Explain the magic equation in calc_cfs_shares() a bit better.

Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
---
 kernel/sched/fair.c |   61 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)

--- a/kernel/sched/fair.c
+++ b/kernel/sched/fair.c
@@ -2633,6 +2633,67 @@ account_entity_dequeue(struct cfs_rq *cf
 
 #ifdef CONFIG_FAIR_GROUP_SCHED
 # ifdef CONFIG_SMP
+/*
+ * All this does is approximate the hierarchical proportion which includes that
+ * global sum we all love to hate.
+ *
+ * That is, the weight of a group entity, is the proportional share of the
+ * group weight based on the group runqueue weights. That is:
+ *
+ *                     tg->weight * grq->load.weight
+ *   ge->load.weight = -----------------------------               (1)
+ *       		  \Sum grq->load.weight
+ *
+ * Now, because computing that sum is prohibitively expensive to compute (been
+ * there, done that) we approximate it with this average stuff. The average
+ * moves slower and therefore the approximation is cheaper and more stable.
+ *
+ * So instead of the above, we substitute:
+ *
+ *   grq->load.weight -> grq->avg.load_avg                         (2)
+ *
+ * which yields the following:
+ *
+ *                     tg->weight * grq->avg.load_avg
+ *   ge->load.weight = ------------------------------              (3)
+ *       		      tg->load_avg
+ *
+ * Where: tg->load_avg ~= \Sum grq->avg.load_avg
+ *
+ * That is shares_avg, and it is right (given the approximation (2)).
+ *
+ * The problem with it is that because the average is slow -- it was designed
+ * to be exactly that of course -- this leads to transients in boundary
+ * conditions. In specific, the case where the group was idle and we start the
+ * one task. It takes time for our CPU's grq->avg.load_avg to build up,
+ * yielding bad latency etc..
+ *
+ * Now, in that special case (1) reduces to:
+ *
+ *                     tg->weight * grq->load.weight
+ *   ge->load.weight = ----------------------------- = tg>weight   (4)
+ *       		  grp->load.weight
+ *
+ * That is, the sum collapses because all other CPUs are idle; the UP scenario.
+ *
+ * So what we do is modify our approximation (3) to approach (4) in the (near)
+ * UP case, like:
+ *
+ *   ge->load.weight =
+ *
+ *              tg->weight * grq->load.weight
+ *     ---------------------------------------------------         (5)
+ *     tg->load_avg - grq->avg.load_avg + grq->load.weight
+ *
+ *
+ * And that is shares_weight and is icky. In the (near) UP case it approaches
+ * (4) while in the normal case it approaches (3). It consistently
+ * overestimates the ge->load.weight and therefore:
+ *
+ *   \Sum ge->load.weight >= tg->weight
+ *
+ * hence icky!
+ */
 static long calc_cfs_shares(struct cfs_rq *cfs_rq)
 {
 	long tg_weight, tg_shares, load, shares;