xref: /openbmc/linux/kernel/sched/loadavg.c (revision 801c1419)
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 */
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 */
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  */
get_avenrun(unsigned long * loads,unsigned long offset,int shift)71 void 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 
calc_load_fold_active(struct rq * this_rq,long adjust)78 long 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  */
108 static unsigned long
fixed_power_int(unsigned long x,unsigned int frac_bits,unsigned int n)109 fixed_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  */
155 unsigned long
calc_load_n(unsigned long load,unsigned long exp,unsigned long active,unsigned int n)156 calc_load_n(unsigned long load, unsigned long exp,
157 	    unsigned long active, unsigned int n)
158 {
159 	return calc_load(load, fixed_power_int(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  */
205 static atomic_long_t calc_load_nohz[2];
206 static int calc_load_idx;
207 
calc_load_write_idx(void)208 static 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 
calc_load_read_idx(void)228 static inline int calc_load_read_idx(void)
229 {
230 	return calc_load_idx & 1;
231 }
232 
calc_load_nohz_fold(struct rq * rq)233 static void calc_load_nohz_fold(struct rq *rq)
234 {
235 	long delta;
236 
237 	delta = calc_load_fold_active(rq, 0);
238 	if (delta) {
239 		int idx = calc_load_write_idx();
240 
241 		atomic_long_add(delta, &calc_load_nohz[idx]);
242 	}
243 }
244 
calc_load_nohz_start(void)245 void 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  */
calc_load_nohz_remote(struct rq * rq)258 void calc_load_nohz_remote(struct rq *rq)
259 {
260 	calc_load_nohz_fold(rq);
261 }
262 
calc_load_nohz_stop(void)263 void 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 
calc_load_nohz_read(void)283 static long calc_load_nohz_read(void)
284 {
285 	int idx = calc_load_read_idx();
286 	long delta = 0;
287 
288 	if (atomic_long_read(&calc_load_nohz[idx]))
289 		delta = atomic_long_xchg(&calc_load_nohz[idx], 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  */
calc_global_nohz(void)303 static 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(&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 		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 
calc_load_nohz_read(void)338 static inline long calc_load_nohz_read(void) { return 0; }
calc_global_nohz(void)339 static 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  */
calc_global_load(void)349 void 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(delta, &calc_load_tasks);
364 
365 	active = atomic_long_read(&calc_load_tasks);
366 	active = active > 0 ? active * FIXED_1 : 0;
367 
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);
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  */
calc_global_load_tick(struct rq * this_rq)385 void 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, 0);
393 	if (delta)
394 		atomic_long_add(delta, &calc_load_tasks);
395 
396 	this_rq->calc_load_update += LOAD_FREQ;
397 }
398