sched/fair: Prepare __update_cpu_load() to handle active tickless

There are some cases where distance between ticks is more than one tick
while the CPU is not idle, e.g. full NOHZ.

However __update_cpu_load() assumes it is the idle tickless case if the
distance between ticks is more than 1, even though it can be the active
tickless case as well. Thus in the active tickless case, updating the CPU
load will not be performed correctly.

Where the current code assumes the load for each tick is zero, this is
(obviously) not true in non-idle tickless case. We can approximately
consider the load ~= this_rq->cpu_load[0] during tickless in non-idle
tickless case.

Signed-off-by: Byungchul Park <byungchul.park@lge.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.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>
Link: http://lkml.kernel.org/r/1444816056-11886-2-git-send-email-byungchul.park@lge.com
Signed-off-by: Ingo Molnar <mingo@kernel.org>

kernel/sched/fair.c

@@ -4283,14 +4283,46 @@ decay_load_missed(unsigned long load, unsigned long missed_updates, int idx)
 	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++;
@@ -4302,8 +4334,9 @@ static void __update_cpu_load(struct rq *this_rq, unsigned long this_load,
 
 		/* 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
@@ -4358,7 +4391,7 @@ static void update_idle_cpu_load(struct rq *this_rq)
 	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);
 }
 
 /*
@@ -4381,7 +4414,7 @@ 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);
 }
@@ -4397,7 +4430,7 @@ void update_cpu_load_active(struct rq *this_rq)
 	 * 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);
 }
 
 /*