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Subject[PATCH 14/16] sched: make __update_entity_runnable_avg() fast
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__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` */



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