#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");
