Root/lib/proportions.c

1/*
2 * Floating proportions
3 *
4 * Copyright (C) 2007 Red Hat, Inc., Peter Zijlstra <pzijlstr@redhat.com>
5 *
6 * Description:
7 *
8 * The floating proportion is a time derivative with an exponentially decaying
9 * history:
10 *
11 * p_{j} = \Sum_{i=0} (dx_{j}/dt_{-i}) / 2^(1+i)
12 *
13 * Where j is an element from {prop_local}, x_{j} is j's number of events,
14 * and i the time period over which the differential is taken. So d/dt_{-i} is
15 * the differential over the i-th last period.
16 *
17 * The decaying history gives smooth transitions. The time differential carries
18 * the notion of speed.
19 *
20 * The denominator is 2^(1+i) because we want the series to be normalised, ie.
21 *
22 * \Sum_{i=0} 1/2^(1+i) = 1
23 *
24 * Further more, if we measure time (t) in the same events as x; so that:
25 *
26 * t = \Sum_{j} x_{j}
27 *
28 * we get that:
29 *
30 * \Sum_{j} p_{j} = 1
31 *
32 * Writing this in an iterative fashion we get (dropping the 'd's):
33 *
34 * if (++x_{j}, ++t > period)
35 * t /= 2;
36 * for_each (j)
37 * x_{j} /= 2;
38 *
39 * so that:
40 *
41 * p_{j} = x_{j} / t;
42 *
43 * We optimize away the '/= 2' for the global time delta by noting that:
44 *
45 * if (++t > period) t /= 2:
46 *
47 * Can be approximated by:
48 *
49 * period/2 + (++t % period/2)
50 *
51 * [ Furthermore, when we choose period to be 2^n it can be written in terms of
52 * binary operations and wraparound artefacts disappear. ]
53 *
54 * Also note that this yields a natural counter of the elapsed periods:
55 *
56 * c = t / (period/2)
57 *
58 * [ Its monotonic increasing property can be applied to mitigate the wrap-
59 * around issue. ]
60 *
61 * This allows us to do away with the loop over all prop_locals on each period
62 * expiration. By remembering the period count under which it was last accessed
63 * as c_{j}, we can obtain the number of 'missed' cycles from:
64 *
65 * c - c_{j}
66 *
67 * We can then lazily catch up to the global period count every time we are
68 * going to use x_{j}, by doing:
69 *
70 * x_{j} /= 2^(c - c_{j}), c_{j} = c
71 */
72
73#include <linux/proportions.h>
74#include <linux/rcupdate.h>
75
76int prop_descriptor_init(struct prop_descriptor *pd, int shift)
77{
78    int err;
79
80    if (shift > PROP_MAX_SHIFT)
81        shift = PROP_MAX_SHIFT;
82
83    pd->index = 0;
84    pd->pg[0].shift = shift;
85    mutex_init(&pd->mutex);
86    err = percpu_counter_init(&pd->pg[0].events, 0);
87    if (err)
88        goto out;
89
90    err = percpu_counter_init(&pd->pg[1].events, 0);
91    if (err)
92        percpu_counter_destroy(&pd->pg[0].events);
93
94out:
95    return err;
96}
97
98/*
99 * We have two copies, and flip between them to make it seem like an atomic
100 * update. The update is not really atomic wrt the events counter, but
101 * it is internally consistent with the bit layout depending on shift.
102 *
103 * We copy the events count, move the bits around and flip the index.
104 */
105void prop_change_shift(struct prop_descriptor *pd, int shift)
106{
107    int index;
108    int offset;
109    u64 events;
110    unsigned long flags;
111
112    if (shift > PROP_MAX_SHIFT)
113        shift = PROP_MAX_SHIFT;
114
115    mutex_lock(&pd->mutex);
116
117    index = pd->index ^ 1;
118    offset = pd->pg[pd->index].shift - shift;
119    if (!offset)
120        goto out;
121
122    pd->pg[index].shift = shift;
123
124    local_irq_save(flags);
125    events = percpu_counter_sum(&pd->pg[pd->index].events);
126    if (offset < 0)
127        events <<= -offset;
128    else
129        events >>= offset;
130    percpu_counter_set(&pd->pg[index].events, events);
131
132    /*
133     * ensure the new pg is fully written before the switch
134     */
135    smp_wmb();
136    pd->index = index;
137    local_irq_restore(flags);
138
139    synchronize_rcu();
140
141out:
142    mutex_unlock(&pd->mutex);
143}
144
145/*
146 * wrap the access to the data in an rcu_read_lock() section;
147 * this is used to track the active references.
148 */
149static struct prop_global *prop_get_global(struct prop_descriptor *pd)
150__acquires(RCU)
151{
152    int index;
153
154    rcu_read_lock();
155    index = pd->index;
156    /*
157     * match the wmb from vcd_flip()
158     */
159    smp_rmb();
160    return &pd->pg[index];
161}
162
163static void prop_put_global(struct prop_descriptor *pd, struct prop_global *pg)
164__releases(RCU)
165{
166    rcu_read_unlock();
167}
168
169static void
170prop_adjust_shift(int *pl_shift, unsigned long *pl_period, int new_shift)
171{
172    int offset = *pl_shift - new_shift;
173
174    if (!offset)
175        return;
176
177    if (offset < 0)
178        *pl_period <<= -offset;
179    else
180        *pl_period >>= offset;
181
182    *pl_shift = new_shift;
183}
184
185/*
186 * PERCPU
187 */
188
189#define PROP_BATCH (8*(1+ilog2(nr_cpu_ids)))
190
191int prop_local_init_percpu(struct prop_local_percpu *pl)
192{
193    spin_lock_init(&pl->lock);
194    pl->shift = 0;
195    pl->period = 0;
196    return percpu_counter_init(&pl->events, 0);
197}
198
199void prop_local_destroy_percpu(struct prop_local_percpu *pl)
200{
201    percpu_counter_destroy(&pl->events);
202}
203
204/*
205 * Catch up with missed period expirations.
206 *
207 * until (c_{j} == c)
208 * x_{j} -= x_{j}/2;
209 * c_{j}++;
210 */
211static
212void prop_norm_percpu(struct prop_global *pg, struct prop_local_percpu *pl)
213{
214    unsigned long period = 1UL << (pg->shift - 1);
215    unsigned long period_mask = ~(period - 1);
216    unsigned long global_period;
217    unsigned long flags;
218
219    global_period = percpu_counter_read(&pg->events);
220    global_period &= period_mask;
221
222    /*
223     * Fast path - check if the local and global period count still match
224     * outside of the lock.
225     */
226    if (pl->period == global_period)
227        return;
228
229    spin_lock_irqsave(&pl->lock, flags);
230    prop_adjust_shift(&pl->shift, &pl->period, pg->shift);
231
232    /*
233     * For each missed period, we half the local counter.
234     * basically:
235     * pl->events >> (global_period - pl->period);
236     */
237    period = (global_period - pl->period) >> (pg->shift - 1);
238    if (period < BITS_PER_LONG) {
239        s64 val = percpu_counter_read(&pl->events);
240
241        if (val < (nr_cpu_ids * PROP_BATCH))
242            val = percpu_counter_sum(&pl->events);
243
244        __percpu_counter_add(&pl->events, -val + (val >> period),
245                    PROP_BATCH);
246    } else
247        percpu_counter_set(&pl->events, 0);
248
249    pl->period = global_period;
250    spin_unlock_irqrestore(&pl->lock, flags);
251}
252
253/*
254 * ++x_{j}, ++t
255 */
256void __prop_inc_percpu(struct prop_descriptor *pd, struct prop_local_percpu *pl)
257{
258    struct prop_global *pg = prop_get_global(pd);
259
260    prop_norm_percpu(pg, pl);
261    __percpu_counter_add(&pl->events, 1, PROP_BATCH);
262    percpu_counter_add(&pg->events, 1);
263    prop_put_global(pd, pg);
264}
265
266/*
267 * identical to __prop_inc_percpu, except that it limits this pl's fraction to
268 * @frac/PROP_FRAC_BASE by ignoring events when this limit has been exceeded.
269 */
270void __prop_inc_percpu_max(struct prop_descriptor *pd,
271               struct prop_local_percpu *pl, long frac)
272{
273    struct prop_global *pg = prop_get_global(pd);
274
275    prop_norm_percpu(pg, pl);
276
277    if (unlikely(frac != PROP_FRAC_BASE)) {
278        unsigned long period_2 = 1UL << (pg->shift - 1);
279        unsigned long counter_mask = period_2 - 1;
280        unsigned long global_count;
281        long numerator, denominator;
282
283        numerator = percpu_counter_read_positive(&pl->events);
284        global_count = percpu_counter_read(&pg->events);
285        denominator = period_2 + (global_count & counter_mask);
286
287        if (numerator > ((denominator * frac) >> PROP_FRAC_SHIFT))
288            goto out_put;
289    }
290
291    percpu_counter_add(&pl->events, 1);
292    percpu_counter_add(&pg->events, 1);
293
294out_put:
295    prop_put_global(pd, pg);
296}
297
298/*
299 * Obtain a fraction of this proportion
300 *
301 * p_{j} = x_{j} / (period/2 + t % period/2)
302 */
303void prop_fraction_percpu(struct prop_descriptor *pd,
304        struct prop_local_percpu *pl,
305        long *numerator, long *denominator)
306{
307    struct prop_global *pg = prop_get_global(pd);
308    unsigned long period_2 = 1UL << (pg->shift - 1);
309    unsigned long counter_mask = period_2 - 1;
310    unsigned long global_count;
311
312    prop_norm_percpu(pg, pl);
313    *numerator = percpu_counter_read_positive(&pl->events);
314
315    global_count = percpu_counter_read(&pg->events);
316    *denominator = period_2 + (global_count & counter_mask);
317
318    prop_put_global(pd, pg);
319}
320
321/*
322 * SINGLE
323 */
324
325int prop_local_init_single(struct prop_local_single *pl)
326{
327    spin_lock_init(&pl->lock);
328    pl->shift = 0;
329    pl->period = 0;
330    pl->events = 0;
331    return 0;
332}
333
334void prop_local_destroy_single(struct prop_local_single *pl)
335{
336}
337
338/*
339 * Catch up with missed period expirations.
340 */
341static
342void prop_norm_single(struct prop_global *pg, struct prop_local_single *pl)
343{
344    unsigned long period = 1UL << (pg->shift - 1);
345    unsigned long period_mask = ~(period - 1);
346    unsigned long global_period;
347    unsigned long flags;
348
349    global_period = percpu_counter_read(&pg->events);
350    global_period &= period_mask;
351
352    /*
353     * Fast path - check if the local and global period count still match
354     * outside of the lock.
355     */
356    if (pl->period == global_period)
357        return;
358
359    spin_lock_irqsave(&pl->lock, flags);
360    prop_adjust_shift(&pl->shift, &pl->period, pg->shift);
361    /*
362     * For each missed period, we half the local counter.
363     */
364    period = (global_period - pl->period) >> (pg->shift - 1);
365    if (likely(period < BITS_PER_LONG))
366        pl->events >>= period;
367    else
368        pl->events = 0;
369    pl->period = global_period;
370    spin_unlock_irqrestore(&pl->lock, flags);
371}
372
373/*
374 * ++x_{j}, ++t
375 */
376void __prop_inc_single(struct prop_descriptor *pd, struct prop_local_single *pl)
377{
378    struct prop_global *pg = prop_get_global(pd);
379
380    prop_norm_single(pg, pl);
381    pl->events++;
382    percpu_counter_add(&pg->events, 1);
383    prop_put_global(pd, pg);
384}
385
386/*
387 * Obtain a fraction of this proportion
388 *
389 * p_{j} = x_{j} / (period/2 + t % period/2)
390 */
391void prop_fraction_single(struct prop_descriptor *pd,
392               struct prop_local_single *pl,
393        long *numerator, long *denominator)
394{
395    struct prop_global *pg = prop_get_global(pd);
396    unsigned long period_2 = 1UL << (pg->shift - 1);
397    unsigned long counter_mask = period_2 - 1;
398    unsigned long global_count;
399
400    prop_norm_single(pg, pl);
401    *numerator = pl->events;
402
403    global_count = percpu_counter_read(&pg->events);
404    *denominator = period_2 + (global_count & counter_mask);
405
406    prop_put_global(pd, pg);
407}
408

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