mm/page-writeback.c



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/*
 * mm/page-writeback.c
 *
 * Copyright (C) 2002, Linus Torvalds.
 * Copyright (C) 2007 Red Hat, Inc., Peter Zijlstra <pzijlstr@redhat.com>
 *
 * Contains functions related to writing back dirty pages at the
 * address_space level.
 *
 * 10Apr2002	Andrew Morton
 *		Initial version
 */

#include <linux/kernel.h>
#include <linux/export.h>
#include <linux/spinlock.h>
#include <linux/fs.h>
#include <linux/mm.h>
#include <linux/swap.h>
#include <linux/slab.h>
#include <linux/pagemap.h>
#include <linux/writeback.h>
#include <linux/init.h>
#include <linux/backing-dev.h>
#include <linux/task_io_accounting_ops.h>
#include <linux/blkdev.h>
#include <linux/mpage.h>
#include <linux/rmap.h>
#include <linux/percpu.h>
#include <linux/notifier.h>
#include <linux/smp.h>
#include <linux/sysctl.h>
#include <linux/cpu.h>
#include <linux/syscalls.h>
#include <linux/buffer_head.h> /* __set_page_dirty_buffers */
#include <linux/pagevec.h>
#include <linux/timer.h>
#include <trace/events/writeback.h>

/*
 * Sleep at most 200ms at a time in balance_dirty_pages().
 */
#define MAX_PAUSE		max(HZ/5, 1)

/*
 * Try to keep balance_dirty_pages() call intervals higher than this many pages
 * by raising pause time to max_pause when falls below it.
 */
#define DIRTY_POLL_THRESH	(128 >> (PAGE_SHIFT - 10))

/*
 * Estimate write bandwidth at 200ms intervals.
 */
#define BANDWIDTH_INTERVAL	max(HZ/5, 1)

#define RATELIMIT_CALC_SHIFT	10

/*
 * After a CPU has dirtied this many pages, balance_dirty_pages_ratelimited
 * will look to see if it needs to force writeback or throttling.
 */
static long ratelimit_pages = 32;

/* The following parameters are exported via /proc/sys/vm */

/*
 * Start background writeback (via writeback threads) at this percentage
 */
int dirty_background_ratio = 10;

/*
 * dirty_background_bytes starts at 0 (disabled) so that it is a function of
 * dirty_background_ratio * the amount of dirtyable memory
 */
unsigned long dirty_background_bytes;

/*
 * free highmem will not be subtracted from the total free memory
 * for calculating free ratios if vm_highmem_is_dirtyable is true
 */
int vm_highmem_is_dirtyable;

/*
 * The generator of dirty data starts writeback at this percentage
 */
int vm_dirty_ratio = 20;

/*
 * vm_dirty_bytes starts at 0 (disabled) so that it is a function of
 * vm_dirty_ratio * the amount of dirtyable memory
 */
unsigned long vm_dirty_bytes;

/*
 * The interval between `kupdate'-style writebacks
 */
unsigned int dirty_writeback_interval = 5 * 100; /* centiseconds */

EXPORT_SYMBOL_GPL(dirty_writeback_interval);

/*
 * The longest time for which data is allowed to remain dirty
 */
unsigned int dirty_expire_interval = 30 * 100; /* centiseconds */

/*
 * Flag that makes the machine dump writes/reads and block dirtyings.
 */
int block_dump;

/*
 * Flag that puts the machine in "laptop mode". Doubles as a timeout in jiffies:
 * a full sync is triggered after this time elapses without any disk activity.
 */
int laptop_mode;

EXPORT_SYMBOL(laptop_mode);

/* End of sysctl-exported parameters */

unsigned long global_dirty_limit;

/*
 * Scale the writeback cache size proportional to the relative writeout speeds.
 *
 * We do this by keeping a floating proportion between BDIs, based on page
 * writeback completions [end_page_writeback()]. Those devices that write out
 * pages fastest will get the larger share, while the slower will get a smaller
 * share.
 *
 * We use page writeout completions because we are interested in getting rid of
 * dirty pages. Having them written out is the primary goal.
 *
 * We introduce a concept of time, a period over which we measure these events,
 * because demand can/will vary over time. The length of this period itself is
 * measured in page writeback completions.
 *
 */
static struct fprop_global writeout_completions;

static void writeout_period(unsigned long t);
/* Timer for aging of writeout_completions */
static struct timer_list writeout_period_timer =
		TIMER_DEFERRED_INITIALIZER(writeout_period, 0, 0);
static unsigned long writeout_period_time = 0;

/*
 * Length of period for aging writeout fractions of bdis. This is an
 * arbitrarily chosen number. The longer the period, the slower fractions will
 * reflect changes in current writeout rate.
 */
#define VM_COMPLETIONS_PERIOD_LEN (3*HZ)

/*
 * Work out the current dirty-memory clamping and background writeout
 * thresholds.
 *
 * The main aim here is to lower them aggressively if there is a lot of mapped
 * memory around.  To avoid stressing page reclaim with lots of unreclaimable
 * pages.  It is better to clamp down on writers than to start swapping, and
 * performing lots of scanning.
 *
 * We only allow 1/2 of the currently-unmapped memory to be dirtied.
 *
 * We don't permit the clamping level to fall below 5% - that is getting rather
 * excessive.
 *
 * We make sure that the background writeout level is below the adjusted
 * clamping level.
 */

/*
 * In a memory zone, there is a certain amount of pages we consider
 * available for the page cache, which is essentially the number of
 * free and reclaimable pages, minus some zone reserves to protect
 * lowmem and the ability to uphold the zone's watermarks without
 * requiring writeback.
 *
 * This number of dirtyable pages is the base value of which the
 * user-configurable dirty ratio is the effictive number of pages that
 * are allowed to be actually dirtied.  Per individual zone, or
 * globally by using the sum of dirtyable pages over all zones.
 *
 * Because the user is allowed to specify the dirty limit globally as
 * absolute number of bytes, calculating the per-zone dirty limit can
 * require translating the configured limit into a percentage of
 * global dirtyable memory first.
 */

static unsigned long highmem_dirtyable_memory(unsigned long total)
{
#ifdef CONFIG_HIGHMEM
	int node;
	unsigned long x = 0;

	for_each_node_state(node, N_HIGH_MEMORY) {
		struct zone *z =
			&NODE_DATA(node)->node_zones[ZONE_HIGHMEM];

		x += zone_page_state(z, NR_FREE_PAGES) +
		     zone_reclaimable_pages(z) - z->dirty_balance_reserve;
	}
	/*
	 * Make sure that the number of highmem pages is never larger
	 * than the number of the total dirtyable memory. This can only
	 * occur in very strange VM situations but we want to make sure
	 * that this does not occur.
	 */
	return min(x, total);
#else
	return 0;
#endif
}

/**
 * global_dirtyable_memory - number of globally dirtyable pages
 *
 * Returns the global number of pages potentially available for dirty
 * page cache.  This is the base value for the global dirty limits.
 */
static unsigned long global_dirtyable_memory(void)
{
	unsigned long x;

	x = global_page_state(NR_FREE_PAGES) + global_reclaimable_pages() -
	    dirty_balance_reserve;

	if (!vm_highmem_is_dirtyable)
		x -= highmem_dirtyable_memory(x);

	return x + 1;	/* Ensure that we never return 0 */
}

/*
 * global_dirty_limits - background-writeback and dirty-throttling thresholds
 *
 * Calculate the dirty thresholds based on sysctl parameters
 * - vm.dirty_background_ratio  or  vm.dirty_background_bytes
 * - vm.dirty_ratio             or  vm.dirty_bytes
 * The dirty limits will be lifted by 1/4 for PF_LESS_THROTTLE (ie. nfsd) and
 * real-time tasks.
 */
void global_dirty_limits(unsigned long *pbackground, unsigned long *pdirty)
{
	unsigned long background;
	unsigned long dirty;
	unsigned long uninitialized_var(available_memory);
	struct task_struct *tsk;

	if (!vm_dirty_bytes || !dirty_background_bytes)
		available_memory = global_dirtyable_memory();

	if (vm_dirty_bytes)
		dirty = DIV_ROUND_UP(vm_dirty_bytes, PAGE_SIZE);
	else
		dirty = (vm_dirty_ratio * available_memory) / 100;

	if (dirty_background_bytes)
		background = DIV_ROUND_UP(dirty_background_bytes, PAGE_SIZE);
	else
		background = (dirty_background_ratio * available_memory) / 100;

	if (background >= dirty)
		background = dirty / 2;
	tsk = current;
	if (tsk->flags & PF_LESS_THROTTLE || rt_task(tsk)) {
		background += background / 4;
		dirty += dirty / 4;
	}
	*pbackground = background;
	*pdirty = dirty;
	trace_global_dirty_state(background, dirty);
}

/**
 * zone_dirtyable_memory - number of dirtyable pages in a zone
 * @zone: the zone
 *
 * Returns the zone's number of pages potentially available for dirty
 * page cache.  This is the base value for the per-zone dirty limits.
 */
static unsigned long zone_dirtyable_memory(struct zone *zone)
{
	/*
	 * The effective global number of dirtyable pages may exclude
	 * highmem as a big-picture measure to keep the ratio between
	 * dirty memory and lowmem reasonable.
	 *
	 * But this function is purely about the individual zone and a
	 * highmem zone can hold its share of dirty pages, so we don't
	 * care about vm_highmem_is_dirtyable here.
	 */
	return zone_page_state(zone, NR_FREE_PAGES) +
	       zone_reclaimable_pages(zone) -
	       zone->dirty_balance_reserve;
}

/**
 * zone_dirty_limit - maximum number of dirty pages allowed in a zone
 * @zone: the zone
 *
 * Returns the maximum number of dirty pages allowed in a zone, based
 * on the zone's dirtyable memory.
 */
static unsigned long zone_dirty_limit(struct zone *zone)
{
	unsigned long zone_memory = zone_dirtyable_memory(zone);
	struct task_struct *tsk = current;
	unsigned long dirty;

	if (vm_dirty_bytes)
		dirty = DIV_ROUND_UP(vm_dirty_bytes, PAGE_SIZE) *
			zone_memory / global_dirtyable_memory();
	else
		dirty = vm_dirty_ratio * zone_memory / 100;

	if (tsk->flags & PF_LESS_THROTTLE || rt_task(tsk))
		dirty += dirty / 4;

	return dirty;
}

/**
 * zone_dirty_ok - tells whether a zone is within its dirty limits
 * @zone: the zone to check
 *
 * Returns %true when the dirty pages in @zone are within the zone's
 * dirty limit, %false if the limit is exceeded.
 */
bool zone_dirty_ok(struct zone *zone)
{
	unsigned long limit = zone_dirty_limit(zone);

	return zone_page_state(zone, NR_FILE_DIRTY) +
	       zone_page_state(zone, NR_UNSTABLE_NFS) +
	       zone_page_state(zone, NR_WRITEBACK) <= limit;
}

int dirty_background_ratio_handler(struct ctl_table *table, int write,
		void __user *buffer, size_t *lenp,
		loff_t *ppos)
{
	int ret;

	ret = proc_dointvec_minmax(table, write, buffer, lenp, ppos);
	if (ret == 0 && write)
		dirty_background_bytes = 0;
	return ret;
}

int dirty_background_bytes_handler(struct ctl_table *table, int write,
		void __user *buffer, size_t *lenp,
		loff_t *ppos)
{
	int ret;

	ret = proc_doulongvec_minmax(table, write, buffer, lenp, ppos);
	if (ret == 0 && write)
		dirty_background_ratio = 0;
	return ret;
}

int dirty_ratio_handler(struct ctl_table *table, int write,
		void __user *buffer, size_t *lenp,
		loff_t *ppos)
{
	int old_ratio = vm_dirty_ratio;
	int ret;

	ret = proc_dointvec_minmax(table, write, buffer, lenp, ppos);
	if (ret == 0 && write && vm_dirty_ratio != old_ratio) {
		writeback_set_ratelimit();
		vm_dirty_bytes = 0;
	}
	return ret;
}

int dirty_bytes_handler(struct ctl_table *table, int write,
		void __user *buffer, size_t *lenp,
		loff_t *ppos)
{
	unsigned long old_bytes = vm_dirty_bytes;
	int ret;

	ret = proc_doulongvec_minmax(table, write, buffer, lenp, ppos);
	if (ret == 0 && write && vm_dirty_bytes != old_bytes) {
		writeback_set_ratelimit();
		vm_dirty_ratio = 0;
	}
	return ret;
}

static unsigned long wp_next_time(unsigned long cur_time)
{
	cur_time += VM_COMPLETIONS_PERIOD_LEN;
	/* 0 has a special meaning... */
	if (!cur_time)
		return 1;
	return cur_time;
}

/*
 * Increment the BDI's writeout completion count and the global writeout
 * completion count. Called from test_clear_page_writeback().
 */
static inline void __bdi_writeout_inc(struct backing_dev_info *bdi)
{
	__inc_bdi_stat(bdi, BDI_WRITTEN);
	__fprop_inc_percpu_max(&writeout_completions, &bdi->completions,
			       bdi->max_prop_frac);
	/* First event after period switching was turned off? */
	if (!unlikely(writeout_period_time)) {
		/*
		 * We can race with other __bdi_writeout_inc calls here but
		 * it does not cause any harm since the resulting time when
		 * timer will fire and what is in writeout_period_time will be
		 * roughly the same.
		 */
		writeout_period_time = wp_next_time(jiffies);
		mod_timer(&writeout_period_timer, writeout_period_time);
	}
}

void bdi_writeout_inc(struct backing_dev_info *bdi)
{
	unsigned long flags;

	local_irq_save(flags);
	__bdi_writeout_inc(bdi);
	local_irq_restore(flags);
}
EXPORT_SYMBOL_GPL(bdi_writeout_inc);

/*
 * Obtain an accurate fraction of the BDI's portion.
 */
static void bdi_writeout_fraction(struct backing_dev_info *bdi,
		long *numerator, long *denominator)
{
	fprop_fraction_percpu(&writeout_completions, &bdi->completions,
				numerator, denominator);
}

/*
 * On idle system, we can be called long after we scheduled because we use
 * deferred timers so count with missed periods.
 */
static void writeout_period(unsigned long t)
{
	int miss_periods = (jiffies - writeout_period_time) /
						 VM_COMPLETIONS_PERIOD_LEN;

	if (fprop_new_period(&writeout_completions, miss_periods + 1)) {
		writeout_period_time = wp_next_time(writeout_period_time +
				miss_periods * VM_COMPLETIONS_PERIOD_LEN);
		mod_timer(&writeout_period_timer, writeout_period_time);
	} else {
		/*
		 * Aging has zeroed all fractions. Stop wasting CPU on period
		 * updates.
		 */
		writeout_period_time = 0;
	}
}

/*
 * bdi_min_ratio keeps the sum of the minimum dirty shares of all
 * registered backing devices, which, for obvious reasons, can not
 * exceed 100%.
 */
static unsigned int bdi_min_ratio;

int bdi_set_min_ratio(struct backing_dev_info *bdi, unsigned int min_ratio)
{
	int ret = 0;

	spin_lock_bh(&bdi_lock);
	if (min_ratio > bdi->max_ratio) {
		ret = -EINVAL;
	} else {
		min_ratio -= bdi->min_ratio;
		if (bdi_min_ratio + min_ratio < 100) {
			bdi_min_ratio += min_ratio;
			bdi->min_ratio += min_ratio;
		} else {
			ret = -EINVAL;
		}
	}
	spin_unlock_bh(&bdi_lock);

	return ret;
}

int bdi_set_max_ratio(struct backing_dev_info *bdi, unsigned max_ratio)
{
	int ret = 0;

	if (max_ratio > 100)
		return -EINVAL;

	spin_lock_bh(&bdi_lock);
	if (bdi->min_ratio > max_ratio) {
		ret = -EINVAL;
	} else {
		bdi->max_ratio = max_ratio;
		bdi->max_prop_frac = (FPROP_FRAC_BASE * max_ratio) / 100;
	}
	spin_unlock_bh(&bdi_lock);

	return ret;
}
EXPORT_SYMBOL(bdi_set_max_ratio);

static unsigned long dirty_freerun_ceiling(unsigned long thresh,
					   unsigned long bg_thresh)
{
	return (thresh + bg_thresh) / 2;
}

static unsigned long hard_dirty_limit(unsigned long thresh)
{
	return max(thresh, global_dirty_limit);
}

/**
 * bdi_dirty_limit - @bdi's share of dirty throttling threshold
 * @bdi: the backing_dev_info to query
 * @dirty: global dirty limit in pages
 *
 * Returns @bdi's dirty limit in pages. The term "dirty" in the context of
 * dirty balancing includes all PG_dirty, PG_writeback and NFS unstable pages.
 *
 * Note that balance_dirty_pages() will only seriously take it as a hard limit
 * when sleeping max_pause per page is not enough to keep the dirty pages under
 * control. For example, when the device is completely stalled due to some error
 * conditions, or when there are 1000 dd tasks writing to a slow 10MB/s USB key.
 * In the other normal situations, it acts more gently by throttling the tasks
 * more (rather than completely block them) when the bdi dirty pages go high.
 *
 * It allocates high/low dirty limits to fast/slow devices, in order to prevent
 * - starving fast devices
 * - piling up dirty pages (that will take long time to sync) on slow devices
 *
 * The bdi's share of dirty limit will be adapting to its throughput and
 * bounded by the bdi->min_ratio and/or bdi->max_ratio parameters, if set.
 */
unsigned long bdi_dirty_limit(struct backing_dev_info *bdi, unsigned long dirty)
{
	u64 bdi_dirty;
	long numerator, denominator;

	/*
	 * Calculate this BDI's share of the dirty ratio.
	 */
	bdi_writeout_fraction(bdi, &numerator, &denominator);

	bdi_dirty = (dirty * (100 - bdi_min_ratio)) / 100;
	bdi_dirty *= numerator;
	do_div(bdi_dirty, denominator);

	bdi_dirty += (dirty * bdi->min_ratio) / 100;
	if (bdi_dirty > (dirty * bdi->max_ratio) / 100)
		bdi_dirty = dirty * bdi->max_ratio / 100;

	return bdi_dirty;
}

/*
 * Dirty position control.
 *
 * (o) global/bdi setpoints
 *
 * We want the dirty pages be balanced around the global/bdi setpoints.
 * When the number of dirty pages is higher/lower than the setpoint, the
 * dirty position control ratio (and hence task dirty ratelimit) will be
 * decreased/increased to bring the dirty pages back to the setpoint.
 *
 *     pos_ratio = 1 << RATELIMIT_CALC_SHIFT
 *
 *     if (dirty < setpoint) scale up   pos_ratio
 *     if (dirty > setpoint) scale down pos_ratio
 *
 *     if (bdi_dirty < bdi_setpoint) scale up   pos_ratio
 *     if (bdi_dirty > bdi_setpoint) scale down pos_ratio
 *
 *     task_ratelimit = dirty_ratelimit * pos_ratio >> RATELIMIT_CALC_SHIFT
 *
 * (o) global control line
 *
 *     ^ pos_ratio
 *     |
 *     |            |<===== global dirty control scope ======>|
 * 2.0 .............*
 *     |            .*
 *     |            . *
 *     |            .   *
 *     |            .     *
 *     |            .        *
 *     |            .            *
 * 1.0 ................................*
 *     |            .                  .     *
 *     |            .                  .          *
 *     |            .                  .              *
 *     |            .                  .                 *
 *     |            .                  .                    *
 *   0 +------------.------------------.----------------------*------------->
 *           freerun^          setpoint^                 limit^   dirty pages
 *
 * (o) bdi control line
 *
 *     ^ pos_ratio
 *     |
 *     |            *
 *     |              *
 *     |                *
 *     |                  *
 *     |                    * |<=========== span ============>|
 * 1.0 .......................*
 *     |                      . *
 *     |                      .   *
 *     |                      .     *
 *     |                      .       *
 *     |                      .         *
 *     |                      .           *
 *     |                      .             *
 *     |                      .               *
 *     |                      .                 *
 *     |                      .                   *
 *     |                      .                     *
 * 1/4 ...............................................* * * * * * * * * * * *
 *     |                      .                         .
 *     |                      .                           .
 *     |                      .                             .
 *   0 +----------------------.-------------------------------.------------->
 *                bdi_setpoint^                    x_intercept^
 *
 * The bdi control line won't drop below pos_ratio=1/4, so that bdi_dirty can
 * be smoothly throttled down to normal if it starts high in situations like
 * - start writing to a slow SD card and a fast disk at the same time. The SD
 *   card's bdi_dirty may rush to many times higher than bdi_setpoint.
 * - the bdi dirty thresh drops quickly due to change of JBOD workload
 */
static unsigned long bdi_position_ratio(struct backing_dev_info *bdi,
					unsigned long thresh,
					unsigned long bg_thresh,
					unsigned long dirty,
					unsigned long bdi_thresh,
					unsigned long bdi_dirty)
{
	unsigned long write_bw = bdi->avg_write_bandwidth;
	unsigned long freerun = dirty_freerun_ceiling(thresh, bg_thresh);
	unsigned long limit = hard_dirty_limit(thresh);
	unsigned long x_intercept;
	unsigned long setpoint;		/* dirty pages' target balance point */
	unsigned long bdi_setpoint;
	unsigned long span;
	long long pos_ratio;		/* for scaling up/down the rate limit */
	long x;

	if (unlikely(dirty >= limit))
		return 0;

	/*
	 * global setpoint
	 *
	 *                           setpoint - dirty 3
	 *        f(dirty) := 1.0 + (----------------)
	 *                           limit - setpoint
	 *
	 * it's a 3rd order polynomial that subjects to
	 *
	 * (1) f(freerun)  = 2.0 => rampup dirty_ratelimit reasonably fast
	 * (2) f(setpoint) = 1.0 => the balance point
	 * (3) f(limit)    = 0   => the hard limit
	 * (4) df/dx      <= 0	 => negative feedback control
	 * (5) the closer to setpoint, the smaller |df/dx| (and the reverse)
	 *     => fast response on large errors; small oscillation near setpoint
	 */
	setpoint = (freerun + limit) / 2;
	x = div_s64((setpoint - dirty) << RATELIMIT_CALC_SHIFT,
		    limit - setpoint + 1);
	pos_ratio = x;
	pos_ratio = pos_ratio * x >> RATELIMIT_CALC_SHIFT;
	pos_ratio = pos_ratio * x >> RATELIMIT_CALC_SHIFT;
	pos_ratio += 1 << RATELIMIT_CALC_SHIFT;

	/*
	 * We have computed basic pos_ratio above based on global situation. If
	 * the bdi is over/under its share of dirty pages, we want to scale
	 * pos_ratio further down/up. That is done by the following mechanism.
	 */

	/*
	 * bdi setpoint
	 *
	 *        f(bdi_dirty) := 1.0 + k * (bdi_dirty - bdi_setpoint)
	 *
	 *                        x_intercept - bdi_dirty
	 *                     := --------------------------
	 *                        x_intercept - bdi_setpoint
	 *
	 * The main bdi control line is a linear function that subjects to
	 *
	 * (1) f(bdi_setpoint) = 1.0
	 * (2) k = - 1 / (8 * write_bw)  (in single bdi case)
	 *     or equally: x_intercept = bdi_setpoint + 8 * write_bw
	 *
	 * For single bdi case, the dirty pages are observed to fluctuate
	 * regularly within range
	 *        [bdi_setpoint - write_bw/2, bdi_setpoint + write_bw/2]
	 * for various filesystems, where (2) can yield in a reasonable 12.5%
	 * fluctuation range for pos_ratio.
	 *
	 * For JBOD case, bdi_thresh (not bdi_dirty!) could fluctuate up to its
	 * own size, so move the slope over accordingly and choose a slope that
	 * yields 100% pos_ratio fluctuation on suddenly doubled bdi_thresh.
	 */
	if (unlikely(bdi_thresh > thresh))
		bdi_thresh = thresh;
	/*
	 * It's very possible that bdi_thresh is close to 0 not because the
	 * device is slow, but that it has remained inactive for long time.
	 * Honour such devices a reasonable good (hopefully IO efficient)
	 * threshold, so that the occasional writes won't be blocked and active
	 * writes can rampup the threshold quickly.
	 */
	bdi_thresh = max(bdi_thresh, (limit - dirty) / 8);
	/*
	 * scale global setpoint to bdi's:
	 *	bdi_setpoint = setpoint * bdi_thresh / thresh
	 */
	x = div_u64((u64)bdi_thresh << 16, thresh + 1);
	bdi_setpoint = setpoint * (u64)x >> 16;
	/*
	 * Use span=(8*write_bw) in single bdi case as indicated by
	 * (thresh - bdi_thresh ~= 0) and transit to bdi_thresh in JBOD case.
	 *
	 *        bdi_thresh                    thresh - bdi_thresh
	 * span = ---------- * (8 * write_bw) + ------------------- * bdi_thresh
	 *          thresh                            thresh
	 */
	span = (thresh - bdi_thresh + 8 * write_bw) * (u64)x >> 16;
	x_intercept = bdi_setpoint + span;

	if (bdi_dirty < x_intercept - span / 4) {
		pos_ratio = div_u64(pos_ratio * (x_intercept - bdi_dirty),
				    x_intercept - bdi_setpoint + 1);
	} else
		pos_ratio /= 4;

	/*
	 * bdi reserve area, safeguard against dirty pool underrun and disk idle
	 * It may push the desired control point of global dirty pages higher
	 * than setpoint.
	 */
	x_intercept = bdi_thresh / 2;
	if (bdi_dirty < x_intercept) {
		if (bdi_dirty > x_intercept / 8)
			pos_ratio = div_u64(pos_ratio * x_intercept, bdi_dirty);
		else
			pos_ratio *= 8;
	}

	return pos_ratio;
}

static void bdi_update_write_bandwidth(struct backing_dev_info *bdi,
				       unsigned long elapsed,
				       unsigned long written)
{
	const unsigned long period = roundup_pow_of_two(3 * HZ);
	unsigned long avg = bdi->avg_write_bandwidth;
	unsigned long old = bdi->write_bandwidth;
	u64 bw;

	/*
	 * bw = written * HZ / elapsed
	 *
	 *                   bw * elapsed + write_bandwidth * (period - elapsed)
	 * write_bandwidth = ---------------------------------------------------
	 *                                          period
	 */
	bw = written - bdi->written_stamp;
	bw *= HZ;
	if (unlikely(elapsed > period)) {
		do_div(bw, elapsed);
		avg = bw;
		goto out;
	}
	bw += (u64)bdi->write_bandwidth * (period - elapsed);
	bw >>= ilog2(period);

	/*
	 * one more level of smoothing, for filtering out sudden spikes
	 */
	if (avg > old && old >= (unsigned long)bw)
		avg -= (avg - old) >> 3;

	if (avg < old && old <= (unsigned long)bw)
		avg += (old - avg) >> 3;

out:
	bdi->write_bandwidth = bw;
	bdi->avg_write_bandwidth = avg;
}

/*
 * The global dirtyable memory and dirty threshold could be suddenly knocked
 * down by a large amount (eg. on the startup of KVM in a swapless system).
 * This may throw the system into deep dirty exceeded state and throttle
 * heavy/light dirtiers alike. To retain good responsiveness, maintain
 * global_dirty_limit for tracking slowly down to the knocked down dirty
 * threshold.
 */
static void update_dirty_limit(unsigned long thresh, unsigned long dirty)
{
	unsigned long limit = global_dirty_limit;

	/*
	 * Follow up in one step.
	 */
	if (limit < thresh) {
		limit = thresh;
		goto update;
	}

	/*
	 * Follow down slowly. Use the higher one as the target, because thresh
	 * may drop below dirty. This is exactly the reason to introduce
	 * global_dirty_limit which is guaranteed to lie above the dirty pages.
	 */
	thresh = max(thresh, dirty);
	if (limit > thresh) {
		limit -= (limit - thresh) >> 5;
		goto update;
	}
	return;
update:
	global_dirty_limit = limit;
}

static void global_update_bandwidth(unsigned long thresh,
				    unsigned long dirty,
				    unsigned long now)
{
	static DEFINE_SPINLOCK(dirty_lock);
	static unsigned long update_time;

	/*
	 * check locklessly first to optimize away locking for the most time
	 */
	if (time_before(now, update_time + BANDWIDTH_INTERVAL))
		return;

	spin_lock(&dirty_lock);
	if (time_after_eq(now, update_time + BANDWIDTH_INTERVAL)) {
		update_dirty_limit(thresh, dirty);
		update_time = now;
	}
	spin_unlock(&dirty_lock);
}

/*
 * Maintain bdi->dirty_ratelimit, the base dirty throttle rate.
 *
 * Normal bdi tasks will be curbed at or below it in long term.
 * Obviously it should be around (write_bw / N) when there are N dd tasks.
 */
static void bdi_update_dirty_ratelimit(struct backing_dev_info *bdi,
				       unsigned long thresh,
				       unsigned long bg_thresh,
				       unsigned long dirty,
				       unsigned long bdi_thresh,
				       unsigned long bdi_dirty,
				       unsigned long dirtied,
				       unsigned long elapsed)
{
	unsigned long freerun = dirty_freerun_ceiling(thresh, bg_thresh);
	unsigned long limit = hard_dirty_limit(thresh);
	unsigned long setpoint = (freerun + limit) / 2;
	unsigned long write_bw = bdi->avg_write_bandwidth;
	unsigned long dirty_ratelimit = bdi->dirty_ratelimit;
	unsigned long dirty_rate;
	unsigned long task_ratelimit;
	unsigned long balanced_dirty_ratelimit;
	unsigned long pos_ratio;
	unsigned long step;
	unsigned long x;

	/*
	 * The dirty rate will match the writeout rate in long term, except
	 * when dirty pages are truncated by userspace or re-dirtied by FS.
	 */
	dirty_rate = (dirtied - bdi->dirtied_stamp) * HZ / elapsed;

	pos_ratio = bdi_position_ratio(bdi, thresh, bg_thresh, dirty,
				       bdi_thresh, bdi_dirty);
	/*
	 * task_ratelimit reflects each dd's dirty rate for the past 200ms.
	 */
	task_ratelimit = (u64)dirty_ratelimit *
					pos_ratio >> RATELIMIT_CALC_SHIFT;
	task_ratelimit++; /* it helps rampup dirty_ratelimit from tiny values */

	/*
	 * A linear estimation of the "balanced" throttle rate. The theory is,
	 * if there are N dd tasks, each throttled at task_ratelimit, the bdi's
	 * dirty_rate will be measured to be (N * task_ratelimit). So the below
	 * formula will yield the balanced rate limit (write_bw / N).
	 *
	 * Note that the expanded form is not a pure rate feedback:
	 *	rate_(i+1) = rate_(i) * (write_bw / dirty_rate)		     (1)
	 * but also takes pos_ratio into account:
	 *	rate_(i+1) = rate_(i) * (write_bw / dirty_rate) * pos_ratio  (2)
	 *
	 * (1) is not realistic because pos_ratio also takes part in balancing
	 * the dirty rate.  Consider the state
	 *	pos_ratio = 0.5						     (3)
	 *	rate = 2 * (write_bw / N)				     (4)
	 * If (1) is used, it will stuck in that state! Because each dd will
	 * be throttled at
	 *	task_ratelimit = pos_ratio * rate = (write_bw / N)	     (5)
	 * yielding
	 *	dirty_rate = N * task_ratelimit = write_bw		     (6)
	 * put (6) into (1) we get
	 *	rate_(i+1) = rate_(i)					     (7)
	 *
	 * So we end up using (2) to always keep
	 *	rate_(i+1) ~= (write_bw / N)				     (8)
	 * regardless of the value of pos_ratio. As long as (8) is satisfied,
	 * pos_ratio is able to drive itself to 1.0, which is not only where
	 * the dirty count meet the setpoint, but also where the slope of
	 * pos_ratio is most flat and hence task_ratelimit is least fluctuated.
	 */
	balanced_dirty_ratelimit = div_u64((u64)task_ratelimit * write_bw,
					   dirty_rate | 1);
	/*
	 * balanced_dirty_ratelimit ~= (write_bw / N) <= write_bw
	 */
	if (unlikely(balanced_dirty_ratelimit > write_bw))
		balanced_dirty_ratelimit = write_bw;

	/*
	 * We could safely do this and return immediately:
	 *
	 *	bdi->dirty_ratelimit = balanced_dirty_ratelimit;
	 *
	 * However to get a more stable dirty_ratelimit, the below elaborated
	 * code makes use of task_ratelimit to filter out singular points and
	 * limit the step size.
	 *
	 * The below code essentially only uses the relative value of
	 *
	 *	task_ratelimit - dirty_ratelimit
	 *	= (pos_ratio - 1) * dirty_ratelimit
	 *
	 * which reflects the direction and size of dirty position error.
	 */

	/*
	 * dirty_ratelimit will follow balanced_dirty_ratelimit iff
	 * task_ratelimit is on the same side of dirty_ratelimit, too.
	 * For example, when
	 * - dirty_ratelimit > balanced_dirty_ratelimit
	 * - dirty_ratelimit > task_ratelimit (dirty pages are above setpoint)
	 * lowering dirty_ratelimit will help meet both the position and rate
	 * control targets. Otherwise, don't update dirty_ratelimit if it will
	 * only help meet the rate target. After all, what the users ultimately
	 * feel and care are stable dirty rate and small position error.
	 *
	 * |task_ratelimit - dirty_ratelimit| is used to limit the step size
	 * and filter out the singular points of balanced_dirty_ratelimit. Which
	 * keeps jumping around randomly and can even leap far away at times
	 * due to the small 200ms estimation period of dirty_rate (we want to
	 * keep that period small to reduce time lags).
	 */
	step = 0;
	if (dirty < setpoint) {
		x = min(bdi->balanced_dirty_ratelimit,
			 min(balanced_dirty_ratelimit, task_ratelimit));
		if (dirty_ratelimit < x)
			step = x - dirty_ratelimit;
	} else {
		x = max(bdi->balanced_dirty_ratelimit,
			 max(balanced_dirty_ratelimit, task_ratelimit));
		if (dirty_ratelimit > x)
			step = dirty_ratelimit - x;
	}

	/*
	 * Don't pursue 100% rate matching. It's impossible since the balanced
	 * rate itself is constantly fluctuating. So decrease the track speed
	 * when it gets close to the target. Helps eliminate pointless tremors.
	 */
	step >>= dirty_ratelimit / (2 * step + 1);
	/*
	 * Limit the tracking speed to avoid overshooting.
	 */
	step = (step + 7) / 8;

	if (dirty_ratelimit < balanced_dirty_ratelimit)
		dirty_ratelimit += step;
	else
		dirty_ratelimit -= step;

	bdi->dirty_ratelimit = max(dirty_ratelimit, 1UL);
	bdi->balanced_dirty_ratelimit = balanced_dirty_ratelimit;

	trace_bdi_dirty_ratelimit(bdi, dirty_rate, task_ratelimit);
}

void __bdi_update_bandwidth(struct backing_dev_info *bdi,
			    unsigned long thresh,
			    unsigned long bg_thresh,
			    unsigned long dirty,
			    unsigned long bdi_thresh,
			    unsigned long bdi_dirty,
			    unsigned long start_time)
{
	unsigned long now = jiffies;
	unsigned long elapsed = now - bdi->bw_time_stamp;
	unsigned long dirtied;
	unsigned long written;

	/*
	 * rate-limit, only update once every 200ms.
	 */
	if (elapsed < BANDWIDTH_INTERVAL)
		return;

	dirtied = percpu_counter_read(&bdi->bdi_stat[BDI_DIRTIED]);
	written = percpu_counter_read(&bdi->bdi_stat[BDI_WRITTEN]);

	/*
	 * Skip quiet periods when disk bandwidth is under-utilized.
	 * (at least 1s idle time between two flusher runs)
	 */
	if (elapsed > HZ && time_before(bdi->bw_time_stamp, start_time))
		goto snapshot;

	if (thresh) {
		global_update_bandwidth(thresh, dirty, now);
		bdi_update_dirty_ratelimit(bdi, thresh, bg_thresh, dirty,
					   bdi_thresh, bdi_dirty,
					   dirtied, elapsed);
	}
	bdi_update_write_bandwidth(bdi, elapsed, written);

snapshot:
	bdi->dirtied_stamp = dirtied;
	bdi->written_stamp = written;
	bdi->bw_time_stamp = now;
}

static void bdi_update_bandwidth(struct backing_dev_info *bdi,
				 unsigned long thresh,
				 unsigned long bg_thresh,
				 unsigned long dirty,
				 unsigned long bdi_thresh,
				 unsigned long bdi_dirty,
				 unsigned long start_time)
{
	if (time_is_after_eq_jiffies(bdi->bw_time_stamp + BANDWIDTH_INTERVAL))
		return;
	spin_lock(&bdi->wb.list_lock);
	__bdi_update_bandwidth(bdi, thresh, bg_thresh, dirty,
			       bdi_thresh, bdi_dirty, start_time);
	spin_unlock(&bdi->wb.list_lock);
}

/*
 * After a task dirtied this many pages, balance_dirty_pages_ratelimited_nr()
 * will look to see if it needs to start dirty throttling.
 *
 * If dirty_poll_interval is too low, big NUMA machines will call the expensive
 * global_page_state() too often. So scale it near-sqrt to the safety margin
 * (the number of pages we may dirty without exceeding the dirty limits).
 */
static unsigned long dirty_poll_interval(unsigned long dirty,
					 unsigned long thresh)
{
	if (thresh > dirty)
		return 1UL << (ilog2(thresh - dirty) >> 1);

	return 1;
}

static long bdi_max_pause(struct backing_dev_info *bdi,
			  unsigned long bdi_dirty)
{
	long bw = bdi->avg_write_bandwidth;
	long t;

	/*
	 * Limit pause time for small memory systems. If sleeping for too long
	 * time, a small pool of dirty/writeback pages may go empty and disk go
	 * idle.
	 *
	 * 8 serves as the safety ratio.
	 */
	t = bdi_dirty / (1 + bw / roundup_pow_of_two(1 + HZ / 8));
	t++;

	return min_t(long, t, MAX_PAUSE);
}

static long bdi_min_pause(struct backing_dev_info *bdi,
			  long max_pause,
			  unsigned long task_ratelimit,
			  unsigned long dirty_ratelimit,
			  int *nr_dirtied_pause)
{
	long hi = ilog2(bdi->avg_write_bandwidth);
	long lo = ilog2(bdi->dirty_ratelimit);
	long t;		/* target pause */
	long pause;	/* estimated next pause */
	int pages;	/* target nr_dirtied_pause */

	/* target for 10ms pause on 1-dd case */
	t = max(1, HZ / 100);

	/*