| // 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 "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 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 += (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; | 
 | } | 
 |  | 
 | /* | 
 |  * a1 = a0 * e + a * (1 - e) | 
 |  */ | 
 | static unsigned long | 
 | calc_load(unsigned long load, unsigned long exp, unsigned long active) | 
 | { | 
 | 	unsigned long newload; | 
 |  | 
 | 	newload = load * exp + active * (FIXED_1 - exp); | 
 | 	if (active >= load) | 
 | 		newload += FIXED_1-1; | 
 |  | 
 | 	return newload / FIXED_1; | 
 | } | 
 |  | 
 | #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 | 
 |  *    accumlating 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; | 
 | } | 
 |  | 
 | void calc_load_nohz_start(void) | 
 | { | 
 | 	struct rq *this_rq = this_rq(); | 
 | 	long delta; | 
 |  | 
 | 	/* | 
 | 	 * We're going into NO_HZ mode, if there's any pending delta, fold it | 
 | 	 * into the pending NO_HZ delta. | 
 | 	 */ | 
 | 	delta = calc_load_fold_active(this_rq, 0); | 
 | 	if (delta) { | 
 | 		int idx = calc_load_write_idx(); | 
 |  | 
 | 		atomic_long_add(delta, &calc_load_nohz[idx]); | 
 | 	} | 
 | } | 
 |  | 
 | 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_fold(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; | 
 | } | 
 |  | 
 | /** | 
 |  * 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 | 
 |  */ | 
 | static 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); | 
 | } | 
 |  | 
 | /* | 
 |  * 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_fold(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(unsigned long ticks) | 
 | { | 
 | 	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_fold(); | 
 | 	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; | 
 | } |