![Thomas Gleixner](/assets/img/avatar_default.png)
Add SPDX license identifiers to all files which: - Have no license information of any form - Have MODULE_LICENCE("GPL*") inside which was used in the initial scan/conversion to ignore the file These files fall under the project license, GPL v2 only. The resulting SPDX license identifier is: GPL-2.0-only Signed-off-by: Thomas Gleixner <tglx@linutronix.de> Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
317 lines
6.5 KiB
C
317 lines
6.5 KiB
C
// SPDX-License-Identifier: GPL-2.0-only
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#define pr_fmt(fmt) "prime numbers: " fmt "\n"
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#include <linux/module.h>
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#include <linux/mutex.h>
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#include <linux/prime_numbers.h>
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#include <linux/slab.h>
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#define bitmap_size(nbits) (BITS_TO_LONGS(nbits) * sizeof(unsigned long))
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struct primes {
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struct rcu_head rcu;
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unsigned long last, sz;
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unsigned long primes[];
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};
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#if BITS_PER_LONG == 64
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static const struct primes small_primes = {
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.last = 61,
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.sz = 64,
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.primes = {
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BIT(2) |
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BIT(3) |
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BIT(5) |
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BIT(7) |
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BIT(11) |
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BIT(13) |
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BIT(17) |
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BIT(19) |
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BIT(23) |
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BIT(29) |
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BIT(31) |
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BIT(37) |
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BIT(41) |
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BIT(43) |
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BIT(47) |
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BIT(53) |
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BIT(59) |
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BIT(61)
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}
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};
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#elif BITS_PER_LONG == 32
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static const struct primes small_primes = {
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.last = 31,
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.sz = 32,
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.primes = {
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BIT(2) |
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BIT(3) |
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BIT(5) |
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BIT(7) |
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BIT(11) |
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BIT(13) |
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BIT(17) |
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BIT(19) |
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BIT(23) |
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BIT(29) |
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BIT(31)
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}
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};
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#else
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#error "unhandled BITS_PER_LONG"
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#endif
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static DEFINE_MUTEX(lock);
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static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);
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static unsigned long selftest_max;
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static bool slow_is_prime_number(unsigned long x)
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{
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unsigned long y = int_sqrt(x);
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while (y > 1) {
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if ((x % y) == 0)
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break;
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y--;
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}
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return y == 1;
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}
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static unsigned long slow_next_prime_number(unsigned long x)
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{
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while (x < ULONG_MAX && !slow_is_prime_number(++x))
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;
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return x;
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}
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static unsigned long clear_multiples(unsigned long x,
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unsigned long *p,
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unsigned long start,
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unsigned long end)
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{
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unsigned long m;
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m = 2 * x;
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if (m < start)
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m = roundup(start, x);
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while (m < end) {
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__clear_bit(m, p);
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m += x;
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}
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return x;
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}
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static bool expand_to_next_prime(unsigned long x)
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{
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const struct primes *p;
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struct primes *new;
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unsigned long sz, y;
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/* Betrand's Postulate (or Chebyshev's theorem) states that if n > 3,
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* there is always at least one prime p between n and 2n - 2.
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* Equivalently, if n > 1, then there is always at least one prime p
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* such that n < p < 2n.
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*
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* http://mathworld.wolfram.com/BertrandsPostulate.html
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* https://en.wikipedia.org/wiki/Bertrand's_postulate
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*/
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sz = 2 * x;
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if (sz < x)
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return false;
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sz = round_up(sz, BITS_PER_LONG);
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new = kmalloc(sizeof(*new) + bitmap_size(sz),
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GFP_KERNEL | __GFP_NOWARN);
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if (!new)
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return false;
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mutex_lock(&lock);
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p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
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if (x < p->last) {
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kfree(new);
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goto unlock;
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}
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/* Where memory permits, track the primes using the
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* Sieve of Eratosthenes. The sieve is to remove all multiples of known
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* primes from the set, what remains in the set is therefore prime.
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*/
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bitmap_fill(new->primes, sz);
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bitmap_copy(new->primes, p->primes, p->sz);
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for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
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new->last = clear_multiples(y, new->primes, p->sz, sz);
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new->sz = sz;
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BUG_ON(new->last <= x);
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rcu_assign_pointer(primes, new);
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if (p != &small_primes)
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kfree_rcu((struct primes *)p, rcu);
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unlock:
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mutex_unlock(&lock);
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return true;
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}
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static void free_primes(void)
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{
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const struct primes *p;
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mutex_lock(&lock);
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p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
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if (p != &small_primes) {
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rcu_assign_pointer(primes, &small_primes);
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kfree_rcu((struct primes *)p, rcu);
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}
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mutex_unlock(&lock);
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}
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/**
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* next_prime_number - return the next prime number
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* @x: the starting point for searching to test
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*
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* A prime number is an integer greater than 1 that is only divisible by
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* itself and 1. The set of prime numbers is computed using the Sieve of
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* Eratoshenes (on finding a prime, all multiples of that prime are removed
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* from the set) enabling a fast lookup of the next prime number larger than
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* @x. If the sieve fails (memory limitation), the search falls back to using
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* slow trial-divison, up to the value of ULONG_MAX (which is reported as the
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* final prime as a sentinel).
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*
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* Returns: the next prime number larger than @x
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*/
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unsigned long next_prime_number(unsigned long x)
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{
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const struct primes *p;
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rcu_read_lock();
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p = rcu_dereference(primes);
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while (x >= p->last) {
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rcu_read_unlock();
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if (!expand_to_next_prime(x))
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return slow_next_prime_number(x);
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rcu_read_lock();
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p = rcu_dereference(primes);
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}
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x = find_next_bit(p->primes, p->last, x + 1);
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rcu_read_unlock();
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return x;
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}
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EXPORT_SYMBOL(next_prime_number);
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/**
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* is_prime_number - test whether the given number is prime
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* @x: the number to test
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*
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* A prime number is an integer greater than 1 that is only divisible by
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* itself and 1. Internally a cache of prime numbers is kept (to speed up
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* searching for sequential primes, see next_prime_number()), but if the number
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* falls outside of that cache, its primality is tested using trial-divison.
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*
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* Returns: true if @x is prime, false for composite numbers.
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*/
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bool is_prime_number(unsigned long x)
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{
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const struct primes *p;
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bool result;
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rcu_read_lock();
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p = rcu_dereference(primes);
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while (x >= p->sz) {
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rcu_read_unlock();
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if (!expand_to_next_prime(x))
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return slow_is_prime_number(x);
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rcu_read_lock();
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p = rcu_dereference(primes);
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}
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result = test_bit(x, p->primes);
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rcu_read_unlock();
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return result;
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}
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EXPORT_SYMBOL(is_prime_number);
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static void dump_primes(void)
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{
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const struct primes *p;
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char *buf;
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buf = kmalloc(PAGE_SIZE, GFP_KERNEL);
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rcu_read_lock();
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p = rcu_dereference(primes);
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if (buf)
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bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
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pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s",
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p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);
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rcu_read_unlock();
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kfree(buf);
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}
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static int selftest(unsigned long max)
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{
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unsigned long x, last;
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if (!max)
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return 0;
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for (last = 0, x = 2; x < max; x++) {
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bool slow = slow_is_prime_number(x);
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bool fast = is_prime_number(x);
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if (slow != fast) {
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pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!",
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x, slow ? "yes" : "no", fast ? "yes" : "no");
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goto err;
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}
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if (!slow)
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continue;
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if (next_prime_number(last) != x) {
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pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu",
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last, x, next_prime_number(last));
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goto err;
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}
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last = x;
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}
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pr_info("selftest(%lu) passed, last prime was %lu", x, last);
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return 0;
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err:
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dump_primes();
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return -EINVAL;
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}
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static int __init primes_init(void)
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{
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return selftest(selftest_max);
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}
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static void __exit primes_exit(void)
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{
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free_primes();
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}
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module_init(primes_init);
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module_exit(primes_exit);
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module_param_named(selftest, selftest_max, ulong, 0400);
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MODULE_AUTHOR("Intel Corporation");
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MODULE_LICENSE("GPL");
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