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
Signed-off-by: Chris Wilson <chris@xxxxxxxxxxxxxxxxxx>
Cc: Lukas Wunner <lukas@xxxxxxxxx>
---
include/linux/prime_numbers.h | 23 +++
lib/Kconfig | 7 +
lib/Makefile | 2 +
lib/prime_numbers.c | 266 +++++++++++++++++++++++++++
tools/testing/selftests/lib/prime_numbers.sh | 15 ++
5 files changed, 313 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..6ba642c3f95d
--- /dev/null
+++ b/include/linux/prime_numbers.h
@@ -0,0 +1,23 @@
+#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 1 (which is only considered prime for convenience
+ * of using for_each_prime_number(), a useful white lie), 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.
+ */
+#define for_each_prime_number(prime, max) \
+ for (prime = 1; 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..02795aa0e820
--- /dev/null
+++ b/lib/prime_numbers.c
@@ -0,0 +1,266 @@
+#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 = { 0x28208a20a08a28acUL }
+};
+#elif BITS_PER_LONG == 32
+static const struct primes small_primes = {
+ .last = 31,
+ .sz = 32,
+ .primes = { 0xa08a28acUL }
+};
+#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 mark_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 const struct primes *expand_to_next_prime(unsigned long x)
+{
+ const struct primes *p;
+ struct primes *new;
+ unsigned long sz, y;
+
+ rcu_read_unlock();
+
+ /* Betrand's Theorem states:
+ * For all n > 1, there exists a prime p: n < p <= 2*n.
+ */
+ sz = 2 * x + 1;
+ if (sz < x)
+ return NULL;
+
+ sz = round_up(sz, BITS_PER_LONG);
+ new = kmalloc(sizeof(*new) + bitmap_size(sz), GFP_KERNEL);
+ if (!new)
+ return NULL;
+
+ mutex_lock(&lock);
+ p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
+ if (x < p->last) {
+ kfree(new);
+ goto relock;
+ }
+
+ /* Where memory permits, track the primes using the
+ * Sieve of Eratosthenes.
+ */
+ bitmap_copy(new->primes, p->primes, p->sz);
+ memset(new->primes + BITS_TO_LONGS(p->sz), -1, bitmap_size(sz - p->sz));
+ for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
+ new->last = mark_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);
+ p = new;
+
+relock:
+ rcu_read_lock();
+ mutex_unlock(&lock);
+ return p;
+}
+
+static const struct primes *get_primes(unsigned long x)
+{
+ const struct primes *p;
+
+ rcu_read_lock();
+ p = rcu_dereference(primes);
+ if (!p || x >= p->last)
+ p = expand_to_next_prime(x);
+
+ /* returns under RCU iff p != NULL */
+ return p;
+}
+
+/**
+ * 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 seive 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;
+
+ p = get_primes(x);
+ if (unlikely(!p))
+ return slow_next_prime_number(x);
+
+ 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;
+
+ p = get_primes(x);
+ if (unlikely(!p))
+ return slow_is_prime_number(x);
+
+ 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;
+
+ rcu_read_lock();
+ p = rcu_dereference(primes);
+ pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx}",
+ p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1]);
+ rcu_read_unlock();
+}
+
+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)
+{
+ 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);
+}
+
+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
--
2.11.0
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