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  1. 28 5月, 2016 18 次提交
  3. 21 5月, 2016 1 次提交
    • Z
      lib/GCD.c: use binary GCD algorithm instead of Euclidean · fff7fb0b
      由 Zhaoxiu Zeng 提交于 
      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: NZhaoxiu Zeng <zhaoxiu.zeng@gmail.com>
Signed-off-by: NGeorge Spelvin <linux@horizon.com>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>
      fff7fb0b
  5. 20 5月, 2016 1 次提交
    • H
      arch: fix has_transparent_hugepage() · fd8cfd30
      由 Hugh Dickins 提交于 
      I've just discovered that the useful-sounding has_transparent_hugepage()
is actually an architecture-dependent minefield: on some arches it only
builds if CONFIG_TRANSPARENT_HUGEPAGE=y, on others it's also there when
not, but on some of those (arm and arm64) it then gives the wrong
answer; and on mips alone it's marked __init, which would crash if
called later (but so far it has not been called later).

Straighten this out: make it available to all configs, with a sensible
default in asm-generic/pgtable.h, removing its definitions from those
arches (arc, arm, arm64, sparc, tile) which are served by the default,
adding #define has_transparent_hugepage has_transparent_hugepage to
those (mips, powerpc, s390, x86) which need to override the default at
runtime, and removing the __init from mips (but maybe that kind of code
should be avoided after init: set a static variable the first time it's
called).
Signed-off-by: NHugh Dickins <hughd@google.com>
Cc: "Kirill A. Shutemov" <kirill.shutemov@linux.intel.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: Andres Lagar-Cavilla <andreslc@google.com>
Cc: Yang Shi <yang.shi@linaro.org>
Cc: Ning Qu <quning@gmail.com>
Cc: Mel Gorman <mgorman@techsingularity.net>
Cc: Konstantin Khlebnikov <koct9i@gmail.com>
Acked-by: NDavid S. Miller <davem@davemloft.net>
Acked-by: Vineet Gupta <vgupta@synopsys.com>		[arch/arc]
Acked-by: Gerald Schaefer <gerald.schaefer@de.ibm.com>	[arch/s390]
Acked-by: NIngo Molnar <mingo@kernel.org>
Signed-off-by: NAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: NLinus Torvalds <torvalds@linux-foundation.org>
      fd8cfd30
  7. 17 5月, 2016 2 次提交
    • J
      MIPS: Fix VZ probe gas errors with binutils <2.24 · bad50d79
      由 James Hogan 提交于 
      The VZ guest register & TLB access macros introduced in commit "MIPS:
Add guest CP0 accessors" use VZ ASE specific instructions that aren't
understood by versions of binutils prior to 2.24.

Add a check for whether the toolchain supports the -mvirt option,
similar to the MSA toolchain check, and implement the accessors using
.word if not.

Due to difficulty in converting compiler specified registers (e.g. "$3")
to usable numbers (e.g. "3") in inline asm, we need to copy to/from a
temporary register, namely the assembler temporary (at/$1), and specify
guest CP0 registers numerically in the gc0 macros.

Fixes: 7eb91118 ("MIPS: Add guest CP0 accessors")
Signed-off-by: NJames Hogan <james.hogan@imgtec.com>
Reported-by: NGuenter Roeck <linux@roeck-us.net>
Cc: linux-mips@linux-mips.org
Cc: linux-kernel@vger.kernel.org
Cc: linux-next@vger.kernel.org
Cc: linux-mips@linux-mips.org
Patchwork: https://patchwork.linux-mips.org/patch/13255/Signed-off-by: NRalf Baechle <ralf@linux-mips.org>
      bad50d79
    • M
      MIPS: MSA: Fix a link error on `_init_msa_upper' with older GCC · e49d3848
      由 Maciej W. Rozycki 提交于 
      Fix a build regression from commit c9017757 ("MIPS: init upper 64b
of vector registers when MSA is first used"):

arch/mips/built-in.o: In function `enable_restore_fp_context':
traps.c:(.text+0xbb90): undefined reference to `_init_msa_upper'
traps.c:(.text+0xbb90): relocation truncated to fit: R_MIPS_26 against `_init_msa_upper'
traps.c:(.text+0xbef0): undefined reference to `_init_msa_upper'
traps.c:(.text+0xbef0): relocation truncated to fit: R_MIPS_26 against `_init_msa_upper'

to !CONFIG_CPU_HAS_MSA configurations with older GCC versions, which are
unable to figure out that calls to `_init_msa_upper' are indeed dead.
Of the many ways to tackle this failure choose the approach we have
already taken in `thread_msa_context_live'.

[ralf@linux-mips.org: Drop patch segment to junk file.]
Signed-off-by: NMaciej W. Rozycki <macro@imgtec.com>
Cc: stable@vger.kernel.org # v3.16+
Cc: linux-mips@linux-mips.org
Patchwork: https://patchwork.linux-mips.org/patch/13271/Signed-off-by: NRalf Baechle <ralf@linux-mips.org>
      e49d3848
  9. 14 5月, 2016 2 次提交
  11. 13 5月, 2016 16 次提交