linux/kernel/time/timer_migration.c

// SPDX-License-Identifier: GPL-2.0-only
/*
 * Infrastructure for migratable timers
 *
 * Copyright(C) 2022 linutronix GmbH
 */
#include <linux/cpuhotplug.h>
#include <linux/slab.h>
#include <linux/smp.h>
#include <linux/spinlock.h>
#include <linux/timerqueue.h>
#include <trace/events/ipi.h>

#include "timer_migration.h"
#include "tick-internal.h"

#define CREATE_TRACE_POINTS
#include <trace/events/timer_migration.h>

/*
 * The timer migration mechanism is built on a hierarchy of groups. The
 * lowest level group contains CPUs, the next level groups of CPU groups
 * and so forth. The CPU groups are kept per node so for the normal case
 * lock contention won't happen across nodes. Depending on the number of
 * CPUs per node even the next level might be kept as groups of CPU groups
 * per node and only the levels above cross the node topology.
 *
 * Example topology for a two node system with 24 CPUs each.
 *
 * LVL 2                           [GRP2:0]
 *                              GRP1:0 = GRP1:M
 *
 * LVL 1            [GRP1:0]                      [GRP1:1]
 *               GRP0:0 - GRP0:2               GRP0:3 - GRP0:5
 *
 * LVL 0  [GRP0:0]  [GRP0:1]  [GRP0:2]  [GRP0:3]  [GRP0:4]  [GRP0:5]
 * CPUS     0-7       8-15      16-23     24-31     32-39     40-47
 *
 * The groups hold a timer queue of events sorted by expiry time. These
 * queues are updated when CPUs go in idle. When they come out of idle
 * ignore flag of events is set.
 *
 * Each group has a designated migrator CPU/group as long as a CPU/group is
 * active in the group. This designated role is necessary to avoid that all
 * active CPUs in a group try to migrate expired timers from other CPUs,
 * which would result in massive lock bouncing.
 *
 * When a CPU is awake, it checks in it's own timer tick the group
 * hierarchy up to the point where it is assigned the migrator role or if
 * no CPU is active, it also checks the groups where no migrator is set
 * (TMIGR_NONE).
 *
 * If it finds expired timers in one of the group queues it pulls them over
 * from the idle CPU and runs the timer function. After that it updates the
 * group and the parent groups if required.
 *
 * CPUs which go idle arm their CPU local timer hardware for the next local
 * (pinned) timer event. If the next migratable timer expires after the
 * next local timer or the CPU has no migratable timer pending then the
 * CPU does not queue an event in the LVL0 group. If the next migratable
 * timer expires before the next local timer then the CPU queues that timer
 * in the LVL0 group. In both cases the CPU marks itself idle in the LVL0
 * group.
 *
 * When CPU comes out of idle and when a group has at least a single active
 * child, the ignore flag of the tmigr_event is set. This indicates, that
 * the event is ignored even if it is still enqueued in the parent groups
 * timer queue. It will be removed when touching the timer queue the next
 * time. This spares locking in active path as the lock protects (after
 * setup) only event information. For more information about locking,
 * please read the section "Locking rules".
 *
 * If the CPU is the migrator of the group then it delegates that role to
 * the next active CPU in the group or sets migrator to TMIGR_NONE when
 * there is no active CPU in the group. This delegation needs to be
 * propagated up the hierarchy so hand over from other leaves can happen at
 * all hierarchy levels w/o doing a search.
 *
 * When the last CPU in the system goes idle, then it drops all migrator
 * duties up to the top level of the hierarchy (LVL2 in the example). It
 * then has to make sure, that it arms it's own local hardware timer for
 * the earliest event in the system.
 *
 *
 * Lifetime rules:
 * ---------------
 *
 * The groups are built up at init time or when CPUs come online. They are
 * not destroyed when a group becomes empty due to offlining. The group
 * just won't participate in the hierarchy management anymore. Destroying
 * groups would result in interesting race conditions which would just make
 * the whole mechanism slow and complex.
 *
 *
 * Locking rules:
 * --------------
 *
 * For setting up new groups and handling events it's required to lock both
 * child and parent group. The lock ordering is always bottom up. This also
 * includes the per CPU locks in struct tmigr_cpu. For updating the migrator and
 * active CPU/group information atomic_try_cmpxchg() is used instead and only
 * the per CPU tmigr_cpu->lock is held.
 *
 * During the setup of groups tmigr_level_list is required. It is protected by
 * @tmigr_mutex.
 *
 * When @timer_base->lock as well as tmigr related locks are required, the lock
 * ordering is: first @timer_base->lock, afterwards tmigr related locks.
 *
 *
 * Protection of the tmigr group state information:
 * ------------------------------------------------
 *
 * The state information with the list of active children and migrator needs to
 * be protected by a sequence counter. It prevents a race when updates in child
 * groups are propagated in changed order. The state update is performed
 * lockless and group wise. The following scenario describes what happens
 * without updating the sequence counter:
 *
 * Therefore, let's take three groups and four CPUs (CPU2 and CPU3 as well
 * as GRP0:1 will not change during the scenario):
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:0, GRP0:1
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = CPU0           migrator = CPU2
 *           active   = CPU0           active   = CPU2
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             active      idle           active      idle
 *
 *
 * 1. CPU0 goes idle. As the update is performed group wise, in the first step
 *    only GRP0:0 is updated. The update of GRP1:0 is pending as CPU0 has to
 *    walk the hierarchy.
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:0, GRP0:1
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *       --> migrator = TMIGR_NONE     migrator = CPU2
 *       --> active   =                active   = CPU2
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *         --> idle        idle           active      idle
 *
 * 2. While CPU0 goes idle and continues to update the state, CPU1 comes out of
 *    idle. CPU1 updates GRP0:0. The update for GRP1:0 is pending as CPU1 also
 *    has to walk the hierarchy. Both CPUs (CPU0 and CPU1) now walk the
 *    hierarchy to perform the needed update from their point of view. The
 *    currently visible state looks the following:
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:0, GRP0:1
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *       --> migrator = CPU1           migrator = CPU2
 *       --> active   = CPU1           active   = CPU2
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle    --> active         active      idle
 *
 * 3. Here is the race condition: CPU1 managed to propagate its changes (from
 *    step 2) through the hierarchy to GRP1:0 before CPU0 (step 1) did. The
 *    active members of GRP1:0 remain unchanged after the update since it is
 *    still valid from CPU1 current point of view:
 *
 *    LVL 1            [GRP1:0]
 *                 --> migrator = GRP0:1
 *                 --> active   = GRP0:0, GRP0:1
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = CPU1           migrator = CPU2
 *           active   = CPU1           active   = CPU2
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        active         active      idle
 *
 * 4. Now CPU0 finally propagates its changes (from step 1) to GRP1:0.
 *
 *    LVL 1            [GRP1:0]
 *                 --> migrator = GRP0:1
 *                 --> active   = GRP0:1
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = CPU1           migrator = CPU2
 *           active   = CPU1           active   = CPU2
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        active         active      idle
 *
 *
 * The race of CPU0 vs. CPU1 led to an inconsistent state in GRP1:0. CPU1 is
 * active and is correctly listed as active in GRP0:0. However GRP1:0 does not
 * have GRP0:0 listed as active, which is wrong. The sequence counter has been
 * added to avoid inconsistent states during updates. The state is updated
 * atomically only if all members, including the sequence counter, match the
 * expected value (compare-and-exchange).
 *
 * Looking back at the previous example with the addition of the sequence
 * counter: The update as performed by CPU0 in step 4 will fail. CPU1 changed
 * the sequence number during the update in step 3 so the expected old value (as
 * seen by CPU0 before starting the walk) does not match.
 *
 * Prevent race between new event and last CPU going inactive
 * ----------------------------------------------------------
 *
 * When the last CPU is going idle and there is a concurrent update of a new
 * first global timer of an idle CPU, the group and child states have to be read
 * while holding the lock in tmigr_update_events(). The following scenario shows
 * what happens, when this is not done.
 *
 * 1. Only CPU2 is active:
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:1
 *                     next_expiry = KTIME_MAX
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = CPU2
 *           active   =                active   = CPU2
 *           next_expiry = KTIME_MAX   next_expiry = KTIME_MAX
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle           active      idle
 *
 * 2. Now CPU 2 goes idle (and has no global timer, that has to be handled) and
 *    propagates that to GRP0:1:
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:1
 *                     next_expiry = KTIME_MAX
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE --> migrator = TMIGR_NONE
 *           active   =            --> active   =
 *           next_expiry = KTIME_MAX   next_expiry = KTIME_MAX
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle       --> idle        idle
 *
 * 3. Now the idle state is propagated up to GRP1:0. As this is now the last
 *    child going idle in top level group, the expiry of the next group event
 *    has to be handed back to make sure no event is lost. As there is no event
 *    enqueued, KTIME_MAX is handed back to CPU2.
 *
 *    LVL 1            [GRP1:0]
 *                 --> migrator = TMIGR_NONE
 *                 --> active   =
 *                     next_expiry = KTIME_MAX
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = TMIGR_NONE
 *           active   =                active   =
 *           next_expiry = KTIME_MAX   next_expiry = KTIME_MAX
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle       --> idle        idle
 *
 * 4. CPU 0 has a new timer queued from idle and it expires at TIMER0. CPU0
 *    propagates that to GRP0:0:
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = TMIGR_NONE
 *                     active   =
 *                     next_expiry = KTIME_MAX
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = TMIGR_NONE
 *           active   =                active   =
 *       --> next_expiry = TIMER0      next_expiry  = KTIME_MAX
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle           idle        idle
 *
 * 5. GRP0:0 is not active, so the new timer has to be propagated to
 *    GRP1:0. Therefore the GRP1:0 state has to be read. When the stalled value
 *    (from step 2) is read, the timer is enqueued into GRP1:0, but nothing is
 *    handed back to CPU0, as it seems that there is still an active child in
 *    top level group.
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = TMIGR_NONE
 *                     active   =
 *                 --> next_expiry = TIMER0
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = TMIGR_NONE
 *           active   =                active   =
 *           next_expiry = TIMER0      next_expiry  = KTIME_MAX
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle           idle        idle
 *
 * This is prevented by reading the state when holding the lock (when a new
 * timer has to be propagated from idle path)::
 *
 *   CPU2 (tmigr_inactive_up())          CPU0 (tmigr_new_timer_up())
 *   --------------------------          ---------------------------
 *   // step 3:
 *   cmpxchg(&GRP1:0->state);
 *   tmigr_update_events() {
 *       spin_lock(&GRP1:0->lock);
 *       // ... update events ...
 *       // hand back first expiry when GRP1:0 is idle
 *       spin_unlock(&GRP1:0->lock);
 *       // ^^^ release state modification
 *   }
 *                                       tmigr_update_events() {
 *                                           spin_lock(&GRP1:0->lock)
 *                                           // ^^^ acquire state modification
 *                                           group_state = atomic_read(&GRP1:0->state)
 *                                           // .... update events ...
 *                                           // hand back first expiry when GRP1:0 is idle
 *                                           spin_unlock(&GRP1:0->lock) <3>
 *                                           // ^^^ makes state visible for other
 *                                           // callers of tmigr_new_timer_up()
 *                                       }
 *
 * When CPU0 grabs the lock directly after cmpxchg, the first timer is reported
 * back to CPU0 and also later on to CPU2. So no timer is missed. A concurrent
 * update of the group state from active path is no problem, as the upcoming CPU
 * will take care of the group events.
 *
 * Required event and timerqueue update after a remote expiry:
 * -----------------------------------------------------------
 *
 * After expiring timers of a remote CPU, a walk through the hierarchy and
 * update of events and timerqueues is required. It is obviously needed if there
 * is a 'new' global timer but also if there is no new global timer but the
 * remote CPU is still idle.
 *
 * 1. CPU0 and CPU1 are idle and have both a global timer expiring at the same
 *    time. So both have an event enqueued in the timerqueue of GRP0:0. CPU3 is
 *    also idle and has no global timer pending. CPU2 is the only active CPU and
 *    thus also the migrator:
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:1
 *                 --> timerqueue = evt-GRP0:0
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = CPU2
 *           active   =                active   = CPU2
 *           groupevt.ignore = false   groupevt.ignore = true
 *           groupevt.cpu = CPU0       groupevt.cpu =
 *           timerqueue = evt-CPU0,    timerqueue =
 *                        evt-CPU1
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle           active      idle
 *
 * 2. CPU2 starts to expire remote timers. It starts with LVL0 group
 *    GRP0:1. There is no event queued in the timerqueue, so CPU2 continues with
 *    the parent of GRP0:1: GRP1:0. In GRP1:0 it dequeues the first event. It
 *    looks at tmigr_event::cpu struct member and expires the pending timer(s)
 *    of CPU0.
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:1
 *                 --> timerqueue =
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = CPU2
 *           active   =                active   = CPU2
 *           groupevt.ignore = false   groupevt.ignore = true
 *       --> groupevt.cpu = CPU0       groupevt.cpu =
 *           timerqueue = evt-CPU0,    timerqueue =
 *                        evt-CPU1
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle           active      idle
 *
 * 3. Some work has to be done after expiring the timers of CPU0. If we stop
 *    here, then CPU1's pending global timer(s) will not expire in time and the
 *    timerqueue of GRP0:0 has still an event for CPU0 enqueued which has just
 *    been processed. So it is required to walk the hierarchy from CPU0's point
 *    of view and update it accordingly. CPU0's event will be removed from the
 *    timerqueue because it has no pending timer. If CPU0 would have a timer
 *    pending then it has to expire after CPU1's first timer because all timers
 *    from this period were just expired. Either way CPU1's event will be first
 *    in GRP0:0's timerqueue and therefore set in the CPU field of the group
 *    event which is then enqueued in GRP1:0's timerqueue as GRP0:0 is still not
 *    active:
 *
 *    LVL 1            [GRP1:0]
 *                     migrator = GRP0:1
 *                     active   = GRP0:1
 *                 --> timerqueue = evt-GRP0:0
 *                   /                \
 *    LVL 0  [GRP0:0]                  [GRP0:1]
 *           migrator = TMIGR_NONE     migrator = CPU2
 *           active   =                active   = CPU2
 *           groupevt.ignore = false   groupevt.ignore = true
 *       --> groupevt.cpu = CPU1       groupevt.cpu =
 *       --> timerqueue = evt-CPU1     timerqueue =
 *              /         \                /         \
 *    CPUs     0           1              2           3
 *             idle        idle           active      idle
 *
 * Now CPU2 (migrator) will continue step 2 at GRP1:0 and will expire the
 * timer(s) of CPU1.
 *
 * The hierarchy walk in step 3 can be skipped if the migrator notices that a
 * CPU of GRP0:0 is active again. The CPU will mark GRP0:0 active and take care
 * of the group as migrator and any needed updates within the hierarchy.
 */

static DEFINE_MUTEX(tmigr_mutex);
static struct list_head *tmigr_level_list __read_mostly;

static unsigned int tmigr_hierarchy_levels __read_mostly;
static unsigned int tmigr_crossnode_level __read_mostly;

static DEFINE_PER_CPU(struct tmigr_cpu, tmigr_cpu);

#define TMIGR_NONE
#define BIT_CNT

static inline bool tmigr_is_not_available(struct tmigr_cpu *tmc)
{}

/*
 * Returns true, when @childmask corresponds to the group migrator or when the
 * group is not active - so no migrator is set.
 */
static bool tmigr_check_migrator(struct tmigr_group *group, u8 childmask)
{}

static bool tmigr_check_migrator_and_lonely(struct tmigr_group *group, u8 childmask)
{}

static bool tmigr_check_lonely(struct tmigr_group *group)
{}

/**
 * struct tmigr_walk - data required for walking the hierarchy
 * @nextexp:		Next CPU event expiry information which is handed into
 *			the timer migration code by the timer code
 *			(get_next_timer_interrupt())
 * @firstexp:		Contains the first event expiry information when
 *			hierarchy is completely idle.  When CPU itself was the
 *			last going idle, information makes sure, that CPU will
 *			be back in time. When using this value in the remote
 *			expiry case, firstexp is stored in the per CPU tmigr_cpu
 *			struct of CPU which expires remote timers. It is updated
 *			in top level group only. Be aware, there could occur a
 *			new top level of the hierarchy between the 'top level
 *			call' in tmigr_update_events() and the check for the
 *			parent group in walk_groups(). Then @firstexp might
 *			contain a value != KTIME_MAX even if it was not the
 *			final top level. This is not a problem, as the worst
 *			outcome is a CPU which might wake up a little early.
 * @evt:		Pointer to tmigr_event which needs to be queued (of idle
 *			child group)
 * @childmask:		groupmask of child group
 * @remote:		Is set, when the new timer path is executed in
 *			tmigr_handle_remote_cpu()
 * @basej:		timer base in jiffies
 * @now:		timer base monotonic
 * @check:		is set if there is the need to handle remote timers;
 *			required in tmigr_requires_handle_remote() only
 * @tmc_active:		this flag indicates, whether the CPU which triggers
 *			the hierarchy walk is !idle in the timer migration
 *			hierarchy. When the CPU is idle and the whole hierarchy is
 *			idle, only the first event of the top level has to be
 *			considered.
 */
struct tmigr_walk {};

up_f;

static void __walk_groups(up_f up, struct tmigr_walk *data,
			  struct tmigr_cpu *tmc)
{}

static void walk_groups(up_f up, struct tmigr_walk *data, struct tmigr_cpu *tmc)
{}

/*
 * Returns the next event of the timerqueue @group->events
 *
 * Removes timers with ignore flag and update next_expiry of the group. Values
 * of the group event are updated in tmigr_update_events() only.
 */
static struct tmigr_event *tmigr_next_groupevt(struct tmigr_group *group)
{}

/*
 * Return the next event (with the expiry equal or before @now)
 *
 * Event, which is returned, is also removed from the queue.
 */
static struct tmigr_event *tmigr_next_expired_groupevt(struct tmigr_group *group,
						       u64 now)
{}

static u64 tmigr_next_groupevt_expires(struct tmigr_group *group)
{}

static bool tmigr_active_up(struct tmigr_group *group,
			    struct tmigr_group *child,
			    struct tmigr_walk *data)
{}

static void __tmigr_cpu_activate(struct tmigr_cpu *tmc)
{}

/**
 * tmigr_cpu_activate() - set this CPU active in timer migration hierarchy
 *
 * Call site timer_clear_idle() is called with interrupts disabled.
 */
void tmigr_cpu_activate(void)
{}

/*
 * Returns true, if there is nothing to be propagated to the next level
 *
 * @data->firstexp is set to expiry of first gobal event of the (top level of
 * the) hierarchy, but only when hierarchy is completely idle.
 *
 * The child and group states need to be read under the lock, to prevent a race
 * against a concurrent tmigr_inactive_up() run when the last CPU goes idle. See
 * also section "Prevent race between new event and last CPU going inactive" in
 * the documentation at the top.
 *
 * This is the only place where the group event expiry value is set.
 */
static
bool tmigr_update_events(struct tmigr_group *group, struct tmigr_group *child,
			 struct tmigr_walk *data)
{}

static bool tmigr_new_timer_up(struct tmigr_group *group,
			       struct tmigr_group *child,
			       struct tmigr_walk *data)
{}

/*
 * Returns the expiry of the next timer that needs to be handled. KTIME_MAX is
 * returned, if an active CPU will handle all the timer migration hierarchy
 * timers.
 */
static u64 tmigr_new_timer(struct tmigr_cpu *tmc, u64 nextexp)
{}

static void tmigr_handle_remote_cpu(unsigned int cpu, u64 now,
				    unsigned long jif)
{}

static bool tmigr_handle_remote_up(struct tmigr_group *group,
				   struct tmigr_group *child,
				   struct tmigr_walk *data)
{}

/**
 * tmigr_handle_remote() - Handle global timers of remote idle CPUs
 *
 * Called from the timer soft interrupt with interrupts enabled.
 */
void tmigr_handle_remote(void)
{}

static bool tmigr_requires_handle_remote_up(struct tmigr_group *group,
					    struct tmigr_group *child,
					    struct tmigr_walk *data)
{}

/**
 * tmigr_requires_handle_remote() - Check the need of remote timer handling
 *
 * Must be called with interrupts disabled.
 */
bool tmigr_requires_handle_remote(void)
{}

/**
 * tmigr_cpu_new_timer() - enqueue next global timer into hierarchy (idle tmc)
 * @nextexp:	Next expiry of global timer (or KTIME_MAX if not)
 *
 * The CPU is already deactivated in the timer migration
 * hierarchy. tick_nohz_get_sleep_length() calls tick_nohz_next_event()
 * and thereby the timer idle path is executed once more. @tmc->wakeup
 * holds the first timer, when the timer migration hierarchy is
 * completely idle.
 *
 * Returns the first timer that needs to be handled by this CPU or KTIME_MAX if
 * nothing needs to be done.
 */
u64 tmigr_cpu_new_timer(u64 nextexp)
{}

static bool tmigr_inactive_up(struct tmigr_group *group,
			      struct tmigr_group *child,
			      struct tmigr_walk *data)
{}

static u64 __tmigr_cpu_deactivate(struct tmigr_cpu *tmc, u64 nextexp)
{}

/**
 * tmigr_cpu_deactivate() - Put current CPU into inactive state
 * @nextexp:	The next global timer expiry of the current CPU
 *
 * Must be called with interrupts disabled.
 *
 * Return: the next event expiry of the current CPU or the next event expiry
 * from the hierarchy if this CPU is the top level migrator or the hierarchy is
 * completely idle.
 */
u64 tmigr_cpu_deactivate(u64 nextexp)
{}

/**
 * tmigr_quick_check() - Quick forecast of next tmigr event when CPU wants to
 *			 go idle
 * @nextevt:	The next global timer expiry of the current CPU
 *
 * Return:
 * * KTIME_MAX		- when it is probable that nothing has to be done (not
 *			  the only one in the level 0 group; and if it is the
 *			  only one in level 0 group, but there are more than a
 *			  single group active on the way to top level)
 * * nextevt		- when CPU is offline and has to handle timer on its own
 *			  or when on the way to top in every group only a single
 *			  child is active but @nextevt is before the lowest
 *			  next_expiry encountered while walking up to top level.
 * * next_expiry	- value of lowest expiry encountered while walking groups
 *			  if only a single child is active on each and @nextevt
 *			  is after this lowest expiry.
 */
u64 tmigr_quick_check(u64 nextevt)
{}

/*
 * tmigr_trigger_active() - trigger a CPU to become active again
 *
 * This function is executed on a CPU which is part of cpu_online_mask, when the
 * last active CPU in the hierarchy is offlining. With this, it is ensured that
 * the other CPU is active and takes over the migrator duty.
 */
static long tmigr_trigger_active(void *unused)
{}

static int tmigr_cpu_offline(unsigned int cpu)
{}

static int tmigr_cpu_online(unsigned int cpu)
{}

static void tmigr_init_group(struct tmigr_group *group, unsigned int lvl,
			     int node)
{}

static struct tmigr_group *tmigr_get_group(unsigned int cpu, int node,
					   unsigned int lvl)
{}

static void tmigr_connect_child_parent(struct tmigr_group *child,
				       struct tmigr_group *parent,
				       bool activate)
{}

static int tmigr_setup_groups(unsigned int cpu, unsigned int node)
{}

static int tmigr_add_cpu(unsigned int cpu)
{}

static int tmigr_cpu_prepare(unsigned int cpu)
{}

static int __init tmigr_init(void)
{}
early_initcall(tmigr_init);