perf bench: Add benchmark of find_next_bit

for_each_set_bit, or similar functions like for_each_cpu, may be hot
within the kernel. If many bits were set then one could imagine on Intel
a "bt" instruction with every bit may be faster than the function call
and word length find_next_bit logic. Add a benchmark to measure this.

This benchmark on AMD rome and Intel skylakex shows "bt" is not a good
option except for very small bitmaps.

Committer testing:

  # perf bench
  Usage:
  	perf bench [<common options>] <collection> <benchmark> [<options>]

          # List of all available benchmark collections:

           sched: Scheduler and IPC benchmarks
         syscall: System call benchmarks
             mem: Memory access benchmarks
            numa: NUMA scheduling and MM benchmarks
           futex: Futex stressing benchmarks
           epoll: Epoll stressing benchmarks
       internals: Perf-internals benchmarks
             all: All benchmarks

  # perf bench mem

          # List of available benchmarks for collection 'mem':

          memcpy: Benchmark for memcpy() functions
          memset: Benchmark for memset() functions
        find_bit: Benchmark for find_bit() functions
             all: Run all memory access benchmarks

  # perf bench mem find_bit
  # Running 'mem/find_bit' benchmark:
  100000 operations 1 bits set of 1 bits
    Average for_each_set_bit took: 730.200 usec (+- 6.468 usec)
    Average test_bit loop took:    366.200 usec (+- 4.652 usec)
  100000 operations 1 bits set of 2 bits
    Average for_each_set_bit took: 781.000 usec (+- 24.247 usec)
    Average test_bit loop took:    550.200 usec (+- 4.152 usec)
  100000 operations 2 bits set of 2 bits
    Average for_each_set_bit took: 1113.400 usec (+- 112.340 usec)
    Average test_bit loop took:    1098.500 usec (+- 182.834 usec)
  100000 operations 1 bits set of 4 bits
    Average for_each_set_bit took: 843.800 usec (+- 8.772 usec)
    Average test_bit loop took:    948.800 usec (+- 10.278 usec)
  100000 operations 2 bits set of 4 bits
    Average for_each_set_bit took: 1185.800 usec (+- 114.345 usec)
    Average test_bit loop took:    1473.200 usec (+- 175.498 usec)
  100000 operations 4 bits set of 4 bits
    Average for_each_set_bit took: 1769.667 usec (+- 233.177 usec)
    Average test_bit loop took:    1864.933 usec (+- 187.470 usec)
  100000 operations 1 bits set of 8 bits
    Average for_each_set_bit took: 898.000 usec (+- 21.755 usec)
    Average test_bit loop took:    1768.400 usec (+- 23.672 usec)
  100000 operations 2 bits set of 8 bits
    Average for_each_set_bit took: 1244.900 usec (+- 116.396 usec)
    Average test_bit loop took:    2201.800 usec (+- 145.398 usec)
  100000 operations 4 bits set of 8 bits
    Average for_each_set_bit took: 1822.533 usec (+- 231.554 usec)
    Average test_bit loop took:    2569.467 usec (+- 168.453 usec)
  100000 operations 8 bits set of 8 bits
    Average for_each_set_bit took: 2845.100 usec (+- 441.365 usec)
    Average test_bit loop took:    3023.300 usec (+- 219.575 usec)
  100000 operations 1 bits set of 16 bits
    Average for_each_set_bit took: 923.400 usec (+- 17.560 usec)
    Average test_bit loop took:    3240.000 usec (+- 16.492 usec)
  100000 operations 2 bits set of 16 bits
    Average for_each_set_bit took: 1264.300 usec (+- 114.034 usec)
    Average test_bit loop took:    3714.400 usec (+- 158.898 usec)
  100000 operations 4 bits set of 16 bits
    Average for_each_set_bit took: 1817.867 usec (+- 222.199 usec)
    Average test_bit loop took:    4015.333 usec (+- 154.162 usec)
  100000 operations 8 bits set of 16 bits
    Average for_each_set_bit took: 2826.350 usec (+- 433.457 usec)
    Average test_bit loop took:    4460.350 usec (+- 210.762 usec)
  100000 operations 16 bits set of 16 bits
    Average for_each_set_bit took: 4615.600 usec (+- 809.350 usec)
    Average test_bit loop took:    5129.960 usec (+- 320.821 usec)
  100000 operations 1 bits set of 32 bits
    Average for_each_set_bit took: 904.400 usec (+- 14.250 usec)
    Average test_bit loop took:    6194.000 usec (+- 29.254 usec)
  100000 operations 2 bits set of 32 bits
    Average for_each_set_bit took: 1252.700 usec (+- 116.432 usec)
    Average test_bit loop took:    6652.400 usec (+- 154.352 usec)
  100000 operations 4 bits set of 32 bits
    Average for_each_set_bit took: 1824.200 usec (+- 229.133 usec)
    Average test_bit loop took:    6961.733 usec (+- 154.682 usec)
  100000 operations 8 bits set of 32 bits
    Average for_each_set_bit took: 2823.950 usec (+- 432.296 usec)
    Average test_bit loop took:    7351.900 usec (+- 193.626 usec)
  100000 operations 16 bits set of 32 bits
    Average for_each_set_bit took: 4552.560 usec (+- 785.141 usec)
    Average test_bit loop took:    7998.360 usec (+- 305.629 usec)
  100000 operations 32 bits set of 32 bits
    Average for_each_set_bit took: 7557.067 usec (+- 1407.702 usec)
    Average test_bit loop took:    9072.400 usec (+- 513.209 usec)
  100000 operations 1 bits set of 64 bits
    Average for_each_set_bit took: 896.800 usec (+- 14.389 usec)
    Average test_bit loop took:    11927.200 usec (+- 68.862 usec)
  100000 operations 2 bits set of 64 bits
    Average for_each_set_bit took: 1230.400 usec (+- 111.731 usec)
    Average test_bit loop took:    12478.600 usec (+- 189.382 usec)
  100000 operations 4 bits set of 64 bits
    Average for_each_set_bit took: 1844.733 usec (+- 244.826 usec)
    Average test_bit loop took:    12911.467 usec (+- 206.246 usec)
  100000 operations 8 bits set of 64 bits
    Average for_each_set_bit took: 2779.300 usec (+- 413.612 usec)
    Average test_bit loop took:    13372.650 usec (+- 239.623 usec)
  100000 operations 16 bits set of 64 bits
    Average for_each_set_bit took: 4423.920 usec (+- 748.240 usec)
    Average test_bit loop took:    13995.800 usec (+- 318.427 usec)
  100000 operations 32 bits set of 64 bits
    Average for_each_set_bit took: 7580.600 usec (+- 1462.407 usec)
    Average test_bit loop took:    15063.067 usec (+- 516.477 usec)
  100000 operations 64 bits set of 64 bits
    Average for_each_set_bit took: 13391.514 usec (+- 2765.371 usec)
    Average test_bit loop took:    16974.914 usec (+- 916.936 usec)
  100000 operations 1 bits set of 128 bits
    Average for_each_set_bit took: 1153.800 usec (+- 124.245 usec)
    Average test_bit loop took:    26959.000 usec (+- 714.047 usec)
  100000 operations 2 bits set of 128 bits
    Average for_each_set_bit took: 1445.200 usec (+- 113.587 usec)
    Average test_bit loop took:    25798.800 usec (+- 512.908 usec)
  100000 operations 4 bits set of 128 bits
    Average for_each_set_bit took: 1990.933 usec (+- 219.362 usec)
    Average test_bit loop took:    25589.400 usec (+- 348.288 usec)
  100000 operations 8 bits set of 128 bits
    Average for_each_set_bit took: 2963.000 usec (+- 419.487 usec)
    Average test_bit loop took:    25690.050 usec (+- 262.025 usec)
  100000 operations 16 bits set of 128 bits
    Average for_each_set_bit took: 4585.200 usec (+- 741.734 usec)
    Average test_bit loop took:    26125.040 usec (+- 274.127 usec)
  100000 operations 32 bits set of 128 bits
    Average for_each_set_bit took: 7626.200 usec (+- 1404.950 usec)
    Average test_bit loop took:    27038.867 usec (+- 442.554 usec)
  100000 operations 64 bits set of 128 bits
    Average for_each_set_bit took: 13343.371 usec (+- 2686.460 usec)
    Average test_bit loop took:    28936.543 usec (+- 883.257 usec)
  100000 operations 128 bits set of 128 bits
    Average for_each_set_bit took: 23442.950 usec (+- 4880.541 usec)
    Average test_bit loop took:    32484.125 usec (+- 1691.931 usec)
  100000 operations 1 bits set of 256 bits
    Average for_each_set_bit took: 1183.000 usec (+- 32.073 usec)
    Average test_bit loop took:    50114.600 usec (+- 198.880 usec)
  100000 operations 2 bits set of 256 bits
    Average for_each_set_bit took: 1550.000 usec (+- 124.550 usec)
    Average test_bit loop took:    50334.200 usec (+- 128.425 usec)
  100000 operations 4 bits set of 256 bits
    Average for_each_set_bit took: 2164.333 usec (+- 246.359 usec)
    Average test_bit loop took:    49959.867 usec (+- 188.035 usec)
  100000 operations 8 bits set of 256 bits
    Average for_each_set_bit took: 3211.200 usec (+- 454.829 usec)
    Average test_bit loop took:    50140.850 usec (+- 176.046 usec)
  100000 operations 16 bits set of 256 bits
    Average for_each_set_bit took: 5181.640 usec (+- 882.726 usec)
    Average test_bit loop took:    51003.160 usec (+- 419.601 usec)
  100000 operations 32 bits set of 256 bits
    Average for_each_set_bit took: 8369.333 usec (+- 1513.150 usec)
    Average test_bit loop took:    52096.700 usec (+- 573.022 usec)
  100000 operations 64 bits set of 256 bits
    Average for_each_set_bit took: 13866.857 usec (+- 2649.393 usec)
    Average test_bit loop took:    53989.600 usec (+- 938.808 usec)
  100000 operations 128 bits set of 256 bits
    Average for_each_set_bit took: 23588.350 usec (+- 4724.222 usec)
    Average test_bit loop took:    57300.625 usec (+- 1625.962 usec)
  100000 operations 256 bits set of 256 bits
    Average for_each_set_bit took: 42752.200 usec (+- 9202.084 usec)
    Average test_bit loop took:    64426.933 usec (+- 3402.326 usec)
  100000 operations 1 bits set of 512 bits
    Average for_each_set_bit took: 1632.000 usec (+- 229.954 usec)
    Average test_bit loop took:    98090.000 usec (+- 1120.435 usec)
  100000 operations 2 bits set of 512 bits
    Average for_each_set_bit took: 1937.700 usec (+- 148.902 usec)
    Average test_bit loop took:    100364.100 usec (+- 1433.219 usec)
  100000 operations 4 bits set of 512 bits
    Average for_each_set_bit took: 2528.000 usec (+- 243.654 usec)
    Average test_bit loop took:    99932.067 usec (+- 955.868 usec)
  100000 operations 8 bits set of 512 bits
    Average for_each_set_bit took: 3734.100 usec (+- 512.359 usec)
    Average test_bit loop took:    98944.750 usec (+- 812.070 usec)
  100000 operations 16 bits set of 512 bits
    Average for_each_set_bit took: 5551.400 usec (+- 846.605 usec)
    Average test_bit loop took:    98691.600 usec (+- 654.753 usec)
  100000 operations 32 bits set of 512 bits
    Average for_each_set_bit took: 8594.500 usec (+- 1446.072 usec)
    Average test_bit loop took:    99176.867 usec (+- 579.990 usec)
  100000 operations 64 bits set of 512 bits
    Average for_each_set_bit took: 13840.743 usec (+- 2527.055 usec)
    Average test_bit loop took:    100758.743 usec (+- 833.865 usec)
  100000 operations 128 bits set of 512 bits
    Average for_each_set_bit took: 23185.925 usec (+- 4532.910 usec)
    Average test_bit loop took:    103786.700 usec (+- 1475.276 usec)
  100000 operations 256 bits set of 512 bits
    Average for_each_set_bit took: 40322.400 usec (+- 8341.802 usec)
    Average test_bit loop took:    109433.378 usec (+- 2742.615 usec)
  100000 operations 512 bits set of 512 bits
    Average for_each_set_bit took: 71804.540 usec (+- 15436.546 usec)
    Average test_bit loop took:    120255.440 usec (+- 5252.777 usec)
  100000 operations 1 bits set of 1024 bits
    Average for_each_set_bit took: 1859.600 usec (+- 27.969 usec)
    Average test_bit loop took:    187676.000 usec (+- 1337.770 usec)
  100000 operations 2 bits set of 1024 bits
    Average for_each_set_bit took: 2273.600 usec (+- 139.420 usec)
    Average test_bit loop took:    188176.000 usec (+- 684.357 usec)
  100000 operations 4 bits set of 1024 bits
    Average for_each_set_bit took: 2940.400 usec (+- 268.213 usec)
    Average test_bit loop took:    189172.600 usec (+- 593.295 usec)
  100000 operations 8 bits set of 1024 bits
    Average for_each_set_bit took: 4224.200 usec (+- 547.933 usec)
    Average test_bit loop took:    190257.250 usec (+- 621.021 usec)
  100000 operations 16 bits set of 1024 bits
    Average for_each_set_bit took: 6090.560 usec (+- 877.975 usec)
    Average test_bit loop took:    190143.880 usec (+- 503.753 usec)
  100000 operations 32 bits set of 1024 bits
    Average for_each_set_bit took: 9178.800 usec (+- 1475.136 usec)
    Average test_bit loop took:    190757.100 usec (+- 494.757 usec)
  100000 operations 64 bits set of 1024 bits
    Average for_each_set_bit took: 14441.457 usec (+- 2545.497 usec)
    Average test_bit loop took:    192299.486 usec (+- 795.251 usec)
  100000 operations 128 bits set of 1024 bits
    Average for_each_set_bit took: 23623.825 usec (+- 4481.182 usec)
    Average test_bit loop took:    194885.550 usec (+- 1300.817 usec)
  100000 operations 256 bits set of 1024 bits
    Average for_each_set_bit took: 40194.956 usec (+- 8109.056 usec)
    Average test_bit loop took:    200259.311 usec (+- 2566.085 usec)
  100000 operations 512 bits set of 1024 bits
    Average for_each_set_bit took: 70983.560 usec (+- 15074.982 usec)
    Average test_bit loop took:    210527.460 usec (+- 4968.980 usec)
  100000 operations 1024 bits set of 1024 bits
    Average for_each_set_bit took: 136530.345 usec (+- 31584.400 usec)
    Average test_bit loop took:    233329.691 usec (+- 10814.036 usec)
  100000 operations 1 bits set of 2048 bits
    Average for_each_set_bit took: 3077.600 usec (+- 76.376 usec)
    Average test_bit loop took:    402154.400 usec (+- 518.571 usec)
  100000 operations 2 bits set of 2048 bits
    Average for_each_set_bit took: 3508.600 usec (+- 148.350 usec)
    Average test_bit loop took:    403814.500 usec (+- 1133.027 usec)
  100000 operations 4 bits set of 2048 bits
    Average for_each_set_bit took: 4219.333 usec (+- 285.844 usec)
    Average test_bit loop took:    404312.533 usec (+- 985.751 usec)
  100000 operations 8 bits set of 2048 bits
    Average for_each_set_bit took: 5670.550 usec (+- 615.238 usec)
    Average test_bit loop took:    405321.800 usec (+- 1038.487 usec)
  100000 operations 16 bits set of 2048 bits
    Average for_each_set_bit took: 7785.080 usec (+- 992.522 usec)
    Average test_bit loop took:    406746.160 usec (+- 1015.478 usec)
  100000 operations 32 bits set of 2048 bits
    Average for_each_set_bit took: 11163.800 usec (+- 1627.320 usec)
    Average test_bit loop took:    406124.267 usec (+- 898.785 usec)
  100000 operations 64 bits set of 2048 bits
    Average for_each_set_bit took: 16964.629 usec (+- 2806.130 usec)
    Average test_bit loop took:    406618.514 usec (+- 798.356 usec)
  100000 operations 128 bits set of 2048 bits
    Average for_each_set_bit took: 27219.625 usec (+- 4988.458 usec)
    Average test_bit loop took:    410149.325 usec (+- 1705.641 usec)
  100000 operations 256 bits set of 2048 bits
    Average for_each_set_bit took: 45138.578 usec (+- 8831.021 usec)
    Average test_bit loop took:    415462.467 usec (+- 2725.418 usec)
  100000 operations 512 bits set of 2048 bits
    Average for_each_set_bit took: 77450.540 usec (+- 15962.238 usec)
    Average test_bit loop took:    426089.180 usec (+- 5171.788 usec)
  100000 operations 1024 bits set of 2048 bits
    Average for_each_set_bit took: 138023.636 usec (+- 29826.959 usec)
    Average test_bit loop took:    446346.636 usec (+- 9904.417 usec)
  100000 operations 2048 bits set of 2048 bits
    Average for_each_set_bit took: 251072.600 usec (+- 55947.692 usec)
    Average test_bit loop took:    484855.983 usec (+- 18970.431 usec)
  #

Signed-off-by: Ian Rogers <irogers@google.com>
Tested-by: Arnaldo Carvalho de Melo <acme@redhat.com>
Cc: Alexander Shishkin <alexander.shishkin@linux.intel.com>
Cc: Andi Kleen <ak@linux.intel.com>
Cc: Jiri Olsa <jolsa@redhat.com>
Cc: Mark Rutland <mark.rutland@arm.com>
Cc: Namhyung Kim <namhyung@kernel.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Stephane Eranian <eranian@google.com>
Cc: Thomas Gleixner <tglx@linutronix.de>
Link: http://lore.kernel.org/lkml/20200729220034.1337168-1-irogers@google.com
Signed-off-by: Arnaldo Carvalho de Melo <acme@redhat.com>

4 files changed, 138 insertions, 0 deletions

diff --git a/tools/perf/bench/Build b/tools/perf/bench/Build
index 560eb9711ea2..dd68a40a790c 100644
--- a/tools/perf/bench/Build
+++ b/tools/perf/bench/Build
@@ -11,6 +11,7 @@ perf-y += epoll-wait.o
 perf-y += epoll-ctl.o
 perf-y += synthesize.o
 perf-y += kallsyms-parse.o
+perf-y += find-bit-bench.o
 
 perf-$(CONFIG_X86_64) += mem-memcpy-x86-64-lib.o
 perf-$(CONFIG_X86_64) += mem-memcpy-x86-64-asm.o
diff --git a/tools/perf/bench/bench.h b/tools/perf/bench/bench.h
index 49bc8ed3042a..2804812d4154 100644
--- a/tools/perf/bench/bench.h
+++ b/tools/perf/bench/bench.h
@@ -36,6 +36,7 @@ int bench_sched_pipe(int argc, const char **argv);
 int bench_syscall_basic(int argc, const char **argv);
 int bench_mem_memcpy(int argc, const char **argv);
 int bench_mem_memset(int argc, const char **argv);
+int bench_mem_find_bit(int argc, const char **argv);
 int bench_futex_hash(int argc, const char **argv);
 int bench_futex_wake(int argc, const char **argv);
 int bench_futex_wake_parallel(int argc, const char **argv);
diff --git a/tools/perf/bench/find-bit-bench.c b/tools/perf/bench/find-bit-bench.c
new file mode 100644
index 000000000000..fa90f3e9d368
--- /dev/null
+++ b/tools/perf/bench/find-bit-bench.c
@@ -0,0 +1,135 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * Benchmark find_next_bit and related bit operations.
+ *
+ * Copyright 2020 Google LLC.
+ */
+#include <stdlib.h>
+#include "bench.h"
+#include "../util/stat.h"
+#include <linux/bitmap.h>
+#include <linux/bitops.h>
+#include <linux/time64.h>
+#include <subcmd/parse-options.h>
+
+static unsigned int outer_iterations = 5;
+static unsigned int inner_iterations = 100000;
+
+static const struct option options[] = {
+	OPT_UINTEGER('i', "outer-iterations", &outer_iterations,
+		"Number of outerer iterations used"),
+	OPT_UINTEGER('j', "inner-iterations", &inner_iterations,
+		"Number of outerer iterations used"),
+	OPT_END()
+};
+
+static const char *const bench_usage[] = {
+	"perf bench mem find_bit <options>",
+	NULL
+};
+
+static unsigned int accumulator;
+static unsigned int use_of_val;
+
+static noinline void workload(int val)
+{
+	use_of_val += val;
+	accumulator++;
+}
+
+#if (defined(__i386__) || defined(__x86_64__)) && defined(__GCC_ASM_FLAG_OUTPUTS__)
+static bool asm_test_bit(long nr, const unsigned long *addr)
+{
+	bool oldbit;
+
+	asm volatile("bt %2,%1"
+		     : "=@ccc" (oldbit)
+		     : "m" (*(unsigned long *)addr), "Ir" (nr) : "memory");
+
+	return oldbit;
+}
+#else
+#define asm_test_bit test_bit
+#endif
+
+static int do_for_each_set_bit(unsigned int num_bits)
+{
+	unsigned long *to_test = bitmap_alloc(num_bits);
+	struct timeval start, end, diff;
+	u64 runtime_us;
+	struct stats fb_time_stats, tb_time_stats;
+	double time_average, time_stddev;
+	unsigned int bit, i, j;
+	unsigned int set_bits, skip;
+	unsigned int old;
+
+	init_stats(&fb_time_stats);
+	init_stats(&tb_time_stats);
+
+	for (set_bits = 1; set_bits <= num_bits; set_bits <<= 1) {
+		bitmap_zero(to_test, num_bits);
+		skip = num_bits / set_bits;
+		for (i = 0; i < num_bits; i += skip)
+			set_bit(i, to_test);
+
+		for (i = 0; i < outer_iterations; i++) {
+			old = accumulator;
+			gettimeofday(&start, NULL);
+			for (j = 0; j < inner_iterations; j++) {
+				for_each_set_bit(bit, to_test, num_bits)
+					workload(bit);
+			}
+			gettimeofday(&end, NULL);
+			assert(old + (inner_iterations * set_bits) == accumulator);
+			timersub(&end, &start, &diff);
+			runtime_us = diff.tv_sec * USEC_PER_SEC + diff.tv_usec;
+			update_stats(&fb_time_stats, runtime_us);
+
+			old = accumulator;
+			gettimeofday(&start, NULL);
+			for (j = 0; j < inner_iterations; j++) {
+				for (bit = 0; bit < num_bits; bit++) {
+					if (asm_test_bit(bit, to_test))
+						workload(bit);
+				}
+			}
+			gettimeofday(&end, NULL);
+			assert(old + (inner_iterations * set_bits) == accumulator);
+			timersub(&end, &start, &diff);
+			runtime_us = diff.tv_sec * USEC_PER_SEC + diff.tv_usec;
+			update_stats(&tb_time_stats, runtime_us);
+		}
+
+		printf("%d operations %d bits set of %d bits\n",
+			inner_iterations, set_bits, num_bits);
+		time_average = avg_stats(&fb_time_stats);
+		time_stddev = stddev_stats(&fb_time_stats);
+		printf("  Average for_each_set_bit took: %.3f usec (+- %.3f usec)\n",
+			time_average, time_stddev);
+		time_average = avg_stats(&tb_time_stats);
+		time_stddev = stddev_stats(&tb_time_stats);
+		printf("  Average test_bit loop took:    %.3f usec (+- %.3f usec)\n",
+			time_average, time_stddev);
+
+		if (use_of_val == accumulator)  /* Try to avoid compiler tricks. */
+			printf("\n");
+	}
+	bitmap_free(to_test);
+	return 0;
+}
+
+int bench_mem_find_bit(int argc, const char **argv)
+{
+	int err = 0, i;
+
+	argc = parse_options(argc, argv, options, bench_usage, 0);
+	if (argc) {
+		usage_with_options(bench_usage, options);
+		exit(EXIT_FAILURE);
+	}
+
+	for (i = 1; i <= 2048; i <<= 1)
+		do_for_each_set_bit(i);
+
+	return err;
+}
diff --git a/tools/perf/builtin-bench.c b/tools/perf/builtin-bench.c
index 4094cbe40ba0..4f176039fc8f 100644
--- a/tools/perf/builtin-bench.c
+++ b/tools/perf/builtin-bench.c
@@ -59,6 +59,7 @@ static struct bench syscall_benchmarks[] = {
 static struct bench mem_benchmarks[] = {
 	{ "memcpy",	"Benchmark for memcpy() functions",		bench_mem_memcpy	},
 	{ "memset",	"Benchmark for memset() functions",		bench_mem_memset	},
+	{ "find_bit",	"Benchmark for find_bit() functions",		bench_mem_find_bit	},
 	{ "all",	"Run all memory access benchmarks",		NULL			},
 	{ NULL,		NULL,						NULL			}
 };