Prime numbers are interesting for testing components that use multiplies and divides, such as testing DRM's struct drm_mm alignment computations.
v2: Move to lib/, add selftest v3: Fix initial constants (exclude 0/1 from being primes) v4: More RCU markup to keep 0day/sparse happy v5: Fix RCU unwind on module exit, add to kselftests v6: Tidy computation of bitmap size v7: for_each_prime_number_from() v8: Compose small-primes using BIT() for easier verification v9: Move rcu dance entirely into callers. v10: Improve quote for Betrand's Postulate (aka Chebyshev's theorem)
Signed-off-by: Chris Wilson chris@chris-wilson.co.uk Cc: Lukas Wunner lukas@wunner.de Reviewed-by: Joonas Lahtinen joonas.lahtinen@linux.intel.com --- include/linux/prime_numbers.h | 37 ++++ lib/Kconfig | 7 + lib/Makefile | 2 + lib/prime_numbers.c | 314 +++++++++++++++++++++++++++ tools/testing/selftests/lib/prime_numbers.sh | 15 ++ 5 files changed, 375 insertions(+) create mode 100644 include/linux/prime_numbers.h create mode 100644 lib/prime_numbers.c create mode 100755 tools/testing/selftests/lib/prime_numbers.sh
diff --git a/include/linux/prime_numbers.h b/include/linux/prime_numbers.h new file mode 100644 index 000000000000..14ec4f567342 --- /dev/null +++ b/include/linux/prime_numbers.h @@ -0,0 +1,37 @@ +#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 */ diff --git a/lib/Kconfig b/lib/Kconfig index 260a80e313b9..1788a1f50d28 100644 --- a/lib/Kconfig +++ b/lib/Kconfig @@ -550,4 +550,11 @@ config STACKDEPOT 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 diff --git a/lib/Makefile b/lib/Makefile index 50144a3aeebd..c664143fd917 100644 --- a/lib/Makefile +++ b/lib/Makefile @@ -197,6 +197,8 @@ obj-$(CONFIG_ASN1) += asn1_decoder.o
obj-$(CONFIG_FONT_SUPPORT) += fonts/
+obj-$(CONFIG_PRIME_NUMBERS) += prime_numbers.o + hostprogs-y := gen_crc32table clean-files := crc32table.h
diff --git a/lib/prime_numbers.c b/lib/prime_numbers.c new file mode 100644 index 000000000000..c9b3c29614aa --- /dev/null +++ b/lib/prime_numbers.c @@ -0,0 +1,314 @@ +#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%27s_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"); diff --git a/tools/testing/selftests/lib/prime_numbers.sh b/tools/testing/selftests/lib/prime_numbers.sh new file mode 100755 index 000000000000..da4cbcd766f5 --- /dev/null +++ b/tools/testing/selftests/lib/prime_numbers.sh @@ -0,0 +1,15 @@ +#!/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