/*
 * mm/page-writeback.c
 *
 * Copyright (C) 2002, Linus Torvalds.
 * Copyright (C) 2007 Red Hat, Inc., Peter Zijlstra
 *
 * 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 <linux/sched/rt.h>
#include <linux/mm_inline.h>
#include <trace/events/writeback.h>

#include "internal.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 */

struct wb_domain global_wb_domain;

/* consolidated parameters for balance_dirty_pages() and its subroutines */
struct dirty_throttle_control {
#ifdef CONFIG_CGROUP_WRITEBACK
        struct wb_domain        *dom;
        struct dirty_throttle_control *gdtc;    /* only set in memcg dtc's */
#endif
        struct bdi_writeback    *wb;
        struct fprop_local_percpu *wb_completions;

        unsigned long           avail;          /* dirtyable */
        unsigned long           dirty;          /* file_dirty + write + nfs */
        unsigned long           thresh;         /* dirty threshold */
        unsigned long           bg_thresh;      /* dirty background threshold */

        unsigned long           wb_dirty;       /* per-wb counterparts */
        unsigned long           wb_thresh;
        unsigned long           wb_bg_thresh;

        unsigned long           pos_ratio;
};

/*
 * 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)

#ifdef CONFIG_CGROUP_WRITEBACK

#define GDTC_INIT(__wb)         .wb = (__wb),                           \
                                .dom = &global_wb_domain,               \
                                .wb_completions = &(__wb)->completions

#define GDTC_INIT_NO_WB         .dom = &global_wb_domain

#define MDTC_INIT(__wb, __gdtc) .wb = (__wb),                           \
                                .dom = mem_cgroup_wb_domain(__wb),      \
                                .wb_completions = &(__wb)->memcg_completions, \
                                .gdtc = __gdtc

static bool mdtc_valid(struct dirty_throttle_control *dtc)
{
        return dtc->dom;
}

static struct wb_domain *dtc_dom(struct dirty_throttle_control *dtc)
{
        return dtc->dom;
}

static struct dirty_throttle_control *mdtc_gdtc(struct dirty_throttle_control *mdtc)
{
        return mdtc->gdtc;
}

static struct fprop_local_percpu *wb_memcg_completions(struct bdi_writeback *wb)
{
        return &wb->memcg_completions;
}

static void wb_min_max_ratio(struct bdi_writeback *wb,
                             unsigned long *minp, unsigned long *maxp)
{
        unsigned long this_bw = wb->avg_write_bandwidth;
        unsigned long tot_bw = atomic_long_read(&wb->bdi->tot_write_bandwidth);
        unsigned long long min = wb->bdi->min_ratio;
        unsigned long long max = wb->bdi->max_ratio;

        /*
         * @wb may already be clean by the time control reaches here and
         * the total may not include its bw.
         */
        if (this_bw < tot_bw) {
                if (min) {
                        min *= this_bw;
                        do_div(min, tot_bw);
                }
                if (max < 100) {
                        max *= this_bw;
                        do_div(max, tot_bw);
                }
        }

        *minp = min;
        *maxp = max;
}

#else   /* CONFIG_CGROUP_WRITEBACK */

#define GDTC_INIT(__wb)         .wb = (__wb),                           \
                                .wb_completions = &(__wb)->completions
#define GDTC_INIT_NO_WB
#define MDTC_INIT(__wb, __gdtc)

static bool mdtc_valid(struct dirty_throttle_control *dtc)
{
        return false;
}

static struct wb_domain *dtc_dom(struct dirty_throttle_control *dtc)
{
        return &global_wb_domain;
}

static struct dirty_throttle_control *mdtc_gdtc(struct dirty_throttle_control *mdtc)
{
        return NULL;
}

static struct fprop_local_percpu *wb_memcg_completions(struct bdi_writeback *wb)
{
        return NULL;
}

static void wb_min_max_ratio(struct bdi_writeback *wb,
                             unsigned long *minp, unsigned long *maxp)
{
        *minp = wb->bdi->min_ratio;
        *maxp = wb->bdi->max_ratio;
}

#endif  /* CONFIG_CGROUP_WRITEBACK */

/*
 * 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.
 */

/**
 * 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)
{
        unsigned long nr_pages;

        nr_pages = zone_page_state(zone, NR_FREE_PAGES);
        nr_pages -= min(nr_pages, zone->dirty_balance_reserve);

        nr_pages += zone_page_state(zone, NR_INACTIVE_FILE);
        nr_pages += zone_page_state(zone, NR_ACTIVE_FILE);

        return nr_pages;
}

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_dirtyable_memory(z);
        }
        /*
         * Unreclaimable memory (kernel memory or anonymous memory
         * without swap) can bring down the dirtyable pages below
         * the zone's dirty balance reserve and the above calculation
         * will underflow.  However we still want to add in nodes
         * which are below threshold (negative values) to get a more
         * accurate calculation but make sure that the total never
         * underflows.
         */
        if ((long)x < 0)
                x = 0;

        /*
         * 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);
        x -= min(x, dirty_balance_reserve);

        x += global_page_state(NR_INACTIVE_FILE);
        x += global_page_state(NR_ACTIVE_FILE);

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

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

/**
 * domain_dirty_limits - calculate thresh and bg_thresh for a wb_domain
 * @dtc: dirty_throttle_control of interest
 *
 * Calculate @dtc->thresh and ->bg_thresh considering
 * vm_dirty_{bytes|ratio} and dirty_background_{bytes|ratio}.  The caller
 * must ensure that @dtc->avail is set before calling this function.  The
 * dirty limits will be lifted by 1/4 for PF_LESS_THROTTLE (ie. nfsd) and
 * real-time tasks.
 */
static void domain_dirty_limits(struct dirty_throttle_control *dtc)
{
        const unsigned long available_memory = dtc->avail;
        struct dirty_throttle_control *gdtc = mdtc_gdtc(dtc);
        unsigned long bytes = vm_dirty_bytes;
        unsigned long bg_bytes = dirty_background_bytes;
        unsigned long ratio = vm_dirty_ratio;
        unsigned long bg_ratio = dirty_background_ratio;
        unsigned long thresh;
        unsigned long bg_thresh;
        struct task_struct *tsk;

        /* gdtc is !NULL iff @dtc is for memcg domain */
        if (gdtc) {
                unsigned long global_avail = gdtc->avail;

                /*
                 * The byte settings can't be applied directly to memcg
                 * domains.  Convert them to ratios by scaling against
                 * globally available memory.
                 */
                if (bytes)
                        ratio = min(DIV_ROUND_UP(bytes, PAGE_SIZE) * 100 /
                                    global_avail, 100UL);
                if (bg_bytes)
                        bg_ratio = min(DIV_ROUND_UP(bg_bytes, PAGE_SIZE) * 100 /
                                       global_avail, 100UL);
                bytes = bg_bytes = 0;
        }

        if (bytes)
                thresh = DIV_ROUND_UP(bytes, PAGE_SIZE);
        else
                thresh = (ratio * available_memory) / 100;

        if (bg_bytes)
                bg_thresh = DIV_ROUND_UP(bg_bytes, PAGE_SIZE);
        else
                bg_thresh = (bg_ratio * available_memory) / 100;

        if (bg_thresh >= thresh)
                bg_thresh = thresh / 2;
        tsk = current;
        if (tsk->flags & PF_LESS_THROTTLE || rt_task(tsk)) {
                bg_thresh += bg_thresh / 4;
                thresh += thresh / 4;
        }
        dtc->thresh = thresh;
        dtc->bg_thresh = bg_thresh;

        /* we should eventually report the domain in the TP */
        if (!gdtc)
                trace_global_dirty_state(bg_thresh, thresh);
}

/**
 * global_dirty_limits - background-writeback and dirty-throttling thresholds
 * @pbackground: out parameter for bg_thresh
 * @pdirty: out parameter for thresh
 *
 * Calculate bg_thresh and thresh for global_wb_domain.  See
 * domain_dirty_limits() for details.
 */
void global_dirty_limits(unsigned long *pbackground, unsigned long *pdirty)
{
        struct dirty_throttle_control gdtc = { GDTC_INIT_NO_WB };

        gdtc.avail = global_dirtyable_memory();
        domain_dirty_limits(&gdtc);

        *pbackground = gdtc.bg_thresh;
        *pdirty = gdtc.thresh;
}

/**
 * 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;
}

static void wb_domain_writeout_inc(struct wb_domain *dom,
                                   struct fprop_local_percpu *completions,
                                   unsigned int max_prop_frac)
{
        __fprop_inc_percpu_max(&dom->completions, completions,
                               max_prop_frac);
        /* First event after period switching was turned off? */
        if (!unlikely(dom->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.
                 */
                dom->period_time = wp_next_time(jiffies);
                mod_timer(&dom->period_timer, dom->period_time);
        }
}

/*
 * Increment @wb's writeout completion count and the global writeout
 * completion count. Called from test_clear_page_writeback().
 */
static inline void __wb_writeout_inc(struct bdi_writeback *wb)
{
        struct wb_domain *cgdom;

        __inc_wb_stat(wb, WB_WRITTEN);
        wb_domain_writeout_inc(&global_wb_domain, &wb->completions,
                               wb->bdi->max_prop_frac);

        cgdom = mem_cgroup_wb_domain(wb);
        if (cgdom)
                wb_domain_writeout_inc(cgdom, wb_memcg_completions(wb),
                                       wb->bdi->max_prop_frac);
}

void wb_writeout_inc(struct bdi_writeback *wb)
{
        unsigned long flags;

        local_irq_save(flags);
        __wb_writeout_inc(wb);
        local_irq_restore(flags);
}
EXPORT_SYMBOL_GPL(wb_writeout_inc);

/*
 * 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)
{
        struct wb_domain *dom = (void *)t;
        int miss_periods = (jiffies - dom->period_time) /
                                                 VM_COMPLETIONS_PERIOD_LEN;

        if (fprop_new_period(&dom->completions, miss_periods + 1)) {
                dom->period_time = wp_next_time(dom->period_time +
                                miss_periods * VM_COMPLETIONS_PERIOD_LEN);
                mod_timer(&dom->period_timer, dom->period_time);
        } else {
                /*
                 * Aging has zeroed all fractions. Stop wasting CPU on period
                 * updates.
                 */
                dom->period_time = 0;
        }
}

int wb_domain_init(struct wb_domain *dom, gfp_t gfp)
{
        memset(dom, 0, sizeof(*dom));

        spin_lock_init(&dom->lock);

        init_timer_deferrable(&dom->period_timer);
        dom->period_timer.function = writeout_period;
        dom->period_timer.data = (unsigned long)dom;

        dom->dirty_limit_tstamp = jiffies;

        return fprop_global_init(&dom->completions, gfp);
}

#ifdef CONFIG_CGROUP_WRITEBACK
void wb_domain_exit(struct wb_domain *dom)
{
        del_timer_sync(&dom->period_timer);
        fprop_global_destroy(&dom->completions);
}
#endif

/*
 * 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(struct wb_domain *dom,
                                      unsigned long thresh)
{
        return max(thresh, dom->dirty_limit);
}

/*
 * Memory which can be further allocated to a memcg domain is capped by
 * system-wide clean memory excluding the amount being used in the domain.
 */
static void mdtc_calc_avail(struct dirty_throttle_control *mdtc,
                            unsigned long filepages, unsigned long headroom)
{
        struct dirty_throttle_control *gdtc = mdtc_gdtc(mdtc);
        unsigned long clean = filepages - min(filepages, mdtc->dirty);
        unsigned long global_clean = gdtc->avail - min(gdtc->avail, gdtc->dirty);
        unsigned long other_clean = global_clean - min(global_clean, clean);

        mdtc->avail = filepages + min(headroom, other_clean);
}

/**
 * __wb_calc_thresh - @wb's share of dirty throttling threshold
 * @dtc: dirty_throttle_context of interest
 *
 * Returns @wb'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 wb 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 wb'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.
 */
static unsigned long __wb_calc_thresh(struct dirty_throttle_control *dtc)
{
        struct wb_domain *dom = dtc_dom(dtc);
        unsigned long thresh = dtc->thresh;
        u64 wb_thresh;
        long numerator, denominator;
        unsigned long wb_min_ratio, wb_max_ratio;

        /*
         * Calculate this BDI's share of the thresh ratio.
         */
        fprop_fraction_percpu(&dom->completions, dtc->wb_completions,
                              &numerator, &denominator);

        wb_thresh = (thresh * (100 - bdi_min_ratio)) / 100;
        wb_thresh *= numerator;
        do_div(wb_thresh, denominator);

        wb_min_max_ratio(dtc->wb, &wb_min_ratio, &wb_max_ratio);

        wb_thresh += (thresh * wb_min_ratio) / 100;
        if (wb_thresh > (thresh * wb_max_ratio) / 100)
                wb_thresh = thresh * wb_max_ratio / 100;

        return wb_thresh;
}

unsigned long wb_calc_thresh(struct bdi_writeback *wb, unsigned long thresh)
{
        struct dirty_throttle_control gdtc = { GDTC_INIT(wb),
                                               .thresh = thresh };
        return __wb_calc_thresh(&gdtc);
}

/*
 *                           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
 */
static long long pos_ratio_polynom(unsigned long setpoint,
                                          unsigned long dirty,
                                          unsigned long limit)
{
        long long pos_ratio;
        long x;

        x = div64_s64(((s64)setpoint - (s64)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;

        return clamp(pos_ratio, 0LL, 2LL << RATELIMIT_CALC_SHIFT);
}

/*
 * Dirty position control.
 *
 * (o) global/bdi setpoints
 *
 * We want the dirty pages be balanced around the global/wb 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 (wb_dirty < wb_setpoint) scale up   pos_ratio
 *     if (wb_dirty > wb_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) wb control line
 *
 *     ^ pos_ratio
 *     |
 *     |            *
 *     |              *
 *     |                *
 *     |                  *
 *     |                    * |<=========== span ============>|
 * 1.0 .......................*
 *     |                      . *
 *     |                      .   *
 *     |                      .     *
 *     |                      .       *
 *     |                      .         *
 *     |                      .           *
 *     |                      .             *
 *     |                      .               *
 *     |                      .                 *
 *     |                      .                   *
 *     |                      .                     *
 * 1/4 ...............................................* * * * * * * * * * * *
 *     |                      .                         .
 *     |                      .                           .
 *     |                      .                             .
 *   0 +----------------------.-------------------------------.------------->
 *                wb_setpoint^                    x_intercept^
 *
 * The wb control line won't drop below pos_ratio=1/4, so that wb_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 wb_dirty may rush to many times higher than wb_setpoint.
 * - the wb dirty thresh drops quickly due to change of JBOD workload
 */
static void wb_position_ratio(struct dirty_throttle_control *dtc)
{
        struct bdi_writeback *wb = dtc->wb;
        unsigned long write_bw = wb->avg_write_bandwidth;
        unsigned long freerun = dirty_freerun_ceiling(dtc->thresh, dtc->bg_thresh);
        unsigned long limit = hard_dirty_limit(dtc_dom(dtc), dtc->thresh);
        unsigned long wb_thresh = dtc->wb_thresh;
        unsigned long x_intercept;
        unsigned long setpoint;         /* dirty pages' target balance point */
        unsigned long wb_setpoint;
        unsigned long span;
        long long pos_ratio;            /* for scaling up/down the rate limit */
        long x;

        dtc->pos_ratio = 0;

        if (unlikely(dtc->dirty >= limit))
                return;

        /*
         * global setpoint
         *
         * See comment for pos_ratio_polynom().
         */
        setpoint = (freerun + limit) / 2;
        pos_ratio = pos_ratio_polynom(setpoint, dtc->dirty, limit);

        /*
         * The strictlimit feature is a tool preventing mistrusted filesystems
         * from growing a large number of dirty pages before throttling. For
         * such filesystems balance_dirty_pages always checks wb counters
         * against wb limits. Even if global "nr_dirty" is under "freerun".
         * This is especially important for fuse which sets bdi->max_ratio to
         * 1% by default. Without strictlimit feature, fuse writeback may
         * consume arbitrary amount of RAM because it is accounted in
         * NR_WRITEBACK_TEMP which is not involved in calculating "nr_dirty".
         *
         * Here, in wb_position_ratio(), we calculate pos_ratio based on
         * two values: wb_dirty and wb_thresh. Let's consider an example:
         * total amount of RAM is 16GB, bdi->max_ratio is equal to 1%, global
         * limits are set by default to 10% and 20% (background and throttle).
         * Then wb_thresh is 1% of 20% of 16GB. This amounts to ~8K pages.
         * wb_calc_thresh(wb, bg_thresh) is about ~4K pages. wb_setpoint is
         * about ~6K pages (as the average of background and throttle wb
         * limits). The 3rd order polynomial will provide positive feedback if
         * wb_dirty is under wb_setpoint and vice versa.
         *
         * Note, that we cannot use global counters in these calculations
         * because we want to throttle process writing to a strictlimit wb
         * much earlier than global "freerun" is reached (~23MB vs. ~2.3GB
         * in the example above).
         */
        if (unlikely(wb->bdi->capabilities & BDI_CAP_STRICTLIMIT)) {
                long long wb_pos_ratio;

                if (dtc->wb_dirty < 8) {
                        dtc->pos_ratio = min_t(long long, pos_ratio * 2,
                                           2 << RATELIMIT_CALC_SHIFT);
                        return;
                }

                if (dtc->wb_dirty >= wb_thresh)
                        return;

                wb_setpoint = dirty_freerun_ceiling(wb_thresh,
                                                    dtc->wb_bg_thresh);

                if (wb_setpoint == 0 || wb_setpoint == wb_thresh)
                        return;

                wb_pos_ratio = pos_ratio_polynom(wb_setpoint, dtc->wb_dirty,
                                                 wb_thresh);

                /*
                 * Typically, for strictlimit case, wb_setpoint << setpoint
                 * and pos_ratio >> wb_pos_ratio. In the other words global
                 * state ("dirty") is not limiting factor and we have to
                 * make decision based on wb counters. But there is an
                 * important case when global pos_ratio should get precedence:
                 * global limits are exceeded (e.g. due to activities on other
                 * wb's) while given strictlimit wb is below limit.
                 *
                 * "pos_ratio * wb_pos_ratio" would work for the case above,
                 * but it would look too non-natural for the case of all
                 * activity in the system coming from a single strictlimit wb
                 * with bdi->max_ratio == 100%.
                 *
                 * Note that min() below somewhat changes the dynamics of the
                 * control system. Normally, pos_ratio value can be well over 3
                 * (when globally we are at freerun and wb is well below wb
                 * setpoint). Now the maximum pos_ratio in the same situation
                 * is 2. We might want to tweak this if we observe the control
                 * system is too slow to adapt.
                 */
                dtc->pos_ratio = min(pos_ratio, wb_pos_ratio);
                return;
        }

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

        /*
         * wb setpoint
         *
         *        f(wb_dirty) := 1.0 + k * (wb_dirty - wb_setpoint)
         *
         *                        x_intercept - wb_dirty
         *                     := --------------------------
         *                        x_intercept - wb_setpoint
         *
         * The main wb control line is a linear function that subjects to
         *
         * (1) f(wb_setpoint) = 1.0
         * (2) k = - 1 / (8 * write_bw)  (in single wb case)
         *     or equally: x_intercept = wb_setpoint + 8 * write_bw
         *
         * For single wb case, the dirty pages are observed to fluctuate
         * regularly within range
         *        [wb_setpoint - write_bw/2, wb_setpoint + write_bw/2]
         * for various filesystems, where (2) can yield in a reasonable 12.5%
         * fluctuation range for pos_ratio.
         *
         * For JBOD case, wb_thresh (not wb_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 wb_thresh.
         */
        if (unlikely(wb_thresh > dtc->thresh))
                wb_thresh = dtc->thresh;
        /*
         * It's very possible that wb_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.
         */

        wb_thresh = max(wb_thresh, (limit - dtc->dirty) / 8);
        /*
         * scale global setpoint to wb's:
         *      wb_setpoint = setpoint * wb_thresh / thresh
         */
        x = div_u64((u64)wb_thresh << 16, dtc->thresh | 1);
        wb_setpoint = setpoint * (u64)x >> 16;
        /*
         * Use span=(8*write_bw) in single wb case as indicated by
         * (thresh - wb_thresh ~= 0) and transit to wb_thresh in JBOD case.
         *
         *        wb_thresh                    thresh - wb_thresh
         * span = --------- * (8 * write_bw) + ------------------ * wb_thresh
         *         thresh                           thresh
         */
        span = (dtc->thresh - wb_thresh + 8 * write_bw) * (u64)x >> 16;
        x_intercept = wb_setpoint + span;

        if (dtc->wb_dirty < x_intercept - span / 4) {
                pos_ratio = div64_u64(pos_ratio * (x_intercept - dtc->wb_dirty),
                                      (x_intercept - wb_setpoint) | 1);
        } else
                pos_ratio /= 4;

        /*
         * wb 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 = wb_thresh / 2;
        if (dtc->wb_dirty < x_intercept) {
                if (dtc->wb_dirty > x_intercept / 8)
                        pos_ratio = div_u64(pos_ratio * x_intercept,
                                            dtc->wb_dirty);
                else
                        pos_ratio *= 8;
        }

        dtc->pos_ratio = pos_ratio;
}

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

        /*
         * bw = written * HZ / elapsed
         *
         *                   bw * elapsed + write_bandwidth * (period - elapsed)
         * write_bandwidth = ---------------------------------------------------
         *                                          period
         *
         * @written may have decreased due to account_page_redirty().
         * Avoid underflowing @bw calculation.
         */
        bw = written - min(written, wb->written_stamp);
        bw *= HZ;
        if (unlikely(elapsed > period)) {
                do_div(bw, elapsed);
                avg = bw;
                goto out;
        }
        bw += (u64)wb->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:
        /* keep avg > 0 to guarantee that tot > 0 if there are dirty wbs */
        avg = max(avg, 1LU);
        if (wb_has_dirty_io(wb)) {
                long delta = avg - wb->avg_write_bandwidth;
                WARN_ON_ONCE(atomic_long_add_return(delta,
                                        &wb->bdi->tot_write_bandwidth) <= 0);
        }
        wb->write_bandwidth = bw;
        wb->avg_write_bandwidth = avg;
}

static void update_dirty_limit(struct dirty_throttle_control *dtc)
{
        struct wb_domain *dom = dtc_dom(dtc);
        unsigned long thresh = dtc->thresh;
        unsigned long limit = dom->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
         * dom->dirty_limit which is guaranteed to lie above the dirty pages.
         */
        thresh = max(thresh, dtc->dirty);
        if (limit > thresh) {
                limit -= (limit - thresh) >> 5;
                goto update;
        }
        return;
update:
        dom->dirty_limit = limit;
}

static void domain_update_bandwidth(struct dirty_throttle_control *dtc,
                                    unsigned long now)
{
        struct wb_domain *dom = dtc_dom(dtc);

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

        spin_lock(&dom->lock);
        if (time_after_eq(now, dom->dirty_limit_tstamp + BANDWIDTH_INTERVAL)) {
                update_dirty_limit(dtc);
                dom->dirty_limit_tstamp = now;
        }
        spin_unlock(&dom->lock);
}

/*
 * Maintain wb->dirty_ratelimit, the base dirty throttle rate.
 *
 * Normal wb 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 wb_update_dirty_ratelimit(struct dirty_throttle_control *dtc,
                                      unsigned long dirtied,
                                      unsigned long elapsed)
{
        struct bdi_writeback *wb = dtc->wb;
        unsigned long dirty = dtc->dirty;
        unsigned long freerun = dirty_freerun_ceiling(dtc->thresh, dtc->bg_thresh);
        unsigned long limit = hard_dirty_limit(dtc_dom(dtc), dtc->thresh);
        unsigned long setpoint = (freerun + limit) / 2;
        unsigned long write_bw = wb->avg_write_bandwidth;
        unsigned long dirty_ratelimit = wb->dirty_ratelimit;
        unsigned long dirty_rate;
        unsigned long task_ratelimit;
        unsigned long balanced_dirty_ratelimit;
        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 - wb->dirtied_stamp) * HZ / elapsed;

        /*
         * task_ratelimit reflects each dd's dirty rate for the past 200ms.
         */
        task_ratelimit = (u64)dirty_ratelimit *
                                        dtc->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 wb'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:
         *
         *      wb->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;

        /*
         * For strictlimit case, calculations above were based on wb counters
         * and limits (starting from pos_ratio = wb_position_ratio() and up to
         * balanced_dirty_ratelimit = task_ratelimit * write_bw / dirty_rate).
         * Hence, to calculate "step" properly, we have to use wb_dirty as
         * "dirty" and wb_setpoint as "setpoint".
         *
         * We rampup dirty_ratelimit forcibly if wb_dirty is low because
         * it's possible that wb_thresh is close to zero due to inactivity
         * of backing device.
         */
        if (unlikely(wb->bdi->capabilities & BDI_CAP_STRICTLIMIT)) {
                dirty = dtc->wb_dirty;
                if (dtc->wb_dirty < 8)
                        setpoint = dtc->wb_dirty + 1;
                else
                        setpoint = (dtc->wb_thresh + dtc->wb_bg_thresh) / 2;
        }

        if (dirty < setpoint) {
                x = min3(wb->balanced_dirty_ratelimit,
                         balanced_dirty_ratelimit, task_ratelimit);
                if (dirty_ratelimit < x)
                        step = x - dirty_ratelimit;
        } else {
                x = max3(wb->balanced_dirty_ratelimit,
                         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;

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

        trace_bdi_dirty_ratelimit(wb, dirty_rate, task_ratelimit);
}

static void __wb_update_bandwidth(struct dirty_throttle_control *gdtc,
                                  struct dirty_throttle_control *mdtc,
                                  unsigned long start_time,
                                  bool update_ratelimit)
{
        struct bdi_writeback *wb = gdtc->wb;
        unsigned long now = jiffies;
        unsigned long elapsed = now - wb->bw_time_stamp;
        unsigned long dirtied;
        unsigned long written;

        lockdep_assert_held(&wb->list_lock);

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

        dirtied = percpu_counter_read(&wb->stat[WB_DIRTIED]);
        written = percpu_counter_read(&wb->stat[WB_WRITTEN]);

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

        if (update_ratelimit) {
                domain_update_bandwidth(gdtc, now);
                wb_update_dirty_ratelimit(gdtc, dirtied, elapsed);

                /*
                 * @mdtc is always NULL if !CGROUP_WRITEBACK but the
                 * compiler has no way to figure that out.  Help it.
                 */
                if (IS_ENABLED(CONFIG_CGROUP_WRITEBACK) && mdtc) {
                        domain_update_bandwidth(mdtc, now);
                        wb_update_dirty_ratelimit(mdtc, dirtied, elapsed);
                }
        }
        wb_update_write_bandwidth(wb, elapsed, written);

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

void wb_update_bandwidth(struct bdi_writeback *wb, unsigned long start_time)
{
        struct dirty_throttle_control gdtc = { GDTC_INIT(wb) };

        __wb_update_bandwidth(&gdtc, NULL, start_time, false);
}

/*
 * After a task dirtied this many pages, balance_dirty_pages_ratelimited()
 * 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 unsigned long wb_max_pause(struct bdi_writeback *wb,
                                  unsigned long wb_dirty)
{
        unsigned long bw = wb->avg_write_bandwidth;
        unsigned 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 = wb_dirty / (1 + bw / roundup_pow_of_two(1 + HZ / 8));
        t++;

        return min_t(unsigned long, t, MAX_PAUSE);
}

static long wb_min_pause(struct bdi_writeback *wb,
                         long max_pause,
                         unsigned long task_ratelimit,
                         unsigned long dirty_ratelimit,
                         int *nr_dirtied_pause)
{
        long hi = ilog2(wb->avg_write_bandwidth);
        long lo = ilog2(wb->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);

        /*
         * Scale up pause time for concurrent dirtiers in order to reduce CPU
         * overheads.
         *
         * (N * 10ms) on 2^N concurrent tasks.
         */
        if (hi > lo)
                t += (hi - lo) * (10 * HZ) / 1024;

        /*
         * This is a bit convoluted. We try to base the next nr_dirtied_pause
         * on the much more stable dirty_ratelimit. However the next pause time
         * will be computed based on task_ratelimit and the two rate limits may
         * depart considerably at some time. Especially if task_ratelimit goes
         * below dirty_ratelimit/2 and the target pause is max_pause, the next
         * pause time will be max_pause*2 _trimmed down_ to max_pause.  As a
         * result task_ratelimit won't be executed faithfully, which could
         * eventually bring down dirty_ratelimit.
         *
         * We apply two rules to fix it up:
         * 1) try to estimate the next pause time and if necessary, use a lower
         *    nr_dirtied_pause so as not to exceed max_pause. When this happens,
         *    nr_dirtied_pause will be "dancing" with task_ratelimit.
         * 2) limit the target pause time to max_pause/2, so that the normal
         *    small fluctuations of task_ratelimit won't trigger rule (1) and
         *    nr_dirtied_pause will remain as stable as dirty_ratelimit.
         */
        t = min(t, 1 + max_pause / 2);
        pages = dirty_ratelimit * t / roundup_pow_of_two(HZ);

        /*
         * Tiny nr_dirtied_pause is found to hurt I/O performance in the test
         * case fio-mmap-randwrite-64k, which does 16*{sync read, async write}.
         * When the 16 consecutive reads are often interrupted by some dirty
         * throttling pause during the async writes, cfq will go into idles
         * (deadline is fine). So push nr_dirtied_pause as high as possible
         * until reaches DIRTY_POLL_THRESH=32 pages.
         */
        if (pages < DIRTY_POLL_THRESH) {
                t = max_pause;
                pages = dirty_ratelimit * t / roundup_pow_of_two(HZ);
                if (pages > DIRTY_POLL_THRESH) {
                        pages = DIRTY_POLL_THRESH;
                        t = HZ * DIRTY_POLL_THRESH / dirty_ratelimit;
                }
        }

        pause = HZ * pages / (task_ratelimit + 1);
        if (pause > max_pause) {
                t = max_pause;
                pages = task_ratelimit * t / roundup_pow_of_two(HZ);
        }

        *nr_dirtied_pause = pages;
        /*
         * The minimal pause time will normally be half the target pause time.
         */
        return pages >= DIRTY_POLL_THRESH ? 1 + t / 2 : t;
}

static inline void wb_dirty_limits(struct dirty_throttle_control *dtc)
{
        struct bdi_writeback *wb = dtc->wb;
        unsigned long wb_reclaimable;

        /*
         * wb_thresh is not treated as some limiting factor as
         * dirty_thresh, due to reasons
         * - in JBOD setup, wb_thresh can fluctuate a lot
         * - in a system with HDD and USB key, the USB key may somehow
         *   go into state (wb_dirty >> wb_thresh) either because
         *   wb_dirty starts high, or because wb_thresh drops low.
         *   In this case we don't want to hard throttle the USB key
         *   dirtiers for 100 seconds until wb_dirty drops under
         *   wb_thresh. Instead the auxiliary wb control line in
         *   wb_position_ratio() will let the dirtier task progress
         *   at some rate <= (write_bw / 2) for bringing down wb_dirty.
         */
        dtc->wb_thresh = __wb_calc_thresh(dtc);
        dtc->wb_bg_thresh = dtc->thresh ?
                div_u64((u64)dtc->wb_thresh * dtc->bg_thresh, dtc->thresh) : 0;

        /*
         * In order to avoid the stacked BDI deadlock we need
         * to ensure we accurately count the 'dirty' pages when
         * the threshold is low.
         *
         * Otherwise it would be possible to get thresh+n pages
         * reported dirty, even though there are thresh-m pages
         * actually dirty; with m+n sitting in the percpu
         * deltas.
         */
        if (dtc->wb_thresh < 2 * wb_stat_error(wb)) {
                wb_reclaimable = wb_stat_sum(wb, WB_RECLAIMABLE);
                dtc->wb_dirty = wb_reclaimable + wb_stat_sum(wb, WB_WRITEBACK);
        } else {
                wb_reclaimable = wb_stat(wb, WB_RECLAIMABLE);
                dtc->wb_dirty = wb_reclaimable + wb_stat(wb, WB_WRITEBACK);
        }
}

/*
 * balance_dirty_pages() must be called by processes which are generating dirty
 * data.  It looks at the number of dirty pages in the machine and will force
 * the caller to wait once crossing the (background_thresh + dirty_thresh) / 2.
 * If we're over `background_thresh' then the writeback threads are woken to
 * perform some writeout.
 */
static void balance_dirty_pages(struct address_space *mapping,
                                struct bdi_writeback *wb,
                                unsigned long pages_dirtied)
{
        struct dirty_throttle_control gdtc_stor = { GDTC_INIT(wb) };
        struct dirty_throttle_control mdtc_stor = { MDTC_INIT(wb, &gdtc_stor) };
        struct dirty_throttle_control * const gdtc = &gdtc_stor;
        struct dirty_throttle_control * const mdtc = mdtc_valid(&mdtc_stor) ?
                                                     &mdtc_stor : NULL;
        struct dirty_throttle_control *sdtc;
        unsigned long nr_reclaimable;   /* = file_dirty + unstable_nfs */
        long period;
        long pause;
        long max_pause;
        long min_pause;
        int nr_dirtied_pause;
        bool dirty_exceeded = false;
        unsigned long task_ratelimit;
        unsigned long dirty_ratelimit;
        struct backing_dev_info *bdi = wb->bdi;
        bool strictlimit = bdi->capabilities & BDI_CAP_STRICTLIMIT;
        unsigned long start_time = jiffies;

        for (;;) {
                unsigned long now = jiffies;
                unsigned long dirty, thresh, bg_thresh;
                unsigned long m_dirty = 0;      /* stop bogus uninit warnings */
                unsigned long m_thresh = 0;
                unsigned long m_bg_thresh = 0;

                /*
                 * Unstable writes are a feature of certain networked
                 * filesystems (i.e. NFS) in which data may have been
                 * written to the server's write cache, but has not yet
                 * been flushed to permanent storage.
                 */
                nr_reclaimable = global_page_state(NR_FILE_DIRTY) +
                                        global_page_state(NR_UNSTABLE_NFS);
                gdtc->avail = global_dirtyable_memory();
                gdtc->dirty = nr_reclaimable + global_page_state(NR_WRITEBACK);

                domain_dirty_limits(gdtc);

                if (unlikely(strictlimit)) {
                        wb_dirty_limits(gdtc);

                        dirty = gdtc->wb_dirty;
                        thresh = gdtc->wb_thresh;
                        bg_thresh = gdtc->wb_bg_thresh;
                } else {
                        dirty = gdtc->dirty;
                        thresh = gdtc->thresh;
                        bg_thresh = gdtc->bg_thresh;
                }

                if (mdtc) {
                        unsigned long filepages, headroom, writeback;

                        /*
                         * If @wb belongs to !root memcg, repeat the same
                         * basic calculations for the memcg domain.
                         */
                        mem_cgroup_wb_stats(wb, &filepages, &headroom,
                                            &mdtc->dirty, &writeback);
                        mdtc->dirty += writeback;
                        mdtc_calc_avail(mdtc, filepages, headroom);

                        domain_dirty_limits(mdtc);

                        if (unlikely(strictlimit)) {
                                wb_dirty_limits(mdtc);
                                m_dirty = mdtc->wb_dirty;
                                m_thresh = mdtc->wb_thresh;
                                m_bg_thresh = mdtc->wb_bg_thresh;
                        } else {
                                m_dirty = mdtc->dirty;
                                m_thresh = mdtc->thresh;
                                m_bg_thresh = mdtc->bg_thresh;
                        }
                }

                /*
                 * Throttle it only when the background writeback cannot
                 * catch-up. This avoids (excessively) small writeouts
                 * when the wb limits are ramping up in case of !strictlimit.
                 *
                 * In strictlimit case make decision based on the wb counters
                 * and limits. Small writeouts when the wb limits are ramping
                 * up are the price we consciously pay for strictlimit-ing.
                 *
                 * If memcg domain is in effect, @dirty should be under
                 * both global and memcg freerun ceilings.
                 */
                if (dirty <= dirty_freerun_ceiling(thresh, bg_thresh) &&
                    (!mdtc ||
                     m_dirty <= dirty_freerun_ceiling(m_thresh, m_bg_thresh))) {
                        unsigned long intv = dirty_poll_interval(dirty, thresh);
                        unsigned long m_intv = ULONG_MAX;

                        current->dirty_paused_when = now;
                        current->nr_dirtied = 0;
                        if (mdtc)
                                m_intv = dirty_poll_interval(m_dirty, m_thresh);
                        current->nr_dirtied_pause = min(intv, m_intv);
                        break;
                }

                if (unlikely(!writeback_in_progress(wb)))
                        wb_start_background_writeback(wb);

                /*
                 * Calculate global domain's pos_ratio and select the
                 * global dtc by default.
                 */
                if (!strictlimit)
                        wb_dirty_limits(gdtc);

                dirty_exceeded = (gdtc->wb_dirty > gdtc->wb_thresh) &&
                        ((gdtc->dirty > gdtc->thresh) || strictlimit);

                wb_position_ratio(gdtc);
                sdtc = gdtc;

                if (mdtc) {
                        /*
                         * If memcg domain is in effect, calculate its
                         * pos_ratio.  @wb should satisfy constraints from
                         * both global and memcg domains.  Choose the one
                         * w/ lower pos_ratio.
                         */
                        if (!strictlimit)
                                wb_dirty_limits(mdtc);

                        dirty_exceeded |= (mdtc->wb_dirty > mdtc->wb_thresh) &&
                                ((mdtc->dirty > mdtc->thresh) || strictlimit);

                        wb_position_ratio(mdtc);
                        if (mdtc->pos_ratio < gdtc->pos_ratio)
                                sdtc = mdtc;
                }

                if (dirty_exceeded && !wb->dirty_exceeded)
                        wb->dirty_exceeded = 1;

                if (time_is_before_jiffies(wb->bw_time_stamp +
                                           BANDWIDTH_INTERVAL)) {
                        spin_lock(&wb->list_lock);
                        __wb_update_bandwidth(gdtc, mdtc, start_time, true);
                        spin_unlock(&wb->list_lock);
                }

                /* throttle according to the chosen dtc */
                dirty_ratelimit = wb->dirty_ratelimit;
                task_ratelimit = ((u64)dirty_ratelimit * sdtc->pos_ratio) >>
                                                        RATELIMIT_CALC_SHIFT;
                max_pause = wb_max_pause(wb, sdtc->wb_dirty);
                min_pause = wb_min_pause(wb, max_pause,
                                         task_ratelimit, dirty_ratelimit,
                                         &nr_dirtied_pause);

                if (unlikely(task_ratelimit == 0)) {
                        period = max_pause;
                        pause = max_pause;
                        goto pause;
                }
                period = HZ * pages_dirtied / task_ratelimit;
                pause = period;
                if (current->dirty_paused_when)
                        pause -= now - current->dirty_paused_when;
                /*
                 * For less than 1s think time (ext3/4 may block the dirtier
                 * for up to 800ms from time to time on 1-HDD; so does xfs,
                 * however at much less frequency), try to compensate it in
                 * future periods by updating the virtual time; otherwise just
                 * do a reset, as it may be a light dirtier.
                 */
                if (pause < min_pause) {
                        trace_balance_dirty_pages(wb,
                                                  sdtc->thresh,
                                                  sdtc->bg_thresh,
                                                  sdtc->dirty,
                                                  sdtc->wb_thresh,
                                                  sdtc->wb_dirty,
                                                  dirty_ratelimit,
                                                  task_ratelimit,
                                                  pages_dirtied,
                                                  period,
                                                  min(pause, 0L),
                                                  start_time);
                        if (pause < -HZ) {
                                current->dirty_paused_when = now;
                                current->nr_dirtied = 0;
                        } else if (period) {
                                current->dirty_paused_when += period;
                                current->nr_dirtied = 0;
                        } else if (current->nr_dirtied_pause <= pages_dirtied)
                                current->nr_dirtied_pause += pages_dirtied;
                        break;
                }
                if (unlikely(pause > max_pause)) {
                        /* for occasional dropped task_ratelimit */
                        now += min(pause - max_pause, max_pause);
                        pause = max_pause;
                }

pause:
                trace_balance_dirty_pages(wb,
                                          sdtc->thresh,
                                          sdtc->bg_thresh,
                                          sdtc->dirty,
                                          sdtc->wb_thresh,
                                          sdtc->wb_dirty,
                                          dirty_ratelimit,
                                          task_ratelimit,
                                          pages_dirtied,
                                          period,
                                          pause,
                                          start_time);
                __set_current_state(TASK_KILLABLE);
                io_schedule_timeout(pause);

                current->dirty_paused_when = now + pause;
                current->nr_dirtied = 0;
                current->nr_dirtied_pause = nr_dirtied_pause;

                /*
                 * This is typically equal to (dirty < thresh) and can also
                 * keep "1000+ dd on a slow USB stick" under control.
                 */
                if (task_ratelimit)
                        break;

                /*
                 * In the case of an unresponding NFS server and the NFS dirty
                 * pages exceeds dirty_thresh, give the other good wb's a pipe
                 * to go through, so that tasks on them still remain responsive.
                 *
                 * In theory 1 page is enough to keep the comsumer-producer
                 * pipe going: the flusher cleans 1 page => the task dirties 1
                 * more page. However wb_dirty has accounting errors.  So use
                 * the larger and more IO friendly wb_stat_error.
                 */
                if (sdtc->wb_dirty <= wb_stat_error(wb))
                        break;

                if (fatal_signal_pending(current))
                        break;
        }

        if (!dirty_exceeded && wb->dirty_exceeded)
                wb->dirty_exceeded = 0;

        if (writeback_in_progress(wb))
                return;

        /*
         * In laptop mode, we wait until hitting the higher threshold before
         * starting background writeout, and then write out all the way down
         * to the lower threshold.  So slow writers cause minimal disk activity.
         *
         * In normal mode, we start background writeout at the lower
         * background_thresh, to keep the amount of dirty memory low.
         */
        if (laptop_mode)
                return;

        if (nr_reclaimable > gdtc->bg_thresh)
                wb_start_background_writeback(wb);
}

static DEFINE_PER_CPU(int, bdp_ratelimits);

/*
 * Normal tasks are throttled by
 *      loop {
 *              dirty tsk->nr_dirtied_pause pages;
 *              take a snap in balance_dirty_pages();
 *      }
 * However there is a worst case. If every task exit immediately when dirtied
 * (tsk->nr_dirtied_pause - 1) pages, balance_dirty_pages() will never be
 * called to throttle the page dirties. The solution is to save the not yet
 * throttled page dirties in dirty_throttle_leaks on task exit and charge them
 * randomly into the running tasks. This works well for the above worst case,
 * as the new task will pick up and accumulate the old task's leaked dirty
 * count and eventually get throttled.
 */
DEFINE_PER_CPU(int, dirty_throttle_leaks) = 0;

/**
 * balance_dirty_pages_ratelimited - balance dirty memory state
 * @mapping: address_space which was dirtied
 *
 * Processes which are dirtying memory should call in here once for each page
 * which was newly dirtied.  The function will periodically check the system's
 * dirty state and will initiate writeback if needed.
 *
 * On really big machines, get_writeback_state is expensive, so try to avoid
 * calling it too often (ratelimiting).  But once we're over the dirty memory
 * limit we decrease the ratelimiting by a lot, to prevent individual processes
 * from overshooting the limit by (ratelimit_pages) each.
 */
void balance_dirty_pages_ratelimited(struct address_space *mapping)
{
        struct inode *inode = mapping->host;
        struct backing_dev_info *bdi = inode_to_bdi(inode);
        struct bdi_writeback *wb = NULL;
        int ratelimit;
        int *p;

        if (!bdi_cap_account_dirty(bdi))
                return;

        if (inode_cgwb_enabled(inode))
                wb = wb_get_create_current(bdi, GFP_KERNEL);
        if (!wb)
                wb = &bdi->wb;

        ratelimit = current->nr_dirtied_pause;
        if (wb->dirty_exceeded)
                ratelimit = min(ratelimit, 32 >> (PAGE_SHIFT - 10));

        preempt_disable();
        /*
         * This prevents one CPU to accumulate too many dirtied pages without
         * calling into balance_dirty_pages(), which can happen when there are
         * 1000+ tasks, all of them start dirtying pages at exactly the same
         * time, hence all honoured too large initial task->nr_dirtied_pause.
         */
        p =  this_cpu_ptr(&bdp_ratelimits);
        if (unlikely(current->nr_dirtied >= ratelimit))
                *p = 0;
        else if (unlikely(*p >= ratelimit_pages)) {
                *p = 0;
                ratelimit = 0;
        }
        /*
         * Pick up the dirtied pages by the exited tasks. This avoids lots of
         * short-lived tasks (eg. gcc invocations in a kernel build) escaping
         * the dirty throttling and livelock other long-run dirtiers.
         */
        p = this_cpu_ptr(&dirty_throttle_leaks);
        if (*p > 0 && current->nr_dirtied < ratelimit) {
                unsigned long nr_pages_dirtied;
                nr_pages_dirtied = min(*p, ratelimit - current->nr_dirtied);
                *p -= nr_pages_dirtied;
                current->nr_dirtied += nr_pages_dirtied;
        }
        preempt_enable();

        if (unlikely(current->nr_dirtied >= ratelimit))
                balance_dirty_pages(mapping, wb, current->nr_dirtied);

        wb_put(wb);
}
EXPORT_SYMBOL(balance_dirty_pages_ratelimited);

/**
 * wb_over_bg_thresh - does @wb need to be written back?
 * @wb: bdi_writeback of interest
 *
 * Determines whether background writeback should keep writing @wb or it's
 * clean enough.  Returns %true if writeback should continue.
 */
bool wb_over_bg_thresh(struct bdi_writeback *wb)
{
        struct dirty_throttle_control gdtc_stor = { GDTC_INIT(wb) };
        struct dirty_throttle_control mdtc_stor = { MDTC_INIT(wb, &gdtc_stor) };
        struct dirty_throttle_control * const gdtc = &gdtc_stor;
        struct dirty_throttle_control * const mdtc = mdtc_valid(&mdtc_stor) ?
                                                     &mdtc_stor : NULL;

        /*
         * Similar to balance_dirty_pages() but ignores pages being written
         * as we're trying to decide whether to put more under writeback.
         */
        gdtc->avail = global_dirtyable_memory();
        gdtc->dirty = global_page_state(NR_FILE_DIRTY) +
                      global_page_state(NR_UNSTABLE_NFS);
        domain_dirty_limits(gdtc);

        if (gdtc->dirty > gdtc->bg_thresh)
                return true;

        if (wb_stat(wb, WB_RECLAIMABLE) > __wb_calc_thresh(gdtc))
                return true;

        if (mdtc) {
                unsigned long filepages, headroom, writeback;

                mem_cgroup_wb_stats(wb, &filepages, &headroom, &mdtc->dirty,
                                    &writeback);
                mdtc_calc_avail(mdtc, filepages, headroom);
                domain_dirty_limits(mdtc);      /* ditto, ignore writeback */

                if (mdtc->dirty > mdtc->bg_thresh)
                        return true;

                if (wb_stat(wb, WB_RECLAIMABLE) > __wb_calc_thresh(mdtc))
                        return true;
        }

        return false;
}

void throttle_vm_writeout(gfp_t gfp_mask)
{
        unsigned long background_thresh;
        unsigned long dirty_thresh;

        for ( ; ; ) {
                global_dirty_limits(&background_thresh, &dirty_thresh);
                dirty_thresh = hard_dirty_limit(&global_wb_domain, dirty_thresh);

                /*
                 * Boost the allowable dirty threshold a bit for page
                 * allocators so they don't get DoS'ed by heavy writers
                 */
                dirty_thresh += dirty_thresh / 10;      /* wheeee... */

                if (global_page_state(NR_UNSTABLE_NFS) +
                        global_page_state(NR_WRITEBACK) <= dirty_thresh)
                                break;
                congestion_wait(BLK_RW_ASYNC, HZ/10);

                /*
                 * The caller might hold locks which can prevent IO completion
                 * or progress in the filesystem.  So we cannot just sit here
                 * waiting for IO to complete.
                 */
                if ((gfp_mask & (__GFP_FS|__GFP_IO)) != (__GFP_FS|__GFP_IO))
                        break;
        }
}

/*
 * sysctl handler for /proc/sys/vm/dirty_writeback_centisecs
 */
int dirty_writeback_centisecs_handler(struct ctl_table *table, int write,
        void __user *buffer, size_t *length, loff_t *ppos)
{
        proc_dointvec(table, write, buffer, length, ppos);
        return 0;
}

#ifdef CONFIG_BLOCK
void laptop_mode_timer_fn(unsigned long data)
{
        struct request_queue *q = (struct request_queue *)data;
        int nr_pages = global_page_state(NR_FILE_DIRTY) +
                global_page_state(NR_UNSTABLE_NFS);
        struct bdi_writeback *wb;

        /*
         * We want to write everything out, not just down to the dirty
         * threshold
         */
        if (!bdi_has_dirty_io(&q->backing_dev_info))
                return;

        rcu_read_lock();
        list_for_each_entry_rcu(wb, &q->backing_dev_info.wb_list, bdi_node)
                if (wb_has_dirty_io(wb))
                        wb_start_writeback(wb, nr_pages, true,
                                           WB_REASON_LAPTOP_TIMER);
        rcu_read_unlock();
}

/*
 * We've spun up the disk and we're in laptop mode: schedule writeback
 * of all dirty data a few seconds from now.  If the flush is already scheduled
 * then push it back - the user is still using the disk.
 */
void laptop_io_completion(struct backing_dev_info *info)
{
        mod_timer(&info->laptop_mode_wb_timer, jiffies + laptop_mode);
}

/*
 * We're in laptop mode and we've just synced. The sync's writes will have
 * caused another writeback to be scheduled by laptop_io_completion.
 * Nothing needs to be written back anymore, so we unschedule the writeback.
 */

void laptop_sync_completion(void)
{
        struct backing_dev_info *bdi;

        rcu_read_lock();

        list_for_each_entry_rcu(bdi, &bdi_list, bdi_list)
                del_timer(&bdi->laptop_mode_wb_timer);

        rcu_read_unlock();
}
#endif

/*
 * If ratelimit_pages is too high then we can get into dirty-data overload
 * if a large number of processes all perform writes at the same time.
 * If it is too low then SMP machines will call the (expensive)
 * get_writeback_state too often.
 *
 * Here we set ratelimit_pages to a level which ensures that when all CPUs are
 * dirtying in parallel, we cannot go more than 3% (1/32) over the dirty memory
 * thresholds.
 */

void writeback_set_ratelimit(void)
{
        struct wb_domain *dom = &global_wb_domain;
        unsigned long background_thresh;
        unsigned long dirty_thresh;

        global_dirty_limits(&background_thresh, &dirty_thresh);
        dom->dirty_limit = dirty_thresh;
        ratelimit_pages = dirty_thresh / (num_online_cpus() * 32);
        if (ratelimit_pages < 16)
                ratelimit_pages = 16;
}

static int
ratelimit_handler(struct notifier_block *self, unsigned long action,
                  void *hcpu)
{

        switch (action & ~CPU_TASKS_FROZEN) {
        case CPU_ONLINE:
        case CPU_DEAD:
                writeback_set_ratelimit();
                return NOTIFY_OK;
        default:
                return NOTIFY_DONE;
        }
}

static struct notifier_block ratelimit_nb = {
        .notifier_call  = ratelimit_handler,
        .next           = NULL,
};

/*
 * Called early on to tune the page writeback dirty limits.
 *
 * We used to scale dirty pages according to how total memory
 * related to pages that could be allocated for buffers (by
 * comparing nr_free_buffer_pages() to vm_total_pages.
 *
 * However, that was when we used "dirty_ratio" to scale with
 * all memory, and we don't do that any more. "dirty_ratio"
 * is now applied to total non-HIGHPAGE memory (by subtracting
 * totalhigh_pages from vm_total_pages), and as such we can't
 * get into the old insane situation any more where we had
 * large amounts of dirty pages compared to a small amount of
 * non-HIGHMEM memory.
 *
 * But we might still want to scale the dirty_ratio by how
 * much memory the box has..
 */
void __init page_writeback_init(void)
{
        BUG_ON(wb_domain_init(&global_wb_domain, GFP_KERNEL));

        writeback_set_ratelimit();
        register_cpu_notifier(&ratelimit_nb);
}

/**
 * tag_pages_for_writeback - tag pages to be written by write_cache_pages
 * @mapping: address space structure to write
 * @start: starting page index
 * @end: ending page index (inclusive)
 *
 * This function scans the page range from @start to @end (inclusive) and tags
 * all pages that have DIRTY tag set with a special TOWRITE tag. The idea is
 * that write_cache_pages (or whoever calls this function) will then use
 * TOWRITE tag to identify pages eligible for writeback.  This mechanism is
 * used to avoid livelocking of writeback by a process steadily creating new
 * dirty pages in the file (thus it is important for this function to be quick
 * so that it can tag pages faster than a dirtying process can create them).
 */
/*
 * We tag pages in batches of WRITEBACK_TAG_BATCH to reduce tree_lock latency.
 */
void tag_pages_for_writeback(struct address_space *mapping,
                             pgoff_t start, pgoff_t end)
{
#define WRITEBACK_TAG_BATCH 4096
        unsigned long tagged;

        do {
                spin_lock_irq(&mapping->tree_lock);
                tagged = radix_tree_range_tag_if_tagged(&mapping->page_tree,
                                &start, end, WRITEBACK_TAG_BATCH,
                                PAGECACHE_TAG_DIRTY, PAGECACHE_TAG_TOWRITE);
                spin_unlock_irq(&mapping->tree_lock);
                WARN_ON_ONCE(tagged > WRITEBACK_TAG_BATCH);
                cond_resched();
                /* We check 'start' to handle wrapping when end == ~0UL */
        } while (tagged >= WRITEBACK_TAG_BATCH && start);
}
EXPORT_SYMBOL(tag_pages_for_writeback);

/**
 * write_cache_pages - walk the list of dirty pages of the given address space and write all of them.
 * @mapping: address space structure to write
 * @wbc: subtract the number of written pages from *@wbc->nr_to_write
 * @writepage: function called for each page
 * @data: data passed to writepage function
 *
 * If a page is already under I/O, write_cache_pages() skips it, even
 * if it's dirty.  This is desirable behaviour for memory-cleaning writeback,
 * but it is INCORRECT for data-integrity system calls such as fsync().  fsync()
 * and msync() need to guarantee that all the data which was dirty at the time
 * the call was made get new I/O started against them.  If wbc->sync_mode is
 * WB_SYNC_ALL then we were called for data integrity and we must wait for
 * existing IO to complete.
 *
 * To avoid livelocks (when other process dirties new pages), we first tag
 * pages which should be written back with TOWRITE tag and only then start
 * writing them. For data-integrity sync we have to be careful so that we do
 * not miss some pages (e.g., because some other process has cleared TOWRITE
 * tag we set). The rule we follow is that TOWRITE tag can be cleared only
 * by the process clearing the DIRTY tag (and submitting the page for IO).
 */
int write_cache_pages(struct address_space *mapping,
                      struct writeback_control *wbc, writepage_t writepage,
                      void *data)
{
        int ret = 0;
        int done = 0;
        struct pagevec pvec;
        int nr_pages;
        pgoff_t uninitialized_var(writeback_index);
        pgoff_t index;
        pgoff_t end;            /* Inclusive */
        pgoff_t done_index;
        int cycled;
        int range_whole = 0;
        int tag;

        pagevec_init(&pvec, 0);
        if (wbc->range_cyclic) {
                writeback_index = mapping->writeback_index; /* prev offset */
                index = writeback_index;
                if (index == 0)
                        cycled = 1;
                else
                        cycled = 0;
                end = -1;
        } else {
                index = wbc->range_start >> PAGE_CACHE_SHIFT;
                end = wbc->range_end >> PAGE_CACHE_SHIFT;
                if (wbc->range_start == 0 && wbc->range_end == LLONG_MAX)
                        range_whole = 1;
                cycled = 1; /* ignore range_cyclic tests */
        }
        if (wbc->sync_mode == WB_SYNC_ALL || wbc->tagged_writepages)
                tag = PAGECACHE_TAG_TOWRITE;
        else
                tag = PAGECACHE_TAG_DIRTY;
retry:
        if (wbc->sync_mode == WB_SYNC_ALL || wbc->tagged_writepages)
                tag_pages_for_writeback(mapping, index, end);
        done_index = index;
        while (!done && (index <= end)) {
                int i;

                nr_pages = pagevec_lookup_tag(&pvec, mapping, &index, tag,
                              min(end - index, (pgoff_t)PAGEVEC_SIZE-1) + 1);
                if (nr_pages == 0)
                        break;

                for (i = 0; i < nr_pages; i++) {
                        struct page *page = pvec.pages[i];

                        /*
                         * At this point, the page may be truncated or
                         * invalidated (changing page->mapping to NULL), or
                         * even swizzled back from swapper_space to tmpfs file
                         * mapping. However, page->index will not change
                         * because we have a reference on the page.
                         */
                        if (page->index > end) {
                                /*
                                 * can't be range_cyclic (1st pass) because
                                 * end == -1 in that case.
                                 */
                                done = 1;
                                break;
                        }

                        done_index = page->index;

                        lock_page(page);

                        /*
                         * Page truncated or invalidated. We can freely skip it
                         * then, even for data integrity operations: the page
                         * has disappeared concurrently, so there could be no
                         * real expectation of this data interity operation
                         * even if there is now a new, dirty page at the same
                         * pagecache address.
                         */
                        if (unlikely(page->mapping != mapping)) {
continue_unlock:
                                unlock_page(page);
                                continue;
                        }

                        if (!PageDirty(page)) {
                                /* someone wrote it for us */
                                goto continue_unlock;
                        }

                        if (PageWriteback(page)) {
                                if (wbc->sync_mode != WB_SYNC_NONE)
                                        wait_on_page_writeback(page);
                                else
                                        goto continue_unlock;
                        }

                        BUG_ON(PageWriteback(page));
                        if (!clear_page_dirty_for_io(page))
                                goto continue_unlock;

                        trace_wbc_writepage(wbc, inode_to_bdi(mapping->host));
                        ret = (*writepage)(page, wbc, data);
                        if (unlikely(ret)) {
                                if (ret == AOP_WRITEPAGE_ACTIVATE) {
                                        unlock_page(page);
                                        ret = 0;
                                } else {
                                        /*
                                         * done_index is set past this page,
                                         * so media errors will not choke
                                         * background writeout for the entire
                                         * file. This has consequences for
                                         * range_cyclic semantics (ie. it may
                                         * not be suitable for data integrity
                                         * writeout).
                                         */
                                        done_index = page->index + 1;
                                        done = 1;
                                        break;
                                }
                        }

                        /*
                         * We stop writing back only if we are not doing
                         * integrity sync. In case of integrity sync we have to
                         * keep going until we have written all the pages
                         * we tagged for writeback prior to entering this loop.
                         */
                        if (--wbc->nr_to_write <= 0 &&
                            wbc->sync_mode == WB_SYNC_NONE) {
                                done = 1;
                                break;
                        }
                }
                pagevec_release(&pvec);
                cond_resched();
        }
        if (!cycled && !done) {
                /*
                 * range_cyclic:
                 * We hit the last page and there is more work to be done: wrap
                 * back to the start of the file
                 */
                cycled = 1;
                index = 0;
                end = writeback_index - 1;
                goto retry;
        }
        if (wbc->range_cyclic || (range_whole && wbc->nr_to_write > 0))
                mapping->writeback_index = done_index;

        return ret;
}
EXPORT_SYMBOL(write_cache_pages);

/*
 * Function used by generic_writepages to call the real writepage
 * function and set the mapping flags on error
 */
static int __writepage(struct page *page, struct writeback_control *wbc,
                       void *data)
{
        struct address_space *mapping = data;
        int ret = mapping->a_ops->writepage(page, wbc);
        mapping_set_error(mapping, ret);
        return ret;
}

/**
 * generic_writepages - walk the list of dirty pages of the given address space and writepage() all of them.
 * @mapping: address space structure to write
 * @wbc: subtract the number of written pages from *@wbc->nr_to_write
 *
 * This is a library function, which implements the writepages()
 * address_space_operation.
 */
int generic_writepages(struct address_space *mapping,
                       struct writeback_control *wbc)
{
        struct blk_plug plug;
        int ret;

        /* deal with chardevs and other special file */
        if (!mapping->a_ops->writepage)
                return 0;

        blk_start_plug(&plug);
        ret = write_cache_pages(mapping, wbc, __writepage, mapping);
        blk_finish_plug(&plug);
        return ret;
}

EXPORT_SYMBOL(generic_writepages);

int do_writepages(struct address_space *mapping, struct writeback_control *wbc)
{
        int ret;

        if (wbc->nr_to_write <= 0)
                return 0;
        if (mapping->a_ops->writepages)
                ret = mapping->a_ops->writepages(mapping, wbc);
        else
                ret = generic_writepages(mapping, wbc);
        return ret;
}

/**
 * write_one_page - write out a single page and optionally wait on I/O
 * @page: the page to write
 * @wait: if true, wait on writeout
 *
 * The page must be locked by the caller and will be unlocked upon return.
 *
 * write_one_page() returns a negative error code if I/O failed.
 */
int write_one_page(struct page *page, int wait)
{
        struct address_space *mapping = page->mapping;
        int ret = 0;
        struct writeback_control wbc = {
                .sync_mode = WB_SYNC_ALL,
                .nr_to_write = 1,
        };

        BUG_ON(!PageLocked(page));

        if (wait)
                wait_on_page_writeback(page);

        if (clear_page_dirty_for_io(page)) {
                page_cache_get(page);
                ret = mapping->a_ops->writepage(page, &wbc);
                if (ret == 0 && wait) {
                        wait_on_page_writeback(page);
                        if (PageError(page))
                                ret = -EIO;
                }
                page_cache_release(page);
        } else {
                unlock_page(page);
        }
        return ret;
}
EXPORT_SYMBOL(write_one_page);

/*
 * For address_spaces which do not use buffers nor write back.
 */
int __set_page_dirty_no_writeback(struct page *page)
{
        if (!PageDirty(page))
                return !TestSetPageDirty(page);
        return 0;
}

/*
 * Helper function for set_page_dirty family.
 *
 * Caller must hold mem_cgroup_begin_page_stat().
 *
 * NOTE: This relies on being atomic wrt interrupts.
 */
void account_page_dirtied(struct page *page, struct address_space *mapping,
                          struct mem_cgroup *memcg)
{
        struct inode *inode = mapping->host;

        trace_writeback_dirty_page(page, mapping);

        if (mapping_cap_account_dirty(mapping)) {
                struct bdi_writeback *wb;

                inode_attach_wb(inode, page);
                wb = inode_to_wb(inode);

                mem_cgroup_inc_page_stat(memcg, MEM_CGROUP_STAT_DIRTY);
                __inc_zone_page_state(page, NR_FILE_DIRTY);
                __inc_zone_page_state(page, NR_DIRTIED);
                __inc_wb_stat(wb, WB_RECLAIMABLE);
                __inc_wb_stat(wb, WB_DIRTIED);
                task_io_account_write(PAGE_CACHE_SIZE);
                current->nr_dirtied++;
                this_cpu_inc(bdp_ratelimits);
        }
}
EXPORT_SYMBOL(account_page_dirtied);

/*
 * Helper function for deaccounting dirty page without writeback.
 *
 * Caller must hold mem_cgroup_begin_page_stat().
 */
void account_page_cleaned(struct page *page, struct address_space *mapping,
                          struct mem_cgroup *memcg, struct bdi_writeback *wb)
{
        if (mapping_cap_account_dirty(mapping)) {
                mem_cgroup_dec_page_stat(memcg, MEM_CGROUP_STAT_DIRTY);
                dec_zone_page_state(page, NR_FILE_DIRTY);
                dec_wb_stat(wb, WB_RECLAIMABLE);
                task_io_account_cancelled_write(PAGE_CACHE_SIZE);
        }
}

/*
 * For address_spaces which do not use buffers.  Just tag the page as dirty in
 * its radix tree.
 *
 * This is also used when a single buffer is being dirtied: we want to set the
 * page dirty in that case, but not all the buffers.  This is a "bottom-up"
 * dirtying, whereas __set_page_dirty_buffers() is a "top-down" dirtying.
 *
 * The caller must ensure this doesn't race with truncation.  Most will simply
 * hold the page lock, but e.g. zap_pte_range() calls with the page mapped and
 * the pte lock held, which also locks out truncation.
 */
int __set_page_dirty_nobuffers(struct page *page)
{
        struct mem_cgroup *memcg;

        memcg = mem_cgroup_begin_page_stat(page);
        if (!TestSetPageDirty(page)) {
                struct address_space *mapping = page_mapping(page);
                unsigned long flags;

                if (!mapping) {
                        mem_cgroup_end_page_stat(memcg);
                        return 1;
                }

                spin_lock_irqsave(&mapping->tree_lock, flags);
                BUG_ON(page_mapping(page) != mapping);
                WARN_ON_ONCE(!PagePrivate(page) && !PageUptodate(page));
                account_page_dirtied(page, mapping, memcg);
                radix_tree_tag_set(&mapping->page_tree, page_index(page),
                                   PAGECACHE_TAG_DIRTY);
                spin_unlock_irqrestore(&mapping->tree_lock, flags);
                mem_cgroup_end_page_stat(memcg);

                if (mapping->host) {
                        /* !PageAnon && !swapper_space */
                        __mark_inode_dirty(mapping->host, I_DIRTY_PAGES);
                }
                return 1;
        }
        mem_cgroup_end_page_stat(memcg);
        return 0;
}
EXPORT_SYMBOL(__set_page_dirty_nobuffers);

/*
 * Call this whenever redirtying a page, to de-account the dirty counters
 * (NR_DIRTIED, BDI_DIRTIED, tsk->nr_dirtied), so that they match the written
 * counters (NR_WRITTEN, BDI_WRITTEN) in long term. The mismatches will lead to
 * systematic errors in balanced_dirty_ratelimit and the dirty pages position
 * control.
 */
void account_page_redirty(struct page *page)
{
        struct address_space *mapping = page->mapping;

        if (mapping && mapping_cap_account_dirty(mapping)) {
                struct inode *inode = mapping->host;
                struct bdi_writeback *wb;
                bool locked;

                wb = unlocked_inode_to_wb_begin(inode, &locked);
                current->nr_dirtied--;
                dec_zone_page_state(page, NR_DIRTIED);
                dec_wb_stat(wb, WB_DIRTIED);
                unlocked_inode_to_wb_end(inode, locked);
        }
}
EXPORT_SYMBOL(account_page_redirty);

/*
 * When a writepage implementation decides that it doesn't want to write this
 * page for some reason, it should redirty the locked page via
 * redirty_page_for_writepage() and it should then unlock the page and return 0
 */
int redirty_page_for_writepage(struct writeback_control *wbc, struct page *page)
{
        int ret;

        wbc->pages_skipped++;
        ret = __set_page_dirty_nobuffers(page);
        account_page_redirty(page);
        return ret;
}
EXPORT_SYMBOL(redirty_page_for_writepage);

/*
 * Dirty a page.
 *
 * For pages with a mapping this should be done under the page lock
 * for the benefit of asynchronous memory errors who prefer a consistent
 * dirty state. This rule can be broken in some special cases,
 * but should be better not to.
 *
 * If the mapping doesn't provide a set_page_dirty a_op, then
 * just fall through and assume that it wants buffer_heads.
 */
int set_page_dirty(struct page *page)
{
        struct address_space *mapping = page_mapping(page);

        if (likely(mapping)) {
                int (*spd)(struct page *) = mapping->a_ops->set_page_dirty;
                /*
                 * readahead/lru_deactivate_page could remain
                 * PG_readahead/PG_reclaim due to race with end_page_writeback
                 * About readahead, if the page is written, the flags would be
                 * reset. So no problem.
                 * About lru_deactivate_page, if the page is redirty, the flag
                 * will be reset. So no problem. but if the page is used by readahead
                 * it will confuse readahead and make it restart the size rampup
                 * process. But it's a trivial problem.
                 */
                if (PageReclaim(page))
                        ClearPageReclaim(page);
#ifdef CONFIG_BLOCK
                if (!spd)
                        spd = __set_page_dirty_buffers;
#endif
                return (*spd)(page);
        }
        if (!PageDirty(page)) {
                if (!TestSetPageDirty(page))
                        return 1;
        }
        return 0;
}
EXPORT_SYMBOL(set_page_dirty);

/*
 * set_page_dirty() is racy if the caller has no reference against
 * page->mapping->host, and if the page is unlocked.  This is because another
 * CPU could truncate the page off the mapping and then free the mapping.
 *
 * Usually, the page _is_ locked, or the caller is a user-space process which
 * holds a reference on the inode by having an open file.
 *
 * In other cases, the page should be locked before running set_page_dirty().
 */
int set_page_dirty_lock(struct page *page)
{
        int ret;

        lock_page(page);
        ret = set_page_dirty(page);
        unlock_page(page);
        return ret;
}
EXPORT_SYMBOL(set_page_dirty_lock);

/*
 * This cancels just the dirty bit on the kernel page itself, it does NOT
 * actually remove dirty bits on any mmap's that may be around. It also
 * leaves the page tagged dirty, so any sync activity will still find it on
 * the dirty lists, and in particular, clear_page_dirty_for_io() will still
 * look at the dirty bits in the VM.
 *
 * Doing this should *normally* only ever be done when a page is truncated,
 * and is not actually mapped anywhere at all. However, fs/buffer.c does
 * this when it notices that somebody has cleaned out all the buffers on a
 * page without actually doing it through the VM. Can you say "ext3 is
 * horribly ugly"? Thought you could.
 */
void cancel_dirty_page(struct page *page)
{
        struct address_space *mapping = page_mapping(page);

        if (mapping_cap_account_dirty(mapping)) {
                struct inode *inode = mapping->host;
                struct bdi_writeback *wb;
                struct mem_cgroup *memcg;
                bool locked;

                memcg = mem_cgroup_begin_page_stat(page);
                wb = unlocked_inode_to_wb_begin(inode, &locked);

                if (TestClearPageDirty(page))
                        account_page_cleaned(page, mapping, memcg, wb);

                unlocked_inode_to_wb_end(inode, locked);
                mem_cgroup_end_page_stat(memcg);
        } else {
                ClearPageDirty(page);
        }
}
EXPORT_SYMBOL(cancel_dirty_page);

/*
 * Clear a page's dirty flag, while caring for dirty memory accounting.
 * Returns true if the page was previously dirty.
 *
 * This is for preparing to put the page under writeout.  We leave the page
 * tagged as dirty in the radix tree so that a concurrent write-for-sync
 * can discover it via a PAGECACHE_TAG_DIRTY walk.  The ->writepage
 * implementation will run either set_page_writeback() or set_page_dirty(),
 * at which stage we bring the page's dirty flag and radix-tree dirty tag
 * back into sync.
 *
 * This incoherency between the page's dirty flag and radix-tree tag is
 * unfortunate, but it only exists while the page is locked.
 */
int clear_page_dirty_for_io(struct page *page)
{
        struct address_space *mapping = page_mapping(page);
        int ret = 0;

        BUG_ON(!PageLocked(page));

        if (mapping && mapping_cap_account_dirty(mapping)) {
                struct inode *inode = mapping->host;
                struct bdi_writeback *wb;
                struct mem_cgroup *memcg;
                bool locked;

                /*
                 * Yes, Virginia, this is indeed insane.
                 *
                 * We use this sequence to make sure that
                 *  (a) we account for dirty stats properly
                 *  (b) we tell the low-level filesystem to
                 *      mark the whole page dirty if it was
                 *      dirty in a pagetable. Only to then
                 *  (c) clean the page again and return 1 to
                 *      cause the writeback.
                 *
                 * This way we avoid all nasty races with the
                 * dirty bit in multiple places and clearing
                 * them concurrently from different threads.
                 *
                 * Note! Normally the "set_page_dirty(page)"
                 * has no effect on the actual dirty bit - since
                 * that will already usually be set. But we
                 * need the side effects, and it can help us
                 * avoid races.
                 *
                 * We basically use the page "master dirty bit"
                 * as a serialization point for all the different
                 * threads doing their things.
                 */
                if (page_mkclean(page))
                        set_page_dirty(page);
                /*
                 * We carefully synchronise fault handlers against
                 * installing a dirty pte and marking the page dirty
                 * at this point.  We do this by having them hold the
                 * page lock while dirtying the page, and pages are
                 * always locked coming in here, so we get the desired
                 * exclusion.
                 */
                memcg = mem_cgroup_begin_page_stat(page);
                wb = unlocked_inode_to_wb_begin(inode, &locked);
                if (TestClearPageDirty(page)) {
                        mem_cgroup_dec_page_stat(memcg, MEM_CGROUP_STAT_DIRTY);
                        dec_zone_page_state(page, NR_FILE_DIRTY);
                        dec_wb_stat(wb, WB_RECLAIMABLE);
                        ret = 1;
                }
                unlocked_inode_to_wb_end(inode, locked);
                mem_cgroup_end_page_stat(memcg);
                return ret;
        }
        return TestClearPageDirty(page);
}
EXPORT_SYMBOL(clear_page_dirty_for_io);

int test_clear_page_writeback(struct page *page)
{
        struct address_space *mapping = page_mapping(page);
        struct mem_cgroup *memcg;
        int ret;

        memcg = mem_cgroup_begin_page_stat(page);
        if (mapping) {
                struct inode *inode = mapping->host;
                struct backing_dev_info *bdi = inode_to_bdi(inode);
                unsigned long flags;

                spin_lock_irqsave(&mapping->tree_lock, flags);
                ret = TestClearPageWriteback(page);
                if (ret) {
                        radix_tree_tag_clear(&mapping->page_tree,
                                                page_index(page),
                                                PAGECACHE_TAG_WRITEBACK);
                        if (bdi_cap_account_writeback(bdi)) {
                                struct bdi_writeback *wb = inode_to_wb(inode);

                                __dec_wb_stat(wb, WB_WRITEBACK);
                                __wb_writeout_inc(wb);
                        }
                }
                spin_unlock_irqrestore(&mapping->tree_lock, flags);
        } else {
                ret = TestClearPageWriteback(page);
        }
        if (ret) {
                mem_cgroup_dec_page_stat(memcg, MEM_CGROUP_STAT_WRITEBACK);
                dec_zone_page_state(page, NR_WRITEBACK);
                inc_zone_page_state(page, NR_WRITTEN);
        }
        mem_cgroup_end_page_stat(memcg);
        return ret;
}

int __test_set_page_writeback(struct page *page, bool keep_write)
{
        struct address_space *mapping = page_mapping(page);
        struct mem_cgroup *memcg;
        int ret;

        memcg = mem_cgroup_begin_page_stat(page);
        if (mapping) {
                struct inode *inode = mapping->host;
                struct backing_dev_info *bdi = inode_to_bdi(inode);
                unsigned long flags;

                spin_lock_irqsave(&mapping->tree_lock, flags);
                ret = TestSetPageWriteback(page);
                if (!ret) {
                        radix_tree_tag_set(&mapping->page_tree,
                                                page_index(page),
                                                PAGECACHE_TAG_WRITEBACK);
                        if (bdi_cap_account_writeback(bdi))
                                __inc_wb_stat(inode_to_wb(inode), WB_WRITEBACK);
                }
                if (!PageDirty(page))
                        radix_tree_tag_clear(&mapping->page_tree,
                                                page_index(page),
                                                PAGECACHE_TAG_DIRTY);
                if (!keep_write)
                        radix_tree_tag_clear(&mapping->page_tree,
                                                page_index(page),
                                                PAGECACHE_TAG_TOWRITE);
                spin_unlock_irqrestore(&mapping->tree_lock, flags);
        } else {
                ret = TestSetPageWriteback(page);
        }
        if (!ret) {
                mem_cgroup_inc_page_stat(memcg, MEM_CGROUP_STAT_WRITEBACK);
                inc_zone_page_state(page, NR_WRITEBACK);
        }
        mem_cgroup_end_page_stat(memcg);
        return ret;

}
EXPORT_SYMBOL(__test_set_page_writeback);

/*
 * Return true if any of the pages in the mapping are marked with the
 * passed tag.
 */
int mapping_tagged(struct address_space *mapping, int tag)
{
        return radix_tree_tagged(&mapping->page_tree, tag);
}
EXPORT_SYMBOL(mapping_tagged);

/**
 * wait_for_stable_page() - wait for writeback to finish, if necessary.
 * @page:       The page to wait on.
 *
 * This function determines if the given page is related to a backing device
 * that requires page contents to be held stable during writeback.  If so, then
 * it will wait for any pending writeback to complete.
 */
void wait_for_stable_page(struct page *page)
{
        if (bdi_cap_stable_pages_required(inode_to_bdi(page->mapping->host)))
                wait_on_page_writeback(page);
}
EXPORT_SYMBOL_GPL(wait_for_stable_page);