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.
12 * Global load-average calculations
14 * We take a distributed and async approach to calculating the global load-avg
15 * in order to minimize overhead.
17 * The global load average is an exponentially decaying average of nr_running +
20 * Once every LOAD_FREQ:
23 * for_each_possible_cpu(cpu)
24 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
26 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
28 * Due to a number of reasons the above turns in the mess below:
30 * - for_each_possible_cpu() is prohibitively expensive on machines with
31 * serious number of CPUs, therefore we need to take a distributed approach
32 * to calculating nr_active.
34 * \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0
35 * = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) }
37 * So assuming nr_active := 0 when we start out -- true per definition, we
38 * can simply take per-CPU deltas and fold those into a global accumulate
39 * to obtain the same result. See calc_load_fold_active().
41 * Furthermore, in order to avoid synchronizing all per-CPU delta folding
42 * across the machine, we assume 10 ticks is sufficient time for every
43 * CPU to have completed this task.
45 * This places an upper-bound on the IRQ-off latency of the machine. Then
46 * again, being late doesn't loose the delta, just wrecks the sample.
48 * - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because
49 * this would add another cross-CPU cacheline miss and atomic operation
50 * to the wakeup path. Instead we increment on whatever CPU the task ran
51 * when it went into uninterruptible state and decrement on whatever CPU
52 * did the wakeup. This means that only the sum of nr_uninterruptible over
53 * all CPUs yields the correct result.
55 * This covers the NO_HZ=n code, for extra head-aches, see the comment below.
58 /* Variables and functions for calc_load */
59 atomic_long_t calc_load_tasks
;
60 unsigned long calc_load_update
;
61 unsigned long avenrun
[3];
62 EXPORT_SYMBOL(avenrun
); /* should be removed */
65 * get_avenrun - get the load average array
66 * @loads: pointer to dest load array
67 * @offset: offset to add
68 * @shift: shift count to shift the result left
70 * These values are estimates at best, so no need for locking.
72 void get_avenrun(unsigned long *loads
, unsigned long offset
, int shift
)
74 loads
[0] = (avenrun
[0] + offset
) << shift
;
75 loads
[1] = (avenrun
[1] + offset
) << shift
;
76 loads
[2] = (avenrun
[2] + offset
) << shift
;
79 long calc_load_fold_active(struct rq
*this_rq
, long adjust
)
81 long nr_active
, delta
= 0;
83 nr_active
= this_rq
->nr_running
- adjust
;
84 nr_active
+= (long)this_rq
->nr_uninterruptible
;
86 if (nr_active
!= this_rq
->calc_load_active
) {
87 delta
= nr_active
- this_rq
->calc_load_active
;
88 this_rq
->calc_load_active
= nr_active
;
95 * fixed_power_int - compute: x^n, in O(log n) time
97 * @x: base of the power
98 * @frac_bits: fractional bits of @x
99 * @n: power to raise @x to.
101 * By exploiting the relation between the definition of the natural power
102 * function: x^n := x*x*...*x (x multiplied by itself for n times), and
103 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
104 * (where: n_i \elem {0, 1}, the binary vector representing n),
105 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
106 * of course trivially computable in O(log_2 n), the length of our binary
110 fixed_power_int(unsigned long x
, unsigned int frac_bits
, unsigned int n
)
112 unsigned long result
= 1UL << frac_bits
;
118 result
+= 1UL << (frac_bits
- 1);
119 result
>>= frac_bits
;
125 x
+= 1UL << (frac_bits
- 1);
134 * a1 = a0 * e + a * (1 - e)
136 * a2 = a1 * e + a * (1 - e)
137 * = (a0 * e + a * (1 - e)) * e + a * (1 - e)
138 * = a0 * e^2 + a * (1 - e) * (1 + e)
140 * a3 = a2 * e + a * (1 - e)
141 * = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
142 * = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
146 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
147 * = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
148 * = a0 * e^n + a * (1 - e^n)
150 * [1] application of the geometric series:
153 * S_n := \Sum x^i = -------------
157 calc_load_n(unsigned long load
, unsigned long exp
,
158 unsigned long active
, unsigned int n
)
160 return calc_load(load
, fixed_power_int(exp
, FSHIFT
, n
), active
);
163 #ifdef CONFIG_NO_HZ_COMMON
165 * Handle NO_HZ for the global load-average.
167 * Since the above described distributed algorithm to compute the global
168 * load-average relies on per-CPU sampling from the tick, it is affected by
171 * The basic idea is to fold the nr_active delta into a global NO_HZ-delta upon
172 * entering NO_HZ state such that we can include this as an 'extra' CPU delta
173 * when we read the global state.
175 * Obviously reality has to ruin such a delightfully simple scheme:
177 * - When we go NO_HZ idle during the window, we can negate our sample
178 * contribution, causing under-accounting.
180 * We avoid this by keeping two NO_HZ-delta counters and flipping them
181 * when the window starts, thus separating old and new NO_HZ load.
183 * The only trick is the slight shift in index flip for read vs write.
187 * |-|-----------|-|-----------|-|-----------|-|
188 * r:0 0 1 1 0 0 1 1 0
189 * w:0 1 1 0 0 1 1 0 0
191 * This ensures we'll fold the old NO_HZ contribution in this window while
192 * accumlating the new one.
194 * - When we wake up from NO_HZ during the window, we push up our
195 * contribution, since we effectively move our sample point to a known
198 * This is solved by pushing the window forward, and thus skipping the
199 * sample, for this CPU (effectively using the NO_HZ-delta for this CPU which
200 * was in effect at the time the window opened). This also solves the issue
201 * of having to deal with a CPU having been in NO_HZ for multiple LOAD_FREQ
204 * When making the ILB scale, we should try to pull this in as well.
206 static atomic_long_t calc_load_nohz
[2];
207 static int calc_load_idx
;
209 static inline int calc_load_write_idx(void)
211 int idx
= calc_load_idx
;
214 * See calc_global_nohz(), if we observe the new index, we also
215 * need to observe the new update time.
220 * If the folding window started, make sure we start writing in the
223 if (!time_before(jiffies
, READ_ONCE(calc_load_update
)))
229 static inline int calc_load_read_idx(void)
231 return calc_load_idx
& 1;
234 void calc_load_nohz_start(void)
236 struct rq
*this_rq
= this_rq();
240 * We're going into NO_HZ mode, if there's any pending delta, fold it
241 * into the pending NO_HZ delta.
243 delta
= calc_load_fold_active(this_rq
, 0);
245 int idx
= calc_load_write_idx();
247 atomic_long_add(delta
, &calc_load_nohz
[idx
]);
251 void calc_load_nohz_stop(void)
253 struct rq
*this_rq
= this_rq();
256 * If we're still before the pending sample window, we're done.
258 this_rq
->calc_load_update
= READ_ONCE(calc_load_update
);
259 if (time_before(jiffies
, this_rq
->calc_load_update
))
263 * We woke inside or after the sample window, this means we're already
264 * accounted through the nohz accounting, so skip the entire deal and
265 * sync up for the next window.
267 if (time_before(jiffies
, this_rq
->calc_load_update
+ 10))
268 this_rq
->calc_load_update
+= LOAD_FREQ
;
271 static long calc_load_nohz_fold(void)
273 int idx
= calc_load_read_idx();
276 if (atomic_long_read(&calc_load_nohz
[idx
]))
277 delta
= atomic_long_xchg(&calc_load_nohz
[idx
], 0);
283 * NO_HZ can leave us missing all per-CPU ticks calling
284 * calc_load_fold_active(), but since a NO_HZ CPU folds its delta into
285 * calc_load_nohz per calc_load_nohz_start(), all we need to do is fold
286 * in the pending NO_HZ delta if our NO_HZ period crossed a load cycle boundary.
288 * Once we've updated the global active value, we need to apply the exponential
289 * weights adjusted to the number of cycles missed.
291 static void calc_global_nohz(void)
293 unsigned long sample_window
;
294 long delta
, active
, n
;
296 sample_window
= READ_ONCE(calc_load_update
);
297 if (!time_before(jiffies
, sample_window
+ 10)) {
299 * Catch-up, fold however many we are behind still
301 delta
= jiffies
- sample_window
- 10;
302 n
= 1 + (delta
/ LOAD_FREQ
);
304 active
= atomic_long_read(&calc_load_tasks
);
305 active
= active
> 0 ? active
* FIXED_1
: 0;
307 avenrun
[0] = calc_load_n(avenrun
[0], EXP_1
, active
, n
);
308 avenrun
[1] = calc_load_n(avenrun
[1], EXP_5
, active
, n
);
309 avenrun
[2] = calc_load_n(avenrun
[2], EXP_15
, active
, n
);
311 WRITE_ONCE(calc_load_update
, sample_window
+ n
* LOAD_FREQ
);
315 * Flip the NO_HZ index...
317 * Make sure we first write the new time then flip the index, so that
318 * calc_load_write_idx() will see the new time when it reads the new
319 * index, this avoids a double flip messing things up.
324 #else /* !CONFIG_NO_HZ_COMMON */
326 static inline long calc_load_nohz_fold(void) { return 0; }
327 static inline void calc_global_nohz(void) { }
329 #endif /* CONFIG_NO_HZ_COMMON */
332 * calc_load - update the avenrun load estimates 10 ticks after the
333 * CPUs have updated calc_load_tasks.
335 * Called from the global timer code.
337 void calc_global_load(unsigned long ticks
)
339 unsigned long sample_window
;
342 sample_window
= READ_ONCE(calc_load_update
);
343 if (time_before(jiffies
, sample_window
+ 10))
347 * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs.
349 delta
= calc_load_nohz_fold();
351 atomic_long_add(delta
, &calc_load_tasks
);
353 active
= atomic_long_read(&calc_load_tasks
);
354 active
= active
> 0 ? active
* FIXED_1
: 0;
356 avenrun
[0] = calc_load(avenrun
[0], EXP_1
, active
);
357 avenrun
[1] = calc_load(avenrun
[1], EXP_5
, active
);
358 avenrun
[2] = calc_load(avenrun
[2], EXP_15
, active
);
360 WRITE_ONCE(calc_load_update
, sample_window
+ LOAD_FREQ
);
363 * In case we went to NO_HZ for multiple LOAD_FREQ intervals
370 * Called from scheduler_tick() to periodically update this CPU's
373 void calc_global_load_tick(struct rq
*this_rq
)
377 if (time_before(jiffies
, this_rq
->calc_load_update
))
380 delta
= calc_load_fold_active(this_rq
, 0);
382 atomic_long_add(delta
, &calc_load_tasks
);
384 this_rq
->calc_load_update
+= LOAD_FREQ
;