sched/fair: Add detailed description to the sched load avg metrics

These sched metrics have become complex enough, so describe them
in detail at their definition.

Signed-off-by: Yuyang Du <yuyang.du@intel.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
[ Fixed the text to improve its spelling and typography. ]
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>
Cc: bsegall@google.com
Cc: dietmar.eggemann@arm.com
Cc: lizefan@huawei.com
Cc: morten.rasmussen@arm.com
Cc: pjt@google.com
Cc: umgwanakikbuti@gmail.com
Cc: vincent.guittot@linaro.org
Link: http://lkml.kernel.org/r/1459829551-21625-4-git-send-email-yuyang.du@intel.com
Signed-off-by: Ingo Molnar <mingo@kernel.org>

include/linux/sched.h

@@ -1211,18 +1211,56 @@ struct load_weight {
 };
 
 /*
- * The load_avg/util_avg accumulates an infinite geometric series.
- * 1) load_avg factors frequency scaling into the amount of time that a
- * sched_entity is runnable on a rq into its weight. For cfs_rq, it is the
- * aggregated such weights of all runnable and blocked sched_entities.
- * 2) util_avg factors frequency and cpu capacity scaling into the amount of time
- * that a sched_entity is running on a CPU, in the range [0..SCHED_CAPACITY_SCALE].
- * For cfs_rq, it is the aggregated such times of all runnable and
+ * The load_avg/util_avg accumulates an infinite geometric series
+ * (see __update_load_avg() in kernel/sched/fair.c).
+ *
+ * [load_avg definition]
+ *
+ *   load_avg = runnable% * scale_load_down(load)
+ *
+ * where runnable% is the time ratio that a sched_entity is runnable.
+ * For cfs_rq, it is the aggregated load_avg of all runnable and
  * blocked sched_entities.
- * The 64 bit load_sum can:
- * 1) for cfs_rq, afford 4353082796 (=2^64/47742/88761) entities with
- * the highest weight (=88761) always runnable, we should not overflow
- * 2) for entity, support any load.weight always runnable
+ *
+ * load_avg may also take frequency scaling into account:
+ *
+ *   load_avg = runnable% * scale_load_down(load) * freq%
+ *
+ * where freq% is the CPU frequency normalized to the highest frequency.
+ *
+ * [util_avg definition]
+ *
+ *   util_avg = running% * SCHED_CAPACITY_SCALE
+ *
+ * where running% is the time ratio that a sched_entity is running on
+ * a CPU. For cfs_rq, it is the aggregated util_avg of all runnable
+ * and blocked sched_entities.
+ *
+ * util_avg may also factor frequency scaling and CPU capacity scaling:
+ *
+ *   util_avg = running% * SCHED_CAPACITY_SCALE * freq% * capacity%
+ *
+ * where freq% is the same as above, and capacity% is the CPU capacity
+ * normalized to the greatest capacity (due to uarch differences, etc).
+ *
+ * N.B., the above ratios (runnable%, running%, freq%, and capacity%)
+ * themselves are in the range of [0, 1]. To do fixed point arithmetics,
+ * we therefore scale them to as large a range as necessary. This is for
+ * example reflected by util_avg's SCHED_CAPACITY_SCALE.
+ *
+ * [Overflow issue]
+ *
+ * The 64-bit load_sum can have 4353082796 (=2^64/47742/88761) entities
+ * with the highest load (=88761), always runnable on a single cfs_rq,
+ * and should not overflow as the number already hits PID_MAX_LIMIT.
+ *
+ * For all other cases (including 32-bit kernels), struct load_weight's
+ * weight will overflow first before we do, because:
+ *
+ *    Max(load_avg) <= Max(load.weight)
+ *
+ * Then it is the load_weight's responsibility to consider overflow
+ * issues.
  */
 struct sched_avg {
 	u64 last_update_time, load_sum;