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>
OpenRISC Linux
==============
This is a port of Linux to the OpenRISC class of microprocessors; the initial
target architecture, specifically, is the 32-bit OpenRISC 1000 family (or1k).
For information about OpenRISC processors and ongoing development:
website http://openrisc.net
For more information about Linux on OpenRISC, please contact South Pole AB.
email: info@southpole.se
website: http://southpole.se
http://southpoleconsulting.com
---------------------------------------------------------------------
Build instructions for OpenRISC toolchain and Linux
===================================================
In order to build and run Linux for OpenRISC, you'll need at least a basic
toolchain and, perhaps, the architectural simulator. Steps to get these bits
in place are outlined here.
1) The toolchain can be obtained from openrisc.net. Instructions for building
a toolchain can be found at:
http://openrisc.net/toolchain-build.html
2) or1ksim (optional)
or1ksim is the architectural simulator which will allow you to actually run
your OpenRISC Linux kernel if you don't have an OpenRISC processor at hand.
git clone git://openrisc.net/jonas/or1ksim-svn
cd or1ksim
./configure --prefix=$OPENRISC_PREFIX
make
make install
3) Linux kernel
Build the kernel as usual
make ARCH=openrisc defconfig
make ARCH=openrisc
4) Run in architectural simulator
Grab the or1ksim platform configuration file (from the or1ksim source) and
together with your freshly built vmlinux, run your kernel with the following
incantation:
sim -f arch/openrisc/or1ksim.cfg vmlinux
---------------------------------------------------------------------
Terminology
===========
In the code, the following particles are used on symbols to limit the scope
to more or less specific processor implementations:
openrisc: the OpenRISC class of processors
or1k: the OpenRISC 1000 family of processors
or1200: the OpenRISC 1200 processor
---------------------------------------------------------------------
History
========
18. 11. 2003 Matjaz Breskvar (phoenix@bsemi.com)
initial port of linux to OpenRISC/or32 architecture.
all the core stuff is implemented and seams usable.
08. 12. 2003 Matjaz Breskvar (phoenix@bsemi.com)
complete change of TLB miss handling.
rewrite of exceptions handling.
fully functional sash-3.6 in default initrd.
a much improved version with changes all around.
10. 04. 2004 Matjaz Breskvar (phoenix@bsemi.com)
alot of bugfixes all over.
ethernet support, functional http and telnet servers.
running many standard linux apps.
26. 06. 2004 Matjaz Breskvar (phoenix@bsemi.com)
port to 2.6.x
30. 11. 2004 Matjaz Breskvar (phoenix@bsemi.com)
lots of bugfixes and enhancments.
added opencores framebuffer driver.
09. 10. 2010 Jonas Bonn (jonas@southpole.se)
major rewrite to bring up to par with upstream Linux 2.6.36
fff7fb0b2d