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 // SPDX-License-Identifier: GPL-2.0
 /*
  * kernel/sched/loadavg.c
  *
  * This file contains the magic bits required to compute the global loadavg
  * figure. Its a silly number but people think its important. We go through
  * great pains to make it work on big machines and tickless kernels.
  */
 
 /*
  * Global load-average calculations
  *
  * We take a distributed and async approach to calculating the global load-avg
  * in order to minimize overhead.
  *
  * The global load average is an exponentially decaying average of nr_running +
  * nr_uninterruptible.
  *
  * Once every LOAD_FREQ:
  *
  *   nr_active = 0;
  *   for_each_possible_cpu(cpu)
  *  nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
  *
  *   avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
  *
  * Due to a number of reasons the above turns in the mess below:
  *
  *  - for_each_possible_cpu() is prohibitively expensive on machines with
  *    serious number of CPUs, therefore we need to take a distributed approach
  *    to calculating nr_active.
  *
  *        \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0
  *                      = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) }
  *
  *    So assuming nr_active := 0 when we start out -- true per definition, we
  *    can simply take per-CPU deltas and fold those into a global accumulate
  *    to obtain the same result. See calc_load_fold_active().
  *
  *    Furthermore, in order to avoid synchronizing all per-CPU delta folding
  *    across the machine, we assume 10 ticks is sufficient time for every
  *    CPU to have completed this task.
  *
  *    This places an upper-bound on the IRQ-off latency of the machine. Then
  *    again, being late doesn't loose the delta, just wrecks the sample.
  *
  *  - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because
  *    this would add another cross-CPU cacheline miss and atomic operation
  *    to the wakeup path. Instead we increment on whatever CPU the task ran
  *    when it went into uninterruptible state and decrement on whatever CPU
  *    did the wakeup. This means that only the sum of nr_uninterruptible over
  *    all CPUs yields the correct result.
  *
  *  This covers the NO_HZ=n code, for extra head-aches, see the comment below.
  */
 
 /* Variables and functions for calc_load */
 atomic_long_t calc_load_tasks;
 unsigned long calc_load_update;
 unsigned long avenrun[3];
 EXPORT_SYMBOL(avenrun); /* should be removed */
 
 /**
  * get_avenrun - get the load average array
  * @loads:  pointer to dest load array
  * @offset: offset to add
  * @shift:  shift count to shift the result left
  *
  * These values are estimates at best, so no need for locking.
  */
 void get_avenrun(unsigned long *loads, unsigned long offset, int shift)
 {
     loads[0] = (avenrun[0] + offset) << shift;
     loads[1] = (avenrun[1] + offset) << shift;
     loads[2] = (avenrun[2] + offset) << shift;
 }
 
 long calc_load_fold_active(struct rq *this_rq, long adjust)
 {
     long nr_active, delta = 0;
 
     nr_active = this_rq->nr_running - adjust;
     nr_active += (int)this_rq->nr_uninterruptible;
 
     if (nr_active != this_rq->calc_load_active) {
         delta = nr_active - this_rq->calc_load_active;
         this_rq->calc_load_active = nr_active;
     }
 
     return delta;
 }
 
 /**
  * fixed_power_int - compute: x^n, in O(log n) time
  *
  * @x:         base of the power
  * @frac_bits: fractional bits of @x
  * @n:         power to raise @x to.
  *
  * By exploiting the relation between the definition of the natural power
  * function: x^n := x*x*...*x (x multiplied by itself for n times), and
  * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
  * (where: n_i \elem {0, 1}, the binary vector representing n),
  * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
  * of course trivially computable in O(log_2 n), the length of our binary
  * vector.
  */
 static unsigned long
 fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n)
 {
     unsigned long result = 1UL << frac_bits;
 
     if (n) {
         for (;;) {
             if (n & 1) {
                 result *= x;
                 result += 1UL << (frac_bits - 1);
                 result >>= frac_bits;
             }
             n >>= 1;
             if (!n)
                 break;
             x *= x;
             x += 1UL << (frac_bits - 1);
             x >>= frac_bits;
         }
     }
 
     return result;
 }
 
 /*
  * a1 = a0 * e + a * (1 - e)
  *
  * a2 = a1 * e + a * (1 - e)
  *    = (a0 * e + a * (1 - e)) * e + a * (1 - e)
  *    = a0 * e^2 + a * (1 - e) * (1 + e)
  *
  * a3 = a2 * e + a * (1 - e)
  *    = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
  *    = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
  *
  *  ...
  *
  * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
  *    = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
  *    = a0 * e^n + a * (1 - e^n)
  *
  * [1] application of the geometric series:
  *
  *              n         1 - x^(n+1)
  *     S_n := \Sum x^i = -------------
  *             i=0          1 - x
  */
 unsigned long
 calc_load_n(unsigned long load, unsigned long exp,
         unsigned long active, unsigned int n)
 {
     return calc_load(load, fixed_power_int(exp, FSHIFT, n), active);
 }
 
 #ifdef CONFIG_NO_HZ_COMMON
 /*
  * Handle NO_HZ for the global load-average.
  *
  * Since the above described distributed algorithm to compute the global
  * load-average relies on per-CPU sampling from the tick, it is affected by
  * NO_HZ.
  *
  * The basic idea is to fold the nr_active delta into a global NO_HZ-delta upon
  * entering NO_HZ state such that we can include this as an 'extra' CPU delta
  * when we read the global state.
  *
  * Obviously reality has to ruin such a delightfully simple scheme:
  *
  *  - When we go NO_HZ idle during the window, we can negate our sample
  *    contribution, causing under-accounting.
  *
  *    We avoid this by keeping two NO_HZ-delta counters and flipping them
  *    when the window starts, thus separating old and new NO_HZ load.
  *
  *    The only trick is the slight shift in index flip for read vs write.
  *
  *        0s            5s            10s           15s
  *          +10           +10           +10           +10
  *        |-|-----------|-|-----------|-|-----------|-|
  *    r:0 0 1           1 0           0 1           1 0
  *    w:0 1 1           0 0           1 1           0 0
  *
  *    This ensures we'll fold the old NO_HZ contribution in this window while
  *    accumulating the new one.
  *
  *  - When we wake up from NO_HZ during the window, we push up our
  *    contribution, since we effectively move our sample point to a known
  *    busy state.
  *
  *    This is solved by pushing the window forward, and thus skipping the
  *    sample, for this CPU (effectively using the NO_HZ-delta for this CPU which
  *    was in effect at the time the window opened). This also solves the issue
  *    of having to deal with a CPU having been in NO_HZ for multiple LOAD_FREQ
  *    intervals.
  *
  * When making the ILB scale, we should try to pull this in as well.
  */
 static atomic_long_t calc_load_nohz[2];
 static int calc_load_idx;
 
 static inline int calc_load_write_idx(void)
 {
     int idx = calc_load_idx;
 
     /*
      * See calc_global_nohz(), if we observe the new index, we also
      * need to observe the new update time.
      */
     smp_rmb();
 
     /*
      * If the folding window started, make sure we start writing in the
      * next NO_HZ-delta.
      */
     if (!time_before(jiffies, READ_ONCE(calc_load_update)))
         idx++;
 
     return idx & 1;
 }
 
 static inline int calc_load_read_idx(void)
 {
     return calc_load_idx & 1;
 }
 
 static void calc_load_nohz_fold(struct rq *rq)
 {
     long delta;
 
     delta = calc_load_fold_active(rq, 0);
     if (delta) {
         int idx = calc_load_write_idx();
 
         atomic_long_add(delta, &calc_load_nohz[idx]);
     }
 }
 
 void calc_load_nohz_start(void)
 {
     /*
      * We're going into NO_HZ mode, if there's any pending delta, fold it
      * into the pending NO_HZ delta.
      */
     calc_load_nohz_fold(this_rq());
 }
 
 /*
  * Keep track of the load for NOHZ_FULL, must be called between
  * calc_load_nohz_{start,stop}().
  */
 void calc_load_nohz_remote(struct rq *rq)
 {
     calc_load_nohz_fold(rq);
 }
 
 void calc_load_nohz_stop(void)
 {
     struct rq *this_rq = this_rq();
 
     /*
      * If we're still before the pending sample window, we're done.
      */
     this_rq->calc_load_update = READ_ONCE(calc_load_update);
     if (time_before(jiffies, this_rq->calc_load_update))
         return;
 
     /*
      * We woke inside or after the sample window, this means we're already
      * accounted through the nohz accounting, so skip the entire deal and
      * sync up for the next window.
      */
     if (time_before(jiffies, this_rq->calc_load_update + 10))
         this_rq->calc_load_update += LOAD_FREQ;
 }
 
 static long calc_load_nohz_read(void)
 {
     int idx = calc_load_read_idx();
     long delta = 0;
 
     if (atomic_long_read(&calc_load_nohz[idx]))
         delta = atomic_long_xchg(&calc_load_nohz[idx], 0);
 
     return delta;
 }
 
 /*
  * NO_HZ can leave us missing all per-CPU ticks calling
  * calc_load_fold_active(), but since a NO_HZ CPU folds its delta into
  * calc_load_nohz per calc_load_nohz_start(), all we need to do is fold
  * in the pending NO_HZ delta if our NO_HZ period crossed a load cycle boundary.
  *
  * Once we've updated the global active value, we need to apply the exponential
  * weights adjusted to the number of cycles missed.
  */
 static void calc_global_nohz(void)
 {
     unsigned long sample_window;
     long delta, active, n;
 
     sample_window = READ_ONCE(calc_load_update);
     if (!time_before(jiffies, sample_window + 10)) {
         /*
          * Catch-up, fold however many we are behind still
          */
         delta = jiffies - sample_window - 10;
         n = 1 + (delta / LOAD_FREQ);
 
         active = atomic_long_read(&calc_load_tasks);
         active = active > 0 ? active * FIXED_1 : 0;
 
         avenrun[0] = calc_load_n(avenrun[0], EXP_1, active, n);
         avenrun[1] = calc_load_n(avenrun[1], EXP_5, active, n);
         avenrun[2] = calc_load_n(avenrun[2], EXP_15, active, n);
 
         WRITE_ONCE(calc_load_update, sample_window + n * LOAD_FREQ);
     }
 
     /*
      * Flip the NO_HZ index...
      *
      * Make sure we first write the new time then flip the index, so that
      * calc_load_write_idx() will see the new time when it reads the new
      * index, this avoids a double flip messing things up.
      */
     smp_wmb();
     calc_load_idx++;
 }
 #else /* !CONFIG_NO_HZ_COMMON */
 
 static inline long calc_load_nohz_read(void) { return 0; }
 static inline void calc_global_nohz(void) { }
 
 #endif /* CONFIG_NO_HZ_COMMON */
 
 /*
  * calc_load - update the avenrun load estimates 10 ticks after the
  * CPUs have updated calc_load_tasks.
  *
  * Called from the global timer code.
  */
 void calc_global_load(void)
 {
     unsigned long sample_window;
     long active, delta;
 
     sample_window = READ_ONCE(calc_load_update);
     if (time_before(jiffies, sample_window + 10))
         return;
 
     /*
      * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs.
      */
     delta = calc_load_nohz_read();
     if (delta)
         atomic_long_add(delta, &calc_load_tasks);
 
     active = atomic_long_read(&calc_load_tasks);
     active = active > 0 ? active * FIXED_1 : 0;
 
     avenrun[0] = calc_load(avenrun[0], EXP_1, active);
     avenrun[1] = calc_load(avenrun[1], EXP_5, active);
     avenrun[2] = calc_load(avenrun[2], EXP_15, active);
 
     WRITE_ONCE(calc_load_update, sample_window + LOAD_FREQ);
 
     /*
      * In case we went to NO_HZ for multiple LOAD_FREQ intervals
      * catch up in bulk.
      */
     calc_global_nohz();
 }
 
 /*
  * Called from scheduler_tick() to periodically update this CPU's
  * active count.
  */
 void calc_global_load_tick(struct rq *this_rq)
 {
     long delta;
 
     if (time_before(jiffies, this_rq->calc_load_update))
         return;
 
     delta  = calc_load_fold_active(this_rq, 0);
     if (delta)
         atomic_long_add(delta, &calc_load_tasks);
 
     this_rq->calc_load_update += LOAD_FREQ;
 }

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