/* | |

* 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/export.h> | |

#include <linux/sched/loadavg.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 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; | |

} |