/*
 * Completely Fair Scheduling (CFS) Class (SCHED_NORMAL/SCHED_BATCH)
 *
 *  Copyright (C) 2007 Red Hat, Inc., Ingo Molnar <mingo@redhat.com>
 *
 *  Interactivity improvements by Mike Galbraith
 *  (C) 2007 Mike Galbraith <efault@gmx.de>
 *
 *  Various enhancements by Dmitry Adamushko.
 *  (C) 2007 Dmitry Adamushko <dmitry.adamushko@gmail.com>
 *
 *  Group scheduling enhancements by Srivatsa Vaddagiri
 *  Copyright IBM Corporation, 2007
 *  Author: Srivatsa Vaddagiri <vatsa@linux.vnet.ibm.com>
 *
 *  Scaled math optimizations by Thomas Gleixner
 *  Copyright (C) 2007, Thomas Gleixner <tglx@linutronix.de>
 *
 *  Adaptive scheduling granularity, math enhancements by Peter Zijlstra
 *  Copyright (C) 2007 Red Hat, Inc., Peter Zijlstra <pzijlstr@redhat.com>
 */

#include <linux/latencytop.h>
#include <linux/sched.h>
#include <linux/cpumask.h>
#include <linux/cpuidle.h>
#include <linux/slab.h>
#include <linux/profile.h>
#include <linux/interrupt.h>
#include <linux/mempolicy.h>
#include <linux/migrate.h>
#include <linux/task_work.h>

#include <trace/events/sched.h>

#include "sched.h"

/*
 * Targeted preemption latency for CPU-bound tasks:
 * (default: 6ms * (1 + ilog(ncpus)), units: nanoseconds)
 *
 * NOTE: this latency value is not the same as the concept of
 * 'timeslice length' - timeslices in CFS are of variable length
 * and have no persistent notion like in traditional, time-slice
 * based scheduling concepts.
 *
 * (to see the precise effective timeslice length of your workload,
 *  run vmstat and monitor the context-switches (cs) field)
 */
unsigned int sysctl_sched_latency = 6000000ULL;
unsigned int normalized_sysctl_sched_latency = 6000000ULL;

/*
 * The initial- and re-scaling of tunables is configurable
 * (default SCHED_TUNABLESCALING_LOG = *(1+ilog(ncpus))
 *
 * Options are:
 * SCHED_TUNABLESCALING_NONE - unscaled, always *1
 * SCHED_TUNABLESCALING_LOG - scaled logarithmical, *1+ilog(ncpus)
 * SCHED_TUNABLESCALING_LINEAR - scaled linear, *ncpus
 */
enum sched_tunable_scaling sysctl_sched_tunable_scaling
	= SCHED_TUNABLESCALING_LOG;

/*
 * Minimal preemption granularity for CPU-bound tasks:
 * (default: 0.75 msec * (1 + ilog(ncpus)), units: nanoseconds)
 */
unsigned int sysctl_sched_min_granularity = 750000ULL;
unsigned int normalized_sysctl_sched_min_granularity = 750000ULL;

/*
 * is kept at sysctl_sched_latency / sysctl_sched_min_granularity
 */
static unsigned int sched_nr_latency = 8;

/*
 * After fork, child runs first. If set to 0 (default) then
 * parent will (try to) run first.
 */
unsigned int sysctl_sched_child_runs_first __read_mostly;

/*
 * SCHED_OTHER wake-up granularity.
 * (default: 1 msec * (1 + ilog(ncpus)), units: nanoseconds)
 *
 * This option delays the preemption effects of decoupled workloads
 * and reduces their over-scheduling. Synchronous workloads will still
 * have immediate wakeup/sleep latencies.
 */
unsigned int sysctl_sched_wakeup_granularity = 1000000UL;
unsigned int normalized_sysctl_sched_wakeup_granularity = 1000000UL;

const_debug unsigned int sysctl_sched_migration_cost = 500000UL;

/*
 * The exponential sliding  window over which load is averaged for shares
 * distribution.
 * (default: 10msec)
 */
unsigned int __read_mostly sysctl_sched_shares_window = 10000000UL;

#ifdef CONFIG_CFS_BANDWIDTH
/*
 * Amount of runtime to allocate from global (tg) to local (per-cfs_rq) pool
 * each time a cfs_rq requests quota.
 *
 * Note: in the case that the slice exceeds the runtime remaining (either due
 * to consumption or the quota being specified to be smaller than the slice)
 * we will always only issue the remaining available time.
 *
 * default: 5 msec, units: microseconds
  */
unsigned int sysctl_sched_cfs_bandwidth_slice = 5000UL;
#endif

static inline void update_load_add(struct load_weight *lw, unsigned long inc)
{
	lw->weight += inc;
	lw->inv_weight = 0;
}

static inline void update_load_sub(struct load_weight *lw, unsigned long dec)
{
	lw->weight -= dec;
	lw->inv_weight = 0;
}

static inline void update_load_set(struct load_weight *lw, unsigned long w)
{
	lw->weight = w;
	lw->inv_weight = 0;
}

/*
 * Increase the granularity value when there are more CPUs,
 * because with more CPUs the 'effective latency' as visible
 * to users decreases. But the relationship is not linear,
 * so pick a second-best guess by going with the log2 of the
 * number of CPUs.
 *
 * This idea comes from the SD scheduler of Con Kolivas:
 */
static int get_update_sysctl_factor(void)
{
	unsigned int cpus = min_t(int, num_online_cpus(), 8);
	unsigned int factor;

	switch (sysctl_sched_tunable_scaling) {
	case SCHED_TUNABLESCALING_NONE:
		factor = 1;
		break;
	case SCHED_TUNABLESCALING_LINEAR:
		factor = cpus;
		break;
	case SCHED_TUNABLESCALING_LOG:
	default:
		factor = 1 + ilog2(cpus);
		break;
	}

	return factor;
}

static void update_sysctl(void)
{
	unsigned int factor = get_update_sysctl_factor();

#define SET_SYSCTL(name) \
	(sysctl_##name = (factor) * normalized_sysctl_##name)
	SET_SYSCTL(sched_min_granularity);
	SET_SYSCTL(sched_latency);
	SET_SYSCTL(sched_wakeup_granularity);
#undef SET_SYSCTL
}

void sched_init_granularity(void)
{
	update_sysctl();
}

#define WMULT_CONST	(~0U)
#define WMULT_SHIFT	32

static void __update_inv_weight(struct load_weight *lw)
{
	unsigned long w;

	if (likely(lw->inv_weight))
		return;

	w = scale_load_down(lw->weight);

	if (BITS_PER_LONG > 32 && unlikely(w >= WMULT_CONST))
		lw->inv_weight = 1;
	else if (unlikely(!w))
		lw->inv_weight = WMULT_CONST;
	else
		lw->inv_weight = WMULT_CONST / w;
}

/*
 * delta_exec * weight / lw.weight
 *   OR
 * (delta_exec * (weight * lw->inv_weight)) >> WMULT_SHIFT
 *
 * Either weight := NICE_0_LOAD and lw \e prio_to_wmult[], in which case
 * we're guaranteed shift stays positive because inv_weight is guaranteed to
 * fit 32 bits, and NICE_0_LOAD gives another 10 bits; therefore shift >= 22.
 *
 * Or, weight =< lw.weight (because lw.weight is the runqueue weight), thus
 * weight/lw.weight <= 1, and therefore our shift will also be positive.
 */
static u64 __calc_delta(u64 delta_exec, unsigned long weight, struct load_weight *lw)
{
	u64 fact = scale_load_down(weight);
	int shift = WMULT_SHIFT;

	__update_inv_weight(lw);

	if (unlikely(fact >> 32)) {
		while (fact >> 32) {
			fact >>= 1;
			shift--;
		}
	}

	/* hint to use a 32x32->64 mul */
	fact = (u64)(u32)fact * lw->inv_weight;

	while (fact >> 32) {
		fact >>= 1;
		shift--;
	}

	return mul_u64_u32_shr(delta_exec, fact, shift);
}


const struct sched_class fair_sched_class;

/**************************************************************
 * CFS operations on generic schedulable entities:
 */

#ifdef CONFIG_FAIR_GROUP_SCHED

/* cpu runqueue to which this cfs_rq is attached */
static inline struct rq *rq_of(struct cfs_rq *cfs_rq)
{
	return cfs_rq->rq;
}

/* An entity is a task if it doesn't "own" a runqueue */
#define entity_is_task(se)	(!se->my_q)

static inline struct task_struct *task_of(struct sched_entity *se)
{
#ifdef CONFIG_SCHED_DEBUG
	WARN_ON_ONCE(!entity_is_task(se));
#endif
	return container_of(se, struct task_struct, se);
}

/* Walk up scheduling entities hierarchy */
#define for_each_sched_entity(se) \
		for (; se; se = se->parent)

static inline struct cfs_rq *task_cfs_rq(struct task_struct *p)
{
	return p->se.cfs_rq;
}

/* runqueue on which this entity is (to be) queued */
static inline struct cfs_rq *cfs_rq_of(struct sched_entity *se)
{
	return se->cfs_rq;
}

/* runqueue "owned" by this group */
static inline struct cfs_rq *group_cfs_rq(struct sched_entity *grp)
{
	return grp->my_q;
}

static void update_cfs_rq_blocked_load(struct cfs_rq *cfs_rq,
				       int force_update);

static inline void list_add_leaf_cfs_rq(struct cfs_rq *cfs_rq)
{
	if (!cfs_rq->on_list) {
		/*
		 * Ensure we either appear before our parent (if already
		 * enqueued) or force our parent to appear after us when it is
		 * enqueued.  The fact that we always enqueue bottom-up
		 * reduces this to two cases.
		 */
		if (cfs_rq->tg->parent &&
		    cfs_rq->tg->parent->cfs_rq[cpu_of(rq_of(cfs_rq))]->on_list) {
			list_add_rcu(&cfs_rq->leaf_cfs_rq_list,
				&rq_of(cfs_rq)->leaf_cfs_rq_list);
		} else {
			list_add_tail_rcu(&cfs_rq->leaf_cfs_rq_list,
				&rq_of(cfs_rq)->leaf_cfs_rq_list);
		}

		cfs_rq->on_list = 1;
		/* We should have no load, but we need to update last_decay. */
		update_cfs_rq_blocked_load(cfs_rq, 0);
	}
}

static inline void list_del_leaf_cfs_rq(struct cfs_rq *cfs_rq)
{
	if (cfs_rq->on_list) {
		list_del_rcu(&cfs_rq->leaf_cfs_rq_list);
		cfs_rq->on_list = 0;
	}
}

/* Iterate thr' all leaf cfs_rq's on a runqueue */
#define for_each_leaf_cfs_rq(rq, cfs_rq) \
	list_for_each_entry_rcu(cfs_rq, &rq->leaf_cfs_rq_list, leaf_cfs_rq_list)

/* Do the two (enqueued) entities belong to the same group ? */
static inline struct cfs_rq *
is_same_group(struct sched_entity *se, struct sched_entity *pse)
{
	if (se->cfs_rq == pse->cfs_rq)
		return se->cfs_rq;

	return NULL;
}

static inline struct sched_entity *parent_entity(struct sched_entity *se)
{
	return se->parent;
}

static void
find_matching_se(struct sched_entity **se, struct sched_entity **pse)
{
	int se_depth, pse_depth;

	/*
	 * preemption test can be made between sibling entities who are in the
	 * same cfs_rq i.e who have a common parent. Walk up the hierarchy of
	 * both tasks until we find their ancestors who are siblings of common
	 * parent.
	 */

	/* First walk up until both entities are at same depth */
	se_depth = (*se)->depth;
	pse_depth = (*pse)->depth;

	while (se_depth > pse_depth) {
		se_depth--;
		*se = parent_entity(*se);
	}

	while (pse_depth > se_depth) {
		pse_depth--;
		*pse = parent_entity(*pse);
	}

	while (!is_same_group(*se, *pse)) {
		*se = parent_entity(*se);
		*pse = parent_entity(*pse);
	}
}

#else	/* !CONFIG_FAIR_GROUP_SCHED */

static inline struct task_struct *task_of(struct sched_entity *se)
{
	return container_of(se, struct task_struct, se);
}

static inline struct rq *rq_of(struct cfs_rq *cfs_rq)
{
	return container_of(cfs_rq, struct rq, cfs);
}

#define entity_is_task(se)	1

#define for_each_sched_entity(se) \
		for (; se; se = NULL)

static inline struct cfs_rq *task_cfs_rq(struct task_struct *p)
{
	return &task_rq(p)->cfs;
}

static inline struct cfs_rq *cfs_rq_of(struct sched_entity *se)
{
	struct task_struct *p = task_of(se);
	struct rq *rq = task_rq(p);

	return &rq->cfs;
}

/* runqueue "owned" by this group */
static inline struct cfs_rq *group_cfs_rq(struct sched_entity *grp)
{
	return NULL;
}

static inline void list_add_leaf_cfs_rq(struct cfs_rq *cfs_rq)
{
}

static inline void list_del_leaf_cfs_rq(struct cfs_rq *cfs_rq)
{
}

#define for_each_leaf_cfs_rq(rq, cfs_rq) \
		for (cfs_rq = &rq->cfs; cfs_rq; cfs_rq = NULL)

static inline struct sched_entity *parent_entity(struct sched_entity *se)
{
	return NULL;
}

static inline void
find_matching_se(struct sched_entity **se, struct sched_entity **pse)
{
}

#endif	/* CONFIG_FAIR_GROUP_SCHED */

static __always_inline
void account_cfs_rq_runtime(struct cfs_rq *cfs_rq, u64 delta_exec);

/**************************************************************
 * Scheduling class tree data structure manipulation methods:
 */

static inline u64 max_vruntime(u64 max_vruntime, u64 vruntime)
{
	s64 delta = (s64)(vruntime - max_vruntime);
	if (delta > 0)
		max_vruntime = vruntime;

	return max_vruntime;
}

static inline u64 min_vruntime(u64 min_vruntime, u64 vruntime)
{
	s64 delta = (s64)(vruntime - min_vruntime);
	if (delta < 0)
		min_vruntime = vruntime;

	return min_vruntime;
}

static inline int entity_before(struct sched_entity *a,
				struct sched_entity *b)
{
	return (s64)(a->vruntime - b->vruntime) < 0;
}

static void update_min_vruntime(struct cfs_rq *cfs_rq)
{
	u64 vruntime = cfs_rq->min_vruntime;

	if (cfs_rq->curr)
		vruntime = cfs_rq->curr->vruntime;

	if (cfs_rq->rb_leftmost) {
		struct sched_entity *se = rb_entry(cfs_rq->rb_leftmost,
						   struct sched_entity,
						   run_node);

		if (!cfs_rq->curr)
			vruntime = se->vruntime;
		else
			vruntime = min_vruntime(vruntime, se->vruntime);
	}

	/* ensure we never gain time by being placed backwards. */
	cfs_rq->min_vruntime = max_vruntime(cfs_rq->min_vruntime, vruntime);
#ifndef CONFIG_64BIT
	smp_wmb();
	cfs_rq->min_vruntime_copy = cfs_rq->min_vruntime;
#endif
}

/*
 * Enqueue an entity into the rb-tree:
 */
static void __enqueue_entity(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	struct rb_node **link = &cfs_rq->tasks_timeline.rb_node;
	struct rb_node *parent = NULL;
	struct sched_entity *entry;
	int leftmost = 1;

	/*
	 * Find the right place in the rbtree:
	 */
	while (*link) {
		parent = *link;
		entry = rb_entry(parent, struct sched_entity, run_node);
		/*
		 * We dont care about collisions. Nodes with
		 * the same key stay together.
		 */
		if (entity_before(se, entry)) {
			link = &parent->rb_left;
		} else {
			link = &parent->rb_right;
			leftmost = 0;
		}
	}

	/*
	 * Maintain a cache of leftmost tree entries (it is frequently
	 * used):
	 */
	if (leftmost)
		cfs_rq->rb_leftmost = &se->run_node;

	rb_link_node(&se->run_node, parent, link);
	rb_insert_color(&se->run_node, &cfs_rq->tasks_timeline);
}

static void __dequeue_entity(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	if (cfs_rq->rb_leftmost == &se->run_node) {
		struct rb_node *next_node;

		next_node = rb_next(&se->run_node);
		cfs_rq->rb_leftmost = next_node;
	}

	rb_erase(&se->run_node, &cfs_rq->tasks_timeline);
}

struct sched_entity *__pick_first_entity(struct cfs_rq *cfs_rq)
{
	struct rb_node *left = cfs_rq->rb_leftmost;

	if (!left)
		return NULL;

	return rb_entry(left, struct sched_entity, run_node);
}

static struct sched_entity *__pick_next_entity(struct sched_entity *se)
{
	struct rb_node *next = rb_next(&se->run_node);

	if (!next)
		return NULL;

	return rb_entry(next, struct sched_entity, run_node);
}

#ifdef CONFIG_SCHED_DEBUG
struct sched_entity *__pick_last_entity(struct cfs_rq *cfs_rq)
{
	struct rb_node *last = rb_last(&cfs_rq->tasks_timeline);

	if (!last)
		return NULL;

	return rb_entry(last, struct sched_entity, run_node);
}

/**************************************************************
 * Scheduling class statistics methods:
 */

int sched_proc_update_handler(struct ctl_table *table, int write,
		void __user *buffer, size_t *lenp,
		loff_t *ppos)
{
	int ret = proc_dointvec_minmax(table, write, buffer, lenp, ppos);
	int factor = get_update_sysctl_factor();

	if (ret || !write)
		return ret;

	sched_nr_latency = DIV_ROUND_UP(sysctl_sched_latency,
					sysctl_sched_min_granularity);

#define WRT_SYSCTL(name) \
	(normalized_sysctl_##name = sysctl_##name / (factor))
	WRT_SYSCTL(sched_min_granularity);
	WRT_SYSCTL(sched_latency);
	WRT_SYSCTL(sched_wakeup_granularity);
#undef WRT_SYSCTL

	return 0;
}
#endif

/*
 * delta /= w
 */
static inline u64 calc_delta_fair(u64 delta, struct sched_entity *se)
{
	if (unlikely(se->load.weight != NICE_0_LOAD))
		delta = __calc_delta(delta, NICE_0_LOAD, &se->load);

	return delta;
}

/*
 * The idea is to set a period in which each task runs once.
 *
 * When there are too many tasks (sched_nr_latency) we have to stretch
 * this period because otherwise the slices get too small.
 *
 * p = (nr <= nl) ? l : l*nr/nl
 */
static u64 __sched_period(unsigned long nr_running)
{
	u64 period = sysctl_sched_latency;
	unsigned long nr_latency = sched_nr_latency;

	if (unlikely(nr_running > nr_latency)) {
		period = sysctl_sched_min_granularity;
		period *= nr_running;
	}

	return period;
}

/*
 * We calculate the wall-time slice from the period by taking a part
 * proportional to the weight.
 *
 * s = p*P[w/rw]
 */
static u64 sched_slice(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	u64 slice = __sched_period(cfs_rq->nr_running + !se->on_rq);

	for_each_sched_entity(se) {
		struct load_weight *load;
		struct load_weight lw;

		cfs_rq = cfs_rq_of(se);
		load = &cfs_rq->load;

		if (unlikely(!se->on_rq)) {
			lw = cfs_rq->load;

			update_load_add(&lw, se->load.weight);
			load = &lw;
		}
		slice = __calc_delta(slice, se->load.weight, load);
	}
	return slice;
}

/*
 * We calculate the vruntime slice of a to-be-inserted task.
 *
 * vs = s/w
 */
static u64 sched_vslice(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	return calc_delta_fair(sched_slice(cfs_rq, se), se);
}

#ifdef CONFIG_SMP
static int select_idle_sibling(struct task_struct *p, int cpu);
static unsigned long task_h_load(struct task_struct *p);

static inline void __update_task_entity_contrib(struct sched_entity *se);

/* Give new task start runnable values to heavy its load in infant time */
void init_task_runnable_average(struct task_struct *p)
{
	u32 slice;

	slice = sched_slice(task_cfs_rq(p), &p->se) >> 10;
	p->se.avg.runnable_avg_sum = slice;
	p->se.avg.runnable_avg_period = slice;
	__update_task_entity_contrib(&p->se);
}
#else
void init_task_runnable_average(struct task_struct *p)
{
}
#endif

/*
 * Update the current task's runtime statistics.
 */
static void update_curr(struct cfs_rq *cfs_rq)
{
	struct sched_entity *curr = cfs_rq->curr;
	u64 now = rq_clock_task(rq_of(cfs_rq));
	u64 delta_exec;

	if (unlikely(!curr))
		return;

	delta_exec = now - curr->exec_start;
	if (unlikely((s64)delta_exec <= 0))
		return;

	curr->exec_start = now;

	schedstat_set(curr->statistics.exec_max,
		      max(delta_exec, curr->statistics.exec_max));

	curr->sum_exec_runtime += delta_exec;
	schedstat_add(cfs_rq, exec_clock, delta_exec);

	curr->vruntime += calc_delta_fair(delta_exec, curr);
	update_min_vruntime(cfs_rq);

	if (entity_is_task(curr)) {
		struct task_struct *curtask = task_of(curr);

		trace_sched_stat_runtime(curtask, delta_exec, curr->vruntime);
		cpuacct_charge(curtask, delta_exec);
		account_group_exec_runtime(curtask, delta_exec);
	}

	account_cfs_rq_runtime(cfs_rq, delta_exec);
}

static void update_curr_fair(struct rq *rq)
{
	update_curr(cfs_rq_of(&rq->curr->se));
}

static inline void
update_stats_wait_start(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	schedstat_set(se->statistics.wait_start, rq_clock(rq_of(cfs_rq)));
}

/*
 * Task is being enqueued - update stats:
 */
static void update_stats_enqueue(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	/*
	 * Are we enqueueing a waiting task? (for current tasks
	 * a dequeue/enqueue event is a NOP)
	 */
	if (se != cfs_rq->curr)
		update_stats_wait_start(cfs_rq, se);
}

static void
update_stats_wait_end(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	schedstat_set(se->statistics.wait_max, max(se->statistics.wait_max,
			rq_clock(rq_of(cfs_rq)) - se->statistics.wait_start));
	schedstat_set(se->statistics.wait_count, se->statistics.wait_count + 1);
	schedstat_set(se->statistics.wait_sum, se->statistics.wait_sum +
			rq_clock(rq_of(cfs_rq)) - se->statistics.wait_start);
#ifdef CONFIG_SCHEDSTATS
	if (entity_is_task(se)) {
		trace_sched_stat_wait(task_of(se),
			rq_clock(rq_of(cfs_rq)) - se->statistics.wait_start);
	}
#endif
	schedstat_set(se->statistics.wait_start, 0);
}

static inline void
update_stats_dequeue(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	/*
	 * Mark the end of the wait period if dequeueing a
	 * waiting task:
	 */
	if (se != cfs_rq->curr)
		update_stats_wait_end(cfs_rq, se);
}

/*
 * We are picking a new current task - update its stats:
 */
static inline void
update_stats_curr_start(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	/*
	 * We are starting a new run period:
	 */
	se->exec_start = rq_clock_task(rq_of(cfs_rq));
}

/**************************************************
 * Scheduling class queueing methods:
 */

#ifdef CONFIG_NUMA_BALANCING
/*
 * Approximate time to scan a full NUMA task in ms. The task scan period is
 * calculated based on the tasks virtual memory size and
 * numa_balancing_scan_size.
 */
unsigned int sysctl_numa_balancing_scan_period_min = 1000;
unsigned int sysctl_numa_balancing_scan_period_max = 60000;

/* Portion of address space to scan in MB */
unsigned int sysctl_numa_balancing_scan_size = 256;

/* Scan @scan_size MB every @scan_period after an initial @scan_delay in ms */
unsigned int sysctl_numa_balancing_scan_delay = 1000;

static unsigned int task_nr_scan_windows(struct task_struct *p)
{
	unsigned long rss = 0;
	unsigned long nr_scan_pages;

	/*
	 * Calculations based on RSS as non-present and empty pages are skipped
	 * by the PTE scanner and NUMA hinting faults should be trapped based
	 * on resident pages
	 */
	nr_scan_pages = sysctl_numa_balancing_scan_size << (20 - PAGE_SHIFT);
	rss = get_mm_rss(p->mm);
	if (!rss)
		rss = nr_scan_pages;

	rss = round_up(rss, nr_scan_pages);
	return rss / nr_scan_pages;
}

/* For sanitys sake, never scan more PTEs than MAX_SCAN_WINDOW MB/sec. */
#define MAX_SCAN_WINDOW 2560

static unsigned int task_scan_min(struct task_struct *p)
{
	unsigned int scan_size = ACCESS_ONCE(sysctl_numa_balancing_scan_size);
	unsigned int scan, floor;
	unsigned int windows = 1;

	if (scan_size < MAX_SCAN_WINDOW)
		windows = MAX_SCAN_WINDOW / scan_size;
	floor = 1000 / windows;

	scan = sysctl_numa_balancing_scan_period_min / task_nr_scan_windows(p);
	return max_t(unsigned int, floor, scan);
}

static unsigned int task_scan_max(struct task_struct *p)
{
	unsigned int smin = task_scan_min(p);
	unsigned int smax;

	/* Watch for min being lower than max due to floor calculations */
	smax = sysctl_numa_balancing_scan_period_max / task_nr_scan_windows(p);
	return max(smin, smax);
}

static void account_numa_enqueue(struct rq *rq, struct task_struct *p)
{
	rq->nr_numa_running += (p->numa_preferred_nid != -1);
	rq->nr_preferred_running += (p->numa_preferred_nid == task_node(p));
}

static void account_numa_dequeue(struct rq *rq, struct task_struct *p)
{
	rq->nr_numa_running -= (p->numa_preferred_nid != -1);
	rq->nr_preferred_running -= (p->numa_preferred_nid == task_node(p));
}

struct numa_group {
	atomic_t refcount;

	spinlock_t lock; /* nr_tasks, tasks */
	int nr_tasks;
	pid_t gid;

	struct rcu_head rcu;
	nodemask_t active_nodes;
	unsigned long total_faults;
	/*
	 * Faults_cpu is used to decide whether memory should move
	 * towards the CPU. As a consequence, these stats are weighted
	 * more by CPU use than by memory faults.
	 */
	unsigned long *faults_cpu;
	unsigned long faults[0];
};

/* Shared or private faults. */
#define NR_NUMA_HINT_FAULT_TYPES 2

/* Memory and CPU locality */
#define NR_NUMA_HINT_FAULT_STATS (NR_NUMA_HINT_FAULT_TYPES * 2)

/* Averaged statistics, and temporary buffers. */
#define NR_NUMA_HINT_FAULT_BUCKETS (NR_NUMA_HINT_FAULT_STATS * 2)

pid_t task_numa_group_id(struct task_struct *p)
{
	return p->numa_group ? p->numa_group->gid : 0;
}

/*
 * The averaged statistics, shared & private, memory & cpu,
 * occupy the first half of the array. The second half of the
 * array is for current counters, which are averaged into the
 * first set by task_numa_placement.
 */
static inline int task_faults_idx(enum numa_faults_stats s, int nid, int priv)
{
	return NR_NUMA_HINT_FAULT_TYPES * (s * nr_node_ids + nid) + priv;
}

static inline unsigned long task_faults(struct task_struct *p, int nid)
{
	if (!p->numa_faults)
		return 0;

	return p->numa_faults[task_faults_idx(NUMA_MEM, nid, 0)] +
		p->numa_faults[task_faults_idx(NUMA_MEM, nid, 1)];
}

static inline unsigned long group_faults(struct task_struct *p, int nid)
{
	if (!p->numa_group)
		return 0;

	return p->numa_group->faults[task_faults_idx(NUMA_MEM, nid, 0)] +
		p->numa_group->faults[task_faults_idx(NUMA_MEM, nid, 1)];
}

static inline unsigned long group_faults_cpu(struct numa_group *group, int nid)
{
	return group->faults_cpu[task_faults_idx(NUMA_MEM, nid, 0)] +
		group->faults_cpu[task_faults_idx(NUMA_MEM, nid, 1)];
}

/* Handle placement on systems where not all nodes are directly connected. */
static unsigned long score_nearby_nodes(struct task_struct *p, int nid,
					int maxdist, bool task)
{
	unsigned long score = 0;
	int node;

	/*
	 * All nodes are directly connected, and the same distance
	 * from each other. No need for fancy placement algorithms.
	 */
	if (sched_numa_topology_type == NUMA_DIRECT)
		return 0;

	/*
	 * This code is called for each node, introducing N^2 complexity,
	 * which should be ok given the number of nodes rarely exceeds 8.
	 */
	for_each_online_node(node) {
		unsigned long faults;
		int dist = node_distance(nid, node);

		/*
		 * The furthest away nodes in the system are not interesting
		 * for placement; nid was already counted.
		 */
		if (dist == sched_max_numa_distance || node == nid)
			continue;

		/*
		 * On systems with a backplane NUMA topology, compare groups
		 * of nodes, and move tasks towards the group with the most
		 * memory accesses. When comparing two nodes at distance
		 * "hoplimit", only nodes closer by than "hoplimit" are part
		 * of each group. Skip other nodes.
		 */
		if (sched_numa_topology_type == NUMA_BACKPLANE &&
					dist > maxdist)
			continue;

		/* Add up the faults from nearby nodes. */
		if (task)
			faults = task_faults(p, node);
		else
			faults = group_faults(p, node);

		/*
		 * On systems with a glueless mesh NUMA topology, there are
		 * no fixed "groups of nodes". Instead, nodes that are not
		 * directly connected bounce traffic through intermediate
		 * nodes; a numa_group can occupy any set of nodes.
		 * The further away a node is, the less the faults count.
		 * This seems to result in good task placement.
		 */
		if (sched_numa_topology_type == NUMA_GLUELESS_MESH) {
			faults *= (sched_max_numa_distance - dist);
			faults /= (sched_max_numa_distance - LOCAL_DISTANCE);
		}

		score += faults;
	}

	return score;
}

/*
 * These return the fraction of accesses done by a particular task, or
 * task group, on a particular numa node.  The group weight is given a
 * larger multiplier, in order to group tasks together that are almost
 * evenly spread out between numa nodes.
 */
static inline unsigned long task_weight(struct task_struct *p, int nid,
					int dist)
{
	unsigned long faults, total_faults;

	if (!p->numa_faults)
		return 0;

	total_faults = p->total_numa_faults;

	if (!total_faults)
		return 0;

	faults = task_faults(p, nid);
	faults += score_nearby_nodes(p, nid, dist, true);

	return 1000 * faults / total_faults;
}

static inline unsigned long group_weight(struct task_struct *p, int nid,
					 int dist)
{
	unsigned long faults, total_faults;

	if (!p->numa_group)
		return 0;

	total_faults = p->numa_group->total_faults;

	if (!total_faults)
		return 0;

	faults = group_faults(p, nid);
	faults += score_nearby_nodes(p, nid, dist, false);

	return 1000 * faults / total_faults;
}

bool should_numa_migrate_memory(struct task_struct *p, struct page * page,
				int src_nid, int dst_cpu)
{
	struct numa_group *ng = p->numa_group;
	int dst_nid = cpu_to_node(dst_cpu);
	int last_cpupid, this_cpupid;

	this_cpupid = cpu_pid_to_cpupid(dst_cpu, current->pid);

	/*
	 * Multi-stage node selection is used in conjunction with a periodic
	 * migration fault to build a temporal task<->page relation. By using
	 * a two-stage filter we remove short/unlikely relations.
	 *
	 * Using P(p) ~ n_p / n_t as per frequentist probability, we can equate
	 * a task's usage of a particular page (n_p) per total usage of this
	 * page (n_t) (in a given time-span) to a probability.
	 *
	 * Our periodic faults will sample this probability and getting the
	 * same result twice in a row, given these samples are fully
	 * independent, is then given by P(n)^2, provided our sample period
	 * is sufficiently short compared to the usage pattern.
	 *
	 * This quadric squishes small probabilities, making it less likely we
	 * act on an unlikely task<->page relation.
	 */
	last_cpupid = page_cpupid_xchg_last(page, this_cpupid);
	if (!cpupid_pid_unset(last_cpupid) &&
				cpupid_to_nid(last_cpupid) != dst_nid)
		return false;

	/* Always allow migrate on private faults */
	if (cpupid_match_pid(p, last_cpupid))
		return true;

	/* A shared fault, but p->numa_group has not been set up yet. */
	if (!ng)
		return true;

	/*
	 * Do not migrate if the destination is not a node that
	 * is actively used by this numa group.
	 */
	if (!node_isset(dst_nid, ng->active_nodes))
		return false;

	/*
	 * Source is a node that is not actively used by this
	 * numa group, while the destination is. Migrate.
	 */
	if (!node_isset(src_nid, ng->active_nodes))
		return true;

	/*
	 * Both source and destination are nodes in active
	 * use by this numa group. Maximize memory bandwidth
	 * by migrating from more heavily used groups, to less
	 * heavily used ones, spreading the load around.
	 * Use a 1/4 hysteresis to avoid spurious page movement.
	 */
	return group_faults(p, dst_nid) < (group_faults(p, src_nid) * 3 / 4);
}

static unsigned long weighted_cpuload(const int cpu);
static unsigned long source_load(int cpu, int type);
static unsigned long target_load(int cpu, int type);
static unsigned long capacity_of(int cpu);
static long effective_load(struct task_group *tg, int cpu, long wl, long wg);

/* Cached statistics for all CPUs within a node */
struct numa_stats {
	unsigned long nr_running;
	unsigned long load;

	/* Total compute capacity of CPUs on a node */
	unsigned long compute_capacity;

	/* Approximate capacity in terms of runnable tasks on a node */
	unsigned long task_capacity;
	int has_free_capacity;
};

/*
 * XXX borrowed from update_sg_lb_stats
 */
static void update_numa_stats(struct numa_stats *ns, int nid)
{
	int smt, cpu, cpus = 0;
	unsigned long capacity;

	memset(ns, 0, sizeof(*ns));
	for_each_cpu(cpu, cpumask_of_node(nid)) {
		struct rq *rq = cpu_rq(cpu);

		ns->nr_running += rq->nr_running;
		ns->load += weighted_cpuload(cpu);
		ns->compute_capacity += capacity_of(cpu);

		cpus++;
	}

	/*
	 * If we raced with hotplug and there are no CPUs left in our mask
	 * the @ns structure is NULL'ed and task_numa_compare() will
	 * not find this node attractive.
	 *
	 * We'll either bail at !has_free_capacity, or we'll detect a huge
	 * imbalance and bail there.
	 */
	if (!cpus)
		return;

	/* smt := ceil(cpus / capacity), assumes: 1 < smt_power < 2 */
	smt = DIV_ROUND_UP(SCHED_CAPACITY_SCALE * cpus, ns->compute_capacity);
	capacity = cpus / smt; /* cores */

	ns->task_capacity = min_t(unsigned, capacity,
		DIV_ROUND_CLOSEST(ns->compute_capacity, SCHED_CAPACITY_SCALE));
	ns->has_free_capacity = (ns->nr_running < ns->task_capacity);
}

struct task_numa_env {
	struct task_struct *p;

	int src_cpu, src_nid;
	int dst_cpu, dst_nid;

	struct numa_stats src_stats, dst_stats;

	int imbalance_pct;
	int dist;

	struct task_struct *best_task;
	long best_imp;
	int best_cpu;
};

static void task_numa_assign(struct task_numa_env *env,
			     struct task_struct *p, long imp)
{
	if (env->best_task)
		put_task_struct(env->best_task);
	if (p)
		get_task_struct(p);

	env->best_task = p;
	env->best_imp = imp;
	env->best_cpu = env->dst_cpu;
}

static bool load_too_imbalanced(long src_load, long dst_load,
				struct task_numa_env *env)
{
	long imb, old_imb;
	long orig_src_load, orig_dst_load;
	long src_capacity, dst_capacity;

	/*
	 * The load is corrected for the CPU capacity available on each node.
	 *
	 * src_load        dst_load
	 * ------------ vs ---------
	 * src_capacity    dst_capacity
	 */
	src_capacity = env->src_stats.compute_capacity;
	dst_capacity = env->dst_stats.compute_capacity;

	/* We care about the slope of the imbalance, not the direction. */
	if (dst_load < src_load)
		swap(dst_load, src_load);

	/* Is the difference below the threshold? */
	imb = dst_load * src_capacity * 100 -
	      src_load * dst_capacity * env->imbalance_pct;
	if (imb <= 0)
		return false;

	/*
	 * The imbalance is above the allowed threshold.
	 * Compare it with the old imbalance.
	 */
	orig_src_load = env->src_stats.load;
	orig_dst_load = env->dst_stats.load;

	if (orig_dst_load < orig_src_load)
		swap(orig_dst_load, orig_src_load);

	old_imb = orig_dst_load * src_capacity * 100 -
		  orig_src_load * dst_capacity * env->imbalance_pct;

	/* Would this change make things worse? */
	return (imb > old_imb);
}

/*
 * This checks if the overall compute and NUMA accesses of the system would
 * be improved if the source tasks was migrated to the target dst_cpu taking
 * into account that it might be best if task running on the dst_cpu should
 * be exchanged with the source task
 */
static void task_numa_compare(struct task_numa_env *env,
			      long taskimp, long groupimp)
{
	struct rq *src_rq = cpu_rq(env->src_cpu);
	struct rq *dst_rq = cpu_rq(env->dst_cpu);
	struct task_struct *cur;
	long src_load, dst_load;
	long load;
	long imp = env->p->numa_group ? groupimp : taskimp;
	long moveimp = imp;
	int dist = env->dist;

	rcu_read_lock();

	raw_spin_lock_irq(&dst_rq->lock);
	cur = dst_rq->curr;
	/*
	 * No need to move the exiting task, and this ensures that ->curr
	 * wasn't reaped and thus get_task_struct() in task_numa_assign()
	 * is safe under RCU read lock.
	 * Note that rcu_read_lock() itself can't protect from the final
	 * put_task_struct() after the last schedule().
	 */
	if ((cur->flags & PF_EXITING) || is_idle_task(cur))
		cur = NULL;
	raw_spin_unlock_irq(&dst_rq->lock);

	/*
	 * Because we have preemption enabled we can get migrated around and
	 * end try selecting ourselves (current == env->p) as a swap candidate.
	 */
	if (cur == env->p)
		goto unlock;

	/*
	 * "imp" is the fault differential for the source task between the
	 * source and destination node. Calculate the total differential for
	 * the source task and potential destination task. The more negative
	 * the value is, the more rmeote accesses that would be expected to
	 * be incurred if the tasks were swapped.
	 */
	if (cur) {
		/* Skip this swap candidate if cannot move to the source cpu */
		if (!cpumask_test_cpu(env->src_cpu, tsk_cpus_allowed(cur)))
			goto unlock;

		/*
		 * If dst and source tasks are in the same NUMA group, or not
		 * in any group then look only at task weights.
		 */
		if (cur->numa_group == env->p->numa_group) {
			imp = taskimp + task_weight(cur, env->src_nid, dist) -
			      task_weight(cur, env->dst_nid, dist);
			/*
			 * Add some hysteresis to prevent swapping the
			 * tasks within a group over tiny differences.
			 */
			if (cur->numa_group)
				imp -= imp/16;
		} else {
			/*
			 * Compare the group weights. If a task is all by
			 * itself (not part of a group), use the task weight
			 * instead.
			 */
			if (cur->numa_group)
				imp += group_weight(cur, env->src_nid, dist) -
				       group_weight(cur, env->dst_nid, dist);
			else
				imp += task_weight(cur, env->src_nid, dist) -
				       task_weight(cur, env->dst_nid, dist);
		}
	}

	if (imp <= env->best_imp && moveimp <= env->best_imp)
		goto unlock;

	if (!cur) {
		/* Is there capacity at our destination? */
		if (env->src_stats.nr_running <= env->src_stats.task_capacity &&
		    !env->dst_stats.has_free_capacity)
			goto unlock;

		goto balance;
	}

	/* Balance doesn't matter much if we're running a task per cpu */
	if (imp > env->best_imp && src_rq->nr_running == 1 &&
			dst_rq->nr_running == 1)
		goto assign;

	/*
	 * In the overloaded case, try and keep the load balanced.
	 */
balance:
	load = task_h_load(env->p);
	dst_load = env->dst_stats.load + load;
	src_load = env->src_stats.load - load;

	if (moveimp > imp && moveimp > env->best_imp) {
		/*
		 * If the improvement from just moving env->p direction is
		 * better than swapping tasks around, check if a move is
		 * possible. Store a slightly smaller score than moveimp,
		 * so an actually idle CPU will win.
		 */
		if (!load_too_imbalanced(src_load, dst_load, env)) {
			imp = moveimp - 1;
			cur = NULL;
			goto assign;
		}
	}

	if (imp <= env->best_imp)
		goto unlock;

	if (cur) {
		load = task_h_load(cur);
		dst_load -= load;
		src_load += load;
	}

	if (load_too_imbalanced(src_load, dst_load, env))
		goto unlock;

	/*
	 * One idle CPU per node is evaluated for a task numa move.
	 * Call select_idle_sibling to maybe find a better one.
	 */
	if (!cur)
		env->dst_cpu = select_idle_sibling(env->p, env->dst_cpu);

assign:
	task_numa_assign(env, cur, imp);
unlock:
	rcu_read_unlock();
}

static void task_numa_find_cpu(struct task_numa_env *env,
				long taskimp, long groupimp)
{
	int cpu;

	for_each_cpu(cpu, cpumask_of_node(env->dst_nid)) {
		/* Skip this CPU if the source task cannot migrate */
		if (!cpumask_test_cpu(cpu, tsk_cpus_allowed(env->p)))
			continue;

		env->dst_cpu = cpu;
		task_numa_compare(env, taskimp, groupimp);
	}
}

static int task_numa_migrate(struct task_struct *p)
{
	struct task_numa_env env = {
		.p = p,

		.src_cpu = task_cpu(p),
		.src_nid = task_node(p),

		.imbalance_pct = 112,

		.best_task = NULL,
		.best_imp = 0,
		.best_cpu = -1
	};
	struct sched_domain *sd;
	unsigned long taskweight, groupweight;
	int nid, ret, dist;
	long taskimp, groupimp;

	/*
	 * Pick the lowest SD_NUMA domain, as that would have the smallest
	 * imbalance and would be the first to start moving tasks about.
	 *
	 * And we want to avoid any moving of tasks about, as that would create
	 * random movement of tasks -- counter the numa conditions we're trying
	 * to satisfy here.
	 */
	rcu_read_lock();
	sd = rcu_dereference(per_cpu(sd_numa, env.src_cpu));
	if (sd)
		env.imbalance_pct = 100 + (sd->imbalance_pct - 100) / 2;
	rcu_read_unlock();

	/*
	 * Cpusets can break the scheduler domain tree into smaller
	 * balance domains, some of which do not cross NUMA boundaries.
	 * Tasks that are "trapped" in such domains cannot be migrated
	 * elsewhere, so there is no point in (re)trying.
	 */
	if (unlikely(!sd)) {
		p->numa_preferred_nid = task_node(p);
		return -EINVAL;
	}

	env.dst_nid = p->numa_preferred_nid;
	dist = env.dist = node_distance(env.src_nid, env.dst_nid);
	taskweight = task_weight(p, env.src_nid, dist);
	groupweight = group_weight(p, env.src_nid, dist);
	update_numa_stats(&env.src_stats, env.src_nid);
	taskimp = task_weight(p, env.dst_nid, dist) - taskweight;
	groupimp = group_weight(p, env.dst_nid, dist) - groupweight;
	update_numa_stats(&env.dst_stats, env.dst_nid);

	/* Try to find a spot on the preferred nid. */
	task_numa_find_cpu(&env, taskimp, groupimp);

	/*
	 * Look at other nodes in these cases:
	 * - there is no space available on the preferred_nid
	 * - the task is part of a numa_group that is interleaved across
	 *   multiple NUMA nodes; in order to better consolidate the group,
	 *   we need to check other locations.
	 */
	if (env.best_cpu == -1 || (p->numa_group &&
			nodes_weight(p->numa_group->active_nodes) > 1)) {
		for_each_online_node(nid) {
			if (nid == env.src_nid || nid == p->numa_preferred_nid)
				continue;

			dist = node_distance(env.src_nid, env.dst_nid);
			if (sched_numa_topology_type == NUMA_BACKPLANE &&
						dist != env.dist) {
				taskweight = task_weight(p, env.src_nid, dist);
				groupweight = group_weight(p, env.src_nid, dist);
			}

			/* Only consider nodes where both task and groups benefit */
			taskimp = task_weight(p, nid, dist) - taskweight;
			groupimp = group_weight(p, nid, dist) - groupweight;
			if (taskimp < 0 && groupimp < 0)
				continue;

			env.dist = dist;
			env.dst_nid = nid;
			update_numa_stats(&env.dst_stats, env.dst_nid);
			task_numa_find_cpu(&env, taskimp, groupimp);
		}
	}

	/*
	 * If the task is part of a workload that spans multiple NUMA nodes,
	 * and is migrating into one of the workload's active nodes, remember
	 * this node as the task's preferred numa node, so the workload can
	 * settle down.
	 * A task that migrated to a second choice node will be better off
	 * trying for a better one later. Do not set the preferred node here.
	 */
	if (p->numa_group) {
		if (env.best_cpu == -1)
			nid = env.src_nid;
		else
			nid = env.dst_nid;

		if (node_isset(nid, p->numa_group->active_nodes))
			sched_setnuma(p, env.dst_nid);
	}

	/* No better CPU than the current one was found. */
	if (env.best_cpu == -1)
		return -EAGAIN;

	/*
	 * Reset the scan period if the task is being rescheduled on an
	 * alternative node to recheck if the tasks is now properly placed.
	 */
	p->numa_scan_period = task_scan_min(p);

	if (env.best_task == NULL) {
		ret = migrate_task_to(p, env.best_cpu);
		if (ret != 0)
			trace_sched_stick_numa(p, env.src_cpu, env.best_cpu);
		return ret;
	}

	ret = migrate_swap(p, env.best_task);
	if (ret != 0)
		trace_sched_stick_numa(p, env.src_cpu, task_cpu(env.best_task));
	put_task_struct(env.best_task);
	return ret;
}

/* Attempt to migrate a task to a CPU on the preferred node. */
static void numa_migrate_preferred(struct task_struct *p)
{
	unsigned long interval = HZ;

	/* This task has no NUMA fault statistics yet */
	if (unlikely(p->numa_preferred_nid == -1 || !p->numa_faults))
		return;

	/* Periodically retry migrating the task to the preferred node */
	interval = min(interval, msecs_to_jiffies(p->numa_scan_period) / 16);
	p->numa_migrate_retry = jiffies + interval;

	/* Success if task is already running on preferred CPU */
	if (task_node(p) == p->numa_preferred_nid)
		return;

	/* Otherwise, try migrate to a CPU on the preferred node */
	task_numa_migrate(p);
}

/*
 * Find the nodes on which the workload is actively running. We do this by
 * tracking the nodes from which NUMA hinting faults are triggered. This can
 * be different from the set of nodes where the workload's memory is currently
 * located.
 *
 * The bitmask is used to make smarter decisions on when to do NUMA page
 * migrations, To prevent flip-flopping, and excessive page migrations, nodes
 * are added when they cause over 6/16 of the maximum number of faults, but
 * only removed when they drop below 3/16.
 */
static void update_numa_active_node_mask(struct numa_group *numa_group)
{
	unsigned long faults, max_faults = 0;
	int nid;

	for_each_online_node(nid) {
		faults = group_faults_cpu(numa_group, nid);
		if (faults > max_faults)
			max_faults = faults;
	}

	for_each_online_node(nid) {
		faults = group_faults_cpu(numa_group, nid);
		if (!node_isset(nid, numa_group->active_nodes)) {
			if (faults > max_faults * 6 / 16)
				node_set(nid, numa_group->active_nodes);
		} else if (faults < max_faults * 3 / 16)
			node_clear(nid, numa_group->active_nodes);
	}
}

/*
 * When adapting the scan rate, the period is divided into NUMA_PERIOD_SLOTS
 * increments. The more local the fault statistics are, the higher the scan
 * period will be for the next scan window. If local/(local+remote) ratio is
 * below NUMA_PERIOD_THRESHOLD (where range of ratio is 1..NUMA_PERIOD_SLOTS)
 * the scan period will decrease. Aim for 70% local accesses.
 */
#define NUMA_PERIOD_SLOTS 10
#define NUMA_PERIOD_THRESHOLD 7

/*
 * Increase the scan period (slow down scanning) if the majority of
 * our memory is already on our local node, or if the majority of
 * the page accesses are shared with other processes.
 * Otherwise, decrease the scan period.
 */
static void update_task_scan_period(struct task_struct *p,
			unsigned long shared, unsigned long private)
{
	unsigned int period_slot;
	int ratio;
	int diff;

	unsigned long remote = p->numa_faults_locality[0];
	unsigned long local = p->numa_faults_locality[1];

	/*
	 * If there were no record hinting faults then either the task is
	 * completely idle or all activity is areas that are not of interest
	 * to automatic numa balancing. Related to that, if there were failed
	 * migration then it implies we are migrating too quickly or the local
	 * node is overloaded. In either case, scan slower
	 */
	if (local + shared == 0 || p->numa_faults_locality[2]) {
		p->numa_scan_period = min(p->numa_scan_period_max,
			p->numa_scan_period << 1);

		p->mm->numa_next_scan = jiffies +
			msecs_to_jiffies(p->numa_scan_period);

		return;
	}

	/*
	 * Prepare to scale scan period relative to the current period.
	 *	 == NUMA_PERIOD_THRESHOLD scan period stays the same
	 *       <  NUMA_PERIOD_THRESHOLD scan period decreases (scan faster)
	 *	 >= NUMA_PERIOD_THRESHOLD scan period increases (scan slower)
	 */
	period_slot = DIV_ROUND_UP(p->numa_scan_period, NUMA_PERIOD_SLOTS);
	ratio = (local * NUMA_PERIOD_SLOTS) / (local + remote);
	if (ratio >= NUMA_PERIOD_THRESHOLD) {
		int slot = ratio - NUMA_PERIOD_THRESHOLD;
		if (!slot)
			slot = 1;
		diff = slot * period_slot;
	} else {
		diff = -(NUMA_PERIOD_THRESHOLD - ratio) * period_slot;

		/*
		 * Scale scan rate increases based on sharing. There is an
		 * inverse relationship between the degree of sharing and
		 * the adjustment made to the scanning period. Broadly
		 * speaking the intent is that there is little point
		 * scanning faster if shared accesses dominate as it may
		 * simply bounce migrations uselessly
		 */
		ratio = DIV_ROUND_UP(private * NUMA_PERIOD_SLOTS, (private + shared + 1));
		diff = (diff * ratio) / NUMA_PERIOD_SLOTS;
	}

	p->numa_scan_period = clamp(p->numa_scan_period + diff,
			task_scan_min(p), task_scan_max(p));
	memset(p->numa_faults_locality, 0, sizeof(p->numa_faults_locality));
}

/*
 * Get the fraction of time the task has been running since the last
 * NUMA placement cycle. The scheduler keeps similar statistics, but
 * decays those on a 32ms period, which is orders of magnitude off
 * from the dozens-of-seconds NUMA balancing period. Use the scheduler
 * stats only if the task is so new there are no NUMA statistics yet.
 */
static u64 numa_get_avg_runtime(struct task_struct *p, u64 *period)
{
	u64 runtime, delta, now;
	/* Use the start of this time slice to avoid calculations. */
	now = p->se.exec_start;
	runtime = p->se.sum_exec_runtime;

	if (p->last_task_numa_placement) {
		delta = runtime - p->last_sum_exec_runtime;
		*period = now - p->last_task_numa_placement;
	} else {
		delta = p->se.avg.runnable_avg_sum;
		*period = p->se.avg.runnable_avg_period;
	}

	p->last_sum_exec_runtime = runtime;
	p->last_task_numa_placement = now;

	return delta;
}

/*
 * Determine the preferred nid for a task in a numa_group. This needs to
 * be done in a way that produces consistent results with group_weight,
 * otherwise workloads might not converge.
 */
static int preferred_group_nid(struct task_struct *p, int nid)
{
	nodemask_t nodes;
	int dist;

	/* Direct connections between all NUMA nodes. */
	if (sched_numa_topology_type == NUMA_DIRECT)
		return nid;

	/*
	 * On a system with glueless mesh NUMA topology, group_weight
	 * scores nodes according to the number of NUMA hinting faults on
	 * both the node itself, and on nearby nodes.
	 */
	if (sched_numa_topology_type == NUMA_GLUELESS_MESH) {
		unsigned long score, max_score = 0;
		int node, max_node = nid;

		dist = sched_max_numa_distance;

		for_each_online_node(node) {
			score = group_weight(p, node, dist);
			if (score > max_score) {
				max_score = score;
				max_node = node;
			}
		}
		return max_node;
	}

	/*
	 * Finding the preferred nid in a system with NUMA backplane
	 * interconnect topology is more involved. The goal is to locate
	 * tasks from numa_groups near each other in the system, and
	 * untangle workloads from different sides of the system. This requires
	 * searching down the hierarchy of node groups, recursively searching
	 * inside the highest scoring group of nodes. The nodemask tricks
	 * keep the complexity of the search down.
	 */
	nodes = node_online_map;
	for (dist = sched_max_numa_distance; dist > LOCAL_DISTANCE; dist--) {
		unsigned long max_faults = 0;
		nodemask_t max_group = NODE_MASK_NONE;
		int a, b;

		/* Are there nodes at this distance from each other? */
		if (!find_numa_distance(dist))
			continue;

		for_each_node_mask(a, nodes) {
			unsigned long faults = 0;
			nodemask_t this_group;
			nodes_clear(this_group);

			/* Sum group's NUMA faults; includes a==b case. */
			for_each_node_mask(b, nodes) {
				if (node_distance(a, b) < dist) {
					faults += group_faults(p, b);
					node_set(b, this_group);
					node_clear(b, nodes);
				}
			}

			/* Remember the top group. */
			if (faults > max_faults) {
				max_faults = faults;
				max_group = this_group;
				/*
				 * subtle: at the smallest distance there is
				 * just one node left in each "group", the
				 * winner is the preferred nid.
				 */
				nid = a;
			}
		}
		/* Next round, evaluate the nodes within max_group. */
		nodes = max_group;
	}
	return nid;
}

static void task_numa_placement(struct task_struct *p)
{
	int seq, nid, max_nid = -1, max_group_nid = -1;
	unsigned long max_faults = 0, max_group_faults = 0;
	unsigned long fault_types[2] = { 0, 0 };
	unsigned long total_faults;
	u64 runtime, period;
	spinlock_t *group_lock = NULL;

	seq = ACCESS_ONCE(p->mm->numa_scan_seq);
	if (p->numa_scan_seq == seq)
		return;
	p->numa_scan_seq = seq;
	p->numa_scan_period_max = task_scan_max(p);

	total_faults = p->numa_faults_locality[0] +
		       p->numa_faults_locality[1];
	runtime = numa_get_avg_runtime(p, &period);

	/* If the task is part of a group prevent parallel updates to group stats */
	if (p->numa_group) {
		group_lock = &p->numa_group->lock;
		spin_lock_irq(group_lock);
	}

	/* Find the node with the highest number of faults */
	for_each_online_node(nid) {
		/* Keep track of the offsets in numa_faults array */
		int mem_idx, membuf_idx, cpu_idx, cpubuf_idx;
		unsigned long faults = 0, group_faults = 0;
		int priv;

		for (priv = 0; priv < NR_NUMA_HINT_FAULT_TYPES; priv++) {
			long diff, f_diff, f_weight;

			mem_idx = task_faults_idx(NUMA_MEM, nid, priv);
			membuf_idx = task_faults_idx(NUMA_MEMBUF, nid, priv);
			cpu_idx = task_faults_idx(NUMA_CPU, nid, priv);
			cpubuf_idx = task_faults_idx(NUMA_CPUBUF, nid, priv);

			/* Decay existing window, copy faults since last scan */
			diff = p->numa_faults[membuf_idx] - p->numa_faults[mem_idx] / 2;
			fault_types[priv] += p->numa_faults[membuf_idx];
			p->numa_faults[membuf_idx] = 0;

			/*
			 * Normalize the faults_from, so all tasks in a group
			 * count according to CPU use, instead of by the raw
			 * number of faults. Tasks with little runtime have
			 * little over-all impact on throughput, and thus their
			 * faults are less important.
			 */
			f_weight = div64_u64(runtime << 16, period + 1);
			f_weight = (f_weight * p->numa_faults[cpubuf_idx]) /
				   (total_faults + 1);
			f_diff = f_weight - p->numa_faults[cpu_idx] / 2;
			p->numa_faults[cpubuf_idx] = 0;

			p->numa_faults[mem_idx] += diff;
			p->numa_faults[cpu_idx] += f_diff;
			faults += p->numa_faults[mem_idx];
			p->total_numa_faults += diff;
			if (p->numa_group) {
				/*
				 * safe because we can only change our own group
				 *
				 * mem_idx represents the offset for a given
				 * nid and priv in a specific region because it
				 * is at the beginning of the numa_faults array.
				 */
				p->numa_group->faults[mem_idx] += diff;
				p->numa_group->faults_cpu[mem_idx] += f_diff;
				p->numa_group->total_faults += diff;
				group_faults += p->numa_group->faults[mem_idx];
			}
		}

		if (faults > max_faults) {
			max_faults = faults;
			max_nid = nid;
		}

		if (group_faults > max_group_faults) {
			max_group_faults = group_faults;
			max_group_nid = nid;
		}
	}

	update_task_scan_period(p, fault_types[0], fault_types[1]);

	if (p->numa_group) {
		update_numa_active_node_mask(p->numa_group);
		spin_unlock_irq(group_lock);
		max_nid = preferred_group_nid(p, max_group_nid);
	}

	if (max_faults) {
		/* Set the new preferred node */
		if (max_nid != p->numa_preferred_nid)
			sched_setnuma(p, max_nid);

		if (task_node(p) != p->numa_preferred_nid)
			numa_migrate_preferred(p);
	}
}

static inline int get_numa_group(struct numa_group *grp)
{
	return atomic_inc_not_zero(&grp->refcount);
}

static inline void put_numa_group(struct numa_group *grp)
{
	if (atomic_dec_and_test(&grp->refcount))
		kfree_rcu(grp, rcu);
}

static void task_numa_group(struct task_struct *p, int cpupid, int flags,
			int *priv)
{
	struct numa_group *grp, *my_grp;
	struct task_struct *tsk;
	bool join = false;
	int cpu = cpupid_to_cpu(cpupid);
	int i;

	if (unlikely(!p->numa_group)) {
		unsigned int size = sizeof(struct numa_group) +
				    4*nr_node_ids*sizeof(unsigned long);

		grp = kzalloc(size, GFP_KERNEL | __GFP_NOWARN);
		if (!grp)
			return;

		atomic_set(&grp->refcount, 1);
		spin_lock_init(&grp->lock);
		grp->gid = p->pid;
		/* Second half of the array tracks nids where faults happen */
		grp->faults_cpu = grp->faults + NR_NUMA_HINT_FAULT_TYPES *
						nr_node_ids;

		node_set(task_node(current), grp->active_nodes);

		for (i = 0; i < NR_NUMA_HINT_FAULT_STATS * nr_node_ids; i++)
			grp->faults[i] = p->numa_faults[i];

		grp->total_faults = p->total_numa_faults;

		grp->nr_tasks++;
		rcu_assign_pointer(p->numa_group, grp);
	}

	rcu_read_lock();
	tsk = ACCESS_ONCE(cpu_rq(cpu)->curr);

	if (!cpupid_match_pid(tsk, cpupid))
		goto no_join;

	grp = rcu_dereference(tsk->numa_group);
	if (!grp)
		goto no_join;

	my_grp = p->numa_group;
	if (grp == my_grp)
		goto no_join;

	/*
	 * Only join the other group if its bigger; if we're the bigger group,
	 * the other task will join us.
	 */
	if (my_grp->nr_tasks > grp->nr_tasks)
		goto no_join;

	/*
	 * Tie-break on the grp address.
	 */
	if (my_grp->nr_tasks == grp->nr_tasks && my_grp > grp)
		goto no_join;

	/* Always join threads in the same process. */
	if (tsk->mm == current->mm)
		join = true;

	/* Simple filter to avoid false positives due to PID collisions */
	if (flags & TNF_SHARED)
		join = true;

	/* Update priv based on whether false sharing was detected */
	*priv = !join;

	if (join && !get_numa_group(grp))
		goto no_join;

	rcu_read_unlock();

	if (!join)
		return;

	BUG_ON(irqs_disabled());
	double_lock_irq(&my_grp->lock, &grp->lock);

	for (i = 0; i < NR_NUMA_HINT_FAULT_STATS * nr_node_ids; i++) {
		my_grp->faults[i] -= p->numa_faults[i];
		grp->faults[i] += p->numa_faults[i];
	}
	my_grp->total_faults -= p->total_numa_faults;
	grp->total_faults += p->total_numa_faults;

	my_grp->nr_tasks--;
	grp->nr_tasks++;

	spin_unlock(&my_grp->lock);
	spin_unlock_irq(&grp->lock);

	rcu_assign_pointer(p->numa_group, grp);

	put_numa_group(my_grp);
	return;

no_join:
	rcu_read_unlock();
	return;
}

void task_numa_free(struct task_struct *p)
{
	struct numa_group *grp = p->numa_group;
	void *numa_faults = p->numa_faults;
	unsigned long flags;
	int i;

	if (grp) {
		spin_lock_irqsave(&grp->lock, flags);
		for (i = 0; i < NR_NUMA_HINT_FAULT_STATS * nr_node_ids; i++)
			grp->faults[i] -= p->numa_faults[i];
		grp->total_faults -= p->total_numa_faults;

		grp->nr_tasks--;
		spin_unlock_irqrestore(&grp->lock, flags);
		RCU_INIT_POINTER(p->numa_group, NULL);
		put_numa_group(grp);
	}

	p->numa_faults = NULL;
	kfree(numa_faults);
}

/*
 * Got a PROT_NONE fault for a page on @node.
 */
void task_numa_fault(int last_cpupid, int mem_node, int pages, int flags)
{
	struct task_struct *p = current;
	bool migrated = flags & TNF_MIGRATED;
	int cpu_node = task_node(current);
	int local = !!(flags & TNF_FAULT_LOCAL);
	int priv;

	if (!numabalancing_enabled)
		return;

	/* for example, ksmd faulting in a user's mm */
	if (!p->mm)
		return;

	/* Allocate buffer to track faults on a per-node basis */
	if (unlikely(!p->numa_faults)) {
		int size = sizeof(*p->numa_faults) *
			   NR_NUMA_HINT_FAULT_BUCKETS * nr_node_ids;

		p->numa_faults = kzalloc(size, GFP_KERNEL|__GFP_NOWARN);
		if (!p->numa_faults)
			return;

		p->total_numa_faults = 0;
		memset(p->numa_faults_locality, 0, sizeof(p->numa_faults_locality));
	}

	/*
	 * First accesses are treated as private, otherwise consider accesses
	 * to be private if the accessing pid has not changed
	 */
	if (unlikely(last_cpupid == (-1 & LAST_CPUPID_MASK))) {
		priv = 1;
	} else {
		priv = cpupid_match_pid(p, last_cpupid);
		if (!priv && !(flags & TNF_NO_GROUP))
			task_numa_group(p, last_cpupid, flags, &priv);
	}

	/*
	 * If a workload spans multiple NUMA nodes, a shared fault that
	 * occurs wholly within the set of nodes that the workload is
	 * actively using should be counted as local. This allows the
	 * scan rate to slow down when a workload has settled down.
	 */
	if (!priv && !local && p->numa_group &&
			node_isset(cpu_node, p->numa_group->active_nodes) &&
			node_isset(mem_node, p->numa_group->active_nodes))
		local = 1;

	task_numa_placement(p);

	/*
	 * Retry task to preferred node migration periodically, in case it
	 * case it previously failed, or the scheduler moved us.
	 */
	if (time_after(jiffies, p->numa_migrate_retry))
		numa_migrate_preferred(p);

	if (migrated)
		p->numa_pages_migrated += pages;
	if (flags & TNF_MIGRATE_FAIL)
		p->numa_faults_locality[2] += pages;

	p->numa_faults[task_faults_idx(NUMA_MEMBUF, mem_node, priv)] += pages;
	p->numa_faults[task_faults_idx(NUMA_CPUBUF, cpu_node, priv)] += pages;
	p->numa_faults_locality[local] += pages;
}

static void reset_ptenuma_scan(struct task_struct *p)
{
	ACCESS_ONCE(p->mm->numa_scan_seq)++;
	p->mm->numa_scan_offset = 0;
}

/*
 * The expensive part of numa migration is done from task_work context.
 * Triggered from task_tick_numa().
 */
void task_numa_work(struct callback_head *work)
{
	unsigned long migrate, next_scan, now = jiffies;
	struct task_struct *p = current;
	struct mm_struct *mm = p->mm;
	struct vm_area_struct *vma;
	unsigned long start, end;
	unsigned long nr_pte_updates = 0;
	long pages;

	WARN_ON_ONCE(p != container_of(work, struct task_struct, numa_work));

	work->next = work; /* protect against double add */
	/*
	 * Who cares about NUMA placement when they're dying.
	 *
	 * NOTE: make sure not to dereference p->mm before this check,
	 * exit_task_work() happens _after_ exit_mm() so we could be called
	 * without p->mm even though we still had it when we enqueued this
	 * work.
	 */
	if (p->flags & PF_EXITING)
		return;

	if (!mm->numa_next_scan) {
		mm->numa_next_scan = now +
			msecs_to_jiffies(sysctl_numa_balancing_scan_delay);
	}

	/*
	 * Enforce maximal scan/migration frequency..
	 */
	migrate = mm->numa_next_scan;
	if (time_before(now, migrate))
		return;

	if (p->numa_scan_period == 0) {
		p->numa_scan_period_max = task_scan_max(p);
		p->numa_scan_period = task_scan_min(p);
	}

	next_scan = now + msecs_to_jiffies(p->numa_scan_period);
	if (cmpxchg(&mm->numa_next_scan, migrate, next_scan) != migrate)
		return;

	/*
	 * Delay this task enough that another task of this mm will likely win
	 * the next time around.
	 */
	p->node_stamp += 2 * TICK_NSEC;

	start = mm->numa_scan_offset;
	pages = sysctl_numa_balancing_scan_size;
	pages <<= 20 - PAGE_SHIFT; /* MB in pages */
	if (!pages)
		return;

	down_read(&mm->mmap_sem);
	vma = find_vma(mm, start);
	if (!vma) {
		reset_ptenuma_scan(p);
		start = 0;
		vma = mm->mmap;
	}
	for (; vma; vma = vma->vm_next) {
		if (!vma_migratable(vma) || !vma_policy_mof(vma))
			continue;

		/*
		 * Shared library pages mapped by multiple processes are not
		 * migrated as it is expected they are cache replicated. Avoid
		 * hinting faults in read-only file-backed mappings or the vdso
		 * as migrating the pages will be of marginal benefit.
		 */
		if (!vma->vm_mm ||
		    (vma->vm_file && (vma->vm_flags & (VM_READ|VM_WRITE)) == (VM_READ)))
			continue;

		/*
		 * Skip inaccessible VMAs to avoid any confusion between
		 * PROT_NONE and NUMA hinting ptes
		 */
		if (!(vma->vm_flags & (VM_READ | VM_EXEC | VM_WRITE)))
			continue;

		do {
			start = max(start, vma->vm_start);
			end = ALIGN(start + (pages << PAGE_SHIFT), HPAGE_SIZE);
			end = min(end, vma->vm_end);
			nr_pte_updates += change_prot_numa(vma, start, end);

			/*
			 * Scan sysctl_numa_balancing_scan_size but ensure that
			 * at least one PTE is updated so that unused virtual
			 * address space is quickly skipped.
			 */
			if (nr_pte_updates)
				pages -= (end - start) >> PAGE_SHIFT;

			start = end;
			if (pages <= 0)
				goto out;

			cond_resched();
		} while (end != vma->vm_end);
	}

out:
	/*
	 * It is possible to reach the end of the VMA list but the last few
	 * VMAs are not guaranteed to the vma_migratable. If they are not, we
	 * would find the !migratable VMA on the next scan but not reset the
	 * scanner to the start so check it now.
	 */
	if (vma)
		mm->numa_scan_offset = start;
	else
		reset_ptenuma_scan(p);
	up_read(&mm->mmap_sem);
}

/*
 * Drive the periodic memory faults..
 */
void task_tick_numa(struct rq *rq, struct task_struct *curr)
{
	struct callback_head *work = &curr->numa_work;
	u64 period, now;

	/*
	 * We don't care about NUMA placement if we don't have memory.
	 */
	if (!curr->mm || (curr->flags & PF_EXITING) || work->next != work)
		return;

	/*
	 * Using runtime rather than walltime has the dual advantage that
	 * we (mostly) drive the selection from busy threads and that the
	 * task needs to have done some actual work before we bother with
	 * NUMA placement.
	 */
	now = curr->se.sum_exec_runtime;
	period = (u64)curr->numa_scan_period * NSEC_PER_MSEC;

	if (now - curr->node_stamp > period) {
		if (!curr->node_stamp)
			curr->numa_scan_period = task_scan_min(curr);
		curr->node_stamp += period;

		if (!time_before(jiffies, curr->mm->numa_next_scan)) {
			init_task_work(work, task_numa_work); /* TODO: move this into sched_fork() */
			task_work_add(curr, work, true);
		}
	}
}
#else
static void task_tick_numa(struct rq *rq, struct task_struct *curr)
{
}

static inline void account_numa_enqueue(struct rq *rq, struct task_struct *p)
{
}

static inline void account_numa_dequeue(struct rq *rq, struct task_struct *p)
{
}
#endif /* CONFIG_NUMA_BALANCING */

static void
account_entity_enqueue(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	update_load_add(&cfs_rq->load, se->load.weight);
	if (!parent_entity(se))
		update_load_add(&rq_of(cfs_rq)->load, se->load.weight);
#ifdef CONFIG_SMP
	if (entity_is_task(se)) {
		struct rq *rq = rq_of(cfs_rq);

		account_numa_enqueue(rq, task_of(se));
		list_add(&se->group_node, &rq->cfs_tasks);
	}
#endif
	cfs_rq->nr_running++;
}

static void
account_entity_dequeue(struct cfs_rq *cfs_rq, struct sched_entity *se)
{
	update_load_sub(&cfs_rq->load, se->load.weight);
	if (!parent_entity(se))
		update_load_sub(&rq_of(cfs_rq)->load, se->load.weight);
	if (entity_is_task(se)) {
		account_numa_dequeue(rq_of(cfs_rq), task_of(se));
		list_del_init(&se->group_node);
	}
	cfs_rq->nr_running--;
}

#ifdef CONFIG_FAIR_GROUP_SCHED
# ifdef CONFIG_SMP
static inline long calc_tg_weight(struct task_group *tg, struct cfs_rq *cfs_rq)
{
	long tg_weight;

	/*
	 * Use this CPU's actual weight instead of the last load_contribution
	 * to gain a more accurate current total weight. See
	 * update_cfs_rq_load_contribution().
	 */
	tg_weight = atomic_long_read(&tg->load_avg);
	tg_weight -= cfs_rq->tg_load_contrib;
	tg_weight += cfs_rq->load.weight;

	return tg_weight;
}

static long calc_cfs_shares(struct cfs_rq *cfs_rq, struct task_group *tg)
{
	long tg_weight, load, shares;

	tg_weight = calc_tg_weight(tg, cfs_rq);
	load = cfs_rq->load.weight;

	shares = (tg->shares * load);
	if (tg_weight)
		shares /= tg_weight;

	if (shares < MIN_SHARES)
		shares = MIN_SHARES;
	if (shares > tg->shares)
		shares = tg->shares;

	return shares;
}
# else /* CONFIG_SMP */
static inline long calc_cfs_shares(struct cfs_rq *cfs_rq, struct task_group *tg)
{
	return tg->shares;
}
# endif /* CONFIG_SMP */
static void reweight_entity(struct cfs_rq *cfs_rq, struct sched_entity *se,
			    unsigned long weight)
{
	if (se->on_rq) {
		/* commit outstanding execution time */
		if (cfs_rq->curr == se)
			update_curr(cfs_rq);
		account_entity_dequeue(cfs_rq, se);
	}

	update_load_set(&se->load, weight);

	if (se->on_rq)
		account_entity_enqueue(cfs_rq, se);
}

static inline int throttled_hierarchy(struct cfs_rq *cfs_rq);

static void update_cfs_shares(struct cfs_rq *cfs_rq)
{
	struct task_group *tg;
	struct sched_entity *se;
	long shares;

	tg = cfs_rq->tg;
	se = tg->se[cpu_of(rq_of(cfs_rq))];
	if (!se || throttled_hierarchy(cfs_rq))
		return;
#ifndef CONFIG_SMP
	if (likely(se->load.weight == tg->shares))
		return;
#endif
	shares = calc_cfs_shares(cfs_rq, tg);

	reweight_entity(cfs_rq_of(se), se, shares);
}
#else /* CONFIG_FAIR_GROUP_SCHED */
static inline void update_cfs_shares(struct cfs_rq *cfs_rq)
{
}
#endif /* CONFIG_FAIR_GROUP_SCHED */

#ifdef CONFIG_SMP
/*
 * We choose a half-life close to 1 scheduling period.
 * Note: The tables below are dependent on this value.
 */
#define LOAD_AVG_PERIOD 32
#define LOAD_AVG_MAX 47742 /* maximum possible load avg */
#define LOAD_AVG_MAX_N 345 /* number of full periods to produce LOAD_MAX_AVG */

/* Precomputed fixed inverse multiplies for multiplication by y^n */
static const u32 runnable_avg_yN_inv[] = {
	0xffffffff, 0xfa83b2da, 0xf5257d14, 0xefe4b99a, 0xeac0c6e6, 0xe5b906e6,
	0xe0ccdeeb, 0xdbfbb796, 0xd744fcc9, 0xd2a81d91, 0xce248c14, 0xc9b9bd85,
	0xc5672a10, 0xc12c4cc9, 0xbd08a39e, 0xb8fbaf46, 0xb504f333, 0xb123f581,
	0xad583ee9, 0xa9a15ab4, 0xa5fed6a9, 0xa2704302, 0x9ef5325f, 0x9b8d39b9,
	0x9837f050, 0x94f4efa8, 0x91c3d373, 0x8ea4398a, 0x8b95c1e3, 0x88980e80,
	0x85aac367, 0x82cd8698,
};

/*
 * Precomputed \Sum y^k { 1<=k<=n }.  These are floor(true_value) to prevent
 * over-estimates when re-combining.
 */
static const u32 runnable_avg_yN_sum[] = {
	    0, 1002, 1982, 2941, 3880, 4798, 5697, 6576, 7437, 8279, 9103,
	 9909,10698,11470,12226,12966,13690,14398,15091,15769,16433,17082,
	17718,18340,18949,