ftrace: Fix stddev calculation in function profiler

When FUNCTION_GRAPH_TRACER is enabled, ftrace can profile kernel functions
and print basic statistics about them. Unfortunately, running stddev
calculation is wrong. This patch corrects it implementing Welford’s method:

        s^2 = 1 / (n * (n-1)) * (n * \Sum (x_i)^2 - (\Sum x_i)^2) .
Link: http://lkml.kernel.org/r/1371031398-24048-1-git-send-email-juri.lelli@gmail.com

Cc: Frederic Weisbecker <fweisbec@gmail.com>
Cc: Ingo Molnar <mingo@redhat.com>
Signed-off-by: Juri Lelli <juri.lelli@gmail.com>
Signed-off-by: Steven Rostedt <rostedt@goodmis.org>

kernel/trace/ftrace.c

@@ -641,12 +641,18 @@ static int function_stat_show(struct seq_file *m, void *v)
 	if (rec->counter <= 1)
 		stddev = 0;
 	else {
-		stddev = rec->time_squared - rec->counter * avg * avg;
+		/*
+		 * Apply Welford's method:
+		 * s^2 = 1 / (n * (n-1)) * (n * \Sum (x_i)^2 - (\Sum x_i)^2)
+		 */
+		stddev = rec->counter * rec->time_squared -
+			 rec->time * rec->time;
+
 		/*
 		 * Divide only 1000 for ns^2 -> us^2 conversion.
 		 * trace_print_graph_duration will divide 1000 again.
 		 */
-		do_div(stddev, (rec->counter - 1) * 1000);
+		do_div(stddev, rec->counter * (rec->counter - 1) * 1000);
 	}
 
 	trace_seq_init(&s);