perf stat: Use stddev_mean in stead of stddev

When we're computing the mean by sampling the distribution,
then the std dev of the mean is related to the std dev of the
sample set by:

  stddev_mean = std_dev / sqrt(N)

Which is exactly what we want.

This results in the error on the mean decreasing with
increasing number of samples.

Also fix the scaled == -1, aka not counted case.

Signed-off-by: Peter Zijlstra <a.p.zijlstra@chello.nl>
LKML-Reference: <new-submission>
Signed-off-by: Ingo Molnar <mingo@elte.hu>

diff --git a/tools/perf/builtin-stat.c b/tools/perf/builtin-stat.c
index 9c6377f..e9424fa 100644 (file)
--- a/tools/perf/builtin-stat.c
+++ b/tools/perf/builtin-stat.c
@@ -75,7 +75,7 @@ static int                    null_run                        =  0;
 static int                     fd[MAX_NR_CPUS][MAX_COUNTERS];
 
 static u64                     event_res[MAX_COUNTERS][3];
-static u64                     event_scaled[MAX_COUNTERS];
+static int                     event_scaled[MAX_COUNTERS];
 
 struct stats
 {
@@ -97,17 +97,31 @@ static double avg_stats(struct stats *stats)
 }
 
 /*
- * stddev = sqrt(1/N (\Sum n_i^2) - avg(n)^2)
+ * http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
+ *
+ *      (\Sum n_i^2) - ((\Sum n_i)^2)/n
+ * s^2  -------------------------------
+ *                   n - 1
+ *
+ * http://en.wikipedia.org/wiki/Stddev
+ *
+ * The std dev of the mean is related to the std dev by:
+ *
+ *             s
+ * s_mean = -------
+ *          sqrt(n)
+ *
  */
 static double stddev_stats(struct stats *stats)
 {
        double avg = stats->sum / run_count;
+       double variance = (stats->sum_sq - stats->sum*avg)/(run_count - 1);
+       double variance_mean = variance / run_count;
 
-       return sqrt(stats->sum_sq/run_count - avg*avg);
+       return sqrt(variance_mean);
 }
 
 struct stats                   event_res_stats[MAX_COUNTERS][3];
-struct stats                   event_scaled_stats[MAX_COUNTERS];
 struct stats                   runtime_nsecs_stats;
 struct stats                   walltime_nsecs_stats;
 struct stats                   runtime_cycles_stats;
@@ -343,11 +357,10 @@ static void abs_printout(int counter, double avg, double stddev)
 static void print_counter(int counter)
 {
        double avg, stddev;
-       int scaled;
+       int scaled = event_scaled[counter];
 
        avg    = avg_stats(&event_res_stats[counter][0]);
        stddev = stddev_stats(&event_res_stats[counter][0]);
-       scaled = avg_stats(&event_scaled_stats[counter]);
 
        if (scaled == -1) {
                fprintf(stderr, " %14s  %-24s\n",