linux/lib/prime_numbers.c

316 lines
6.5 KiB
C
Raw Normal View History

#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);
lib/prime_numbers: Suppress warn on kmalloc failure The allocation for the bitmap may become very large, larger than MAX_ORDER, for large requests. We fail gracefully by falling back to trail-division, so disable the warning from kmalloc: 521.961092] WARNING: CPU: 0 PID: 30637 at mm/page_alloc.c:3548 __alloc_pages_slowpath+0x237/0x9a0 [ 521.961105] Modules linked in: i915(+) drm_kms_helper intel_gtt prime_numbers [last unloaded: drm_kms_helper] [ 521.961126] CPU: 0 PID: 30637 Comm: drv_selftest Tainted: G U W 4.10.0-rc3+ #321 [ 521.961137] Hardware name: / , BIOS PYBSWCEL.86A.0027.2015.0507.1758 05/07/2015 [ 521.961148] Call Trace: [ 521.961161] dump_stack+0x4d/0x6f [ 521.961172] __warn+0xc1/0xe0 [ 521.961181] warn_slowpath_null+0x18/0x20 [ 521.961189] __alloc_pages_slowpath+0x237/0x9a0 [ 521.961200] ? sg_init_table+0x1a/0x40 [ 521.961208] ? get_page_from_freelist+0x3fa/0x910 [ 521.961275] ? i915_gem_object_get_sg+0x272/0x2b0 [i915] [ 521.961285] __alloc_pages_nodemask+0x1ea/0x220 [ 521.961295] kmalloc_order+0x1c/0x50 [ 521.961304] __kmalloc+0x115/0x170 [ 521.961314] expand_to_next_prime+0x43/0x180 [prime_numbers] [ 521.961324] next_prime_number+0x47/0xc0 [prime_numbers] [ 521.961377] igt_vma_rotate+0x386/0x590 [i915] [ 521.961429] i915_subtests+0x37/0xc0 [i915] [ 521.961481] i915_vma_mock_selftests+0x3d/0x70 [i915] [ 521.961532] run_selftests+0x16e/0x1f0 [i915] [ 521.961541] ? 0xffffffffa02a4000 [ 521.961592] i915_mock_selftests+0x29/0x40 [i915] [ 521.961638] i915_init+0xa/0x5e [i915] [ 521.961646] ? 0xffffffffa02a4000 [ 521.961655] do_one_initcall+0x3e/0x160 [ 521.961664] ? __vunmap+0x7c/0xc0 [ 521.961672] ? vfree+0x29/0x70 [ 521.961680] ? kmem_cache_alloc+0xcf/0x120 [ 521.961690] do_init_module+0x55/0x1c4 [ 521.961699] load_module+0x1f3f/0x25b0 [ 521.961707] ? __symbol_put+0x40/0x40 [ 521.961716] ? kernel_read_file+0x100/0x190 [ 521.961725] SYSC_finit_module+0xbc/0xf0 [ 521.961734] SyS_finit_module+0x9/0x10 [ 521.961744] entry_SYSCALL_64_fastpath+0x17/0x98 [ 521.961752] RIP: 0033:0x7f111aca4119 [ 521.961760] RSP: 002b:00007ffd8be6cbe8 EFLAGS: 00000246 ORIG_RAX: 0000000000000139 [ 521.961773] RAX: ffffffffffffffda RBX: 0000000000000006 RCX: 00007f111aca4119 [ 521.961781] RDX: 0000000000000000 RSI: 000055dfc18bc8e0 RDI: 0000000000000006 [ 521.961789] RBP: 00007ffd8be6bbe0 R08: 0000000000000000 R09: 0000000000000000 [ 521.961796] R10: 0000000000000006 R11: 0000000000000246 R12: 0000000000000005 [ 521.961805] R13: 000055dfc18bd3a0 R14: 00007ffd8be6bbc0 R15: 0000000000000005 Signed-off-by: Chris Wilson <chris@chris-wilson.co.uk> Cc: Joonas Lahtinen <joonas.lahtinen@linux.intel.com> Cc: Daniel Vetter <daniel.vetter@intel.com> Reviewed-by: Joonas Lahtinen <joonas.lahtinen@linux.intel.com> Signed-off-by: Daniel Vetter <daniel.vetter@ffwll.ch> Link: http://patchwork.freedesktop.org/patch/msgid/20170113235119.22528-1-chris@chris-wilson.co.uk
2017-01-14 00:51:19 +01:00
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");