1 /*
  2  * Copyright (c) 2018, 2019, Red Hat, Inc. All rights reserved.
  3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  4  *
  5  * This code is free software; you can redistribute it and/or modify it
  6  * under the terms of the GNU General Public License version 2 only, as
  7  * published by the Free Software Foundation.
  8  *
  9  * This code is distributed in the hope that it will be useful, but WITHOUT
 10  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 11  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 12  * version 2 for more details (a copy is included in the LICENSE file that
 13  * accompanied this code).
 14  *
 15  * You should have received a copy of the GNU General Public License version
 16  * 2 along with this work; if not, write to the Free Software Foundation,
 17  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 18  *
 19  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 20  * or visit www.oracle.com if you need additional information or have any
 21  * questions.
 22  *
 23  */
 24 
 25 #include "precompiled.hpp"
 26 
 27 #include "gc/shenandoah/heuristics/shenandoahAdaptiveHeuristics.hpp"
 28 #include "gc/shenandoah/shenandoahCollectionSet.hpp"
 29 #include "gc/shenandoah/shenandoahFreeSet.hpp"
 30 #include "gc/shenandoah/shenandoahGeneration.hpp"
 31 #include "gc/shenandoah/shenandoahHeapRegion.inline.hpp"
 32 #include "gc/shenandoah/shenandoahYoungGeneration.hpp"
 33 #include "logging/log.hpp"
 34 #include "logging/logTag.hpp"
 35 #include "utilities/quickSort.hpp"
 36 
 37 // These constants are used to adjust the margin of error for the moving
 38 // average of the allocation rate and cycle time. The units are standard
 39 // deviations.
 40 const double ShenandoahAdaptiveHeuristics::FULL_PENALTY_SD = 0.2;
 41 const double ShenandoahAdaptiveHeuristics::DEGENERATE_PENALTY_SD = 0.1;
 42 
 43 // These are used to decide if we want to make any adjustments at all
 44 // at the end of a successful concurrent cycle.
 45 const double ShenandoahAdaptiveHeuristics::LOWEST_EXPECTED_AVAILABLE_AT_END = -0.5;
 46 const double ShenandoahAdaptiveHeuristics::HIGHEST_EXPECTED_AVAILABLE_AT_END = 0.5;
 47 
 48 // These values are the confidence interval expressed as standard deviations.
 49 // At the minimum confidence level, there is a 25% chance that the true value of
 50 // the estimate (average cycle time or allocation rate) is not more than
 51 // MINIMUM_CONFIDENCE standard deviations away from our estimate. Similarly, the
 52 // MAXIMUM_CONFIDENCE interval here means there is a one in a thousand chance
 53 // that the true value of our estimate is outside the interval. These are used
 54 // as bounds on the adjustments applied at the outcome of a GC cycle.
 55 const double ShenandoahAdaptiveHeuristics::MINIMUM_CONFIDENCE = 0.319; // 25%
 56 const double ShenandoahAdaptiveHeuristics::MAXIMUM_CONFIDENCE = 3.291; // 99.9%
 57 
 58 const uint ShenandoahAdaptiveHeuristics::MINIMUM_RESIZE_INTERVAL = 10;
 59 
 60 ShenandoahAdaptiveHeuristics::ShenandoahAdaptiveHeuristics(ShenandoahGeneration* generation) :
 61   ShenandoahHeuristics(generation),
 62   _margin_of_error_sd(ShenandoahAdaptiveInitialConfidence),
 63   _spike_threshold_sd(ShenandoahAdaptiveInitialSpikeThreshold),
 64   _last_trigger(OTHER),
 65   _available(Moving_Average_Samples, ShenandoahAdaptiveDecayFactor) { }
 66 
 67 ShenandoahAdaptiveHeuristics::~ShenandoahAdaptiveHeuristics() {}
 68 
 69 void ShenandoahAdaptiveHeuristics::choose_collection_set_from_regiondata(ShenandoahCollectionSet* cset,
 70                                                                          RegionData* data, size_t size,
 71                                                                          size_t actual_free) {
 72   size_t garbage_threshold = ShenandoahHeapRegion::region_size_bytes() * ShenandoahGarbageThreshold / 100;
 73   size_t ignore_threshold = ShenandoahHeapRegion::region_size_bytes() * ShenandoahIgnoreGarbageThreshold / 100;
 74   ShenandoahHeap* heap = ShenandoahHeap::heap();
 75 
 76   // The logic for cset selection in adaptive is as follows:
 77   //
 78   //   1. We cannot get cset larger than available free space. Otherwise we guarantee OOME
 79   //      during evacuation, and thus guarantee full GC. In practice, we also want to let
 80   //      application to allocate something. This is why we limit CSet to some fraction of
 81   //      available space. In non-overloaded heap, max_cset would contain all plausible candidates
 82   //      over garbage threshold.
 83   //
 84   //   2. We should not get cset too low so that free threshold would not be met right
 85   //      after the cycle. Otherwise we get back-to-back cycles for no reason if heap is
 86   //      too fragmented. In non-overloaded non-fragmented heap min_garbage would be around zero.
 87   //
 88   // Therefore, we start by sorting the regions by garbage. Then we unconditionally add the best candidates
 89   // before we meet min_garbage. Then we add all candidates that fit with a garbage threshold before
 90   // we hit max_cset. When max_cset is hit, we terminate the cset selection. Note that in this scheme,
 91   // ShenandoahGarbageThreshold is the soft threshold which would be ignored until min_garbage is hit.
 92 
 93   // In generational mode, the sort order within the data array is not strictly descending amounts of garbage.  In
 94   // particular, regions that have reached tenure age will be sorted into this array before younger regions that contain
 95   // more garbage.  This represents one of the reasons why we keep looking at regions even after we decide, for example,
 96   // to exclude one of the regions because it might require evacuation of too much live data.
 97   bool is_generational = heap->mode()->is_generational();
 98   bool is_global = (_generation->generation_mode() == GLOBAL);
 99   size_t capacity = heap->young_generation()->max_capacity();
100 
101   // cur_young_garbage represents the amount of memory to be reclaimed from young-gen.  In the case that live objects
102   // are known to be promoted out of young-gen, we count this as cur_young_garbage because this memory is reclaimed
103   // from young-gen and becomes available to serve future young-gen allocation requests.
104   size_t cur_young_garbage = 0;
105 
106   // Better select garbage-first regions
107   QuickSort::sort<RegionData>(data, (int)size, compare_by_garbage, false);
108 
109   if (is_generational) {
110     if (is_global) {
111       size_t max_young_cset    = (size_t) (heap->get_young_evac_reserve() / ShenandoahEvacWaste);
112       size_t young_cur_cset = 0;
113       size_t max_old_cset    = (size_t) (heap->get_old_evac_reserve() / ShenandoahEvacWaste);
114       size_t old_cur_cset = 0;
115       size_t free_target = (capacity * ShenandoahMinFreeThreshold) / 100 + max_young_cset;
116       size_t min_garbage = (free_target > actual_free) ? (free_target - actual_free) : 0;
117 
118       log_info(gc, ergo)("Adaptive CSet Selection for GLOBAL. Max Young Evacuation: " SIZE_FORMAT
119                          "%s, Max Old Evacuation: " SIZE_FORMAT "%s, Actual Free: " SIZE_FORMAT "%s.",
120                          byte_size_in_proper_unit(max_young_cset),    proper_unit_for_byte_size(max_young_cset),
121                          byte_size_in_proper_unit(max_old_cset),    proper_unit_for_byte_size(max_old_cset),
122                          byte_size_in_proper_unit(actual_free), proper_unit_for_byte_size(actual_free));
123 
124       for (size_t idx = 0; idx < size; idx++) {
125         ShenandoahHeapRegion* r = data[idx]._region;
126         bool add_region = false;
127         if (r->is_old()) {
128           size_t new_cset = old_cur_cset + r->get_live_data_bytes();
129           if ((new_cset <= max_old_cset) && (r->garbage() > garbage_threshold)) {
130             add_region = true;
131             old_cur_cset = new_cset;
132           }
133         } else if (cset->is_preselected(r->index())) {
134           assert(r->age() >= InitialTenuringThreshold, "Preselected regions must have tenure age");
135           // Entire region will be promoted, This region does not impact young-gen or old-gen evacuation reserve.
136           // This region has been pre-selected and its impact on promotion reserve is already accounted for.
137           add_region = true;
138           // r->used() is r->garbage() + r->get_live_data_bytes()
139           // Since all live data in this region is being evacuated from young-gen, it is as if this memory
140           // is garbage insofar as young-gen is concerned.  Counting this as garbage reduces the need to
141           // reclaim highly utilized young-gen regions just for the sake of finding min_garbage to reclaim
142           // within youn-gen memory.
143           cur_young_garbage += r->used();
144         } else if (r->age() < InitialTenuringThreshold) {
145           size_t new_cset = young_cur_cset + r->get_live_data_bytes();
146           size_t region_garbage = r->garbage();
147           size_t new_garbage = cur_young_garbage + region_garbage;
148           bool add_regardless = (region_garbage > ignore_threshold) && (new_garbage < min_garbage);
149           if ((new_cset <= max_young_cset) && (add_regardless || (region_garbage > garbage_threshold))) {
150             add_region = true;
151             young_cur_cset = new_cset;
152             cur_young_garbage = new_garbage;
153           }
154         }
155         // Note that we do not add aged regions if they were not pre-selected.  The reason they were not preselected
156         // is because there is not sufficient room in old-gen to hold their to-be-promoted live objects.
157 
158         if (add_region) {
159           cset->add_region(r);
160         }
161       }
162     } else {
163       // This is young-gen collection or a mixed evacuation.  If this is mixed evacuation, the old-gen candidate regions
164       // have already been added.
165       size_t max_cset    = (size_t) (heap->get_young_evac_reserve() / ShenandoahEvacWaste);
166       size_t cur_cset = 0;
167       size_t free_target = (capacity * ShenandoahMinFreeThreshold) / 100 + max_cset;
168       size_t min_garbage = (free_target > actual_free) ? (free_target - actual_free) : 0;
169 
170       log_info(gc, ergo)("Adaptive CSet Selection for YOUNG. Max Evacuation: " SIZE_FORMAT "%s, Actual Free: " SIZE_FORMAT "%s.",
171                          byte_size_in_proper_unit(max_cset),    proper_unit_for_byte_size(max_cset),
172                          byte_size_in_proper_unit(actual_free), proper_unit_for_byte_size(actual_free));
173 
174       for (size_t idx = 0; idx < size; idx++) {
175         ShenandoahHeapRegion* r = data[idx]._region;
176         bool add_region = false;
177 
178         if (!r->is_old()) {
179           if (cset->is_preselected(r->index())) {
180             assert(r->age() >= InitialTenuringThreshold, "Preselected regions must have tenure age");
181             // Entire region will be promoted, This region does not impact young-gen evacuation reserve.  Memory has already
182             // been set aside to hold evacuation results as advance_promotion_reserve.
183             add_region = true;
184             // Since all live data in this region is being evacuated from young-gen, it is as if this memory
185             // is garbage insofar as young-gen is concerned.  Counting this as garbage reduces the need to
186             // reclaim highly utilized young-gen regions just for the sake of finding min_garbage to reclaim
187             // within youn-gen memory
188             cur_young_garbage += r->get_live_data_bytes();
189           } else if  (r->age() < InitialTenuringThreshold) {
190             size_t new_cset = cur_cset + r->get_live_data_bytes();
191             size_t region_garbage = r->garbage();
192             size_t new_garbage = cur_young_garbage + region_garbage;
193             bool add_regardless = (region_garbage > ignore_threshold) && (new_garbage < min_garbage);
194             if ((new_cset <= max_cset) && (add_regardless || (region_garbage > garbage_threshold))) {
195               add_region = true;
196               cur_cset = new_cset;
197               cur_young_garbage = new_garbage;
198             }
199           }
200           // Note that we do not add aged regions if they were not pre-selected.  The reason they were not preselected
201           // is because there is not sufficient room in old-gen to hold their to-be-promoted live objects.
202 
203           if (add_region) {
204             cset->add_region(r);
205           }
206         }
207       }
208     }
209   } else {
210     // Traditional Shenandoah (non-generational)
211     size_t capacity    = ShenandoahHeap::heap()->soft_max_capacity();
212     size_t max_cset    = (size_t)((1.0 * capacity / 100 * ShenandoahEvacReserve) / ShenandoahEvacWaste);
213     size_t free_target = (capacity * ShenandoahMinFreeThreshold) / 100 + max_cset;
214     size_t min_garbage = (free_target > actual_free) ? (free_target - actual_free) : 0;
215 
216     log_info(gc, ergo)("Adaptive CSet Selection. Max Evacuation: " SIZE_FORMAT "%s, Actual Free: " SIZE_FORMAT "%s.",
217                          byte_size_in_proper_unit(max_cset),    proper_unit_for_byte_size(max_cset),
218                          byte_size_in_proper_unit(actual_free), proper_unit_for_byte_size(actual_free));
219 
220     size_t cur_cset = 0;
221     size_t cur_garbage = 0;
222 
223     for (size_t idx = 0; idx < size; idx++) {
224       ShenandoahHeapRegion* r = data[idx]._region;
225       size_t new_cset = cur_cset + r->get_live_data_bytes();
226       size_t region_garbage = r->garbage();
227       size_t new_garbage = cur_garbage + region_garbage;
228       bool add_regardless = (region_garbage > ignore_threshold) && (new_garbage < min_garbage);
229       if ((new_cset <= max_cset) && (add_regardless || (region_garbage > garbage_threshold))) {
230         cset->add_region(r);
231         cur_cset = new_cset;
232         cur_garbage = new_garbage;
233       }
234     }
235   }
236 }
237 
238 void ShenandoahAdaptiveHeuristics::record_cycle_start() {
239   ShenandoahHeuristics::record_cycle_start();
240   _allocation_rate.allocation_counter_reset();
241   ++_cycles_since_last_resize;
242 }
243 
244 void ShenandoahAdaptiveHeuristics::record_success_concurrent(bool abbreviated) {
245   ShenandoahHeuristics::record_success_concurrent(abbreviated);
246 
247   size_t available = MIN2(_generation->available(), ShenandoahHeap::heap()->free_set()->available());
248 
249   double z_score = 0.0;
250   double available_sd = _available.sd();
251   if (available_sd > 0) {
252     double available_avg = _available.avg();
253     z_score = (double(available) - available_avg) / available_sd;
254     log_debug(gc, ergo)("%s Available: " SIZE_FORMAT " %sB, z-score=%.3f. Average available: %.1f %sB +/- %.1f %sB.",
255                         _generation->name(),
256                         byte_size_in_proper_unit(available), proper_unit_for_byte_size(available), z_score,
257                         byte_size_in_proper_unit(available_avg), proper_unit_for_byte_size(available_avg),
258                         byte_size_in_proper_unit(available_sd), proper_unit_for_byte_size(available_sd));
259   }
260 
261   _available.add(double(available));
262 
263   // In the case when a concurrent GC cycle completes successfully but with an
264   // unusually small amount of available memory we will adjust our trigger
265   // parameters so that they are more likely to initiate a new cycle.
266   // Conversely, when a GC cycle results in an above average amount of available
267   // memory, we will adjust the trigger parameters to be less likely to initiate
268   // a GC cycle.
269   //
270   // The z-score we've computed is in no way statistically related to the
271   // trigger parameters, but it has the nice property that worse z-scores for
272   // available memory indicate making larger adjustments to the trigger
273   // parameters. It also results in fewer adjustments as the application
274   // stabilizes.
275   //
276   // In order to avoid making endless and likely unnecessary adjustments to the
277   // trigger parameters, the change in available memory (with respect to the
278   // average) at the end of a cycle must be beyond these threshold values.
279   if (z_score < LOWEST_EXPECTED_AVAILABLE_AT_END ||
280       z_score > HIGHEST_EXPECTED_AVAILABLE_AT_END) {
281     // The sign is flipped because a negative z-score indicates that the
282     // available memory at the end of the cycle is below average. Positive
283     // adjustments make the triggers more sensitive (i.e., more likely to fire).
284     // The z-score also gives us a measure of just how far below normal. This
285     // property allows us to adjust the trigger parameters proportionally.
286     //
287     // The `100` here is used to attenuate the size of our adjustments. This
288     // number was chosen empirically. It also means the adjustments at the end of
289     // a concurrent cycle are an order of magnitude smaller than the adjustments
290     // made for a degenerated or full GC cycle (which themselves were also
291     // chosen empirically).
292     adjust_last_trigger_parameters(z_score / -100);
293   }
294 }
295 
296 void ShenandoahAdaptiveHeuristics::record_success_degenerated() {
297   ShenandoahHeuristics::record_success_degenerated();
298   // Adjust both trigger's parameters in the case of a degenerated GC because
299   // either of them should have triggered earlier to avoid this case.
300   adjust_margin_of_error(DEGENERATE_PENALTY_SD);
301   adjust_spike_threshold(DEGENERATE_PENALTY_SD);
302 }
303 
304 void ShenandoahAdaptiveHeuristics::record_success_full() {
305   ShenandoahHeuristics::record_success_full();
306   // Adjust both trigger's parameters in the case of a full GC because
307   // either of them should have triggered earlier to avoid this case.
308   adjust_margin_of_error(FULL_PENALTY_SD);
309   adjust_spike_threshold(FULL_PENALTY_SD);
310 }
311 
312 static double saturate(double value, double min, double max) {
313   return MAX2(MIN2(value, max), min);
314 }
315 
316 bool ShenandoahAdaptiveHeuristics::should_start_gc() {
317   size_t max_capacity = _generation->max_capacity();
318   size_t capacity = _generation->soft_max_capacity();
319   size_t available = _generation->available();
320   size_t allocated = _generation->bytes_allocated_since_gc_start();
321 
322   log_debug(gc)("should_start_gc (%s)? available: " SIZE_FORMAT ", soft_max_capacity: " SIZE_FORMAT
323                 ", max_capacity: " SIZE_FORMAT ", allocated: " SIZE_FORMAT,
324                 _generation->name(), available, capacity, max_capacity, allocated);
325 
326   // The collector reserve may eat into what the mutator is allowed to use. Make sure we are looking
327   // at what is available to the mutator when deciding whether to start a GC.
328   size_t usable = ShenandoahHeap::heap()->free_set()->available();
329   if (usable < available) {
330     log_debug(gc)("Usable (" SIZE_FORMAT "%s) is less than available (" SIZE_FORMAT "%s)",
331                   byte_size_in_proper_unit(usable), proper_unit_for_byte_size(usable),
332                   byte_size_in_proper_unit(available), proper_unit_for_byte_size(available));
333     available = usable;
334   }
335 
336   // Allocation spikes are a characteristic of both the application ahd the JVM configuration.  On the JVM command line,
337   // the application developer may want to supply a hint of the nature of spikes that are inherent in the application
338   // workload, and this information would normally be independent of heap size (not a percentage thereof).  On the
339   // other hand, some allocation spikes are correlated with JVM configuration.  For example, there are allocation
340   // spikes at the starts of concurrent marking and evacuation to refresh all local allocation buffers.  The nature
341   // of these spikes is determined by LAB min and max sizes and numbers of threads, but also on frequency of GC passes,
342   // and on "periodic" behavior of these threads  If GC frequency is much higher than the periodic trigger for mutator
343   // threads, then many of the mutator threads may be able to "sit out" of most GC passes.  Though the thread's stack
344   // must be scanned, the thread does not need to refresh its LABs if it sits idle throughout the duration of the GC
345   // pass.  The best prediction for this aspect of spikes in allocation patterns is probably recent past history.
346   // TODO: and dive deeper into _gc_time_penalties as this may also need to be corrected
347 
348   // Check if allocation headroom is still okay. This also factors in:
349   //   1. Some space to absorb allocation spikes (ShenandoahAllocSpikeFactor)
350   //   2. Accumulated penalties from Degenerated and Full GC
351   size_t allocation_headroom = available;
352   size_t spike_headroom = capacity / 100 * ShenandoahAllocSpikeFactor;
353   size_t penalties      = capacity / 100 * _gc_time_penalties;
354 
355   allocation_headroom -= MIN2(allocation_headroom, penalties);
356   allocation_headroom -= MIN2(allocation_headroom, spike_headroom);
357 
358   // Track allocation rate even if we decide to start a cycle for other reasons.
359   double rate = _allocation_rate.sample(allocated);
360   _last_trigger = OTHER;
361 
362   size_t min_threshold = min_free_threshold();
363 
364   if (allocation_headroom < min_threshold) {
365     log_info(gc)("Trigger (%s): Free (" SIZE_FORMAT "%s) is below minimum threshold (" SIZE_FORMAT "%s)",
366                  _generation->name(),
367                  byte_size_in_proper_unit(allocation_headroom), proper_unit_for_byte_size(allocation_headroom),
368                  byte_size_in_proper_unit(min_threshold),       proper_unit_for_byte_size(min_threshold));
369     return resize_and_evaluate();
370   }
371 
372   // Check if we need to learn a bit about the application
373   const size_t max_learn = ShenandoahLearningSteps;
374   if (_gc_times_learned < max_learn) {
375     size_t init_threshold = capacity / 100 * ShenandoahInitFreeThreshold;
376     if (allocation_headroom < init_threshold) {
377       log_info(gc)("Trigger (%s): Learning " SIZE_FORMAT " of " SIZE_FORMAT ". Free (" SIZE_FORMAT "%s) is below initial threshold (" SIZE_FORMAT "%s)",
378                    _generation->name(), _gc_times_learned + 1, max_learn,
379                    byte_size_in_proper_unit(allocation_headroom), proper_unit_for_byte_size(allocation_headroom),
380                    byte_size_in_proper_unit(init_threshold),      proper_unit_for_byte_size(init_threshold));
381       return true;
382     }
383   }
384 
385   //  Rationale:
386   //    The idea is that there is an average allocation rate and there are occasional abnormal bursts (or spikes) of
387   //    allocations that exceed the average allocation rate.  What do these spikes look like?
388   //
389   //    1. At certain phase changes, we may discard large amounts of data and replace it with large numbers of newly
390   //       allocated objects.  This "spike" looks more like a phase change.  We were in steady state at M bytes/sec
391   //       allocation rate and now we're in a "reinitialization phase" that looks like N bytes/sec.  We need the "spike"
392   //       accomodation to give us enough runway to recalibrate our "average allocation rate".
393   //
394   //   2. The typical workload changes.  "Suddenly", our typical workload of N TPS increases to N+delta TPS.  This means
395   //       our average allocation rate needs to be adjusted.  Once again, we need the "spike" accomodation to give us
396   //       enough runway to recalibrate our "average allocation rate".
397   //
398   //    3. Though there is an "average" allocation rate, a given workload's demand for allocation may be very bursty.  We
399   //       allocate a bunch of LABs during the 5 ms that follow completion of a GC, then we perform no more allocations for
400   //       the next 150 ms.  It seems we want the "spike" to represent the maximum divergence from average within the
401   //       period of time between consecutive evaluation of the should_start_gc() service.  Here's the thinking:
402   //
403   //       a) Between now and the next time I ask whether should_start_gc(), we might experience a spike representing
404   //          the anticipated burst of allocations.  If that would put us over budget, then we should start GC immediately.
405   //       b) Between now and the anticipated depletion of allocation pool, there may be two or more bursts of allocations.
406   //          If there are more than one of these bursts, we can "approximate" that these will be separated by spans of
407   //          time with very little or no allocations so the "average" allocation rate should be a suitable approximation
408   //          of how this will behave.
409   //
410   //    For cases 1 and 2, we need to "quickly" recalibrate the average allocation rate whenever we detect a change
411   //    in operation mode.  We want some way to decide that the average rate has changed.  Make average allocation rate
412   //    computations an independent effort.
413 
414 
415   // TODO: Account for inherent delays in responding to GC triggers
416   //  1. It has been observed that delays of 200 ms or greater are common between the moment we return true from should_start_gc()
417   //     and the moment at which we begin execution of the concurrent reset phase.  Add this time into the calculation of
418   //     avg_cycle_time below.  (What is "this time"?  Perhaps we should remember recent history of this delay for the
419   //     running workload and use the maximum delay recently seen for "this time".)
420   //  2. The frequency of inquiries to should_start_gc() is adaptive, ranging between ShenandoahControlIntervalMin and
421   //     ShenandoahControlIntervalMax.  The current control interval (or the max control interval) should also be added into
422   //     the calculation of avg_cycle_time below.
423 
424   double avg_cycle_time = _gc_cycle_time_history->davg() + (_margin_of_error_sd * _gc_cycle_time_history->dsd());
425 
426   size_t last_live_memory = get_last_live_memory();
427   size_t penultimate_live_memory = get_penultimate_live_memory();
428   double original_cycle_time = avg_cycle_time;
429   if ((penultimate_live_memory < last_live_memory) && (penultimate_live_memory != 0)) {
430     // If the live-memory size is growing, our estimates of cycle time are based on lighter workload, so adjust.
431     // TODO: Be more precise about how to scale when live memory is growing.  Existing code is a very rough approximation
432     // tuned with very limited workload observations.
433     avg_cycle_time = (avg_cycle_time * 2 * last_live_memory) / penultimate_live_memory;
434   } else {
435     int degen_cycles = degenerated_cycles_in_a_row();
436     if (degen_cycles > 0) {
437       // If we've degenerated recently, we might be waiting too long between triggers so adjust trigger forward.
438       // TODO: Be more precise about how to scale when we've experienced recent degenerated GC.  Existing code is a very
439       // rough approximation tuned with very limited workload observations.
440       avg_cycle_time += degen_cycles * avg_cycle_time;
441     }
442   }
443 
444   double avg_alloc_rate = _allocation_rate.upper_bound(_margin_of_error_sd);
445   log_debug(gc)("%s: average GC time: %.2f ms, allocation rate: %.0f %s/s",
446     _generation->name(), avg_cycle_time * 1000, byte_size_in_proper_unit(avg_alloc_rate), proper_unit_for_byte_size(avg_alloc_rate));
447 
448   if (avg_cycle_time > allocation_headroom / avg_alloc_rate) {
449     if (avg_cycle_time > original_cycle_time) {
450       log_debug(gc)("%s: average GC time adjusted from: %.2f ms to %.2f ms because upward trend in live memory retention",
451                     _generation->name(), original_cycle_time, avg_cycle_time);
452     }
453 
454     log_info(gc)("Trigger (%s): Average GC time (%.2f ms) is above the time for average allocation rate (%.0f %sB/s) to deplete free headroom (" SIZE_FORMAT "%s) (margin of error = %.2f)",
455                  _generation->name(), avg_cycle_time * 1000,
456                  byte_size_in_proper_unit(avg_alloc_rate), proper_unit_for_byte_size(avg_alloc_rate),
457                  byte_size_in_proper_unit(allocation_headroom), proper_unit_for_byte_size(allocation_headroom),
458                  _margin_of_error_sd);
459 
460     log_info(gc, ergo)("Free headroom: " SIZE_FORMAT "%s (free) - " SIZE_FORMAT "%s (spike) - " SIZE_FORMAT "%s (penalties) = " SIZE_FORMAT "%s",
461                        byte_size_in_proper_unit(available),           proper_unit_for_byte_size(available),
462                        byte_size_in_proper_unit(spike_headroom),      proper_unit_for_byte_size(spike_headroom),
463                        byte_size_in_proper_unit(penalties),           proper_unit_for_byte_size(penalties),
464                        byte_size_in_proper_unit(allocation_headroom), proper_unit_for_byte_size(allocation_headroom));
465 
466     _last_trigger = RATE;
467     return resize_and_evaluate();
468   }
469 
470   bool is_spiking = _allocation_rate.is_spiking(rate, _spike_threshold_sd);
471   if (is_spiking && avg_cycle_time > allocation_headroom / rate) {
472     log_info(gc)("Trigger (%s): Average GC time (%.2f ms) is above the time for instantaneous allocation rate (%.0f %sB/s) to deplete free headroom (" SIZE_FORMAT "%s) (spike threshold = %.2f)",
473                  _generation->name(), avg_cycle_time * 1000,
474                  byte_size_in_proper_unit(rate), proper_unit_for_byte_size(rate),
475                  byte_size_in_proper_unit(allocation_headroom), proper_unit_for_byte_size(allocation_headroom),
476 
477                  _spike_threshold_sd);
478     _last_trigger = SPIKE;
479     return resize_and_evaluate();
480   }
481 
482   return ShenandoahHeuristics::should_start_gc();
483 }
484 
485 bool ShenandoahAdaptiveHeuristics::resize_and_evaluate() {
486   ShenandoahHeap* heap = ShenandoahHeap::heap();
487   if (!heap->mode()->is_generational()) {
488     // We only attempt to resize the generations in generational mode.
489     return true;
490   }
491 
492   if (_cycles_since_last_resize <= MINIMUM_RESIZE_INTERVAL) {
493     log_info(gc, ergo)("Not resizing %s for another " UINT32_FORMAT " cycles.",
494         _generation->name(),  _cycles_since_last_resize);
495     return true;
496   }
497 
498   if (!heap->generation_sizer()->transfer_capacity(_generation)) {
499     // We could not enlarge our generation, so we must start a gc cycle.
500     log_info(gc, ergo)("Could not increase size of %s, begin gc cycle.", _generation->name());
501     return true;
502   }
503 
504   log_info(gc)("Increased size of %s generation, re-evaluate trigger criteria", _generation->name());
505   return should_start_gc();
506 }
507 
508 void ShenandoahAdaptiveHeuristics::adjust_last_trigger_parameters(double amount) {
509   switch (_last_trigger) {
510     case RATE:
511       adjust_margin_of_error(amount);
512       break;
513     case SPIKE:
514       adjust_spike_threshold(amount);
515       break;
516     case OTHER:
517       // nothing to adjust here.
518       break;
519     default:
520       ShouldNotReachHere();
521   }
522 }
523 
524 void ShenandoahAdaptiveHeuristics::adjust_margin_of_error(double amount) {
525   _margin_of_error_sd = saturate(_margin_of_error_sd + amount, MINIMUM_CONFIDENCE, MAXIMUM_CONFIDENCE);
526   log_debug(gc, ergo)("Margin of error now %.2f", _margin_of_error_sd);
527 }
528 
529 void ShenandoahAdaptiveHeuristics::adjust_spike_threshold(double amount) {
530   _spike_threshold_sd = saturate(_spike_threshold_sd - amount, MINIMUM_CONFIDENCE, MAXIMUM_CONFIDENCE);
531   log_debug(gc, ergo)("Spike threshold now: %.2f", _spike_threshold_sd);
532 }
533 
534 ShenandoahAllocationRate::ShenandoahAllocationRate() :
535   _last_sample_time(os::elapsedTime()),
536   _last_sample_value(0),
537   _interval_sec(1.0 / ShenandoahAdaptiveSampleFrequencyHz),
538   _rate(int(ShenandoahAdaptiveSampleSizeSeconds * ShenandoahAdaptiveSampleFrequencyHz), ShenandoahAdaptiveDecayFactor),
539   _rate_avg(int(ShenandoahAdaptiveSampleSizeSeconds * ShenandoahAdaptiveSampleFrequencyHz), ShenandoahAdaptiveDecayFactor) {
540 }
541 
542 double ShenandoahAllocationRate::sample(size_t allocated) {
543   double now = os::elapsedTime();
544   double rate = 0.0;
545   if (now - _last_sample_time > _interval_sec) {
546     if (allocated >= _last_sample_value) {
547       rate = instantaneous_rate(now, allocated);
548       _rate.add(rate);
549       _rate_avg.add(_rate.avg());
550     }
551 
552     _last_sample_time = now;
553     _last_sample_value = allocated;
554   }
555   return rate;
556 }
557 
558 double ShenandoahAllocationRate::upper_bound(double sds) const {
559   // Here we are using the standard deviation of the computed running
560   // average, rather than the standard deviation of the samples that went
561   // into the moving average. This is a much more stable value and is tied
562   // to the actual statistic in use (moving average over samples of averages).
563   return _rate.davg() + (sds * _rate_avg.dsd());
564 }
565 
566 void ShenandoahAllocationRate::allocation_counter_reset() {
567   _last_sample_time = os::elapsedTime();
568   _last_sample_value = 0;
569 }
570 
571 bool ShenandoahAllocationRate::is_spiking(double rate, double threshold) const {
572   if (rate <= 0.0) {
573     return false;
574   }
575 
576   double sd = _rate.sd();
577   if (sd > 0) {
578     // There is a small chance that that rate has already been sampled, but it
579     // seems not to matter in practice.
580     double z_score = (rate - _rate.avg()) / sd;
581     if (z_score > threshold) {
582       return true;
583     }
584   }
585   return false;
586 }
587 
588 double ShenandoahAllocationRate::instantaneous_rate(size_t allocated) const {
589   return instantaneous_rate(os::elapsedTime(), allocated);
590 }
591 
592 double ShenandoahAllocationRate::instantaneous_rate(double time, size_t allocated) const {
593   size_t last_value = _last_sample_value;
594   double last_time = _last_sample_time;
595   size_t allocation_delta = (allocated > last_value) ? (allocated - last_value) : 0;
596   double time_delta_sec = time - last_time;
597   return (time_delta_sec > 0)  ? (allocation_delta / time_delta_sec) : 0;
598 }