9cbSAndy Shevchenko 		BIT(29) |
56*2c64e9cbSAndy Shevchenko 		BIT(31)
57*2c64e9cbSAndy Shevchenko 	}
58*2c64e9cbSAndy Shevchenko };
59*2c64e9cbSAndy Shevchenko #else
60*2c64e9cbSAndy Shevchenko #error "unhandled BITS_PER_LONG"
61*2c64e9cbSAndy Shevchenko #endif
62*2c64e9cbSAndy Shevchenko 
63*2c64e9cbSAndy Shevchenko static DEFINE_MUTEX(lock);
64*2c64e9cbSAndy Shevchenko static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);
65*2c64e9cbSAndy Shevchenko 
66*2c64e9cbSAndy Shevchenko static unsigned long selftest_max;
67*2c64e9cbSAndy Shevchenko 
68*2c64e9cbSAndy Shevchenko static bool slow_is_prime_number(unsigned long x)
69*2c64e9cbSAndy Shevchenko {
70*2c64e9cbSAndy Shevchenko 	unsigned long y = int_sqrt(x);
71*2c64e9cbSAndy Shevchenko 
72*2c64e9cbSAndy Shevchenko 	while (y > 1) {
73*2c64e9cbSAndy Shevchenko 		if ((x % y) == 0)
74*2c64e9cbSAndy Shevchenko 			break;
75*2c64e9cbSAndy Shevchenko 		y--;
76*2c64e9cbSAndy Shevchenko 	}
77*2c64e9cbSAndy Shevchenko 
78*2c64e9cbSAndy Shevchenko 	return y == 1;
79*2c64e9cbSAndy Shevchenko }
80*2c64e9cbSAndy Shevchenko 
81*2c64e9cbSAndy Shevchenko static unsigned long slow_next_prime_number(unsigned long x)
82*2c64e9cbSAndy Shevchenko {
83*2c64e9cbSAndy Shevchenko 	while (x < ULONG_MAX && !slow_is_prime_number(++x))
84*2c64e9cbSAndy Shevchenko 		;
85*2c64e9cbSAndy Shevchenko 
86*2c64e9cbSAndy Shevchenko 	return x;
87*2c64e9cbSAndy Shevchenko }
88*2c64e9cbSAndy Shevchenko 
89*2c64e9cbSAndy Shevchenko static unsigned long clear_multiples(unsigned long x,
90*2c64e9cbSAndy Shevchenko 				     unsigned long *p,
91*2c64e9cbSAndy Shevchenko 				     unsigned long start,
92*2c64e9cbSAndy Shevchenko 				     unsigned long end)
93*2c64e9cbSAndy Shevchenko {
94*2c64e9cbSAndy Shevchenko 	unsigned long m;
95*2c64e9cbSAndy Shevchenko 
96*2c64e9cbSAndy Shevchenko 	m = 2 * x;
97*2c64e9cbSAndy Shevchenko 	if (m < start)
98*2c64e9cbSAndy Shevchenko 		m = roundup(start, x);
99*2c64e9cbSAndy Shevchenko 
100*2c64e9cbSAndy Shevchenko 	while (m < end) {
101*2c64e9cbSAndy Shevchenko 		__clear_bit(m, p);
102*2c64e9cbSAndy Shevchenko 		m += x;
103*2c64e9cbSAndy Shevchenko 	}
104*2c64e9cbSAndy Shevchenko 
105*2c64e9cbSAndy Shevchenko 	return x;
106*2c64e9cbSAndy Shevchenko }
107*2c64e9cbSAndy Shevchenko 
108*2c64e9cbSAndy Shevchenko static bool expand_to_next_prime(unsigned long x)
109*2c64e9cbSAndy Shevchenko {
110*2c64e9cbSAndy Shevchenko 	const struct primes *p;
111*2c64e9cbSAndy Shevchenko 	struct primes *new;
112*2c64e9cbSAndy Shevchenko 	unsigned long sz, y;
113*2c64e9cbSAndy Shevchenko 
114*2c64e9cbSAndy Shevchenko 	/* Betrand's Postulate (or Chebyshev's theorem) states that if n > 3,
115*2c64e9cbSAndy Shevchenko 	 * there is always at least one prime p between n and 2n - 2.
116*2c64e9cbSAndy Shevchenko 	 * Equivalently, if n > 1, then there is always at least one prime p
117*2c64e9cbSAndy Shevchenko 	 * such that n < p < 2n.
118*2c64e9cbSAndy Shevchenko 	 *
119*2c64e9cbSAndy Shevchenko 	 * http://mathworld.wolfram.com/BertrandsPostulate.html
120*2c64e9cbSAndy Shevchenko 	 * https://en.wikipedia.org/wiki/Bertrand's_postulate
121*2c64e9cbSAndy Shevchenko 	 */
122*2c64e9cbSAndy Shevchenko 	sz = 2 * x;
123*2c64e9cbSAndy Shevchenko 	if (sz < x)
124*2c64e9cbSAndy Shevchenko 		return false;
125*2c64e9cbSAndy Shevchenko 
126*2c64e9cbSAndy Shevchenko 	sz = round_up(sz, BITS_PER_LONG);
127*2c64e9cbSAndy Shevchenko 	new = kmalloc(sizeof(*new) + bitmap_size(sz),
128*2c64e9cbSAndy Shevchenko 		      GFP_KERNEL | __GFP_NOWARN);
129*2c64e9cbSAndy Shevchenko 	if (!new)
130*2c64e9cbSAndy Shevchenko 		return false;
131*2c64e9cbSAndy Shevchenko 
132*2c64e9cbSAndy Shevchenko 	mutex_lock(&lock);
133*2c64e9cbSAndy Shevchenko 	p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
134*2c64e9cbSAndy Shevchenko 	if (x < p->last) {
135*2c64e9cbSAndy Shevchenko 		kfree(new);
136*2c64e9cbSAndy Shevchenko 		goto unlock;
137*2c64e9cbSAndy Shevchenko 	}
138*2c64e9cbSAndy Shevchenko 
139*2c64e9cbSAndy Shevchenko 	/* Where memory permits, track the primes using the
140*2c64e9cbSAndy Shevchenko 	 * Sieve of Eratosthenes. The sieve is to remove all multiples of known
141*2c64e9cbSAndy Shevchenko 	 * primes from the set, what remains in the set is therefore prime.
142*2c64e9cbSAndy Shevchenko 	 */
143*2c64e9cbSAndy Shevchenko 	bitmap_fill(new->primes, sz);
144*2c64e9cbSAndy Shevchenko 	bitmap_copy(new->primes, p->primes, p->sz);
145*2c64e9cbSAndy Shevchenko 	for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
146*2c64e9cbSAndy Shevchenko 		new->last = clear_multiples(y, new->primes, p->sz, sz);
147*2c64e9cbSAndy Shevchenko 	new->sz = sz;
148*2c64e9cbSAndy Shevchenko 
149*2c64e9cbSAndy Shevchenko 	BUG_ON(new->last <= x);
150*2c64e9cbSAndy Shevchenko 
151*2c64e9cbSAndy Shevchenko 	rcu_assign_pointer(primes, new);
152*2c64e9cbSAndy Shevchenko 	if (p != &small_primes)
153*2c64e9cbSAndy Shevchenko 		kfree_rcu((struct primes *)p, rcu);
154*2c64e9cbSAndy Shevchenko 
155*2c64e9cbSAndy Shevchenko unlock:
156*2c64e9cbSAndy Shevchenko 	mutex_unlock(&lock);
157*2c64e9cbSAndy Shevchenko 	return true;
158*2c64e9cbSAndy Shevchenko }
159*2c64e9cbSAndy Shevchenko 
160*2c64e9cbSAndy Shevchenko static void free_primes(void)
161*2c64e9cbSAndy Shevchenko {
162*2c64e9cbSAndy Shevchenko 	const struct primes *p;
163*2c64e9cbSAndy Shevchenko 
164*2c64e9cbSAndy Shevchenko 	mutex_lock(&lock);
165*2c64e9cbSAndy Shevchenko 	p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
166*2c64e9cbSAndy Shevchenko 	if (p != &small_primes) {
167*2c64e9cbSAndy Shevchenko 		rcu_assign_pointer(primes, &small_primes);
168*2c64e9cbSAndy Shevchenko 		kfree_rcu((struct primes *)p, rcu);
169*2c64e9cbSAndy Shevchenko 	}
170*2c64e9cbSAndy Shevchenko 	mutex_unlock(&lock);
171*2c64e9cbSAndy Shevchenko }
172*2c64e9cbSAndy Shevchenko 
173*2c64e9cbSAndy Shevchenko /**
174*2c64e9cbSAndy Shevchenko  * next_prime_number - return the next prime number
175*2c64e9cbSAndy Shevchenko  * @x: the starting point for searching to test
176*2c64e9cbSAndy Shevchenko  *
177*2c64e9cbSAndy Shevchenko  * A prime number is an integer greater than 1 that is only divisible by
178*2c64e9cbSAndy Shevchenko  * itself and 1.  The set of prime numbers is computed using the Sieve of
179*2c64e9cbSAndy Shevchenko  * Eratoshenes (on finding a prime, all multiples of that prime are removed
180*2c64e9cbSAndy Shevchenko  * from the set) enabling a fast lookup of the next prime number larger than
181*2c64e9cbSAndy Shevchenko  * @x. If the sieve fails (memory limitation), the search falls back to using
182*2c64e9cbSAndy Shevchenko  * slow trial-divison, up to the value of ULONG_MAX (which is reported as the
183*2c64e9cbSAndy Shevchenko  * final prime as a sentinel).
184*2c64e9cbSAndy Shevchenko  *
185*2c64e9cbSAndy Shevchenko  * Returns: the next prime number larger than @x
186*2c64e9cbSAndy Shevchenko  */
187*2c64e9cbSAndy Shevchenko unsigned long next_prime_number(unsigned long x)
188*2c64e9cbSAndy Shevchenko {
189*2c64e9cbSAndy Shevchenko 	const struct primes *p;
190*2c64e9cbSAndy Shevchenko 
191*2c64e9cbSAndy Shevchenko 	rcu_read_lock();
192*2c64e9cbSAndy Shevchenko 	p = rcu_dereference(primes);
193*2c64e9cbSAndy Shevchenko 	while (x >= p->last) {
194*2c64e9cbSAndy Shevchenko 		rcu_read_unlock();
195*2c64e9cbSAndy Shevchenko 
196*2c64e9cbSAndy Shevchenko 		if (!expand_to_next_prime(x))
197*2c64e9cbSAndy Shevchenko 			return slow_next_prime_number(x);
198*2c64e9cbSAndy Shevchenko 
199*2c64e9cbSAndy Shevchenko 		rcu_read_lock();
200*2c64e9cbSAndy Shevchenko 		p = rcu_dereference(primes);
201*2c64e9cbSAndy Shevchenko 	}
202*2c64e9cbSAndy Shevchenko 	x = find_next_bit(p->primes, p->last, x + 1);
203*2c64e9cbSAndy Shevchenko 	rcu_read_unlock();
204*2c64e9cbSAndy Shevchenko 
205*2c64e9cbSAndy Shevchenko 	return x;
206*2c64e9cbSAndy Shevchenko }
207*2c64e9cbSAndy Shevchenko EXPORT_SYMBOL(next_prime_number);
208*2c64e9cbSAndy Shevchenko 
209*2c64e9cbSAndy Shevchenko /**
210*2c64e9cbSAndy Shevchenko  * is_prime_number - test whether the given number is prime
211*2c64e9cbSAndy Shevchenko  * @x: the number to test
212*2c64e9cbSAndy Shevchenko  *
213*2c64e9cbSAndy Shevchenko  * A prime number is an integer greater than 1 that is only divisible by
214*2c64e9cbSAndy Shevchenko  * itself and 1. Internally a cache of prime numbers is kept (to speed up
215*2c64e9cbSAndy Shevchenko  * searching for sequential primes, see next_prime_number()), but if the number
216*2c64e9cbSAndy Shevchenko  * falls outside of that cache, its primality is tested using trial-divison.
217*2c64e9cbSAndy Shevchenko  *
218*2c64e9cbSAndy Shevchenko  * Returns: true if @x is prime, false for composite numbers.
219*2c64e9cbSAndy Shevchenko  */
220*2c64e9cbSAndy Shevchenko bool is_prime_number(unsigned long x)
221*2c64e9cbSAndy Shevchenko {
222*2c64e9cbSAndy Shevchenko 	const struct primes *p;
223*2c64e9cbSAndy Shevchenko 	bool result;
224*2c64e9cbSAndy Shevchenko 
225*2c64e9cbSAndy Shevchenko 	rcu_read_lock();
226*2c64e9cbSAndy Shevchenko 	p = rcu_dereference(primes);
227*2c64e9cbSAndy Shevchenko 	while (x >= p->sz) {
228*2c64e9cbSAndy Shevchenko 		rcu_read_unlock();
229*2c64e9cbSAndy Shevchenko 
230*2c64e9cbSAndy Shevchenko 		if (!expand_to_next_prime(x))
231*2c64e9cbSAndy Shevchenko 			return slow_is_prime_number(x);
232*2c64e9cbSAndy Shevchenko 
233*2c64e9cbSAndy Shevchenko 		rcu_read_lock();
234*2c64e9cbSAndy Shevchenko 		p = rcu_dereference(primes);
235*2c64e9cbSAndy Shevchenko 	}
236*2c64e9cbSAndy Shevchenko 	result = test_bit(x, p->primes);
237*2c64e9cbSAndy Shevchenko 	rcu_read_unlock();
238*2c64e9cbSAndy Shevchenko 
239*2c64e9cbSAndy Shevchenko 	return result;
240*2c64e9cbSAndy Shevchenko }
241*2c64e9cbSAndy Shevchenko EXPORT_SYMBOL(is_prime_number);
242*2c64e9cbSAndy Shevchenko 
243*2c64e9cbSAndy Shevchenko static void dump_primes(void)
244*2c64e9cbSAndy Shevchenko {
245*2c64e9cbSAndy Shevchenko 	const struct primes *p;
246*2c64e9cbSAndy Shevchenko 	char *buf;
247*2c64e9cbSAndy Shevchenko 
248*2c64e9cbSAndy Shevchenko 	buf = kmalloc(PAGE_SIZE, GFP_KERNEL);
249*2c64e9cbSAndy Shevchenko 
250*2c64e9cbSAndy Shevchenko 	rcu_read_lock();
251*2c64e9cbSAndy Shevchenko 	p = rcu_dereference(primes);
252*2c64e9cbSAndy Shevchenko 
253*2c64e9cbSAndy Shevchenko 	if (buf)
254*2c64e9cbSAndy Shevchenko 		bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
255*2c64e9cbSAndy Shevchenko 	pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s",
256*2c64e9cbSAndy Shevchenko 		p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);
257*2c64e9cbSAndy Shevchenko 
258*2c64e9cbSAndy Shevchenko 	rcu_read_unlock();
259*2c64e9cbSAndy Shevchenko 
260*2c64e9cbSAndy Shevchenko 	kfree(buf);
261*2c64e9cbSAndy Shevchenko }
262*2c64e9cbSAndy Shevchenko 
263*2c64e9cbSAndy Shevchenko static int selftest(unsigned long max)
264*2c64e9cbSAndy Shevchenko {
265*2c64e9cbSAndy Shevchenko 	unsigned long x, last;
266*2c64e9cbSAndy Shevchenko 
267*2c64e9cbSAndy Shevchenko 	if (!max)
268*2c64e9cbSAndy Shevchenko 		return 0;
269*2c64e9cbSAndy Shevchenko 
270*2c64e9cbSAndy Shevchenko 	for (last = 0, x = 2; x < max; x++) {
271*2c64e9cbSAndy Shevchenko 		bool slow = slow_is_prime_number(x);
272*2c64e9cbSAndy Shevchenko 		bool fast = is_prime_number(x);
273*2c64e9cbSAndy Shevchenko 
274*2c64e9cbSAndy Shevchenko 		if (slow != fast) {
275*2c64e9cbSAndy Shevchenko 			pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!",
276*2c64e9cbSAndy Shevchenko 			       x, slow ? "yes" : "no", fast ? "yes" : "no");
277*2c64e9cbSAndy Shevchenko 			goto err;
278*2c64e9cbSAndy Shevchenko 		}
279*2c64e9cbSAndy Shevchenko 
280*2c64e9cbSAndy Shevchenko 		if (!slow)
281*2c64e9cbSAndy Shevchenko 			continue;
282*2c64e9cbSAndy Shevchenko 
283*2c64e9cbSAndy Shevchenko 		if (next_prime_number(last) != x) {
284*2c64e9cbSAndy Shevchenko 			pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu",
285*2c64e9cbSAndy Shevchenko 			       last, x, next_prime_number(last));
286*2c64e9cbSAndy Shevchenko 			goto err;
287*2c64e9cbSAndy Shevchenko 		}
288*2c64e9cbSAndy Shevchenko 		last = x;
289*2c64e9cbSAndy Shevchenko 	}
290*2c64e9cbSAndy Shevchenko 
291*2c64e9cbSAndy Shevchenko 	pr_info("selftest(%lu) passed, last prime was %lu", x, last);
292*2c64e9cbSAndy Shevchenko 	return 0;
293*2c64e9cbSAndy Shevchenko 
294*2c64e9cbSAndy Shevchenko err:
295*2c64e9cbSAndy Shevchenko 	dump_primes();
296*2c64e9cbSAndy Shevchenko 	return -EINVAL;
297*2c64e9cbSAndy Shevchenko }
298*2c64e9cbSAndy Shevchenko 
299*2c64e9cbSAndy Shevchenko static int __init primes_init(void)
300*2c64e9cbSAndy Shevchenko {
301*2c64e9cbSAndy Shevchenko 	return selftest(selftest_max);
302*2c64e9cbSAndy Shevchenko }
303*2c64e9cbSAndy Shevchenko 
304*2c64e9cbSAndy Shevchenko static void __exit primes_exit(void)
305*2c64e9cbSAndy Shevchenko {
306*2c64e9cbSAndy Shevchenko 	free_primes();
307*2c64e9cbSAndy Shevchenko }
308*2c64e9cbSAndy Shevchenko 
309*2c64e9cbSAndy Shevchenko module_init(primes_init);
310*2c64e9cbSAndy Shevchenko module_exit(primes_exit);
311*2c64e9cbSAndy Shevchenko 
312*2c64e9cbSAndy Shevchenko module_param_named(selftest, selftest_max, ulong, 0400);
313*2c64e9cbSAndy Shevchenko 
314*2c64e9cbSAndy Shevchenko MODULE_AUTHOR("Intel Corporation");
315*2c64e9cbSAndy Shevchenko MODULE_LICENSE("GPL");
316