sched/fair: Optimize sum computation with a lookup table

__compute_runnable_contrib() uses a loop to compute sum, whereas a
table lookup can do it faster in a constant amount of time.

The program to generate the constants is located at:

  Documentation/scheduler/sched-avg.txt
Signed-off-by: Yuyang Du <yuyang.du@intel.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Reviewed-by: Morten Rasmussen <morten.rasmussen@arm.com>
Acked-by: Vincent Guittot <vincent.guittot@linaro.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Mike Galbraith <efault@gmx.de>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: bsegall@google.com
Cc: dietmar.eggemann@arm.com
Cc: juri.lelli@arm.com
Cc: pjt@google.com
Link: http://lkml.kernel.org/r/1462226078-31904-2-git-send-email-yuyang.du@intel.comSigned-off-by: Ingo Molnar <mingo@kernel.org>

kernel/sched/fair.c

@@ -2602,6 +2602,16 @@ static const u32 runnable_avg_yN_sum[] = {
 	17718,18340,18949,19545,20128,20698,21256,21802,22336,22859,23371,
 };
 
+/*
+ * Precomputed \Sum y^k { 1<=k<=n, where n%32=0). Values are rolled down to
+ * lower integers. See Documentation/scheduler/sched-avg.txt how these
+ * were generated:
+ */
+static const u32 __accumulated_sum_N32[] = {
+	    0, 23371, 35056, 40899, 43820, 45281,
+	46011, 46376, 46559, 46650, 46696, 46719,
+};
+
 /*
  * Approximate:
  *   val * y^n,    where y^32 ~= 0.5 (~1 scheduling period)
@@ -2650,14 +2660,9 @@ static u32 __compute_runnable_contrib(u64 n)
 	else if (unlikely(n >= LOAD_AVG_MAX_N))
 		return LOAD_AVG_MAX;
 
-	/* Compute \Sum k^n combining precomputed values for k^i, \Sum k^j */
-	do {
-		contrib /= 2; /* y^LOAD_AVG_PERIOD = 1/2 */
-		contrib += runnable_avg_yN_sum[LOAD_AVG_PERIOD];
-
-		n -= LOAD_AVG_PERIOD;
-	} while (n > LOAD_AVG_PERIOD);
-
+	/* Since n < LOAD_AVG_MAX_N, n/LOAD_AVG_PERIOD < 11 */
+	contrib = __accumulated_sum_N32[n/LOAD_AVG_PERIOD];
+	n %= LOAD_AVG_PERIOD;
 	contrib = decay_load(contrib, n);
 	return contrib + runnable_avg_yN_sum[n];
 }