lib: Add an iterator to generate primes

Primes are useful as input sources since they should not fall into any
patterns that may be optimised by the drivers.

An example of use this in a test driver:

	uint32_t seqno, inc, count;

	seqno = inc = count = 0;
	do {
		inc = igt_next_prime_number(inc);
		if (seqno + inc < seqno)
			break;
		seqno += inc;
		/* igt_assert_eq(test_inc(inc), seqno); */
		count++;
	} while (1);
	printf("count=%u, seqno=%u, last=%u\n", count, seqno, inc);

and prints "count=27878, seqno=4294845817, last=323381", or for simply
generating the set of the first N prime numbers, use

	for_each_prime_number(prime, 100)
		printf("%lu ", prime);

which prints

1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 64 67 71 73 79 83 89
97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181
191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397
401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503
509 521

Note that 1 is included in the set of prime numbers for convenience
above. Mathematicians beware!

The set of primes is computed using the Sieve of Eratosthenes, which
basically just keeps a list of all multiples - any number not in list is
therefore prime. As a bitmask of all integers is kept, it can be quite
memory intensive for very large primes. A fallback to "trial division"
is available just in case, but for large primes that is much slower.

Signed-off-by: Chris Wilson <chris@chris-wilson.co.uk>

1 files changed, 178 insertions, 0 deletions

diff --git a/lib/igt_primes.c b/lib/igt_primes.c
new file mode 100644
index 00000000..d5232e54
--- /dev/null
+++ b/lib/igt_primes.c
@@ -0,0 +1,178 @@
+/*
+ * Copyright © 2016 Intel Corporation
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
+ */
+
+#include "igt_primes.h"
+
+#include <stdlib.h>
+#include <stdbool.h>
+#include <string.h>
+#include <math.h>
+
+#define BITS_PER_CHAR 8
+#define BITS_PER_LONG (sizeof(long)*BITS_PER_CHAR)
+
+#define BITMAP_FIRST_WORD_MASK(start) (~0UL << ((start) & (BITS_PER_LONG - 1)))
+#define BITMAP_LAST_WORD_MASK(nbits) (~0UL >> (-(nbits) & (BITS_PER_LONG - 1)))
+
+#define __round_mask(x, y) ((__typeof__(x))((y)-1))
+#define round_up(x, y) ((((x)-1) | __round_mask(x, y))+1)
+#define round_down(x, y) ((x) & ~__round_mask(x, y))
+
+#define min(x, y) ({                            \
+	typeof(x) _min1 = (x);                  \
+	typeof(y) _min2 = (y);                  \
+	(void) (&_min1 == &_min2);              \
+	_min1 < _min2 ? _min1 : _min2;		\
+})
+
+#define max(x, y) ({                            \
+	typeof(x) _max1 = (x);                  \
+	typeof(y) _max2 = (y);                  \
+	(void) (&_max1 == &_max2);              \
+	_max1 > _max2 ? _max1 : _max2;		\
+})
+
+static inline unsigned long __bit__(unsigned long nr)
+{
+	return 1UL << (nr % BITS_PER_LONG);
+}
+
+static inline void set_bit(unsigned long nr, unsigned long *addr)
+{
+	addr[nr / BITS_PER_LONG] |= __bit__(nr);
+}
+
+static inline void clear_bit(unsigned long nr, unsigned long *addr)
+{
+	addr[nr / BITS_PER_LONG] &= ~__bit__(nr);
+}
+
+static inline bool test_bit(unsigned long nr, const unsigned long *addr)
+{
+	return addr[nr / BITS_PER_LONG] & __bit__(nr);
+}
+
+static unsigned long
+__find_next_bit(const unsigned long *addr,
+		unsigned long nbits, unsigned long start,
+		unsigned long invert)
+{
+	unsigned long tmp;
+
+	if (!nbits || start >= nbits)
+		return nbits;
+
+	tmp = addr[start / BITS_PER_LONG] ^ invert;
+
+	/* Handle 1st word. */
+	tmp &= BITMAP_FIRST_WORD_MASK(start);
+	start = round_down(start, BITS_PER_LONG);
+
+	while (!tmp) {
+		start += BITS_PER_LONG;
+		if (start >= nbits)
+			return nbits;
+
+		tmp = addr[start / BITS_PER_LONG] ^ invert;
+	}
+
+	return min(start + __builtin_ffsl(tmp) - 1, nbits);
+}
+
+static unsigned long find_next_bit(const unsigned long *addr,
+		unsigned long size,
+		unsigned long offset)
+{
+	return __find_next_bit(addr, size, offset, 0UL);
+}
+
+static unsigned long slow_next_prime_number(unsigned long x)
+{
+	for (;;) {
+		unsigned long y = sqrt(++x) + 1;
+		while (y > 1) {
+			if ((x % y) == 0)
+				break;
+			y--;
+		}
+		if (y == 1)
+			return x;
+	}
+}
+
+static unsigned long mark_multiples(unsigned long x,
+				    unsigned long *primes,
+				    unsigned long start,
+				    unsigned long end)
+{
+	unsigned long m;
+
+	m = 2*x;
+	if (m < start)
+		m = (start / x + 1) * x;
+
+	while (m < end) {
+		clear_bit(m, primes);
+		m += x;
+	}
+
+	return x;
+}
+
+unsigned long igt_next_prime_number(unsigned long x)
+{
+	static unsigned long *primes;
+	static unsigned long last, last_sz;
+
+	if (x == 0)
+		return 1; /* a white lie for for_each_prime_number() */
+	if (x == 1)
+		return 2;
+
+	if (x >= last) {
+		unsigned long sz, y;
+		unsigned long *nprimes;
+
+		sz = x*x;
+		if (sz < x)
+			return slow_next_prime_number(x);
+
+		sz = round_up(sz, BITS_PER_LONG);
+		nprimes = realloc(primes, sz / sizeof(long));
+		if (!nprimes)
+			return slow_next_prime_number(x);
+
+		/* Where memory permits, track the primes using the
+		 * Sieve of Eratosthenes.
+		 */
+		memset(nprimes + last_sz / BITS_PER_LONG,
+		       0xff, (sz - last_sz) / sizeof(long));
+		for (y = 2UL; y < sz; y = find_next_bit(nprimes, sz, y + 1))
+			last = mark_multiples(y, nprimes, last_sz, sz);
+
+		primes = nprimes;
+		last_sz = sz;
+	}
+
+	return find_next_bit(primes, last, x + 1);
+}