/*
* 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 "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 nr_active, delta = 0;
nr_active = this_rq->nr_running;
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)
{
load *= exp;
load += active * (FIXED_1 - exp);
load += 1UL << (FSHIFT - 1);
return load >> FSHIFT;
}
#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 idle-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 idle-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 idle contribution in this window while
* accumlating the new one.
*
* - When we wake up from NO_HZ idle 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 idle-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 NOHZ idle 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_idle[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 idle-delta.
*/
if (!time_before(jiffies, calc_load_update))
idx++;
return idx & 1;
}
static inline int calc_load_read_idx(void)
{
return calc_load_idx & 1;
}
void calc_load_enter_idle(void)
{
struct rq *this_rq = this_rq();
long delta;
/*
* We're going into NOHZ mode, if there's any pending delta, fold it
* into the pending idle delta.
*/
delta = calc_load_fold_active(this_rq);
if (delta) {
int idx = calc_load_write_idx();
atomic_long_add(delta, &calc_load_idle[idx]);
}
}
void calc_load_exit_idle(void)
{
struct rq *this_rq = this_rq();
/*
* If we're still before the sample window, we're done.
*/
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.
*/
this_rq->calc_load_update = calc_load_update;
if (time_before(jiffies, this_rq->calc_load_update + 10))
this_rq->calc_load_update += LOAD_FREQ;
}
static long calc_load_fold_idle(void)
{
int idx = calc_load_read_idx();
long delta = 0;
if (atomic_long_read(&calc_load_idle[idx]))
delta = atomic_long_xchg(&calc_load_idle[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_account_active(), but since an idle CPU folds its delta into
* calc_load_tasks_idle per calc_load_account_idle(), all we need to do is fold
* in the pending idle delta if our idle 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)
{
long delta, active, n;
if (!time_before(jiffies, calc_load_update + 10)) {
/*
* Catch-up, fold however many we are behind still
*/
delta = jiffies - calc_load_update - 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);
calc_load_update += n * LOAD_FREQ;
}
/*
* Flip the idle 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_fold_idle(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)
{
long active, delta;
if (time_before(jiffies, calc_load_update + 10))
return;
/*
* Fold the 'old' idle-delta to include all NO_HZ cpus.
*/
delta = calc_load_fold_idle();
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);
calc_load_update += LOAD_FREQ;
/*
* In case we idled 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);
if (delta)
atomic_long_add(delta, &calc_load_tasks);
this_rq->calc_load_update += LOAD_FREQ;
}