1// SPDX-License-Identifier: GPL-2.0
2/*
3 * kernel/sched/loadavg.c
4 *
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.
8 */
9
10/*
11 * Global load-average calculations
12 *
13 * We take a distributed and async approach to calculating the global load-avg
14 * in order to minimize overhead.
15 *
16 * The global load average is an exponentially decaying average of nr_running +
17 * nr_uninterruptible.
18 *
19 * Once every LOAD_FREQ:
20 *
21 * nr_active = 0;
22 * for_each_possible_cpu(cpu)
23 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
24 *
25 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
26 *
27 * Due to a number of reasons the above turns in the mess below:
28 *
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.
32 *
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) }
35 *
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().
39 *
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.
43 *
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.
46 *
47 * - cpu_rq()->nr_uninterruptible isn't accurately tracked per-CPU because
48 * this would add another cross-CPU cacheline 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.
53 *
54 * This covers the NO_HZ=n code, for extra head-aches, see the comment below.
55 */
56
57/* Variables and functions for calc_load */
58atomic_long_t calc_load_tasks;
59unsigned long calc_load_update;
60unsigned long avenrun[3];
61EXPORT_SYMBOL(avenrun); /* should be removed */
62
63/**
64 * get_avenrun - get the load average array
65 * @loads: pointer to dest load array
66 * @offset: offset to add
67 * @shift: shift count to shift the result left
68 *
69 * These values are estimates at best, so no need for locking.
70 */
71void get_avenrun(unsigned long *loads, unsigned long offset, int shift)
72{
73 loads[0] = (avenrun[0] + offset) << shift;
74 loads[1] = (avenrun[1] + offset) << shift;
75 loads[2] = (avenrun[2] + offset) << shift;
76}
77
78long calc_load_fold_active(struct rq *this_rq, long adjust)
79{
80 long nr_active, delta = 0;
81
82 nr_active = this_rq->nr_running - adjust;
83 nr_active += (int)this_rq->nr_uninterruptible;
84
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;
88 }
89
90 return delta;
91}
92
93/**
94 * fixed_power_int - compute: x^n, in O(log n) time
95 *
96 * @x: base of the power
97 * @frac_bits: fractional bits of @x
98 * @n: power to raise @x to.
99 *
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
106 * vector.
107 */
108static unsigned long
109fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n)
110{
111 unsigned long result = 1UL << frac_bits;
112
113 if (n) {
114 for (;;) {
115 if (n & 1) {
116 result *= x;
117 result += 1UL << (frac_bits - 1);
118 result >>= frac_bits;
119 }
120 n >>= 1;
121 if (!n)
122 break;
123 x *= x;
124 x += 1UL << (frac_bits - 1);
125 x >>= frac_bits;
126 }
127 }
128
129 return result;
130}
131
132/*
133 * a1 = a0 * e + a * (1 - e)
134 *
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)
138 *
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)
142 *
143 * ...
144 *
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)
148 *
149 * [1] application of the geometric series:
150 *
151 * n 1 - x^(n+1)
152 * S_n := \Sum x^i = -------------
153 * i=0 1 - x
154 */
155unsigned long
156calc_load_n(unsigned long load, unsigned long exp,
157 unsigned long active, unsigned int n)
158{
159 return calc_load(load, exp: fixed_power_int(x: exp, FSHIFT, n), active);
160}
161
162#ifdef CONFIG_NO_HZ_COMMON
163/*
164 * Handle NO_HZ for the global load-average.
165 *
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
168 * NO_HZ.
169 *
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.
173 *
174 * Obviously reality has to ruin such a delightfully simple scheme:
175 *
176 * - When we go NO_HZ idle during the window, we can negate our sample
177 * contribution, causing under-accounting.
178 *
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.
181 *
182 * The only trick is the slight shift in index flip for read vs write.
183 *
184 * 0s 5s 10s 15s
185 * +10 +10 +10 +10
186 * |-|-----------|-|-----------|-|-----------|-|
187 * r:0 0 1 1 0 0 1 1 0
188 * w:0 1 1 0 0 1 1 0 0
189 *
190 * This ensures we'll fold the old NO_HZ contribution in this window while
191 * accumulating the new one.
192 *
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
195 * busy state.
196 *
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
201 * intervals.
202 *
203 * When making the ILB scale, we should try to pull this in as well.
204 */
205static atomic_long_t calc_load_nohz[2];
206static int calc_load_idx;
207
208static inline int calc_load_write_idx(void)
209{
210 int idx = calc_load_idx;
211
212 /*
213 * See calc_global_nohz(), if we observe the new index, we also
214 * need to observe the new update time.
215 */
216 smp_rmb();
217
218 /*
219 * If the folding window started, make sure we start writing in the
220 * next NO_HZ-delta.
221 */
222 if (!time_before(jiffies, READ_ONCE(calc_load_update)))
223 idx++;
224
225 return idx & 1;
226}
227
228static inline int calc_load_read_idx(void)
229{
230 return calc_load_idx & 1;
231}
232
233static void calc_load_nohz_fold(struct rq *rq)
234{
235 long delta;
236
237 delta = calc_load_fold_active(this_rq: rq, adjust: 0);
238 if (delta) {
239 int idx = calc_load_write_idx();
240
241 atomic_long_add(i: delta, v: &calc_load_nohz[idx]);
242 }
243}
244
245void calc_load_nohz_start(void)
246{
247 /*
248 * We're going into NO_HZ mode, if there's any pending delta, fold it
249 * into the pending NO_HZ delta.
250 */
251 calc_load_nohz_fold(this_rq());
252}
253
254/*
255 * Keep track of the load for NOHZ_FULL, must be called between
256 * calc_load_nohz_{start,stop}().
257 */
258void calc_load_nohz_remote(struct rq *rq)
259{
260 calc_load_nohz_fold(rq);
261}
262
263void calc_load_nohz_stop(void)
264{
265 struct rq *this_rq = this_rq();
266
267 /*
268 * If we're still before the pending sample window, we're done.
269 */
270 this_rq->calc_load_update = READ_ONCE(calc_load_update);
271 if (time_before(jiffies, this_rq->calc_load_update))
272 return;
273
274 /*
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.
278 */
279 if (time_before(jiffies, this_rq->calc_load_update + 10))
280 this_rq->calc_load_update += LOAD_FREQ;
281}
282
283static long calc_load_nohz_read(void)
284{
285 int idx = calc_load_read_idx();
286 long delta = 0;
287
288 if (atomic_long_read(v: &calc_load_nohz[idx]))
289 delta = atomic_long_xchg(v: &calc_load_nohz[idx], new: 0);
290
291 return delta;
292}
293
294/*
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.
299 *
300 * Once we've updated the global active value, we need to apply the exponential
301 * weights adjusted to the number of cycles missed.
302 */
303static void calc_global_nohz(void)
304{
305 unsigned long sample_window;
306 long delta, active, n;
307
308 sample_window = READ_ONCE(calc_load_update);
309 if (!time_before(jiffies, sample_window + 10)) {
310 /*
311 * Catch-up, fold however many we are behind still
312 */
313 delta = jiffies - sample_window - 10;
314 n = 1 + (delta / LOAD_FREQ);
315
316 active = atomic_long_read(v: &calc_load_tasks);
317 active = active > 0 ? active * FIXED_1 : 0;
318
319 avenrun[0] = calc_load_n(load: avenrun[0], EXP_1, active, n);
320 avenrun[1] = calc_load_n(load: avenrun[1], EXP_5, active, n);
321 avenrun[2] = calc_load_n(load: avenrun[2], EXP_15, active, n);
322
323 WRITE_ONCE(calc_load_update, sample_window + n * LOAD_FREQ);
324 }
325
326 /*
327 * Flip the NO_HZ index...
328 *
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.
332 */
333 smp_wmb();
334 calc_load_idx++;
335}
336#else /* !CONFIG_NO_HZ_COMMON */
337
338static inline long calc_load_nohz_read(void) { return 0; }
339static inline void calc_global_nohz(void) { }
340
341#endif /* CONFIG_NO_HZ_COMMON */
342
343/*
344 * calc_load - update the avenrun load estimates 10 ticks after the
345 * CPUs have updated calc_load_tasks.
346 *
347 * Called from the global timer code.
348 */
349void calc_global_load(void)
350{
351 unsigned long sample_window;
352 long active, delta;
353
354 sample_window = READ_ONCE(calc_load_update);
355 if (time_before(jiffies, sample_window + 10))
356 return;
357
358 /*
359 * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs.
360 */
361 delta = calc_load_nohz_read();
362 if (delta)
363 atomic_long_add(i: delta, v: &calc_load_tasks);
364
365 active = atomic_long_read(v: &calc_load_tasks);
366 active = active > 0 ? active * FIXED_1 : 0;
367
368 avenrun[0] = calc_load(load: avenrun[0], EXP_1, active);
369 avenrun[1] = calc_load(load: avenrun[1], EXP_5, active);
370 avenrun[2] = calc_load(load: avenrun[2], EXP_15, active);
371
372 WRITE_ONCE(calc_load_update, sample_window + LOAD_FREQ);
373
374 /*
375 * In case we went to NO_HZ for multiple LOAD_FREQ intervals
376 * catch up in bulk.
377 */
378 calc_global_nohz();
379}
380
381/*
382 * Called from scheduler_tick() to periodically update this CPU's
383 * active count.
384 */
385void calc_global_load_tick(struct rq *this_rq)
386{
387 long delta;
388
389 if (time_before(jiffies, this_rq->calc_load_update))
390 return;
391
392 delta = calc_load_fold_active(this_rq, adjust: 0);
393 if (delta)
394 atomic_long_add(i: delta, v: &calc_load_tasks);
395
396 this_rq->calc_load_update += LOAD_FREQ;
397}
398

source code of linux/kernel/sched/loadavg.c