From fff7fb0b2d908dec779783d8eaf3d7725230f75e Mon Sep 17 00:00:00 2001 From: Zhaoxiu Zeng Date: Fri, 20 May 2016 17:03:57 -0700 Subject: lib/GCD.c: use binary GCD algorithm instead of Euclidean 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 #include #include #include #include #include #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 Signed-off-by: George Spelvin Signed-off-by: Andrew Morton Signed-off-by: Linus Torvalds --- arch/m68k/Kconfig.cpu | 11 +++++++++++ 1 file changed, 11 insertions(+) (limited to 'arch/m68k') diff --git a/arch/m68k/Kconfig.cpu b/arch/m68k/Kconfig.cpu index c1beb5a..8ace920 100644 --- a/arch/m68k/Kconfig.cpu +++ b/arch/m68k/Kconfig.cpu @@ -40,6 +40,7 @@ config M68000 select CPU_HAS_NO_MULDIV64 select CPU_HAS_NO_UNALIGNED select GENERIC_CSUM + select CPU_NO_EFFICIENT_FFS help The Freescale (was Motorola) 68000 CPU is the first generation of the well known M68K family of processors. The CPU core as well as @@ -51,6 +52,7 @@ config MCPU32 bool select CPU_HAS_NO_BITFIELDS select CPU_HAS_NO_UNALIGNED + select CPU_NO_EFFICIENT_FFS help The Freescale (was then Motorola) CPU32 is a CPU core that is based on the 68020 processor. For the most part it is used in @@ -130,6 +132,7 @@ config M5206 depends on !MMU select COLDFIRE_SW_A7 select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Motorola ColdFire 5206 processor support. @@ -138,6 +141,7 @@ config M5206e depends on !MMU select COLDFIRE_SW_A7 select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Motorola ColdFire 5206e processor support. @@ -163,6 +167,7 @@ config M5249 depends on !MMU select COLDFIRE_SW_A7 select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Motorola ColdFire 5249 processor support. @@ -171,6 +176,7 @@ config M525x depends on !MMU select COLDFIRE_SW_A7 select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Freescale (Motorola) Coldfire 5251/5253 processor support. @@ -189,6 +195,7 @@ config M5272 depends on !MMU select COLDFIRE_SW_A7 select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Motorola ColdFire 5272 processor support. @@ -217,6 +224,7 @@ config M5307 select COLDFIRE_SW_A7 select HAVE_CACHE_CB select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Motorola ColdFire 5307 processor support. @@ -242,6 +250,7 @@ config M5407 select COLDFIRE_SW_A7 select HAVE_CACHE_CB select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Motorola ColdFire 5407 processor support. @@ -251,6 +260,7 @@ config M547x select MMU_COLDFIRE if MMU select HAVE_CACHE_CB select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Freescale ColdFire 5470/5471/5472/5473/5474/5475 processor support. @@ -260,6 +270,7 @@ config M548x select M54xx select HAVE_CACHE_CB select HAVE_MBAR + select CPU_NO_EFFICIENT_FFS help Freescale ColdFire 5480/5481/5482/5483/5484/5485 processor support. -- cgit v1.1