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1/*
2 * kernel/sched/loadavg.c
3 *
4 * This file contains the magic bits required to compute the global loadavg
5 * figure. Its a silly number but people think its important. We go through
6 * great pains to make it work on big machines and tickless kernels.
7 */
8
9#include <linux/export.h>
10
11#include "sched.h"
12
13/*
14 * Global load-average calculations
15 *
16 * We take a distributed and async approach to calculating the global load-avg
17 * in order to minimize overhead.
18 *
19 * The global load average is an exponentially decaying average of nr_running +
20 * nr_uninterruptible.
21 *
22 * Once every LOAD_FREQ:
23 *
24 * nr_active = 0;
25 * for_each_possible_cpu(cpu)
26 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
27 *
28 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
29 *
30 * Due to a number of reasons the above turns in the mess below:
31 *
32 * - for_each_possible_cpu() is prohibitively expensive on machines with
33 * serious number of cpus, therefore we need to take a distributed approach
34 * to calculating nr_active.
35 *
36 * \Sum_i x_i(t) = \Sum_i x_i(t) - x_i(t_0) | x_i(t_0) := 0
37 * = \Sum_i { \Sum_j=1 x_i(t_j) - x_i(t_j-1) }
38 *
39 * So assuming nr_active := 0 when we start out -- true per definition, we
40 * can simply take per-cpu deltas and fold those into a global accumulate
41 * to obtain the same result. See calc_load_fold_active().
42 *
43 * Furthermore, in order to avoid synchronizing all per-cpu delta folding
44 * across the machine, we assume 10 ticks is sufficient time for every
45 * cpu to have completed this task.
46 *
47 * This places an upper-bound on the IRQ-off latency of the machine. Then
48 * again, being late doesn't loose the delta, just wrecks the sample.
49 *
50 * - cpu_rq()->nr_uninterruptible isn't accurately tracked per-cpu because
51 * this would add another cross-cpu cacheline miss and atomic operation
52 * to the wakeup path. Instead we increment on whatever cpu the task ran
53 * when it went into uninterruptible state and decrement on whatever cpu
54 * did the wakeup. This means that only the sum of nr_uninterruptible over
55 * all cpus yields the correct result.
56 *
57 * This covers the NO_HZ=n code, for extra head-aches, see the comment below.
58 */
59
60/* Variables and functions for calc_load */
61atomic_long_t calc_load_tasks;
62unsigned long calc_load_update;
63unsigned long avenrun[3];
64EXPORT_SYMBOL(avenrun); /* should be removed */
65
66/**
67 * get_avenrun - get the load average array
68 * @loads: pointer to dest load array
69 * @offset: offset to add
70 * @shift: shift count to shift the result left
71 *
72 * These values are estimates at best, so no need for locking.
73 */
74void get_avenrun(unsigned long *loads, unsigned long offset, int shift)
75{
76 loads[0] = (avenrun[0] + offset) << shift;
77 loads[1] = (avenrun[1] + offset) << shift;
78 loads[2] = (avenrun[2] + offset) << shift;
79}
80
81long calc_load_fold_active(struct rq *this_rq)
82{
83 long nr_active, delta = 0;
84
85 nr_active = this_rq->nr_running;
86 nr_active += (long)this_rq->nr_uninterruptible;
87
88 if (nr_active != this_rq->calc_load_active) {
89 delta = nr_active - this_rq->calc_load_active;
90 this_rq->calc_load_active = nr_active;
91 }
92
93 return delta;
94}
95
96/*
97 * a1 = a0 * e + a * (1 - e)
98 */
99static unsigned long
100calc_load(unsigned long load, unsigned long exp, unsigned long active)
101{
102 load *= exp;
103 load += active * (FIXED_1 - exp);
104 load += 1UL << (FSHIFT - 1);
105 return load >> FSHIFT;
106}
107
108#ifdef CONFIG_NO_HZ_COMMON
109/*
110 * Handle NO_HZ for the global load-average.
111 *
112 * Since the above described distributed algorithm to compute the global
113 * load-average relies on per-cpu sampling from the tick, it is affected by
114 * NO_HZ.
115 *
116 * The basic idea is to fold the nr_active delta into a global idle-delta upon
117 * entering NO_HZ state such that we can include this as an 'extra' cpu delta
118 * when we read the global state.
119 *
120 * Obviously reality has to ruin such a delightfully simple scheme:
121 *
122 * - When we go NO_HZ idle during the window, we can negate our sample
123 * contribution, causing under-accounting.
124 *
125 * We avoid this by keeping two idle-delta counters and flipping them
126 * when the window starts, thus separating old and new NO_HZ load.
127 *
128 * The only trick is the slight shift in index flip for read vs write.
129 *
130 * 0s 5s 10s 15s
131 * +10 +10 +10 +10
132 * |-|-----------|-|-----------|-|-----------|-|
133 * r:0 0 1 1 0 0 1 1 0
134 * w:0 1 1 0 0 1 1 0 0
135 *
136 * This ensures we'll fold the old idle contribution in this window while
137 * accumlating the new one.
138 *
139 * - When we wake up from NO_HZ idle during the window, we push up our
140 * contribution, since we effectively move our sample point to a known
141 * busy state.
142 *
143 * This is solved by pushing the window forward, and thus skipping the
144 * sample, for this cpu (effectively using the idle-delta for this cpu which
145 * was in effect at the time the window opened). This also solves the issue
146 * of having to deal with a cpu having been in NOHZ idle for multiple
147 * LOAD_FREQ intervals.
148 *
149 * When making the ILB scale, we should try to pull this in as well.
150 */
151static atomic_long_t calc_load_idle[2];
152static int calc_load_idx;
153
154static inline int calc_load_write_idx(void)
155{
156 int idx = calc_load_idx;
157
158 /*
159 * See calc_global_nohz(), if we observe the new index, we also
160 * need to observe the new update time.
161 */
162 smp_rmb();
163
164 /*
165 * If the folding window started, make sure we start writing in the
166 * next idle-delta.
167 */
168 if (!time_before(jiffies, calc_load_update))
169 idx++;
170
171 return idx & 1;
172}
173
174static inline int calc_load_read_idx(void)
175{
176 return calc_load_idx & 1;
177}
178
179void calc_load_enter_idle(void)
180{
181 struct rq *this_rq = this_rq();
182 long delta;
183
184 /*
185 * We're going into NOHZ mode, if there's any pending delta, fold it
186 * into the pending idle delta.
187 */
188 delta = calc_load_fold_active(this_rq);
189 if (delta) {
190 int idx = calc_load_write_idx();
191
192 atomic_long_add(delta, &calc_load_idle[idx]);
193 }
194}
195
196void calc_load_exit_idle(void)
197{
198 struct rq *this_rq = this_rq();
199
200 /*
201 * If we're still before the sample window, we're done.
202 */
203 if (time_before(jiffies, this_rq->calc_load_update))
204 return;
205
206 /*
207 * We woke inside or after the sample window, this means we're already
208 * accounted through the nohz accounting, so skip the entire deal and
209 * sync up for the next window.
210 */
211 this_rq->calc_load_update = calc_load_update;
212 if (time_before(jiffies, this_rq->calc_load_update + 10))
213 this_rq->calc_load_update += LOAD_FREQ;
214}
215
216static long calc_load_fold_idle(void)
217{
218 int idx = calc_load_read_idx();
219 long delta = 0;
220
221 if (atomic_long_read(&calc_load_idle[idx]))
222 delta = atomic_long_xchg(&calc_load_idle[idx], 0);
223
224 return delta;
225}
226
227/**
228 * fixed_power_int - compute: x^n, in O(log n) time
229 *
230 * @x: base of the power
231 * @frac_bits: fractional bits of @x
232 * @n: power to raise @x to.
233 *
234 * By exploiting the relation between the definition of the natural power
235 * function: x^n := x*x*...*x (x multiplied by itself for n times), and
236 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
237 * (where: n_i \elem {0, 1}, the binary vector representing n),
238 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
239 * of course trivially computable in O(log_2 n), the length of our binary
240 * vector.
241 */
242static unsigned long
243fixed_power_int(unsigned long x, unsigned int frac_bits, unsigned int n)
244{
245 unsigned long result = 1UL << frac_bits;
246
247 if (n) {
248 for (;;) {
249 if (n & 1) {
250 result *= x;
251 result += 1UL << (frac_bits - 1);
252 result >>= frac_bits;
253 }
254 n >>= 1;
255 if (!n)
256 break;
257 x *= x;
258 x += 1UL << (frac_bits - 1);
259 x >>= frac_bits;
260 }
261 }
262
263 return result;
264}
265
266/*
267 * a1 = a0 * e + a * (1 - e)
268 *
269 * a2 = a1 * e + a * (1 - e)
270 * = (a0 * e + a * (1 - e)) * e + a * (1 - e)
271 * = a0 * e^2 + a * (1 - e) * (1 + e)
272 *
273 * a3 = a2 * e + a * (1 - e)
274 * = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
275 * = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
276 *
277 * ...
278 *
279 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
280 * = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
281 * = a0 * e^n + a * (1 - e^n)
282 *
283 * [1] application of the geometric series:
284 *
285 * n 1 - x^(n+1)
286 * S_n := \Sum x^i = -------------
287 * i=0 1 - x
288 */
289static unsigned long
290calc_load_n(unsigned long load, unsigned long exp,
291 unsigned long active, unsigned int n)
292{
293 return calc_load(load, fixed_power_int(exp, FSHIFT, n), active);
294}
295
296/*
297 * NO_HZ can leave us missing all per-cpu ticks calling
298 * calc_load_account_active(), but since an idle CPU folds its delta into
299 * calc_load_tasks_idle per calc_load_account_idle(), all we need to do is fold
300 * in the pending idle delta if our idle period crossed a load cycle boundary.
301 *
302 * Once we've updated the global active value, we need to apply the exponential
303 * weights adjusted to the number of cycles missed.
304 */
305static void calc_global_nohz(void)
306{
307 long delta, active, n;
308
309 if (!time_before(jiffies, calc_load_update + 10)) {
310 /*
311 * Catch-up, fold however many we are behind still
312 */
313 delta = jiffies - calc_load_update - 10;
314 n = 1 + (delta / LOAD_FREQ);
315
316 active = atomic_long_read(&calc_load_tasks);
317 active = active > 0 ? active * FIXED_1 : 0;
318
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);
322
323 calc_load_update += n * LOAD_FREQ;
324 }
325
326 /*
327 * Flip the idle 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_fold_idle(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(unsigned long ticks)
350{
351 long active, delta;
352
353 if (time_before(jiffies, calc_load_update + 10))
354 return;
355
356 /*
357 * Fold the 'old' idle-delta to include all NO_HZ cpus.
358 */
359 delta = calc_load_fold_idle();
360 if (delta)
361 atomic_long_add(delta, &calc_load_tasks);
362
363 active = atomic_long_read(&calc_load_tasks);
364 active = active > 0 ? active * FIXED_1 : 0;
365
366 avenrun[0] = calc_load(avenrun[0], EXP_1, active);
367 avenrun[1] = calc_load(avenrun[1], EXP_5, active);
368 avenrun[2] = calc_load(avenrun[2], EXP_15, active);
369
370 calc_load_update += LOAD_FREQ;
371
372 /*
373 * In case we idled for multiple LOAD_FREQ intervals, catch up in bulk.
374 */
375 calc_global_nohz();
376}
377
378/*
379 * Called from scheduler_tick() to periodically update this CPU's
380 * active count.
381 */
382void calc_global_load_tick(struct rq *this_rq)
383{
384 long delta;
385
386 if (time_before(jiffies, this_rq->calc_load_update))
387 return;
388
389 delta = calc_load_fold_active(this_rq);
390 if (delta)
391 atomic_long_add(delta, &calc_load_tasks);
392
393 this_rq->calc_load_update += LOAD_FREQ;
394}