Re: [PATCH v4 1/2] sched: make __update_cpu_load() handle active tickless case

[Peter Zijlstra <peterz@infradead.org>]

On Wed, Oct 14, 2015 at 06:47:35PM +0900, byungchul.park@lge.com wrote:
> 
> cpu_load(n) = (1 - 1/s) * cpu_load(n-1) + (1/s) * L

So I've been taught to use subscripts, not arguments, for progressive
values of the same thing. However I can see the recursive nature of you
definition so I can well imagine people having different views on it.

>             , where n = the current tick - 1, s = scale
> 
>             = A * cpu_load(n-1) + B
>             , where A = 1 - 1/s, B = (1/s) * L
> 
>             = A * (A * cpu_load(n-2) + B) + B
> 
>             = A * (A * (A * cpu_load(n-3) + B) + B) + B
> 
>             = A^3 * cpu_load(n-3) + A^2 * B + A * B + B
> 
>             = A^i * cpu_load(n-i) + (A^(i-1) + A^(i-2) + ... + 1) * B
>             , where i = pending_updates - 1

You missed an opportunity here, if you take i==n you avoid the need for
i entirely.

>             = A^i * cpu_load(n-i) + B * (A^i - 1) / (A - 1)
>             , by geometric series formula for sum

That's wrong; the limited geometric series expands to:

  a * (1 - r^n) / (1 - r)

Which would give: A^i * cpu_load(n-i) + B * (1 - A^i) / (1 - A)

>             = (1 - 1/s)^i * (cpu_load(n-i) - L) + L
>             , by extending A and B

This appears to be correct however, I think your above mistake must have
been one copying.

I've rewritten the things a little; does this look good to you?

---
Subject: sched: make __update_cpu_load() handle active tickless case
From: Byungchul Park <byungchul.park@lge.com>
Date: Wed, 14 Oct 2015 18:47:35 +0900

XXX write new changelog...

Cc: mingo@kernel.org
Signed-off-by: Byungchul Park <byungchul.park@lge.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Link: http://lkml.kernel.org/r/1444816056-11886-2-git-send-email-byungchul.park@lge.com
---
 kernel/sched/fair.c |   49 +++++++++++++++++++++++++++++++++++++++++--------
 1 file changed, 41 insertions(+), 8 deletions(-)

--- a/kernel/sched/fair.c
+++ b/kernel/sched/fair.c
@@ -4298,14 +4298,46 @@ decay_load_missed(unsigned long load, un
 	return load;
 }
 
-/*
+/**
+ * __update_cpu_load - update the rq->cpu_load[] statistics
+ * @this_rq: The rq to update statistics for
+ * @this_load: The current load
+ * @pending_updates: The number of missed updates
+ * @active: !0 for NOHZ_FULL
+ *
  * Update rq->cpu_load[] statistics. This function is usually called every
- * scheduler tick (TICK_NSEC). With tickless idle this will not be called
- * every tick. We fix it up based on jiffies.
+ * scheduler tick (TICK_NSEC).
+ *
+ * This function computes a decaying average:
+ *
+ *   load[i]' = (1 - 1/2^i) * load[i] + (1/2^i) * load
+ *
+ * Because of NOHZ it might not get called on every tick which gives need for
+ * the @pending_updates argument.
+ *
+ *   load[i]_n = (1 - 1/2^i) * load[i]_n-1 + (1/2^i) * load_n-1
+ *             = A * load[i]_n-1 + B ; A := (1 - 1/2^i), B := (1/2^i) * load
+ *             = A * (A * load[i]_n-2 + B) + B
+ *             = A * (A * (A * load[i]_n-3 + B) + B) + B
+ *             = A^3 * load[i]_n-3 + (A^2 + A + 1) * B
+ *             = A^n * load[i]_0 + (A^(n-1) + A^(n-2) + ... + 1) * B
+ *             = A^n * load[i]_0 + ((1 - A^n) / (1 - A)) * B
+ *             = (1 - 1/2^i)^n * (load[i]_0 - load) + load
+ *
+ * In the above we've assumed load_n := load, which is true for NOHZ_FULL as
+ * any change in load would have resulted in the tick being turned back on.
+ *
+ * For regular NOHZ, this reduces to:
+ *
+ *   load[i]_n = (1 - 1/2^i)^n * load[i]_0
+ *
+ * see decay_load_misses(). For NOHZ_FULL we get to subtract and add the extra
+ * term. See the @active paramter.
  */
 static void __update_cpu_load(struct rq *this_rq, unsigned long this_load,
-			      unsigned long pending_updates)
+			      unsigned long pending_updates, int active)
 {
+	unsigned long tickless_load = active ? this_rq->cpu_load[0] : 0;
 	int i, scale;
 
 	this_rq->nr_load_updates++;
@@ -4317,8 +4349,9 @@ static void __update_cpu_load(struct rq
 
 		/* scale is effectively 1 << i now, and >> i divides by scale */
 
-		old_load = this_rq->cpu_load[i];
+		old_load = this_rq->cpu_load[i] - tickless_load;
 		old_load = decay_load_missed(old_load, pending_updates - 1, i);
+		old_load += tickless_load;
 		new_load = this_load;
 		/*
 		 * Round up the averaging division if load is increasing. This
@@ -4373,7 +4406,7 @@ static void update_idle_cpu_load(struct
 	pending_updates = curr_jiffies - this_rq->last_load_update_tick;
 	this_rq->last_load_update_tick = curr_jiffies;
 
-	__update_cpu_load(this_rq, load, pending_updates);
+	__update_cpu_load(this_rq, load, pending_updates, 0);
 }
 
 /*
@@ -4396,7 +4429,7 @@ void update_cpu_load_nohz(void)
 		 * We were idle, this means load 0, the current load might be
 		 * !0 due to remote wakeups and the sort.
 		 */
-		__update_cpu_load(this_rq, 0, pending_updates);
+		__update_cpu_load(this_rq, 0, pending_updates, 0);
 	}
 	raw_spin_unlock(&this_rq->lock);
 }
@@ -4412,7 +4445,7 @@ void update_cpu_load_active(struct rq *t
 	 * See the mess around update_idle_cpu_load() / update_cpu_load_nohz().
 	 */
 	this_rq->last_load_update_tick = jiffies;
-	__update_cpu_load(this_rq, load, 1);
+	__update_cpu_load(this_rq, load, 1, 1);
 }
 
 /*