2 * kernel/sched/loadavg.c
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.
9 #include <linux/export.h>
14 * Global load-average calculations
16 * We take a distributed and async approach to calculating the global load-avg
17 * in order to minimize overhead.
19 * The global load average is an exponentially decaying average of nr_running +
22 * Once every LOAD_FREQ:
25 * for_each_possible_cpu(cpu)
26 * nr_active += cpu_of(cpu)->nr_running + cpu_of(cpu)->nr_uninterruptible;
28 * avenrun[n] = avenrun[0] * exp_n + nr_active * (1 - exp_n)
30 * Due to a number of reasons the above turns in the mess below:
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.
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) }
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().
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.
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.
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.
57 * This covers the NO_HZ=n code, for extra head-aches, see the comment below.
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 */
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
72 * These values are estimates at best, so no need for locking.
74 void get_avenrun(unsigned long *loads
, unsigned long offset
, int shift
)
76 loads
[0] = (avenrun
[0] + offset
) << shift
;
77 loads
[1] = (avenrun
[1] + offset
) << shift
;
78 loads
[2] = (avenrun
[2] + offset
) << shift
;
81 long calc_load_fold_active(struct rq
*this_rq
, long adjust
)
83 long nr_active
, delta
= 0;
85 nr_active
= this_rq
->nr_running
- adjust
;
86 nr_active
+= (long)this_rq
->nr_uninterruptible
;
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
;
97 * a1 = a0 * e + a * (1 - e)
100 calc_load(unsigned long load
, unsigned long exp
, unsigned long active
)
102 unsigned long newload
;
104 newload
= load
* exp
+ active
* (FIXED_1
- exp
);
106 newload
+= FIXED_1
-1;
108 return newload
/ FIXED_1
;
111 #ifdef CONFIG_NO_HZ_COMMON
113 * Handle NO_HZ for the global load-average.
115 * Since the above described distributed algorithm to compute the global
116 * load-average relies on per-cpu sampling from the tick, it is affected by
119 * The basic idea is to fold the nr_active delta into a global idle-delta upon
120 * entering NO_HZ state such that we can include this as an 'extra' cpu delta
121 * when we read the global state.
123 * Obviously reality has to ruin such a delightfully simple scheme:
125 * - When we go NO_HZ idle during the window, we can negate our sample
126 * contribution, causing under-accounting.
128 * We avoid this by keeping two idle-delta counters and flipping them
129 * when the window starts, thus separating old and new NO_HZ load.
131 * The only trick is the slight shift in index flip for read vs write.
135 * |-|-----------|-|-----------|-|-----------|-|
136 * r:0 0 1 1 0 0 1 1 0
137 * w:0 1 1 0 0 1 1 0 0
139 * This ensures we'll fold the old idle contribution in this window while
140 * accumlating the new one.
142 * - When we wake up from NO_HZ idle during the window, we push up our
143 * contribution, since we effectively move our sample point to a known
146 * This is solved by pushing the window forward, and thus skipping the
147 * sample, for this cpu (effectively using the idle-delta for this cpu which
148 * was in effect at the time the window opened). This also solves the issue
149 * of having to deal with a cpu having been in NOHZ idle for multiple
150 * LOAD_FREQ intervals.
152 * When making the ILB scale, we should try to pull this in as well.
154 static atomic_long_t calc_load_idle
[2];
155 static int calc_load_idx
;
157 static inline int calc_load_write_idx(void)
159 int idx
= calc_load_idx
;
162 * See calc_global_nohz(), if we observe the new index, we also
163 * need to observe the new update time.
168 * If the folding window started, make sure we start writing in the
171 if (!time_before(jiffies
, calc_load_update
))
177 static inline int calc_load_read_idx(void)
179 return calc_load_idx
& 1;
182 void calc_load_enter_idle(void)
184 struct rq
*this_rq
= this_rq();
188 * We're going into NOHZ mode, if there's any pending delta, fold it
189 * into the pending idle delta.
191 delta
= calc_load_fold_active(this_rq
, 0);
193 int idx
= calc_load_write_idx();
195 atomic_long_add(delta
, &calc_load_idle
[idx
]);
199 void calc_load_exit_idle(void)
201 struct rq
*this_rq
= this_rq();
204 * If we're still before the sample window, we're done.
206 if (time_before(jiffies
, this_rq
->calc_load_update
))
210 * We woke inside or after the sample window, this means we're already
211 * accounted through the nohz accounting, so skip the entire deal and
212 * sync up for the next window.
214 this_rq
->calc_load_update
= calc_load_update
;
215 if (time_before(jiffies
, this_rq
->calc_load_update
+ 10))
216 this_rq
->calc_load_update
+= LOAD_FREQ
;
219 static long calc_load_fold_idle(void)
221 int idx
= calc_load_read_idx();
224 if (atomic_long_read(&calc_load_idle
[idx
]))
225 delta
= atomic_long_xchg(&calc_load_idle
[idx
], 0);
231 * fixed_power_int - compute: x^n, in O(log n) time
233 * @x: base of the power
234 * @frac_bits: fractional bits of @x
235 * @n: power to raise @x to.
237 * By exploiting the relation between the definition of the natural power
238 * function: x^n := x*x*...*x (x multiplied by itself for n times), and
239 * the binary encoding of numbers used by computers: n := \Sum n_i * 2^i,
240 * (where: n_i \elem {0, 1}, the binary vector representing n),
241 * we find: x^n := x^(\Sum n_i * 2^i) := \Prod x^(n_i * 2^i), which is
242 * of course trivially computable in O(log_2 n), the length of our binary
246 fixed_power_int(unsigned long x
, unsigned int frac_bits
, unsigned int n
)
248 unsigned long result
= 1UL << frac_bits
;
254 result
+= 1UL << (frac_bits
- 1);
255 result
>>= frac_bits
;
261 x
+= 1UL << (frac_bits
- 1);
270 * a1 = a0 * e + a * (1 - e)
272 * a2 = a1 * e + a * (1 - e)
273 * = (a0 * e + a * (1 - e)) * e + a * (1 - e)
274 * = a0 * e^2 + a * (1 - e) * (1 + e)
276 * a3 = a2 * e + a * (1 - e)
277 * = (a0 * e^2 + a * (1 - e) * (1 + e)) * e + a * (1 - e)
278 * = a0 * e^3 + a * (1 - e) * (1 + e + e^2)
282 * an = a0 * e^n + a * (1 - e) * (1 + e + ... + e^n-1) [1]
283 * = a0 * e^n + a * (1 - e) * (1 - e^n)/(1 - e)
284 * = a0 * e^n + a * (1 - e^n)
286 * [1] application of the geometric series:
289 * S_n := \Sum x^i = -------------
293 calc_load_n(unsigned long load
, unsigned long exp
,
294 unsigned long active
, unsigned int n
)
296 return calc_load(load
, fixed_power_int(exp
, FSHIFT
, n
), active
);
300 * NO_HZ can leave us missing all per-cpu ticks calling
301 * calc_load_account_active(), but since an idle CPU folds its delta into
302 * calc_load_tasks_idle per calc_load_account_idle(), all we need to do is fold
303 * in the pending idle delta if our idle period crossed a load cycle boundary.
305 * Once we've updated the global active value, we need to apply the exponential
306 * weights adjusted to the number of cycles missed.
308 static void calc_global_nohz(void)
310 long delta
, active
, n
;
312 if (!time_before(jiffies
, calc_load_update
+ 10)) {
314 * Catch-up, fold however many we are behind still
316 delta
= jiffies
- calc_load_update
- 10;
317 n
= 1 + (delta
/ LOAD_FREQ
);
319 active
= atomic_long_read(&calc_load_tasks
);
320 active
= active
> 0 ? active
* FIXED_1
: 0;
322 avenrun
[0] = calc_load_n(avenrun
[0], EXP_1
, active
, n
);
323 avenrun
[1] = calc_load_n(avenrun
[1], EXP_5
, active
, n
);
324 avenrun
[2] = calc_load_n(avenrun
[2], EXP_15
, active
, n
);
326 calc_load_update
+= n
* LOAD_FREQ
;
330 * Flip the idle index...
332 * Make sure we first write the new time then flip the index, so that
333 * calc_load_write_idx() will see the new time when it reads the new
334 * index, this avoids a double flip messing things up.
339 #else /* !CONFIG_NO_HZ_COMMON */
341 static inline long calc_load_fold_idle(void) { return 0; }
342 static inline void calc_global_nohz(void) { }
344 #endif /* CONFIG_NO_HZ_COMMON */
347 * calc_load - update the avenrun load estimates 10 ticks after the
348 * CPUs have updated calc_load_tasks.
350 * Called from the global timer code.
352 void calc_global_load(unsigned long ticks
)
356 if (time_before(jiffies
, calc_load_update
+ 10))
360 * Fold the 'old' idle-delta to include all NO_HZ cpus.
362 delta
= calc_load_fold_idle();
364 atomic_long_add(delta
, &calc_load_tasks
);
366 active
= atomic_long_read(&calc_load_tasks
);
367 active
= active
> 0 ? active
* FIXED_1
: 0;
369 avenrun
[0] = calc_load(avenrun
[0], EXP_1
, active
);
370 avenrun
[1] = calc_load(avenrun
[1], EXP_5
, active
);
371 avenrun
[2] = calc_load(avenrun
[2], EXP_15
, active
);
373 calc_load_update
+= LOAD_FREQ
;
376 * In case we idled for multiple LOAD_FREQ intervals, catch up in bulk.
382 * Called from scheduler_tick() to periodically update this CPU's
385 void calc_global_load_tick(struct rq
*this_rq
)
389 if (time_before(jiffies
, this_rq
->calc_load_update
))
392 delta
= calc_load_fold_active(this_rq
, 0);
394 atomic_long_add(delta
, &calc_load_tasks
);
396 this_rq
->calc_load_update
+= LOAD_FREQ
;