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Linux/kernel/sched/loadavg.c

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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 */
 61 atomic_long_t calc_load_tasks;
 62 unsigned long calc_load_update;
 63 unsigned long avenrun[3];
 64 EXPORT_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  */
 74 void 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 
 81 long 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  */
 99 static unsigned long
100 calc_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  */
151 static atomic_long_t calc_load_idle[2];
152 static int calc_load_idx;
153 
154 static 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 
174 static inline int calc_load_read_idx(void)
175 {
176         return calc_load_idx & 1;
177 }
178 
179 void 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 
196 void 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 
216 static 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  */
242 static unsigned long
243 fixed_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  */
289 static unsigned long
290 calc_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  */
305 static 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 
338 static inline long calc_load_fold_idle(void) { return 0; }
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  */
349 void 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  */
382 void 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 }
395 

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