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#include "sched.h"
10
11/*
12 * Global load-average calculations
13 *
14 * We take a distributed and async approach to calculating the global load-avg
15 * in order to minimize overhead.
16 *
17 * The global load average is an exponentially decaying average of nr_running +
18 * nr_uninterruptible.
19 *
20 * Once every LOAD_FREQ:
21 *
22 * nr_active = 0;
23 * for_each_possible_cpu(cpu)
24 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
25 *
26 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
27 *
28 * Due to a number of reasons the above turns in the mess below:
29 *
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.
33 *
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) }
36 *
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().
40 *
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.
44 *
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.
47 *
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.
54 *
55 * This covers the NO_HZ=n code, for extra head-aches, see the comment below.
56 */
57
58/* Variables and functions for calc_load */
59atomic_long_t calc_load_tasks;
60unsigned long calc_load_update;
61unsigned long avenrun[3];
62EXPORT_SYMBOL(avenrun); /* should be removed */
63
64/**
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
69 *
70 * These values are estimates at best, so no need for locking.
71 */
72void get_avenrun(unsigned long *loads, unsigned long offset, int shift)
73{
74 loads[0] = (avenrun[0] + offset) << shift;
75 loads[1] = (avenrun[1] + offset) << shift;
76 loads[2] = (avenrun[2] + offset) << shift;
77}
78
79long calc_load_fold_active(struct rq *this_rq, long adjust)
80{
81 long nr_active, delta = 0;
82
83 nr_active = this_rq->nr_running - adjust;
84 nr_active += (long)this_rq->nr_uninterruptible;
85
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;
89 }
90
91 return delta;
92}
93
94/**
95 * fixed_power_int - compute: x^n, in O(log n) time
96 *
97 * @x: base of the power
98 * @frac_bits: fractional bits of @x
99 * @n: power to raise @x to.
100 *
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
107 * vector.
108 */
109static unsigned long
110fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n)
111{
112 unsigned long result = 1UL << frac_bits;
113
114 if (n) {
115 for (;;) {
116 if (n & 1) {
117 result *= x;
118 result += 1UL << (frac_bits - 1);
119 result >>= frac_bits;
120 }
121 n >>= 1;
122 if (!n)
123 break;
124 x *= x;
125 x += 1UL << (frac_bits - 1);
126 x >>= frac_bits;
127 }
128 }
129
130 return result;
131}
132
133/*
134 * a1 = a0 * e + a * (1 - e)
135 *
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)
139 *
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)
143 *
144 * ...
145 *
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)
149 *
150 * [1] application of the geometric series:
151 *
152 * n 1 - x^(n+1)
153 * S_n := \Sum x^i = -------------
154 * i=0 1 - x
155 */
156unsigned long
157calc_load_n(unsigned long load, unsigned long exp,
158 unsigned long active, unsigned int n)
159{
160 return calc_load(load, fixed_power_int(exp, FSHIFT, n), active);
161}
162
163#ifdef CONFIG_NO_HZ_COMMON
164/*
165 * Handle NO_HZ for the global load-average.
166 *
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
169 * NO_HZ.
170 *
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.
174 *
175 * Obviously reality has to ruin such a delightfully simple scheme:
176 *
177 * - When we go NO_HZ idle during the window, we can negate our sample
178 * contribution, causing under-accounting.
179 *
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.
182 *
183 * The only trick is the slight shift in index flip for read vs write.
184 *
185 * 0s 5s 10s 15s
186 * +10 +10 +10 +10
187 * |-|-----------|-|-----------|-|-----------|-|
188 * r:0 0 1 1 0 0 1 1 0
189 * w:0 1 1 0 0 1 1 0 0
190 *
191 * This ensures we'll fold the old NO_HZ contribution in this window while
192 * accumlating the new one.
193 *
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
196 * busy state.
197 *
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
202 * intervals.
203 *
204 * When making the ILB scale, we should try to pull this in as well.
205 */
206static atomic_long_t calc_load_nohz[2];
207static int calc_load_idx;
208
209static inline int calc_load_write_idx(void)
210{
211 int idx = calc_load_idx;
212
213 /*
214 * See calc_global_nohz(), if we observe the new index, we also
215 * need to observe the new update time.
216 */
217 smp_rmb();
218
219 /*
220 * If the folding window started, make sure we start writing in the
221 * next NO_HZ-delta.
222 */
223 if (!time_before(jiffies, READ_ONCE(calc_load_update)))
224 idx++;
225
226 return idx & 1;
227}
228
229static inline int calc_load_read_idx(void)
230{
231 return calc_load_idx & 1;
232}
233
234void calc_load_nohz_start(void)
235{
236 struct rq *this_rq = this_rq();
237 long delta;
238
239 /*
240 * We're going into NO_HZ mode, if there's any pending delta, fold it
241 * into the pending NO_HZ delta.
242 */
243 delta = calc_load_fold_active(this_rq, 0);
244 if (delta) {
245 int idx = calc_load_write_idx();
246
247 atomic_long_add(delta, &calc_load_nohz[idx]);
248 }
249}
250
251void calc_load_nohz_stop(void)
252{
253 struct rq *this_rq = this_rq();
254
255 /*
256 * If we're still before the pending sample window, we're done.
257 */
258 this_rq->calc_load_update = READ_ONCE(calc_load_update);
259 if (time_before(jiffies, this_rq->calc_load_update))
260 return;
261
262 /*
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.
266 */
267 if (time_before(jiffies, this_rq->calc_load_update + 10))
268 this_rq->calc_load_update += LOAD_FREQ;
269}
270
271static long calc_load_nohz_fold(void)
272{
273 int idx = calc_load_read_idx();
274 long delta = 0;
275
276 if (atomic_long_read(&calc_load_nohz[idx]))
277 delta = atomic_long_xchg(&calc_load_nohz[idx], 0);
278
279 return delta;
280}
281
282/*
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.
287 *
288 * Once we've updated the global active value, we need to apply the exponential
289 * weights adjusted to the number of cycles missed.
290 */
291static void calc_global_nohz(void)
292{
293 unsigned long sample_window;
294 long delta, active, n;
295
296 sample_window = READ_ONCE(calc_load_update);
297 if (!time_before(jiffies, sample_window + 10)) {
298 /*
299 * Catch-up, fold however many we are behind still
300 */
301 delta = jiffies - sample_window - 10;
302 n = 1 + (delta / LOAD_FREQ);
303
304 active = atomic_long_read(&calc_load_tasks);
305 active = active > 0 ? active * FIXED_1 : 0;
306
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);
310
311 WRITE_ONCE(calc_load_update, sample_window + n * LOAD_FREQ);
312 }
313
314 /*
315 * Flip the NO_HZ index...
316 *
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.
320 */
321 smp_wmb();
322 calc_load_idx++;
323}
324#else /* !CONFIG_NO_HZ_COMMON */
325
326static inline long calc_load_nohz_fold(void) { return 0; }
327static inline void calc_global_nohz(void) { }
328
329#endif /* CONFIG_NO_HZ_COMMON */
330
331/*
332 * calc_load - update the avenrun load estimates 10 ticks after the
333 * CPUs have updated calc_load_tasks.
334 *
335 * Called from the global timer code.
336 */
337void calc_global_load(unsigned long ticks)
338{
339 unsigned long sample_window;
340 long active, delta;
341
342 sample_window = READ_ONCE(calc_load_update);
343 if (time_before(jiffies, sample_window + 10))
344 return;
345
346 /*
347 * Fold the 'old' NO_HZ-delta to include all NO_HZ CPUs.
348 */
349 delta = calc_load_nohz_fold();
350 if (delta)
351 atomic_long_add(delta, &calc_load_tasks);
352
353 active = atomic_long_read(&calc_load_tasks);
354 active = active > 0 ? active * FIXED_1 : 0;
355
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);
359
360 WRITE_ONCE(calc_load_update, sample_window + LOAD_FREQ);
361
362 /*
363 * In case we went to NO_HZ for multiple LOAD_FREQ intervals
364 * catch up in bulk.
365 */
366 calc_global_nohz();
367}
368
369/*
370 * Called from scheduler_tick() to periodically update this CPU's
371 * active count.
372 */
373void calc_global_load_tick(struct rq *this_rq)
374{
375 long delta;
376
377 if (time_before(jiffies, this_rq->calc_load_update))
378 return;
379
380 delta = calc_load_fold_active(this_rq, 0);
381 if (delta)
382 atomic_long_add(delta, &calc_load_tasks);
383
384 this_rq->calc_load_update += LOAD_FREQ;
385}
386