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
  76 /*
  77  * Limit the time part in order to ensure there are some bits left for the
  78  * cycle counter.
  79  */
  80 #define PROP_MAX_SHIFT (3*BITS_PER_LONG/4)
  81
  82 int prop_descriptor_init(struct prop_descriptor *pd, int shift)
  83 {
  84         int err;
  85
  86         if (shift > PROP_MAX_SHIFT)
  87                 shift = PROP_MAX_SHIFT;
  88
  89         pd->index = 0;
  90         pd->pg[0].shift = shift;
  91         mutex_init(&pd->mutex);
  92         err = percpu_counter_init_irq(&pd->pg[0].events, 0);
  93         if (err)
  94                 goto out;
  95
  96         err = percpu_counter_init_irq(&pd->pg[1].events, 0);
  97         if (err)
  98                 percpu_counter_destroy(&pd->pg[0].events);
  99
 100 out:
 101         return err;
 102 }
 103
 104 /*
 105  * We have two copies, and flip between them to make it seem like an atomic
 106  * update. The update is not really atomic wrt the events counter, but
 107  * it is internally consistent with the bit layout depending on shift.
 108  *
 109  * We copy the events count, move the bits around and flip the index.
 110  */
 111 void prop_change_shift(struct prop_descriptor *pd, int shift)
 112 {
 113         int index;
 114         int offset;
 115         u64 events;
 116         unsigned long flags;
 117
 118         if (shift > PROP_MAX_SHIFT)
 119                 shift = PROP_MAX_SHIFT;
 120
 121         mutex_lock(&pd->mutex);
 122
 123         index = pd->index ^ 1;
 124         offset = pd->pg[pd->index].shift - shift;
 125         if (!offset)
 126                 goto out;
 127
 128         pd->pg[index].shift = shift;
 129
 130         local_irq_save(flags);
 131         events = percpu_counter_sum(&pd->pg[pd->index].events);
 132         if (offset < 0)
 133                 events <<= -offset;
 134         else
 135                 events >>= offset;
 136         percpu_counter_set(&pd->pg[index].events, events);
 137
 138         /*
 139          * ensure the new pg is fully written before the switch
 140          */
 141         smp_wmb();
 142         pd->index = index;
 143         local_irq_restore(flags);
 144
 145         synchronize_rcu();
 146
 147 out:
 148         mutex_unlock(&pd->mutex);
 149 }
 150
 151 /*
 152  * wrap the access to the data in an rcu_read_lock() section;
 153  * this is used to track the active references.
 154  */
 155 static struct prop_global *prop_get_global(struct prop_descriptor *pd)
 156 {
 157         int index;
 158
 159         rcu_read_lock();
 160         index = pd->index;
 161         /*
 162          * match the wmb from vcd_flip()
 163          */
 164         smp_rmb();
 165         return &pd->pg[index];
 166 }
 167
 168 static void prop_put_global(struct prop_descriptor *pd, struct prop_global *pg)
 169 {
 170         rcu_read_unlock();
 171 }
 172
 173 static void
 174 prop_adjust_shift(int *pl_shift, unsigned long *pl_period, int new_shift)
 175 {
 176         int offset = *pl_shift - new_shift;
 177
 178         if (!offset)
 179                 return;
 180
 181         if (offset < 0)
 182                 *pl_period <<= -offset;
 183         else
 184                 *pl_period >>= offset;
 185
 186         *pl_shift = new_shift;
 187 }
 188
 189 /*
 190  * PERCPU
 191  */
 192
 193 #define PROP_BATCH (8*(1+ilog2(nr_cpu_ids)))
 194
 195 int prop_local_init_percpu(struct prop_local_percpu *pl)
 196 {
 197         spin_lock_init(&pl->lock);
 198         pl->shift = 0;
 199         pl->period = 0;
 200         return percpu_counter_init_irq(&pl->events, 0);
 201 }
 202
 203 void prop_local_destroy_percpu(struct prop_local_percpu *pl)
 204 {
 205         percpu_counter_destroy(&pl->events);
 206 }
 207
 208 /*
 209  * Catch up with missed period expirations.
 210  *
 211  *   until (c_{j} == c)
 212  *     x_{j} -= x_{j}/2;
 213  *     c_{j}++;
 214  */
 215 static
 216 void prop_norm_percpu(struct prop_global *pg, struct prop_local_percpu *pl)
 217 {
 218         unsigned long period = 1UL << (pg->shift - 1);
 219         unsigned long period_mask = ~(period - 1);
 220         unsigned long global_period;
 221         unsigned long flags;
 222
 223         global_period = percpu_counter_read(&pg->events);
 224         global_period &= period_mask;
 225
 226         /*
 227          * Fast path - check if the local and global period count still match
 228          * outside of the lock.
 229          */
 230         if (pl->period == global_period)
 231                 return;
 232
 233         spin_lock_irqsave(&pl->lock, flags);
 234         prop_adjust_shift(&pl->shift, &pl->period, pg->shift);
 235
 236         /*
 237          * For each missed period, we half the local counter.
 238          * basically:
 239          *   pl->events >> (global_period - pl->period);
 240          */
 241         period = (global_period - pl->period) >> (pg->shift - 1);
 242         if (period < BITS_PER_LONG) {
 243                 s64 val = percpu_counter_read(&pl->events);
 244
 245                 if (val < (nr_cpu_ids * PROP_BATCH))
 246                         val = percpu_counter_sum(&pl->events);
 247
 248                 __percpu_counter_add(&pl->events, -val + (val >> period),
 249                                         PROP_BATCH);
 250         } else
 251                 percpu_counter_set(&pl->events, 0);
 252
 253         pl->period = global_period;
 254         spin_unlock_irqrestore(&pl->lock, flags);
 255 }
 256
 257 /*
 258  *   ++x_{j}, ++t
 259  */
 260 void __prop_inc_percpu(struct prop_descriptor *pd, struct prop_local_percpu *pl)
 261 {
 262         struct prop_global *pg = prop_get_global(pd);
 263
 264         prop_norm_percpu(pg, pl);
 265         __percpu_counter_add(&pl->events, 1, PROP_BATCH);
 266         percpu_counter_add(&pg->events, 1);
 267         prop_put_global(pd, pg);
 268 }
 269
 270 /*
 271  * Obtain a fraction of this proportion
 272  *
 273  *   p_{j} = x_{j} / (period/2 + t % period/2)
 274  */
 275 void prop_fraction_percpu(struct prop_descriptor *pd,
 276                 struct prop_local_percpu *pl,
 277                 long *numerator, long *denominator)
 278 {
 279         struct prop_global *pg = prop_get_global(pd);
 280         unsigned long period_2 = 1UL << (pg->shift - 1);
 281         unsigned long counter_mask = period_2 - 1;
 282         unsigned long global_count;
 283
 284         prop_norm_percpu(pg, pl);
 285         *numerator = percpu_counter_read_positive(&pl->events);
 286
 287         global_count = percpu_counter_read(&pg->events);
 288         *denominator = period_2 + (global_count & counter_mask);
 289
 290         prop_put_global(pd, pg);
 291 }
 292
 293 /*
 294  * SINGLE
 295  */
 296
 297 int prop_local_init_single(struct prop_local_single *pl)
 298 {
 299         spin_lock_init(&pl->lock);
 300         pl->shift = 0;
 301         pl->period = 0;
 302         pl->events = 0;
 303         return 0;
 304 }
 305
 306 void prop_local_destroy_single(struct prop_local_single *pl)
 307 {
 308 }
 309
 310 /*
 311  * Catch up with missed period expirations.
 312  */
 313 static
 314 void prop_norm_single(struct prop_global *pg, struct prop_local_single *pl)
 315 {
 316         unsigned long period = 1UL << (pg->shift - 1);
 317         unsigned long period_mask = ~(period - 1);
 318         unsigned long global_period;
 319         unsigned long flags;
 320
 321         global_period = percpu_counter_read(&pg->events);
 322         global_period &= period_mask;
 323
 324         /*
 325          * Fast path - check if the local and global period count still match
 326          * outside of the lock.
 327          */
 328         if (pl->period == global_period)
 329                 return;
 330
 331         spin_lock_irqsave(&pl->lock, flags);
 332         prop_adjust_shift(&pl->shift, &pl->period, pg->shift);
 333         /*
 334          * For each missed period, we half the local counter.
 335          */
 336         period = (global_period - pl->period) >> (pg->shift - 1);
 337         if (likely(period < BITS_PER_LONG))
 338                 pl->events >>= period;
 339         else
 340                 pl->events = 0;
 341         pl->period = global_period;
 342         spin_unlock_irqrestore(&pl->lock, flags);
 343 }
 344
 345 /*
 346  *   ++x_{j}, ++t
 347  */
 348 void __prop_inc_single(struct prop_descriptor *pd, struct prop_local_single *pl)
 349 {
 350         struct prop_global *pg = prop_get_global(pd);
 351
 352         prop_norm_single(pg, pl);
 353         pl->events++;
 354         percpu_counter_add(&pg->events, 1);
 355         prop_put_global(pd, pg);
 356 }
 357
 358 /*
 359  * Obtain a fraction of this proportion
 360  *
 361  *   p_{j} = x_{j} / (period/2 + t % period/2)
 362  */
 363 void prop_fraction_single(struct prop_descriptor *pd,
 364                 struct prop_local_single *pl,
 365                 long *numerator, long *denominator)
 366 {
 367         struct prop_global *pg = prop_get_global(pd);
 368         unsigned long period_2 = 1UL << (pg->shift - 1);
 369         unsigned long counter_mask = period_2 - 1;
 370         unsigned long global_count;
 371
 372         prop_norm_single(pg, pl);
 373         *numerator = pl->events;
 374
 375         global_count = percpu_counter_read(&pg->events);
 376         *denominator = period_2 + (global_count & counter_mask);
 377
 378         prop_put_global(pd, pg);
 379 }