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fff7fb0b2d
The binary GCD algorithm is based on the following facts:
1. If a and b are all evens, then gcd(a,b) = 2 * gcd(a/2, b/2)
2. If a is even and b is odd, then gcd(a,b) = gcd(a/2, b)
3. If a and b are all odds, then gcd(a,b) = gcd((a-b)/2, b) = gcd((a+b)/2, b)
Even on x86 machines with reasonable division hardware, the binary
algorithm runs about 25% faster (80% the execution time) than the
division-based Euclidian algorithm.
On platforms like Alpha and ARMv6 where division is a function call to
emulation code, it's even more significant.
There are two variants of the code here, depending on whether a fast
__ffs (find least significant set bit) instruction is available. This
allows the unpredictable branches in the bit-at-a-time shifting loop to
be eliminated.
If fast __ffs is not available, the "even/odd" GCD variant is used.
I use the following code to benchmark:
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <time.h>
#include <unistd.h>
#define swap(a, b) \
do { \
a ^= b; \
b ^= a; \
a ^= b; \
} while (0)
unsigned long gcd0(unsigned long a, unsigned long b)
{
unsigned long r;
if (a < b) {
swap(a, b);
}
if (b == 0)
return a;
while ((r = a % b) != 0) {
a = b;
b = r;
}
return b;
}
unsigned long gcd1(unsigned long a, unsigned long b)
{
unsigned long r = a | b;
if (!a || !b)
return r;
b >>= __builtin_ctzl(b);
for (;;) {
a >>= __builtin_ctzl(a);
if (a == b)
return a << __builtin_ctzl(r);
if (a < b)
swap(a, b);
a -= b;
}
}
unsigned long gcd2(unsigned long a, unsigned long b)
{
unsigned long r = a | b;
if (!a || !b)
return r;
r &= -r;
while (!(b & r))
b >>= 1;
for (;;) {
while (!(a & r))
a >>= 1;
if (a == b)
return a;
if (a < b)
swap(a, b);
a -= b;
a >>= 1;
if (a & r)
a += b;
a >>= 1;
}
}
unsigned long gcd3(unsigned long a, unsigned long b)
{
unsigned long r = a | b;
if (!a || !b)
return r;
b >>= __builtin_ctzl(b);
if (b == 1)
return r & -r;
for (;;) {
a >>= __builtin_ctzl(a);
if (a == 1)
return r & -r;
if (a == b)
return a << __builtin_ctzl(r);
if (a < b)
swap(a, b);
a -= b;
}
}
unsigned long gcd4(unsigned long a, unsigned long b)
{
unsigned long r = a | b;
if (!a || !b)
return r;
r &= -r;
while (!(b & r))
b >>= 1;
if (b == r)
return r;
for (;;) {
while (!(a & r))
a >>= 1;
if (a == r)
return r;
if (a == b)
return a;
if (a < b)
swap(a, b);
a -= b;
a >>= 1;
if (a & r)
a += b;
a >>= 1;
}
}
static unsigned long (*gcd_func[])(unsigned long a, unsigned long b) = {
gcd0, gcd1, gcd2, gcd3, gcd4,
};
#define TEST_ENTRIES (sizeof(gcd_func) / sizeof(gcd_func[0]))
#if defined(__x86_64__)
#define rdtscll(val) do { \
unsigned long __a,__d; \
__asm__ __volatile__("rdtsc" : "=a" (__a), "=d" (__d)); \
(val) = ((unsigned long long)__a) | (((unsigned long long)__d)<<32); \
} while(0)
static unsigned long long benchmark_gcd_func(unsigned long (*gcd)(unsigned long, unsigned long),
unsigned long a, unsigned long b, unsigned long *res)
{
unsigned long long start, end;
unsigned long long ret;
unsigned long gcd_res;
rdtscll(start);
gcd_res = gcd(a, b);
rdtscll(end);
if (end >= start)
ret = end - start;
else
ret = ~0ULL - start + 1 + end;
*res = gcd_res;
return ret;
}
#else
static inline struct timespec read_time(void)
{
struct timespec time;
clock_gettime(CLOCK_PROCESS_CPUTIME_ID, &time);
return time;
}
static inline unsigned long long diff_time(struct timespec start, struct timespec end)
{
struct timespec temp;
if ((end.tv_nsec - start.tv_nsec) < 0) {
temp.tv_sec = end.tv_sec - start.tv_sec - 1;
temp.tv_nsec = 1000000000ULL + end.tv_nsec - start.tv_nsec;
} else {
temp.tv_sec = end.tv_sec - start.tv_sec;
temp.tv_nsec = end.tv_nsec - start.tv_nsec;
}
return temp.tv_sec * 1000000000ULL + temp.tv_nsec;
}
static unsigned long long benchmark_gcd_func(unsigned long (*gcd)(unsigned long, unsigned long),
unsigned long a, unsigned long b, unsigned long *res)
{
struct timespec start, end;
unsigned long gcd_res;
start = read_time();
gcd_res = gcd(a, b);
end = read_time();
*res = gcd_res;
return diff_time(start, end);
}
#endif
static inline unsigned long get_rand()
{
if (sizeof(long) == 8)
return (unsigned long)rand() << 32 | rand();
else
return rand();
}
int main(int argc, char **argv)
{
unsigned int seed = time(0);
int loops = 100;
int repeats = 1000;
unsigned long (*res)[TEST_ENTRIES];
unsigned long long elapsed[TEST_ENTRIES];
int i, j, k;
for (;;) {
int opt = getopt(argc, argv, "n:r:s:");
/* End condition always first */
if (opt == -1)
break;
switch (opt) {
case 'n':
loops = atoi(optarg);
break;
case 'r':
repeats = atoi(optarg);
break;
case 's':
seed = strtoul(optarg, NULL, 10);
break;
default:
/* You won't actually get here. */
break;
}
}
res = malloc(sizeof(unsigned long) * TEST_ENTRIES * loops);
memset(elapsed, 0, sizeof(elapsed));
srand(seed);
for (j = 0; j < loops; j++) {
unsigned long a = get_rand();
/* Do we have args? */
unsigned long b = argc > optind ? strtoul(argv[optind], NULL, 10) : get_rand();
unsigned long long min_elapsed[TEST_ENTRIES];
for (k = 0; k < repeats; k++) {
for (i = 0; i < TEST_ENTRIES; i++) {
unsigned long long tmp = benchmark_gcd_func(gcd_func[i], a, b, &res[j][i]);
if (k == 0 || min_elapsed[i] > tmp)
min_elapsed[i] = tmp;
}
}
for (i = 0; i < TEST_ENTRIES; i++)
elapsed[i] += min_elapsed[i];
}
for (i = 0; i < TEST_ENTRIES; i++)
printf("gcd%d: elapsed %llu\n", i, elapsed[i]);
k = 0;
srand(seed);
for (j = 0; j < loops; j++) {
unsigned long a = get_rand();
unsigned long b = argc > optind ? strtoul(argv[optind], NULL, 10) : get_rand();
for (i = 1; i < TEST_ENTRIES; i++) {
if (res[j][i] != res[j][0])
break;
}
if (i < TEST_ENTRIES) {
if (k == 0) {
k = 1;
fprintf(stderr, "Error:\n");
}
fprintf(stderr, "gcd(%lu, %lu): ", a, b);
for (i = 0; i < TEST_ENTRIES; i++)
fprintf(stderr, "%ld%s", res[j][i], i < TEST_ENTRIES - 1 ? ", " : "\n");
}
}
if (k == 0)
fprintf(stderr, "PASS\n");
free(res);
return 0;
}
Compiled with "-O2", on "VirtualBox 4.4.0-22-generic #38-Ubuntu x86_64" got:
zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10
gcd0: elapsed 10174
gcd1: elapsed 2120
gcd2: elapsed 2902
gcd3: elapsed 2039
gcd4: elapsed 2812
PASS
zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10
gcd0: elapsed 9309
gcd1: elapsed 2280
gcd2: elapsed 2822
gcd3: elapsed 2217
gcd4: elapsed 2710
PASS
zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10
gcd0: elapsed 9589
gcd1: elapsed 2098
gcd2: elapsed 2815
gcd3: elapsed 2030
gcd4: elapsed 2718
PASS
zhaoxiuzeng@zhaoxiuzeng-VirtualBox:~/develop$ ./gcd -r 500000 -n 10
gcd0: elapsed 9914
gcd1: elapsed 2309
gcd2: elapsed 2779
gcd3: elapsed 2228
gcd4: elapsed 2709
PASS
[akpm@linux-foundation.org: avoid #defining a CONFIG_ variable]
Signed-off-by: Zhaoxiu Zeng <zhaoxiu.zeng@gmail.com>
Signed-off-by: George Spelvin <linux@horizon.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
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| .. | ||
| 842 | ||
| fonts | ||
| lz4 | ||
| lzo | ||
| mpi | ||
| raid6 | ||
| reed_solomon | ||
| xz | ||
| zlib_deflate | ||
| zlib_inflate | ||
| .gitignore | ||
| argv_split.c | ||
| asn1_decoder.c | ||
| assoc_array.c | ||
| atomic64.c | ||
| atomic64_test.c | ||
| audit.c | ||
| bcd.c | ||
| bch.c | ||
| bitmap.c | ||
| bitrev.c | ||
| bsearch.c | ||
| btree.c | ||
| bug.c | ||
| build_OID_registry | ||
| bust_spinlocks.c | ||
| check_signature.c | ||
| checksum.c | ||
| clz_ctz.c | ||
| clz_tab.c | ||
| cmdline.c | ||
| compat_audit.c | ||
| cordic.c | ||
| cpu-notifier-error-inject.c | ||
| cpu_rmap.c | ||
| cpumask.c | ||
| crc-ccitt.c | ||
| crc-itu-t.c | ||
| crc-t10dif.c | ||
| crc7.c | ||
| crc8.c | ||
| crc16.c | ||
| crc32.c | ||
| crc32defs.h | ||
| ctype.c | ||
| debug_info.c | ||
| debug_locks.c | ||
| debugobjects.c | ||
| dec_and_lock.c | ||
| decompress.c | ||
| decompress_bunzip2.c | ||
| decompress_inflate.c | ||
| decompress_unlz4.c | ||
| decompress_unlzma.c | ||
| decompress_unlzo.c | ||
| decompress_unxz.c | ||
| devres.c | ||
| digsig.c | ||
| div64.c | ||
| dma-debug.c | ||
| dma-noop.c | ||
| dump_stack.c | ||
| dynamic_debug.c | ||
| dynamic_queue_limits.c | ||
| earlycpio.c | ||
| extable.c | ||
| fault-inject.c | ||
| fdt.c | ||
| fdt_empty_tree.c | ||
| fdt_ro.c | ||
| fdt_rw.c | ||
| fdt_strerror.c | ||
| fdt_sw.c | ||
| fdt_wip.c | ||
| find_bit.c | ||
| flex_array.c | ||
| flex_proportions.c | ||
| gcd.c | ||
| gen_crc32table.c | ||
| genalloc.c | ||
| glob.c | ||
| halfmd4.c | ||
| hexdump.c | ||
| hweight.c | ||
| idr.c | ||
| inflate.c | ||
| int_sqrt.c | ||
| interval_tree.c | ||
| interval_tree_test.c | ||
| iomap.c | ||
| iomap_copy.c | ||
| iommu-common.c | ||
| iommu-helper.c | ||
| ioremap.c | ||
| iov_iter.c | ||
| irq_poll.c | ||
| irq_regs.c | ||
| is_single_threaded.c | ||
| jedec_ddr_data.c | ||
| kasprintf.c | ||
| Kconfig | ||
| Kconfig.debug | ||
| Kconfig.kasan | ||
| Kconfig.kgdb | ||
| Kconfig.kmemcheck | ||
| Kconfig.ubsan | ||
| kfifo.c | ||
| klist.c | ||
| kobject.c | ||
| kobject_uevent.c | ||
| kstrtox.c | ||
| kstrtox.h | ||
| lcm.c | ||
| libcrc32c.c | ||
| list_debug.c | ||
| list_sort.c | ||
| llist.c | ||
| locking-selftest-hardirq.h | ||
| locking-selftest-mutex.h | ||
| locking-selftest-rlock-hardirq.h | ||
| locking-selftest-rlock-softirq.h | ||
| locking-selftest-rlock.h | ||
| locking-selftest-rsem.h | ||
| locking-selftest-softirq.h | ||
| locking-selftest-spin-hardirq.h | ||
| locking-selftest-spin-softirq.h | ||
| locking-selftest-spin.h | ||
| locking-selftest-wlock-hardirq.h | ||
| locking-selftest-wlock-softirq.h | ||
| locking-selftest-wlock.h | ||
| locking-selftest-wsem.h | ||
| locking-selftest.c | ||
| lockref.c | ||
| lru_cache.c | ||
| Makefile | ||
| md5.c | ||
| memory-notifier-error-inject.c | ||
| memweight.c | ||
| net_utils.c | ||
| netdev-notifier-error-inject.c | ||
| nlattr.c | ||
| nmi_backtrace.c | ||
| nodemask.c | ||
| notifier-error-inject.c | ||
| notifier-error-inject.h | ||
| of-reconfig-notifier-error-inject.c | ||
| oid_registry.c | ||
| once.c | ||
| parser.c | ||
| pci_iomap.c | ||
| percpu-refcount.c | ||
| percpu_counter.c | ||
| percpu_ida.c | ||
| percpu_test.c | ||
| plist.c | ||
| pm-notifier-error-inject.c | ||
| radix-tree.c | ||
| random32.c | ||
| ratelimit.c | ||
| rational.c | ||
| rbtree.c | ||
| rbtree_test.c | ||
| reciprocal_div.c | ||
| rhashtable.c | ||
| scatterlist.c | ||
| seq_buf.c | ||
| sg_pool.c | ||
| sg_split.c | ||
| sha1.c | ||
| show_mem.c | ||
| smp_processor_id.c | ||
| sort.c | ||
| stackdepot.c | ||
| stmp_device.c | ||
| string.c | ||
| string_helpers.c | ||
| strncpy_from_user.c | ||
| strnlen_user.c | ||
| swiotlb.c | ||
| syscall.c | ||
| test-kstrtox.c | ||
| test-string_helpers.c | ||
| test_bitmap.c | ||
| test_bpf.c | ||
| test_firmware.c | ||
| test_hexdump.c | ||
| test_kasan.c | ||
| test_module.c | ||
| test_printf.c | ||
| test_rhashtable.c | ||
| test_static_key_base.c | ||
| test_static_keys.c | ||
| test_user_copy.c | ||
| textsearch.c | ||
| timerqueue.c | ||
| ts_bm.c | ||
| ts_fsm.c | ||
| ts_kmp.c | ||
| ubsan.c | ||
| ubsan.h | ||
| ucs2_string.c | ||
| usercopy.c | ||
| uuid.c | ||
| vsprintf.c | ||