[PATCH 14/16] sched: make __update_entity_runnable_avg() fast

[Paul Turner <pjt@google.com>]

__update_entity_runnable_avg forms the core of maintaining an entity's runnable
load average.  In this function we charge the accumulated run-time since last
update and handle appropriate decay.  In some cases, e.g. a waking task, this
time interval may be much larger than our period unit.

Fortunately we can exploit some properties of our series to perform decay for a
blocked update in constant time and account the contribution for a running
update in essentially-constant* time.

[*]: For any running entity they should be performing updates at the tick which
gives us a soft limit of 1 jiffy between updates, and we can compute up to a
32 jiffy update in a single pass.

Signed-off-by: Paul Turner <pjt@google.com>
Signed-off-by: Ben Segall <bsegall@google.com>
---
 kernel/sched/fair.c |  122 +++++++++++++++++++++++++++++++++++++++++----------
 1 files changed, 97 insertions(+), 25 deletions(-)

diff --git a/kernel/sched/fair.c b/kernel/sched/fair.c
index f67842f..89c353c 100644
--- a/kernel/sched/fair.c
+++ b/kernel/sched/fair.c
@@ -884,17 +884,87 @@ static inline void update_cfs_shares(struct cfs_rq *cfs_rq)
 
 #ifdef CONFIG_SMP
 /*
+ * We choose a half-life close to 1 scheduling period.
+ * Note: The tables below are dependent on this value.
+ */
+#define LOAD_AVG_PERIOD 32
+#define LOAD_AVG_MAX 46742 /* maximum possible load avg */
+#define LOAD_AVG_MAX_N 516 /* number of full periods it takes to produce max */
+
+/* Precomputed fixed inverse multiplies for multiplication by y^n */
+static const u32 runnable_avg_yN_inv[] = {
+	0xffffffff, 0xfa83b2db, 0xf5257d15, 0xefe4b99b, 0xeac0c6e7, 0xe5b906e7,
+	0xe0ccdeec, 0xdbfbb797, 0xd744fcca, 0xd2a81d91, 0xce248c15, 0xc9b9bd86,
+	0xc5672a11, 0xc12c4cca, 0xbd08a39f, 0xb8fbaf47, 0xb504f333, 0xb123f581,
+	0xad583eea, 0xa9a15ab4, 0xa5fed6a9, 0xa2704303, 0x9ef53260, 0x9b8d39b9,
+	0x9837f051, 0x94f4efa8, 0x91c3d373, 0x8ea4398b, 0x8b95c1e3, 0x88980e80,
+	0x85aac367, 0x82cd8698,
+};
+
+/* Precomputed \Sum y^k { 1<=k<=n } */
+static const u32 runnable_avg_yN_sum[] = {
+	    0, 1002, 1982, 2941, 3880, 4798, 5697, 6576, 7437, 8279, 9103,
+	 9909,10698,11470,12226,12966,13690,14398,15091,15769,16433,17082,
+	17718,18340,18949,19545,20128,20698,21256,21802,22336,22859,23371,
+};
+
+/*
  * Approximate:
  *   val * y^n,    where y^32 ~= 0.5 (~1 scheduling period)
  */
-static __always_inline u64 decay_load(u64 val, int n)
+static __always_inline u64 decay_load(u64 val, u64 n)
 {
-	for (; n && val; n--) {
-		val *= 4008;
-		val >>= 12;
+	int local_n;
+	if (!n)
+		return val;
+	else if (unlikely(n > LOAD_AVG_PERIOD * 63))
+		return 0;
+
+	/* will be 32 bits if that's desirable */
+	local_n = n;
+
+	/*
+	 * As y^PERIOD = 1/2, we can combine
+	 *    y^n = 1/2^(n/PERIOD) * k^(n%PERIOD)
+	 * With a look-up table which covers k^n (n<PERIOD)
+	 *
+	 * To achieve constant time decay_load.
+	 */
+	if (unlikely(local_n >= LOAD_AVG_PERIOD)) {
+		val >>= local_n / LOAD_AVG_PERIOD;
+		n %= LOAD_AVG_PERIOD;
 	}
 
-	return val;
+	val *= runnable_avg_yN_inv[local_n];
+	return SRR(val, 32);
+}
+
+/*
+ * For updates fully spanning n periods, the contribution to runnable
+ * average will be: \Sum 1024*y^n
+ *
+ * We can compute this reasonably efficiently by combining:
+ *   y^PERIOD = 1/2 with precomputed \Sum 1024*y^n {for  n <PERIOD}
+ */
+static u32 __compute_runnable_contrib(int n)
+{
+	u32 contrib = 0;
+
+	if (likely(n <= LOAD_AVG_PERIOD))
+		return runnable_avg_yN_sum[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);
+
+	contrib = decay_load(contrib, n);
+	return contrib + runnable_avg_yN_sum[n];
 }
 
 /* We can represent the historical contribution to runnable average as the
@@ -928,7 +998,8 @@ static __always_inline int __update_entity_runnable_avg(u64 now,
 							struct sched_avg *sa,
 							int runnable)
 {
-	u64 delta;
+	u64 delta, periods;
+	u32 runnable_contrib;
 	int delta_w, decayed = 0;
 
 	delta = now - sa->last_runnable_update;
@@ -962,25 +1033,26 @@ static __always_inline int __update_entity_runnable_avg(u64 now,
 		 * period and accrue it.
 		 */
 		delta_w = 1024 - delta_w;
-		BUG_ON(delta_w > delta);
-		do {
-			if (runnable)
-				sa->runnable_avg_sum += delta_w;
-			sa->runnable_avg_period += delta_w;
-
-			/*
-			 * Remainder of delta initiates a new period, roll over
-			 * the previous.
-			 */
-			sa->runnable_avg_sum =
-				decay_load(sa->runnable_avg_sum, 1);
-			sa->runnable_avg_period =
-				decay_load(sa->runnable_avg_period, 1);
-
-			delta -= delta_w;
-			/* New period is empty */
-			delta_w = 1024;
-		} while (delta >= 1024);
+		if (runnable)
+			sa->runnable_avg_sum += delta_w;
+		sa->runnable_avg_period += delta_w;
+
+		delta -= delta_w;
+
+		/* Figure out how many additional periods this update spans */
+		periods = delta / 1024;
+		delta %= 1024;
+
+		sa->runnable_avg_sum = decay_load(sa->runnable_avg_sum,
+						  periods + 1);
+		sa->runnable_avg_period = decay_load(sa->runnable_avg_period,
+						     periods + 1);
+
+		/* Efficiently calculate \sum (1..n_period) 1024*y^i */
+		runnable_contrib = __compute_runnable_contrib(periods);
+		if (runnable)
+			sa->runnable_avg_sum += runnable_contrib;
+		sa->runnable_avg_period += runnable_contrib;
 	}
 
 	/* Remainder of delta accrued against u_0` */