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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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