[PATCH 1/4] sched/fair: Optimize sum computation with a lookup table

[Yuyang Du]

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

The following python script can be used to generate the constants:

print " #:     yN_inv   yN_sum"
print "-----------------------"
y = (0.5)**(1/32.0)
x = 2**32
xx = 1024
for i in range(0, 32):
	if i == 0:
		x = x-1
		xx = xx*y
	else:
		x = x*y
		xx = int(xx*y + 1024*y)
	print "%2d: %#x %8d" % (i, int(x), int(xx))

print " #:  sum_N32"
print "------------"
xxx = xx
for i in range(0, 11):
	if i == 0:
		xxx = xx
	else:
		xxx = xxx/2 + xx
	print "%2d: %8d" % (i, xxx)

Signed-off-by: Yuyang Du <yuyang.du@xxxxxxxxx>
Reviewed-by: Morten Rasmussen <morten.rasmussen@xxxxxxx>
---
 kernel/sched/fair.c | 20 ++++++++++++--------
 1 file changed, 12 insertions(+), 8 deletions(-)

diff --git a/kernel/sched/fair.c b/kernel/sched/fair.c
index b8cc1c3..6e0eec0 100644
--- a/kernel/sched/fair.c
+++ b/kernel/sched/fair.c
@@ -2603,6 +2603,15 @@ static const u32 runnable_avg_yN_sum[] = {
 };
 
 /*
+ * Precomputed \Sum y^k { 1<=k<=n, where n%32=0). Values are rolled down to
+ * lower integers.
+ */
+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 +2659,9 @@ 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>>5]; /* =n/LOAD_AVG_PERIOD */
+	n %= LOAD_AVG_PERIOD;
 	contrib = decay_load(contrib, n);
 	return contrib + runnable_avg_yN_sum[n];
 }
-- 
2.1.4