Merge #12048: Use best-fit strategy in Arena, now O(log(n)) instead O(n)

5fbf7c4 fix nits: variable naming, typos (Martin Ankerl)
1e0ee90 Use best-fit strategy in Arena, now O(log(n)) instead O(n) (Martin Ankerl)

Pull request description:

  This replaces the first-fit algorithm used in the Arena with a best-fit. According to "Dynamic Storage Allocation: A Survey and Critical Review", Wilson et. al. 1995, http://www.scs.stanford.edu/14wi-cs140/sched/readings/wilson.pdf, both startegies work well in practice.

  The advantage of using best-fit is that we can switch the O(n) allocation to O(log(n)). Additionally, some previously O(log(n)) operations are now O(1) operations by using hash maps. The end effect is that the benchmark runs about 2.5 times faster on my machine:

      # Benchmark, evals, iterations, total, min, max, median
      old: BenchLockedPool, 5, 530, 5.25749, 0.00196938, 0.00199755, 0.00198172
      new: BenchLockedPool, 5, 1300, 5.11313, 0.000781493, 0.000793314, 0.00078606

  I've run all unit tests and benchmarks, and increased the number of iterations so that BenchLockedPool takes about 5 seconds again.

Tree-SHA512: 6551e384671f93f10c60df530a29a1954bd265cc305411f665a8756525e5afe2873a8032c797d00b6e8c07e16d9827465d0b662875433147381474a44119ccce

2 files changed, 59 insertions, 30 deletions

diff --git a/src/support/lockedpool.cpp b/src/support/lockedpool.cpp
index 1401188a2b..f10fd07c63 100644
--- a/src/support/lockedpool.cpp
+++ b/src/support/lockedpool.cpp
@@ -47,7 +47,9 @@ Arena::Arena(void *base_in, size_t size_in, size_t alignment_in):
     base(static_cast<char*>(base_in)), end(static_cast<char*>(base_in) + size_in), alignment(alignment_in)
 {
     // Start with one free chunk that covers the entire arena
-    chunks_free.emplace(base, size_in);
+    auto it = size_to_free_chunk.emplace(size_in, base);
+    chunks_free.emplace(base, it);
+    chunks_free_end.emplace(base + size_in, it);
 }
 
 Arena::~Arena()
@@ -63,26 +65,30 @@ void* Arena::alloc(size_t size)
     if (size == 0)
         return nullptr;
 
-    // Pick a large enough free-chunk
-    auto it = std::find_if(chunks_free.begin(), chunks_free.end(),
-        [=](const std::map<char*, size_t>::value_type& chunk){ return chunk.second >= size; });
-    if (it == chunks_free.end())
+    // Pick a large enough free-chunk. Returns an iterator pointing to the first element that is not less than key.
+    // This allocation strategy is best-fit. According to "Dynamic Storage Allocation: A Survey and Critical Review",
+    // Wilson et. al. 1995, http://www.scs.stanford.edu/14wi-cs140/sched/readings/wilson.pdf, best-fit and first-fit
+    // policies seem to work well in practice.
+    auto size_ptr_it = size_to_free_chunk.lower_bound(size);
+    if (size_ptr_it == size_to_free_chunk.end())
         return nullptr;
 
     // Create the used-chunk, taking its space from the end of the free-chunk
-    auto alloced = chunks_used.emplace(it->first + it->second - size, size).first;
-    if (!(it->second -= size))
-        chunks_free.erase(it);
-    return reinterpret_cast<void*>(alloced->first);
-}
-
-/* extend the Iterator if other begins at its end */
-template <class Iterator, class Pair> bool extend(Iterator it, const Pair& other) {
-    if (it->first + it->second == other.first) {
-        it->second += other.second;
-        return true;
+    const size_t size_remaining = size_ptr_it->first - size;
+    auto alloced = chunks_used.emplace(size_ptr_it->second + size_remaining, size).first;
+    chunks_free_end.erase(size_ptr_it->second + size_ptr_it->first);
+    if (size_ptr_it->first == size) {
+        // whole chunk is used up
+        chunks_free.erase(size_ptr_it->second);
+    } else {
+        // still some memory left in the chunk
+        auto it_remaining = size_to_free_chunk.emplace(size_remaining, size_ptr_it->second);
+        chunks_free[size_ptr_it->second] = it_remaining;
+        chunks_free_end.emplace(size_ptr_it->second + size_remaining, it_remaining);
     }
-    return false;
+    size_to_free_chunk.erase(size_ptr_it);
+
+    return reinterpret_cast<void*>(alloced->first);
 }
 
 void Arena::free(void *ptr)
@@ -97,16 +103,30 @@ void Arena::free(void *ptr)
     if (i == chunks_used.end()) {
         throw std::runtime_error("Arena: invalid or double free");
     }
-    auto freed = *i;
+    std::pair<char*, size_t> freed = *i;
     chunks_used.erase(i);
 
-    // Add space to free map, coalescing contiguous chunks
-    auto next = chunks_free.upper_bound(freed.first);
-    auto prev = (next == chunks_free.begin()) ? chunks_free.end() : std::prev(next);
-    if (prev == chunks_free.end() || !extend(prev, freed))
-        prev = chunks_free.emplace_hint(next, freed);
-    if (next != chunks_free.end() && extend(prev, *next))
+    // coalesce freed with previous chunk
+    auto prev = chunks_free_end.find(freed.first);
+    if (prev != chunks_free_end.end()) {
+        freed.first -= prev->second->first;
+        freed.second += prev->second->first;
+        size_to_free_chunk.erase(prev->second);
+        chunks_free_end.erase(prev);
+    }
+
+    // coalesce freed with chunk after freed
+    auto next = chunks_free.find(freed.first + freed.second);
+    if (next != chunks_free.end()) {
+        freed.second += next->second->first;
+        size_to_free_chunk.erase(next->second);
         chunks_free.erase(next);
+    }
+
+    // Add/set space with coalesced free chunk
+    auto it = size_to_free_chunk.emplace(freed.second, freed.first);
+    chunks_free[freed.first] = it;
+    chunks_free_end[freed.first + freed.second] = it;
 }
 
 Arena::Stats Arena::stats() const
@@ -115,7 +135,7 @@ Arena::Stats Arena::stats() const
     for (const auto& chunk: chunks_used)
         r.used += chunk.second;
     for (const auto& chunk: chunks_free)
-        r.free += chunk.second;
+        r.free += chunk.second->first;
     r.total = r.used + r.free;
     return r;
 }
diff --git a/src/support/lockedpool.h b/src/support/lockedpool.h
index fc85e6c73c..ccfae16701 100644
--- a/src/support/lockedpool.h
+++ b/src/support/lockedpool.h
@@ -10,6 +10,7 @@
 #include <map>
 #include <mutex>
 #include <memory>
+#include <unordered_map>
 
 /**
  * OS-dependent allocation and deallocation of locked/pinned memory pages.
@@ -88,11 +89,19 @@ public:
      */
     bool addressInArena(void *ptr) const { return ptr >= base && ptr < end; }
 private:
-    /** Map of chunk address to chunk information. This class makes use of the
-     * sorted order to merge previous and next chunks during deallocation.
-     */
-    std::map<char*, size_t> chunks_free;
-    std::map<char*, size_t> chunks_used;
+    typedef std::multimap<size_t, char*> SizeToChunkSortedMap;
+    /** Map to enable O(log(n)) best-fit allocation, as it's sorted by size */
+    SizeToChunkSortedMap size_to_free_chunk;
+
+    typedef std::unordered_map<char*, SizeToChunkSortedMap::const_iterator> ChunkToSizeMap;
+    /** Map from begin of free chunk to its node in size_to_free_chunk */
+    ChunkToSizeMap chunks_free;
+    /** Map from end of free chunk to its node in size_to_free_chunk */
+    ChunkToSizeMap chunks_free_end;
+
+    /** Map from begin of used chunk to its size */
+    std::unordered_map<char*, size_t> chunks_used;
+
     /** Base address of arena */
     char* base;
     /** End address of arena */