sched/fair: Update scale invariance of PELT

The current implementation of load tracking invariance scales the
contribution with current frequency and uarch performance (only for
utilization) of the CPU. One main result of this formula is that the
figures are capped by current capacity of CPU. Another one is that the
load_avg is not invariant because not scaled with uarch.

The util_avg of a periodic task that runs r time slots every p time slots
varies in the range :

    U * (1-y^r)/(1-y^p) * y^i < Utilization < U * (1-y^r)/(1-y^p)

with U is the max util_avg value = SCHED_CAPACITY_SCALE

At a lower capacity, the range becomes:

    U * C * (1-y^r')/(1-y^p) * y^i' < Utilization <  U * C * (1-y^r')/(1-y^p)

with C reflecting the compute capacity ratio between current capacity and
max capacity.

so C tries to compensate changes in (1-y^r') but it can't be accurate.

Instead of scaling the contribution value of PELT algo, we should scale the
running time. The PELT signal aims to track the amount of computation of
tasks and/or rq so it seems more correct to scale the running time to
reflect the effective amount of computation done since the last update.

In order to be fully invariant, we need to apply the same amount of
running time and idle time whatever the current capacity. Because running
at lower capacity implies that the task will run longer, we have to ensure
that the same amount of idle time will be applied when system becomes idle
and no idle time has been "stolen". But reaching the maximum utilization
value (SCHED_CAPACITY_SCALE) means that the task is seen as an
always-running task whatever the capacity of the CPU (even at max compute
capacity). In this case, we can discard this "stolen" idle times which
becomes meaningless.

In order to achieve this time scaling, a new clock_pelt is created per rq.
The increase of this clock scales with current capacity when something
is running on rq and synchronizes with clock_task when rq is idle. With
this mechanism, we ensure the same running and idle time whatever the
current capacity. This also enables to simplify the pelt algorithm by
removing all references of uarch and frequency and applying the same
contribution to utilization and loads. Furthermore, the scaling is done
only once per update of clock (update_rq_clock_task()) instead of during
each update of sched_entities and cfs/rt/dl_rq of the rq like the current
implementation. This is interesting when cgroup are involved as shown in
the results below:

On a hikey (octo Arm64 platform).
Performance cpufreq governor and only shallowest c-state to remove variance
generated by those power features so we only track the impact of pelt algo.

each test runs 16 times:

	./perf bench sched pipe
	(higher is better)
	kernel	tip/sched/core     + patch
	        ops/seconds        ops/seconds         diff
	root    59652(+/- 0.18%)   59876(+/- 0.24%)    +0.38%
	level1  55608(+/- 0.27%)   55923(+/- 0.24%)    +0.57%
	level2  52115(+/- 0.29%)   52564(+/- 0.22%)    +0.86%

	hackbench -l 1000
	(lower is better)
	kernel	tip/sched/core     + patch
	        duration(sec)      duration(sec)        diff
	root    4.453(+/- 2.37%)   4.383(+/- 2.88%)     -1.57%
	level1  4.859(+/- 8.50%)   4.830(+/- 7.07%)     -0.60%
	level2  5.063(+/- 9.83%)   4.928(+/- 9.66%)     -2.66%

Then, the responsiveness of PELT is improved when CPU is not running at max
capacity with this new algorithm. I have put below some examples of
duration to reach some typical load values according to the capacity of the
CPU with current implementation and with this patch. These values has been
computed based on the geometric series and the half period value:

  Util (%)     max capacity  half capacity(mainline)  half capacity(w/ patch)
  972 (95%)    138ms         not reachable            276ms
  486 (47.5%)  30ms          138ms                     60ms
  256 (25%)    13ms           32ms                     26ms

On my hikey (octo Arm64 platform) with schedutil governor, the time to
reach max OPP when starting from a null utilization, decreases from 223ms
with current scale invariance down to 121ms with the new algorithm.

Signed-off-by: Vincent Guittot <>
Signed-off-by: Peter Zijlstra (Intel) <>
Cc: Linus Torvalds <>
Cc: Mike Galbraith <>
Cc: Peter Zijlstra <>
Cc: Thomas Gleixner <>
Signed-off-by: Ingo Molnar <>
8 files changed