// SPDX-License-Identifier: GPL-2.0-only
#define pr_fmt(fmt) "prime numbers: " fmt

#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\n",
                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!\n",
                               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\n",
                               last, x, next_prime_number(last));
                        goto err;
                }
                last = x;
        }

        pr_info("%s(%lu) passed, last prime was %lu\n", __func__, 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");