1 // SPDX-License-Identifier: GPL-2.0
3 * kernel/sched/loadavg.c
5 * This file contains the magic bits required to compute the global loadavg
6 * figure. Its a silly number but people think its important. We go through
7 * great pains to make it work on big machines and tickless kernels.
11 * Global load-average calculations
13 * We take a distributed and async approach to calculating the global load-avg
14 * in order to minimize overhead.
16 * The global load average is an exponentially decaying average of nr_running +
19 * Once every LOAD_FREQ:
22 * for_each_possible_cpu(cpu)
23 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
25 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
27 * Due to a number of reasons the above turns in the mess below:
29 * - for_each_possible_cpu() is prohibitively expensive on machines with
30 * serious number of CPUs, therefore we need to take a distributed approach
31 * to calculating nr_active.
33 * \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0
34 * = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) }
36 * So assuming nr_active := 0 when we start out -- true per definition, we
37 * can simply take per-CPU deltas and fold those into a global accumulate
38 * to obtain the same result. See calc_load_fold_active().
40 * Furthermore, in order to avoid synchronizing all per-CPU delta folding
41 * across the machine, we assume 10 ticks is sufficient time for every
42 * CPU to have completed this task.
44 * This places an upper-bound on the IRQ-off latency of the machine. Then
45 * again, being late doesn't loose the delta, just wrecks the sample.
47 * - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because
48 * this would add another cross-CPU cache-line miss and atomic operation
49 * to the wakeup path. Instead we increment on whatever CPU the task ran
50 * when it went into uninterruptible state and decrement on whatever CPU
51 * did the wakeup. This means that only the sum of nr_uninterruptible over
52 * all CPUs yields the correct result.
54 * This covers the NO_HZ=n code, for extra head-aches, see the comment below.
57 /* Variables and functions for calc_load */
58 atomic_long_t calc_load_tasks
;
59 unsigned long calc_load_update
;
60 unsigned long avenrun
[3];
61 EXPORT_SYMBOL(avenrun
); /* should be removed */
64 * get_avenrun - get the load average array
65 * @loads: pointer to destination load array
66 * @offset: offset to add
67 * @shift: shift count to shift the result left
69 * These values are estimates at best, so no need for locking.
71 void get_avenrun(unsigned long *loads
, unsigned long offset
, int shift
)
73 loads
[0] = (avenrun
[0] + offset
) << shift
;
74 loads
[1] = (avenrun
[1] + offset
) << shift
;
75 loads
[2] = (avenrun
[2] + offset
) << shift
;
78 long calc_load_fold_active(struct rq
*this_rq
, long adjust
)
80 long nr_active
, delta
= 0;
82 nr_active
= this_rq
->nr_running
- adjust
;
83 nr_active
+= (int)this_rq
->nr_uninterruptible
;
85 if (nr_active
!= this_rq
->calc_load_active
) {
86 delta
= nr_active
- this_rq
->calc_load_active
;
87 this_rq
->calc_load_active
= nr_active
;
94 * fixed_power_int - compute: x^n, in O(log n) time
96 * @x: base of the power
97 * @frac_bits: fractional bits of @x
98 * @n: power to raise @x to.
100 * By exploiting the relation between the definition of the natural power
101 * function: x^n := x*x*...*x (x multiplied by itself for n times), and
102 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
103 * (where: n_i \elem {0, 1}, the binary vector representing n),
104 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
105 * of course trivially computable in O(log_2 n), the length of our binary
109 fixed_power_int(unsigned long x
, unsigned int frac_bits
, unsigned int n
)
111 unsigned long result
= 1UL << frac_bits
;
117 result
+= 1UL << (frac_bits
- 1);
118 result
>>= frac_bits
;
124 x
+= 1UL << (frac_bits
- 1);
133 * a1 = a0 * e + a * (1 - e)
135 * a2 = a1 * e + a * (1 - e)
136 * = (a0 * e + a * (1 - e)) * e + a * (1 - e)
137 * = a0 * e^2 + a * (1 - e) * (1 + e)
139 * a3 = a2 * e + a * (1 - e)
140 * = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
141 * = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
145 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
146 * = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
147 * = a0 * e^n + a * (1 - e^n)
149 * [1] application of the geometric series:
152 * S_n := \Sum x^i = -------------
156 calc_load_n(unsigned long load
, unsigned long exp
,
157 unsigned long active
, unsigned int n
)
159 return calc_load(load
, fixed_power_int(exp
, FSHIFT
, n
), active
);
162 #ifdef CONFIG_NO_HZ_COMMON
164 * Handle NO_HZ for the global load-average.
166 * Since the above described distributed algorithm to compute the global
167 * load-average relies on per-CPU sampling from the tick, it is affected by
170 * The basic idea is to fold the nr_active delta into a global NO_HZ-delta upon
171 * entering NO_HZ state such that we can include this as an 'extra' CPU delta
172 * when we read the global state.
174 * Obviously reality has to ruin such a delightfully simple scheme:
176 * - When we go NO_HZ idle during the window, we can negate our sample
177 * contribution, causing under-accounting.
179 * We avoid this by keeping two NO_HZ-delta counters and flipping them
180 * when the window starts, thus separating old and new NO_HZ load.
182 * The only trick is the slight shift in index flip for read vs write.
186 * |-|-----------|-|-----------|-|-----------|-|
187 * r:0 0 1 1 0 0 1 1 0
188 * w:0 1 1 0 0 1 1 0 0
190 * This ensures we'll fold the old NO_HZ contribution in this window while
191 * accumulating the new one.
193 * - When we wake up from NO_HZ during the window, we push up our
194 * contribution, since we effectively move our sample point to a known
197 * This is solved by pushing the window forward, and thus skipping the
198 * sample, for this CPU (effectively using the NO_HZ-delta for this CPU which
199 * was in effect at the time the window opened). This also solves the issue
200 * of having to deal with a CPU having been in NO_HZ for multiple LOAD_FREQ
203 * When making the ILB scale, we should try to pull this in as well.
205 static atomic_long_t calc_load_nohz
[2];
206 static int calc_load_idx
;
208 static inline int calc_load_write_idx(void)
210 int idx
= calc_load_idx
;
213 * See calc_global_nohz(), if we observe the new index, we also
214 * need to observe the new update time.
219 * If the folding window started, make sure we start writing in the
222 if (!time_before(jiffies
, READ_ONCE(calc_load_update
)))
228 static inline int calc_load_read_idx(void)
230 return calc_load_idx
& 1;
233 static void calc_load_nohz_fold(struct rq
*rq
)
237 delta
= calc_load_fold_active(rq
, 0);
239 int idx
= calc_load_write_idx();
241 atomic_long_add(delta
, &calc_load_nohz
[idx
]);
245 void calc_load_nohz_start(void)
248 * We're going into NO_HZ mode, if there's any pending delta, fold it
249 * into the pending NO_HZ delta.
251 calc_load_nohz_fold(this_rq());
255 * Keep track of the load for NOHZ_FULL, must be called between
256 * calc_load_nohz_{start,stop}().
258 void calc_load_nohz_remote(struct rq
*rq
)
260 calc_load_nohz_fold(rq
);
263 void calc_load_nohz_stop(void)
265 struct rq
*this_rq
= this_rq();
268 * If we're still before the pending sample window, we're done.
270 this_rq
->calc_load_update
= READ_ONCE(calc_load_update
);
271 if (time_before(jiffies
, this_rq
->calc_load_update
))
275 * We woke inside or after the sample window, this means we're already
276 * accounted through the nohz accounting, so skip the entire deal and
277 * sync up for the next window.
279 if (time_before(jiffies
, this_rq
->calc_load_update
+ 10))
280 this_rq
->calc_load_update
+= LOAD_FREQ
;
283 static long calc_load_nohz_read(void)
285 int idx
= calc_load_read_idx();
288 if (atomic_long_read(&calc_load_nohz
[idx
]))
289 delta
= atomic_long_xchg(&calc_load_nohz
[idx
], 0);
295 * NO_HZ can leave us missing all per-CPU ticks calling
296 * calc_load_fold_active(), but since a NO_HZ CPU folds its delta into
297 * calc_load_nohz per calc_load_nohz_start(), all we need to do is fold
298 * in the pending NO_HZ delta if our NO_HZ period crossed a load cycle boundary.
300 * Once we've updated the global active value, we need to apply the exponential
301 * weights adjusted to the number of cycles missed.
303 static void calc_global_nohz(void)
305 unsigned long sample_window
;
306 long delta
, active
, n
;
308 sample_window
= READ_ONCE(calc_load_update
);
309 if (!time_before(jiffies
, sample_window
+ 10)) {
311 * Catch-up, fold however many we are behind still
313 delta
= jiffies
- sample_window
- 10;
314 n
= 1 + (delta
/ LOAD_FREQ
);
316 active
= atomic_long_read(&calc_load_tasks
);
317 active
= active
> 0 ? active
* FIXED_1
: 0;
319 avenrun
[0] = calc_load_n(avenrun
[0], EXP_1
, active
, n
);
320 avenrun
[1] = calc_load_n(avenrun
[1], EXP_5
, active
, n
);
321 avenrun
[2] = calc_load_n(avenrun
[2], EXP_15
, active
, n
);
323 WRITE_ONCE(calc_load_update
, sample_window
+ n
* LOAD_FREQ
);
327 * Flip the NO_HZ index...
329 * Make sure we first write the new time then flip the index, so that
330 * calc_load_write_idx() will see the new time when it reads the new
331 * index, this avoids a double flip messing things up.
336 #else /* !CONFIG_NO_HZ_COMMON */
338 static inline long calc_load_nohz_read(void) { return 0; }
339 static inline void calc_global_nohz(void) { }
341 #endif /* CONFIG_NO_HZ_COMMON */
344 * calc_load - update the avenrun load estimates 10 ticks after the
345 * CPUs have updated calc_load_tasks.
347 * Called from the global timer code.
349 void calc_global_load(void)
351 unsigned long sample_window
;
354 sample_window
= READ_ONCE(calc_load_update
);
355 if (time_before(jiffies
, sample_window
+ 10))
359 * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs.
361 delta
= calc_load_nohz_read();
363 atomic_long_add(delta
, &calc_load_tasks
);
365 active
= atomic_long_read(&calc_load_tasks
);
366 active
= active
> 0 ? active
* FIXED_1
: 0;
368 avenrun
[0] = calc_load(avenrun
[0], EXP_1
, active
);
369 avenrun
[1] = calc_load(avenrun
[1], EXP_5
, active
);
370 avenrun
[2] = calc_load(avenrun
[2], EXP_15
, active
);
372 WRITE_ONCE(calc_load_update
, sample_window
+ LOAD_FREQ
);
375 * In case we went to NO_HZ for multiple LOAD_FREQ intervals
382 * Called from sched_tick() to periodically update this CPU's
385 void calc_global_load_tick(struct rq
*this_rq
)
389 if (time_before(jiffies
, this_rq
->calc_load_update
))
392 delta
= calc_load_fold_active(this_rq
, 0);
394 atomic_long_add(delta
, &calc_load_tasks
);
396 this_rq
->calc_load_update
+= LOAD_FREQ
;