// 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. */ #include <linux/sched/nohz.h> #include "sched.h" /* * 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 cache-line 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 destination 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 += (long)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 sched_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; }
