On Wed, Oct 14, 2015 at 06:47:35PM +0900, byungchul.p...@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.p...@lge.com> Date: Wed, 14 Oct 2015 18:47:35 +0900 XXX write new changelog... Cc: mi...@kernel.org Signed-off-by: Byungchul Park <byungchul.p...@lge.com> Signed-off-by: Peter Zijlstra (Intel) <pet...@infradead.org> Link: http://lkml.kernel.org/r/1444816056-11886-2-git-send-email-byungchul.p...@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); } /* -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to majord...@vger.kernel.org More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
