stats: Fix computation of summed standard deviation

Fix the computation of standard deviation for a group
of jobs. Please see the below link for the
approximation formula used.
<http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance

The formula was originally presented here:
<ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/79/773/
CS-TR-79-773.pdf>

Signed-off-by: Yu-ju Hong <yjhong@google.com>
Signed-off-by: Jens Axboe <jaxboe@fusionio.com>

diff --git a/stat.c b/stat.c
index 9f22c6e159c3c1a4c0a6a411d2d7da4a78b63aad..8be4be5761cbfda454da47f541965a67115c6b26 100644 (file)
--- a/stat.c
+++ b/stat.c
@@ -474,21 +474,28 @@ static void sum_stat(struct io_stat *dst, struct io_stat *src, int nr)
 
        dst->min_val = min(dst->min_val, src->min_val);
        dst->max_val = max(dst->max_val, src->max_val);
-       dst->samples += src->samples;
 
        /*
-        * Needs a new method for calculating stddev, we cannot just
-        * average them we do below for nr > 1
+        * Compute new mean and S after the merge
+        * <http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
+        *  #Parallel_algorithm>
         */
        if (nr == 1) {
                mean = src->mean;
                S = src->S;
        } else {
-               mean = ((src->mean * (double) (nr - 1))
-                               + dst->mean) / ((double) nr);
-               S = ((src->S * (double) (nr - 1)) + dst->S) / ((double) nr);
+               double delta = src->mean - dst->mean;
+
+               mean = ((src->mean * src->samples) +
+                       (dst->mean * dst->samples)) /
+                       (dst->samples + src->samples);
+
+               S =  src->S + dst->S + pow(delta, 2.0) *
+                       (dst->samples * src->samples) /
+                       (dst->samples + src->samples);
        }
 
+       dst->samples += src->samples;
        dst->mean = mean;
        dst->S = S;
 }