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 =========================
 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 and arm64 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/arm/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.

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