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![Zhaoxiu Zeng](/assets/img/avatar_default.png)
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>
215 lines
5.1 KiB
Text
215 lines
5.1 KiB
Text
config NIOS2
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def_bool y
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select CLKSRC_OF
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select GENERIC_ATOMIC64
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select GENERIC_CLOCKEVENTS
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select GENERIC_CPU_DEVICES
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select GENERIC_IRQ_PROBE
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select GENERIC_IRQ_SHOW
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select HAVE_ARCH_TRACEHOOK
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select HAVE_ARCH_KGDB
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select IRQ_DOMAIN
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select MODULES_USE_ELF_RELA
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select OF
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select OF_EARLY_FLATTREE
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select SOC_BUS
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select SPARSE_IRQ
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select USB_ARCH_HAS_HCD if USB_SUPPORT
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select CPU_NO_EFFICIENT_FFS
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config GENERIC_CSUM
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def_bool y
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config GENERIC_HWEIGHT
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def_bool y
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config GENERIC_CALIBRATE_DELAY
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def_bool y
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config NO_IOPORT_MAP
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def_bool y
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config HAS_DMA
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def_bool y
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config FPU
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def_bool n
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config SWAP
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def_bool n
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config RWSEM_GENERIC_SPINLOCK
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def_bool y
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config TRACE_IRQFLAGS_SUPPORT
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def_bool n
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source "init/Kconfig"
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menu "Kernel features"
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source "kernel/Kconfig.preempt"
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source "kernel/Kconfig.freezer"
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source "kernel/Kconfig.hz"
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source "mm/Kconfig"
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config FORCE_MAX_ZONEORDER
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int "Maximum zone order"
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range 9 20
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default "11"
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help
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The kernel memory allocator divides physically contiguous memory
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blocks into "zones", where each zone is a power of two number of
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pages. This option selects the largest power of two that the kernel
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keeps in the memory allocator. If you need to allocate very large
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blocks of physically contiguous memory, then you may need to
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increase this value.
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This config option is actually maximum order plus one. For example,
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a value of 11 means that the largest free memory block is 2^10 pages.
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endmenu
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source "arch/nios2/platform/Kconfig.platform"
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menu "Processor type and features"
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config MMU
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def_bool y
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config NR_CPUS
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int
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default "1"
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config NIOS2_ALIGNMENT_TRAP
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bool "Catch alignment trap"
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default y
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help
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Nios II CPUs cannot fetch/store data which is not bus aligned,
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i.e., a 2 or 4 byte fetch must start at an address divisible by
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2 or 4. Any non-aligned load/store instructions will be trapped and
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emulated in software if you say Y here, which has a performance
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impact.
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comment "Boot options"
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config CMDLINE_BOOL
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bool "Default bootloader kernel arguments"
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default y
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config CMDLINE
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string "Default kernel command string"
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default ""
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depends on CMDLINE_BOOL
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help
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On some platforms, there is currently no way for the boot loader to
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pass arguments to the kernel. For these platforms, you can supply
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some command-line options at build time by entering them here. In
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other cases you can specify kernel args so that you don't have
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to set them up in board prom initialization routines.
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config CMDLINE_FORCE
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bool "Force default kernel command string"
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depends on CMDLINE_BOOL
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help
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Set this to have arguments from the default kernel command string
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override those passed by the boot loader.
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config NIOS2_CMDLINE_IGNORE_DTB
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bool "Ignore kernel command string from DTB"
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depends on CMDLINE_BOOL
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depends on !CMDLINE_FORCE
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default y
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help
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Set this to ignore the bootargs property from the devicetree's
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chosen node and fall back to CMDLINE if nothing is passed.
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config NIOS2_PASS_CMDLINE
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bool "Passed kernel command line from u-boot"
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default n
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help
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Use bootargs env variable from u-boot for kernel command line.
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will override "Default kernel command string".
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Say N if you are unsure.
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config NIOS2_BOOT_LINK_OFFSET
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hex "Link address offset for booting"
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default "0x00500000"
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help
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This option allows you to set the link address offset of the zImage.
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This can be useful if you are on a board which has a small amount of
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memory.
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endmenu
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menu "Advanced setup"
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config ADVANCED_OPTIONS
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bool "Prompt for advanced kernel configuration options"
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help
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comment "Default settings for advanced configuration options are used"
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depends on !ADVANCED_OPTIONS
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config NIOS2_KERNEL_MMU_REGION_BASE_BOOL
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bool "Set custom kernel MMU region base address"
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depends on ADVANCED_OPTIONS
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help
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This option allows you to set the virtual address of the kernel MMU region.
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Say N here unless you know what you are doing.
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config NIOS2_KERNEL_MMU_REGION_BASE
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hex "Virtual base address of the kernel MMU region " if NIOS2_KERNEL_MMU_REGION_BASE_BOOL
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default "0x80000000"
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help
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This option allows you to set the virtual base address of the kernel MMU region.
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config NIOS2_KERNEL_REGION_BASE_BOOL
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bool "Set custom kernel region base address"
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depends on ADVANCED_OPTIONS
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help
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This option allows you to set the virtual address of the kernel region.
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Say N here unless you know what you are doing.
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config NIOS2_KERNEL_REGION_BASE
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hex "Virtual base address of the kernel region " if NIOS2_KERNEL_REGION_BASE_BOOL
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default "0xc0000000"
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config NIOS2_IO_REGION_BASE_BOOL
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bool "Set custom I/O region base address"
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depends on ADVANCED_OPTIONS
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help
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This option allows you to set the virtual address of the I/O region.
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Say N here unless you know what you are doing.
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config NIOS2_IO_REGION_BASE
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hex "Virtual base address of the I/O region" if NIOS2_IO_REGION_BASE_BOOL
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default "0xe0000000"
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endmenu
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menu "Executable file formats"
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source "fs/Kconfig.binfmt"
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endmenu
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source "net/Kconfig"
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source "drivers/Kconfig"
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source "fs/Kconfig"
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source "arch/nios2/Kconfig.debug"
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source "security/Kconfig"
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source "crypto/Kconfig"
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source "lib/Kconfig"
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