=========================
Capacity Aware Scheduling
=========================

1. CPU Capacity
===============

1.1 Introduction
----------------

Conventional, homogeneous SMP platforms are composed of purely identical
CPUs. Heterogeneous platforms on the other hand are composed of CPUs with
different performance characteristics - on such platforms, not all CPUs can be
considered equal.

CPU capacity is a measure of the performance a CPU can reach, normalized against
the most performant CPU in the system. Heterogeneous systems are also called
asymmetric CPU capacity systems, as they contain CPUs of different capacities.

Disparity in maximum attainable performance (IOW in maximum CPU capacity) stems
from two factors:

- not all CPUs may have the same microarchitecture (µarch).
- with Dynamic Voltage and Frequency Scaling (DVFS), not all CPUs may be
  physically able to attain the higher Operating Performance Points (OPP).

Arm big.LITTLE systems are an example of both. The big CPUs are more
performance-oriented than the LITTLE ones (more pipeline stages, bigger caches,
smarter predictors, etc), and can usually reach higher OPPs than the LITTLE ones
can.

CPU performance is usually expressed in Millions of Instructions Per Second
(MIPS), which can also be expressed as a given amount of instructions attainable
per Hz, leading to::

  capacity(cpu) = work_per_hz(cpu) * max_freq(cpu)

1.2 Scheduler terms
-------------------

Two different capacity values are used within the scheduler. A CPU's
``capacity_orig`` is its maximum attainable capacity, i.e. its maximum
attainable performance level. A CPU's ``capacity`` is its ``capacity_orig`` to
which some loss of available performance (e.g. time spent handling IRQs) is
subtracted.

Note that a CPU's ``capacity`` is solely intended to be used by the CFS class,
while ``capacity_orig`` is class-agnostic. The rest of this document will use
the term ``capacity`` interchangeably with ``capacity_orig`` for the sake of
brevity.

1.3 Platform examples
---------------------

1.3.1 Identical OPPs
~~~~~~~~~~~~~~~~~~~~

Consider an hypothetical dual-core asymmetric CPU capacity system where

- work_per_hz(CPU0) = W
- work_per_hz(CPU1) = W/2
- all CPUs are running at the same fixed frequency

By the above definition of capacity:

- capacity(CPU0) = C
- capacity(CPU1) = C/2

To draw the parallel with Arm big.LITTLE, CPU0 would be a big while CPU1 would
be a LITTLE.

With a workload that periodically does a fixed amount of work, you will get an
execution trace like so::

 CPU0 work ^
           |     ____                ____                ____
           |    |    |              |    |              |    |
           +----+----+----+----+----+----+----+----+----+----+-> time

 CPU1 work ^
           |     _________           _________           ____
           |    |         |         |         |         |
           +----+----+----+----+----+----+----+----+----+----+-> time

CPU0 has the highest capacity in the system (C), and completes a fixed amount of
work W in T units of time. On the other hand, CPU1 has half the capacity of
CPU0, and thus only completes W/2 in T.

1.3.2 Different max OPPs
~~~~~~~~~~~~~~~~~~~~~~~~

Usually, CPUs of different capacity values also have different maximum
OPPs. Consider the same CPUs as above (i.e. same work_per_hz()) with:

- max_freq(CPU0) = F
- max_freq(CPU1) = 2/3 * F

This yields:

- capacity(CPU0) = C
- capacity(CPU1) = C/3

Executing the same workload as described in 1.3.1, which each CPU running at its
maximum frequency results in::

 CPU0 work ^
           |     ____                ____                ____
           |    |    |              |    |              |    |
           +----+----+----+----+----+----+----+----+----+----+-> time

                            workload on CPU1
 CPU1 work ^
           |     ______________      ______________      ____
           |    |              |    |              |    |
           +----+----+----+----+----+----+----+----+----+----+-> time

1.4 Representation caveat
-------------------------

It should be noted that having a *single* value to represent differences in CPU
performance is somewhat of a contentious point. The relative performance
difference between two different µarchs could be X% on integer operations, Y% on
floating point operations, Z% on branches, and so on. Still, results using this
simple approach have been satisfactory for now.

2. Task utilization
===================

2.1 Introduction
----------------

Capacity aware scheduling requires an expression of a task's requirements with
regards to CPU capacity. Each scheduler class can express this differently, and
while task utilization is specific to CFS, it is convenient to describe it here
in order to introduce more generic concepts.

Task utilization is a percentage meant to represent the throughput requirements
of a task. A simple approximation of it is the task's duty cycle, i.e.::

  task_util(p) = duty_cycle(p)

On an SMP system with fixed frequencies, 100% utilization suggests the task is a
busy loop. Conversely, 10% utilization hints it is a small periodic task that
spends more time sleeping than executing. Variable CPU frequencies and
asymmetric CPU capacities complexify this somewhat; the following sections will
expand on these.

2.2 Frequency invariance
------------------------

One issue that needs to be taken into account is that a workload's duty cycle is
directly impacted by the current OPP the CPU is running at. Consider running a
periodic workload at a given frequency F::

  CPU work ^
           |     ____                ____                ____
           |    |    |              |    |              |    |
           +----+----+----+----+----+----+----+----+----+----+-> time

This yields duty_cycle(p) == 25%.

Now, consider running the *same* workload at frequency F/2::

  CPU work ^
           |     _________           _________           ____
           |    |         |         |         |         |
           +----+----+----+----+----+----+----+----+----+----+-> time

This yields duty_cycle(p) == 50%, despite the task having the exact same
behaviour (i.e. executing the same amount of work) in both executions.

The task utilization signal can be made frequency invariant using the following
formula::

  task_util_freq_inv(p) = duty_cycle(p) * (curr_frequency(cpu) / max_frequency(cpu))

Applying this formula to the two examples above yields a frequency invariant
task utilization of 25%.

2.3 CPU invariance
------------------

CPU capacity has a similar effect on task utilization in that running an
identical workload on CPUs of different capacity values will yield different
duty cycles.

Consider the system described in 1.3.2., i.e.::

- capacity(CPU0) = C
- capacity(CPU1) = C/3

Executing a given periodic workload on each CPU at their maximum frequency would
result in::

 CPU0 work ^
           |     ____                ____                ____
           |    |    |              |    |              |    |
           +----+----+----+----+----+----+----+----+----+----+-> time

 CPU1 work ^
           |     ______________      ______________      ____
           |    |              |    |              |    |
           +----+----+----+----+----+----+----+----+----+----+-> time

IOW,

- duty_cycle(p) == 25% if p runs on CPU0 at its maximum frequency
- duty_cycle(p) == 75% if p runs on CPU1 at its maximum frequency

The task utilization signal can be made CPU invariant using the following
formula::

  task_util_cpu_inv(p) = duty_cycle(p) * (capacity(cpu) / max_capacity)

with ``max_capacity`` being the highest CPU capacity value in the
system. Applying this formula to the above example above yields a CPU
invariant task utilization of 25%.

2.4 Invariant task utilization
------------------------------

Both frequency and CPU invariance need to be applied to task utilization in
order to obtain a truly invariant signal. The pseudo-formula for a task
utilization that is both CPU and frequency invariant is thus, for a given
task p::

                                     curr_frequency(cpu)   capacity(cpu)
  task_util_inv(p) = duty_cycle(p) * ------------------- * -------------
                                     max_frequency(cpu)    max_capacity

In other words, invariant task utilization describes the behaviour of a task as
if it were running on the highest-capacity CPU in the system, running at its
maximum frequency.

Any mention of task utilization in the following sections will imply its
invariant form.

2.5 Utilization estimation
--------------------------

Without a crystal ball, task behaviour (and thus task utilization) cannot
accurately be predicted the moment a task first becomes runnable. The CFS class
maintains a handful of CPU and task signals based on the Per-Entity Load
Tracking (PELT) mechanism, one of those yielding an *average* utilization (as
opposed to instantaneous).

This means that while the capacity aware scheduling criteria will be written
considering a "true" task utilization (using a crystal ball), the implementation
will only ever be able to use an estimator thereof.

3. Capacity aware scheduling requirements
=========================================

3.1 CPU capacity
----------------

Linux cannot currently figure out CPU capacity on its own, this information thus
needs to be handed to it. Architectures must define arch_scale_cpu_capacity()
for that purpose.

The arm, arm64, and RISC-V architectures directly map this to the arch_topology driver
CPU scaling data, which is derived from the capacity-dmips-mhz CPU binding; see
Documentation/devicetree/bindings/cpu/cpu-capacity.txt.

3.2 Frequency invariance
------------------------

As stated in 2.2, capacity-aware scheduling requires a frequency-invariant task
utilization. Architectures must define arch_scale_freq_capacity(cpu) for that
purpose.

Implementing this function requires figuring out at which frequency each CPU
have been running at. One way to implement this is to leverage hardware counters
whose increment rate scale with a CPU's current frequency (APERF/MPERF on x86,
AMU on arm64). Another is to directly hook into cpufreq frequency transitions,
when the kernel is aware of the switched-to frequency (also employed by
arm/arm64).

4. Scheduler topology
=====================

During the construction of the sched domains, the scheduler will figure out
whether the system exhibits asymmetric CPU capacities. Should that be the
case:

- The sched_asym_cpucapacity static key will be enabled.
- The SD_ASYM_CPUCAPACITY_FULL flag will be set at the lowest sched_domain
  level that spans all unique CPU capacity values.
- The SD_ASYM_CPUCAPACITY flag will be set for any sched_domain that spans
  CPUs with any range of asymmetry.

The sched_asym_cpucapacity static key is intended to guard sections of code that
cater to asymmetric CPU capacity systems. Do note however that said key is
*system-wide*. Imagine the following setup using cpusets::

  capacity    C/2          C
            ________    ________
           /        \  /        \
  CPUs     0  1  2  3  4  5  6  7
           \__/  \______________/
  cpusets   cs0         cs1

Which could be created via:

.. code-block:: sh

  mkdir /sys/fs/cgroup/cpuset/cs0
  echo 0-1 > /sys/fs/cgroup/cpuset/cs0/cpuset.cpus
  echo 0 > /sys/fs/cgroup/cpuset/cs0/cpuset.mems

  mkdir /sys/fs/cgroup/cpuset/cs1
  echo 2-7 > /sys/fs/cgroup/cpuset/cs1/cpuset.cpus
  echo 0 > /sys/fs/cgroup/cpuset/cs1/cpuset.mems

  echo 0 > /sys/fs/cgroup/cpuset/cpuset.sched_load_balance

Since there *is* CPU capacity asymmetry in the system, the
sched_asym_cpucapacity static key will be enabled. However, the sched_domain
hierarchy of CPUs 0-1 spans a single capacity value: SD_ASYM_CPUCAPACITY isn't
set in that hierarchy, it describes an SMP island and should be treated as such.

Therefore, the 'canonical' pattern for protecting codepaths that cater to
asymmetric CPU capacities is to:

- Check the sched_asym_cpucapacity static key
- If it is enabled, then also check for the presence of SD_ASYM_CPUCAPACITY in
  the sched_domain hierarchy (if relevant, i.e. the codepath targets a specific
  CPU or group thereof)

5. Capacity aware scheduling implementation
===========================================

5.1 CFS
-------

5.1.1 Capacity fitness
~~~~~~~~~~~~~~~~~~~~~~

The main capacity scheduling criterion of CFS is::

  task_util(p) < capacity(task_cpu(p))

This is commonly called the capacity fitness criterion, i.e. CFS must ensure a
task "fits" on its CPU. If it is violated, the task will need to achieve more
work than what its CPU can provide: it will be CPU-bound.

Furthermore, uclamp lets userspace specify a minimum and a maximum utilization
value for a task, either via sched_setattr() or via the cgroup interface (see
Documentation/admin-guide/cgroup-v2.rst). As its name imply, this can be used to
clamp task_util() in the previous criterion.

5.1.2 Wakeup CPU selection
~~~~~~~~~~~~~~~~~~~~~~~~~~

CFS task wakeup CPU selection follows the capacity fitness criterion described
above. On top of that, uclamp is used to clamp the task utilization values,
which lets userspace have more leverage over the CPU selection of CFS
tasks. IOW, CFS wakeup CPU selection searches for a CPU that satisfies::

  clamp(task_util(p), task_uclamp_min(p), task_uclamp_max(p)) < capacity(cpu)

By using uclamp, userspace can e.g. allow a busy loop (100% utilization) to run
on any CPU by giving it a low uclamp.max value. Conversely, it can force a small
periodic task (e.g. 10% utilization) to run on the highest-performance CPUs by
giving it a high uclamp.min value.

.. note::

  Wakeup CPU selection in CFS can be eclipsed by Energy Aware Scheduling
  (EAS), which is described in Documentation/scheduler/sched-energy.rst.

5.1.3 Load balancing
~~~~~~~~~~~~~~~~~~~~

A pathological case in the wakeup CPU selection occurs when a task rarely
sleeps, if at all - it thus rarely wakes up, if at all. Consider::

  w == wakeup event

  capacity(CPU0) = C
  capacity(CPU1) = C / 3

                           workload on CPU0
  CPU work ^
           |     _________           _________           ____
           |    |         |         |         |         |
           +----+----+----+----+----+----+----+----+----+----+-> time
                w                   w                   w

                           workload on CPU1
  CPU work ^
           |     ____________________________________________
           |    |
           +----+----+----+----+----+----+----+----+----+----+->
                w

This workload should run on CPU0, but if the task either:

- was improperly scheduled from the start (inaccurate initial
  utilization estimation)
- was properly scheduled from the start, but suddenly needs more
  processing power

then it might become CPU-bound, IOW ``task_util(p) > capacity(task_cpu(p))``;
the CPU capacity scheduling criterion is violated, and there may not be any more
wakeup event to fix this up via wakeup CPU selection.

Tasks that are in this situation are dubbed "misfit" tasks, and the mechanism
put in place to handle this shares the same name. Misfit task migration
leverages the CFS load balancer, more specifically the active load balance part
(which caters to migrating currently running tasks). When load balance happens,
a misfit active load balance will be triggered if a misfit task can be migrated
to a CPU with more capacity than its current one.

5.2 RT
------

5.2.1 Wakeup CPU selection
~~~~~~~~~~~~~~~~~~~~~~~~~~

RT task wakeup CPU selection searches for a CPU that satisfies::

  task_uclamp_min(p) <= capacity(task_cpu(cpu))

while still following the usual priority constraints. If none of the candidate
CPUs can satisfy this capacity criterion, then strict priority based scheduling
is followed and CPU capacities are ignored.

5.3 DL
------

5.3.1 Wakeup CPU selection
~~~~~~~~~~~~~~~~~~~~~~~~~~

DL task wakeup CPU selection searches for a CPU that satisfies::

  task_bandwidth(p) < capacity(task_cpu(p))

while still respecting the usual bandwidth and deadline constraints. If
none of the candidate CPUs can satisfy this capacity criterion, then the
task will remain on its current CPU.
