lib: Add a simple prime number generator

#ifndef __LINUX_PRIME_NUMBERS_H

#define __LINUX_PRIME_NUMBERS_H

#include <linux/types.h>

bool is_prime_number(unsigned long x);

unsigned long next_prime_number(unsigned long x);

/**

 * for_each_prime_number - iterate over each prime upto a value

 * @prime: the current prime number in this iteration

 * @max: the upper limit

 *

 * Starting from the first prime number 2 iterate over each prime number up to

 * the @max value. On each iteration, @prime is set to the current prime number.

 * @max should be less than ULONG_MAX to ensure termination. To begin with

 * @prime set to 1 on the first iteration use for_each_prime_number_from()

 * instead.

 */

#define for_each_prime_number(prime, max) \

	for_each_prime_number_from((prime), 2, (max))

/**

 * for_each_prime_number_from - iterate over each prime upto a value

 * @prime: the current prime number in this iteration

 * @from: the initial value

 * @max: the upper limit

 *

 * Starting from @from iterate over each successive prime number up to the

 * @max value. On each iteration, @prime is set to the current prime number.

 * @max should be less than ULONG_MAX, and @from less than @max, to ensure

 * termination.

 */

#define for_each_prime_number_from(prime, from, max) \

	for (prime = (from); prime <= (max); prime = next_prime_number(prime))

#endif /* !__LINUX_PRIME_NUMBERS_H */

config SBITMAP

	bool

config PRIME_NUMBERS

	tristate "Prime number generator"

	default n

	help

	  Provides a helper module to generate prime numbers. Useful for writing

	  test code, especially when checking multiplication and divison.

endmenu

obj-$(CONFIG_FONT_SUPPORT) += fonts/

obj-$(CONFIG_PRIME_NUMBERS) += prime_numbers.o

hostprogs-y	:= gen_crc32table

clean-files	:= crc32table.h

#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);

	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");

#!/bin/sh

# Checks fast/slow prime_number generation for inconsistencies

if ! /sbin/modprobe -q -r prime_numbers; then

	echo "prime_numbers: [SKIP]"

	exit 77

fi

if /sbin/modprobe -q prime_numbers selftest=65536; then

	/sbin/modprobe -q -r prime_numbers

	echo "prime_numbers: ok"

else

	echo "prime_numbers: [FAIL]"

	exit 1

fi