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authorZhaoxiu Zeng <zhaoxiu.zeng@gmail.com>2016-05-20 17:03:57 -0700
committerLinus Torvalds <torvalds@linux-foundation.org>2016-05-20 17:58:30 -0700
commitfff7fb0b2d908dec779783d8eaf3d7725230f75e (patch)
tree907c5d69832b2f05c3c56272d8b6e87114e9a5f4
parent3bcadd6fa6c4fd07ace3626357c824eb532488a6 (diff)
downloadlinux-fff7fb0b2d908dec779783d8eaf3d7725230f75e.tar.gz
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 <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>
-rw-r--r--arch/Kconfig3
-rw-r--r--arch/alpha/Kconfig1
-rw-r--r--arch/arc/Kconfig1
-rw-r--r--arch/arm/mm/Kconfig3
-rw-r--r--arch/h8300/Kconfig1
-rw-r--r--arch/m32r/Kconfig1
-rw-r--r--arch/m68k/Kconfig.cpu11
-rw-r--r--arch/metag/Kconfig1
-rw-r--r--arch/microblaze/Kconfig1
-rw-r--r--arch/mips/include/asm/cpu-features.h10
-rw-r--r--arch/nios2/Kconfig1
-rw-r--r--arch/openrisc/Kconfig1
-rw-r--r--arch/parisc/Kconfig1
-rw-r--r--arch/s390/Kconfig1
-rw-r--r--arch/score/Kconfig1
-rw-r--r--arch/sh/Kconfig1
-rw-r--r--arch/sparc/Kconfig1
-rw-r--r--lib/gcd.c77
18 files changed, 107 insertions, 10 deletions
diff --git a/arch/Kconfig b/arch/Kconfig
index 8f84fd268dee..b16e74e4b5af 100644
--- a/arch/Kconfig
+++ b/arch/Kconfig
@@ -647,4 +647,7 @@ config COMPAT_OLD_SIGACTION
config ARCH_NO_COHERENT_DMA_MMAP
bool
+config CPU_NO_EFFICIENT_FFS
+ def_bool n
+
source "kernel/gcov/Kconfig"
diff --git a/arch/alpha/Kconfig b/arch/alpha/Kconfig
index fe99f894e57d..7f312d80b43b 100644
--- a/arch/alpha/Kconfig
+++ b/arch/alpha/Kconfig
@@ -26,6 +26,7 @@ config ALPHA
select MODULES_USE_ELF_RELA
select ODD_RT_SIGACTION
select OLD_SIGSUSPEND
+ select CPU_NO_EFFICIENT_FFS if !ALPHA_EV67
help
The Alpha is a 64-bit general-purpose processor designed and
marketed by the Digital Equipment Corporation of blessed memory,
diff --git a/arch/arc/Kconfig b/arch/arc/Kconfig
index 8894f7e7e3de..0dcbacfdea4b 100644
--- a/arch/arc/Kconfig
+++ b/arch/arc/Kconfig
@@ -107,6 +107,7 @@ choice
config ISA_ARCOMPACT
bool "ARCompact ISA"
+ select CPU_NO_EFFICIENT_FFS
help
The original ARC ISA of ARC600/700 cores
diff --git a/arch/arm/mm/Kconfig b/arch/arm/mm/Kconfig
index 55347662e5ed..cb569b65a54d 100644
--- a/arch/arm/mm/Kconfig
+++ b/arch/arm/mm/Kconfig
@@ -421,18 +421,21 @@ config CPU_32v3
select CPU_USE_DOMAINS if MMU
select NEED_KUSER_HELPERS
select TLS_REG_EMUL if SMP || !MMU
+ select CPU_NO_EFFICIENT_FFS
config CPU_32v4
bool
select CPU_USE_DOMAINS if MMU
select NEED_KUSER_HELPERS
select TLS_REG_EMUL if SMP || !MMU
+ select CPU_NO_EFFICIENT_FFS
config CPU_32v4T
bool
select CPU_USE_DOMAINS if MMU
select NEED_KUSER_HELPERS
select TLS_REG_EMUL if SMP || !MMU
+ select CPU_NO_EFFICIENT_FFS
config CPU_32v5
bool
diff --git a/arch/h8300/Kconfig b/arch/h8300/Kconfig
index 986ea84caaed..aa232de2d4bc 100644
--- a/arch/h8300/Kconfig
+++ b/arch/h8300/Kconfig
@@ -20,6 +20,7 @@ config H8300
select HAVE_KERNEL_GZIP
select HAVE_KERNEL_LZO
select HAVE_ARCH_KGDB
+ select CPU_NO_EFFICIENT_FFS
config RWSEM_GENERIC_SPINLOCK
def_bool y
diff --git a/arch/m32r/Kconfig b/arch/m32r/Kconfig
index c82b29253991..3cc8498fe0fe 100644
--- a/arch/m32r/Kconfig
+++ b/arch/m32r/Kconfig
@@ -17,6 +17,7 @@ config M32R
select ARCH_USES_GETTIMEOFFSET
select MODULES_USE_ELF_RELA
select HAVE_DEBUG_STACKOVERFLOW
+ select CPU_NO_EFFICIENT_FFS
config SBUS
bool
diff --git a/arch/m68k/Kconfig.cpu b/arch/m68k/Kconfig.cpu
index c1beb5ae181f..8ace920ca24a 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.
diff --git a/arch/metag/Kconfig b/arch/metag/Kconfig
index e47a08d72819..5b7a45d99cfb 100644
--- a/arch/metag/Kconfig
+++ b/arch/metag/Kconfig
@@ -30,6 +30,7 @@ config METAG
select OF
select OF_EARLY_FLATTREE
select SPARSE_IRQ
+ select CPU_NO_EFFICIENT_FFS
config STACKTRACE_SUPPORT
def_bool y
diff --git a/arch/microblaze/Kconfig b/arch/microblaze/Kconfig
index 3d793b55f60c..f17c3a4fb697 100644
--- a/arch/microblaze/Kconfig
+++ b/arch/microblaze/Kconfig
@@ -32,6 +32,7 @@ config MICROBLAZE
select OF_EARLY_FLATTREE
select TRACING_SUPPORT
select VIRT_TO_BUS
+ select CPU_NO_EFFICIENT_FFS
config SWAP
def_bool n
diff --git a/arch/mips/include/asm/cpu-features.h b/arch/mips/include/asm/cpu-features.h
index e6f19fc61bf2..e961c8a7ea66 100644
--- a/arch/mips/include/asm/cpu-features.h
+++ b/arch/mips/include/asm/cpu-features.h
@@ -204,6 +204,16 @@
#endif
#endif
+/* __builtin_constant_p(cpu_has_mips_r) && cpu_has_mips_r */
+#if !((defined(cpu_has_mips32r1) && cpu_has_mips32r1) || \
+ (defined(cpu_has_mips32r2) && cpu_has_mips32r2) || \
+ (defined(cpu_has_mips32r6) && cpu_has_mips32r6) || \
+ (defined(cpu_has_mips64r1) && cpu_has_mips64r1) || \
+ (defined(cpu_has_mips64r2) && cpu_has_mips64r2) || \
+ (defined(cpu_has_mips64r6) && cpu_has_mips64r6))
+#define CPU_NO_EFFICIENT_FFS 1
+#endif
+
#ifndef cpu_has_mips_1
# define cpu_has_mips_1 (!cpu_has_mips_r6)
#endif
diff --git a/arch/nios2/Kconfig b/arch/nios2/Kconfig
index 87ca653eb5f3..51a56c8b04b4 100644
--- a/arch/nios2/Kconfig
+++ b/arch/nios2/Kconfig
@@ -15,6 +15,7 @@ config NIOS2
select SOC_BUS
select SPARSE_IRQ
select USB_ARCH_HAS_HCD if USB_SUPPORT
+ select CPU_NO_EFFICIENT_FFS
config GENERIC_CSUM
def_bool y
diff --git a/arch/openrisc/Kconfig b/arch/openrisc/Kconfig
index e118c02cc79a..142cb057c41b 100644
--- a/arch/openrisc/Kconfig
+++ b/arch/openrisc/Kconfig
@@ -25,6 +25,7 @@ config OPENRISC
select MODULES_USE_ELF_RELA
select HAVE_DEBUG_STACKOVERFLOW
select OR1K_PIC
+ select CPU_NO_EFFICIENT_FFS if !OPENRISC_HAVE_INST_FF1
config MMU
def_bool y
diff --git a/arch/parisc/Kconfig b/arch/parisc/Kconfig
index 88cfaa8af78e..3d498a676551 100644
--- a/arch/parisc/Kconfig
+++ b/arch/parisc/Kconfig
@@ -32,6 +32,7 @@ config PARISC
select HAVE_ARCH_AUDITSYSCALL
select HAVE_ARCH_SECCOMP_FILTER
select ARCH_NO_COHERENT_DMA_MMAP
+ select CPU_NO_EFFICIENT_FFS
help
The PA-RISC microprocessor is designed by Hewlett-Packard and used
diff --git a/arch/s390/Kconfig b/arch/s390/Kconfig
index 1c3c43d9d1b5..a8c259059adf 100644
--- a/arch/s390/Kconfig
+++ b/arch/s390/Kconfig
@@ -123,6 +123,7 @@ config S390
select HAVE_ARCH_AUDITSYSCALL
select HAVE_ARCH_EARLY_PFN_TO_NID
select HAVE_ARCH_JUMP_LABEL
+ select CPU_NO_EFFICIENT_FFS if !HAVE_MARCH_Z9_109_FEATURES
select HAVE_ARCH_SECCOMP_FILTER
select HAVE_ARCH_SOFT_DIRTY
select HAVE_ARCH_TRACEHOOK
diff --git a/arch/score/Kconfig b/arch/score/Kconfig
index 366e1b599a7b..507d63181389 100644
--- a/arch/score/Kconfig
+++ b/arch/score/Kconfig
@@ -14,6 +14,7 @@ config SCORE
select VIRT_TO_BUS
select MODULES_USE_ELF_REL
select CLONE_BACKWARDS
+ select CPU_NO_EFFICIENT_FFS
choice
prompt "System type"
diff --git a/arch/sh/Kconfig b/arch/sh/Kconfig
index f6254341c065..e803a836cb7c 100644
--- a/arch/sh/Kconfig
+++ b/arch/sh/Kconfig
@@ -20,6 +20,7 @@ config SUPERH
select PERF_USE_VMALLOC
select HAVE_DEBUG_KMEMLEAK
select HAVE_KERNEL_GZIP
+ select CPU_NO_EFFICIENT_FFS
select HAVE_KERNEL_BZIP2
select HAVE_KERNEL_LZMA
select HAVE_KERNEL_XZ
diff --git a/arch/sparc/Kconfig b/arch/sparc/Kconfig
index 1012f7ffcdf5..546293d9e6c5 100644
--- a/arch/sparc/Kconfig
+++ b/arch/sparc/Kconfig
@@ -42,6 +42,7 @@ config SPARC
select ODD_RT_SIGACTION
select OLD_SIGSUSPEND
select ARCH_HAS_SG_CHAIN
+ select CPU_NO_EFFICIENT_FFS
config SPARC32
def_bool !64BIT
diff --git a/lib/gcd.c b/lib/gcd.c
index 3657f129d7b8..135ee6407a5e 100644
--- a/lib/gcd.c
+++ b/lib/gcd.c
@@ -2,20 +2,77 @@
#include <linux/gcd.h>
#include <linux/export.h>
-/* Greatest common divisor */
+/*
+ * This implements the binary GCD algorithm. (Often attributed to Stein,
+ * but as Knuth has noted, appears in a first-century Chinese math text.)
+ *
+ * This is faster than the division-based algorithm even on x86, which
+ * has decent hardware division.
+ */
+
+#if !defined(CONFIG_CPU_NO_EFFICIENT_FFS) && !defined(CPU_NO_EFFICIENT_FFS)
+
+/* If __ffs is available, the even/odd algorithm benchmarks slower. */
unsigned long gcd(unsigned long a, unsigned long b)
{
- unsigned long r;
+ unsigned long r = a | b;
+
+ if (!a || !b)
+ return r;
- if (a < b)
- swap(a, b);
+ b >>= __ffs(b);
+ if (b == 1)
+ return r & -r;
- if (!b)
- return a;
- while ((r = a % b) != 0) {
- a = b;
- b = r;
+ for (;;) {
+ a >>= __ffs(a);
+ if (a == 1)
+ return r & -r;
+ if (a == b)
+ return a << __ffs(r);
+
+ if (a < b)
+ swap(a, b);
+ a -= b;
}
- return b;
}
+
+#else
+
+/* If normalization is done by loops, the even/odd algorithm is a win. */
+unsigned long gcd(unsigned long a, unsigned long b)
+{
+ unsigned long r = a | b;
+
+ if (!a || !b)
+ return r;
+
+ /* Isolate lsbit of 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;
+ }
+}
+
+#endif
+
EXPORT_SYMBOL_GPL(gcd);