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Date: Tue, 20 Oct 2015 09:49:32 +0900
From: Byungchul Park <byungchul.park@....com>
To: Peter Zijlstra <peterz@...radead.org>
Cc: mingo@...nel.org, linux-kernel@...r.kernel.org, fweisbec@...il.com,
tglx@...utronix.de
Subject: Re: [PATCH v4 1/2] sched: make __update_cpu_load() handle active
tickless case
On Mon, Oct 19, 2015 at 03:16:18PM +0200, Peter Zijlstra wrote:
> On Wed, Oct 14, 2015 at 06:47:35PM +0900, byungchul.park@....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.
i don't think so. as i said, _n_ is the current tick -1 and _i_ is
pending_updates - 1. we cannot take i == n, but should keep (n-i).
>
> > = 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:
NO, that's not wrong. it doesn't matter at all.
a * (1 - r^n) / (1 - r)
= a * (-1)(r^n - 1) / (-1)(r - 1)
= a * (r^n - 1) / (r - 1)
i mean these two are exactly same.
>
> a * (1 - r^n) / (1 - r)
but i think this is also good one.
>
> 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?
however, your expressions and descriptions below look better than me,
except some logical errors. could you keep my logical flow unchagned?
thanks anyway,
byungchul
>
> ---
> Subject: sched: make __update_cpu_load() handle active tickless case
> From: Byungchul Park <byungchul.park@....com>
> Date: Wed, 14 Oct 2015 18:47:35 +0900
>
> XXX write new changelog...
>
> Cc: mingo@...nel.org
> Signed-off-by: Byungchul Park <byungchul.park@....com>
> Signed-off-by: Peter Zijlstra (Intel) <peterz@...radead.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);
> }
>
> /*
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