Use prime for ConcurrentDictionary initial size (#421)

* initial

* fix

* tests

* 137

* link

* link .net

* comments

* comments

Author: bitfaster

BitFaster.Caching.UnitTests/HashTablePrimesTests.cs

@@ -0,0 +1,121 @@
+using System.Collections.Generic;
+using System;
+using BitFaster.Caching;
+using FluentAssertions;
+using Xunit;
+using Xunit.Abstractions;
+
+namespace BitFaster.Caching.UnitTests
+{
+    public class HashTablePrimesTests
+    {
+        private readonly ITestOutputHelper testOutputHelper;
+
+        public HashTablePrimesTests(ITestOutputHelper testOutputHelper)
+        {
+            this.testOutputHelper = testOutputHelper;
+        }
+
+        [Theory]
+        [InlineData(3, 7)]
+        [InlineData(8, 11)]
+        [InlineData(12, 17)]
+        [InlineData(132, 137)]
+        [InlineData(500, 137)]
+        public void NextPrimeGreaterThan(int input, int nextPrime)
+        {
+            HashTablePrimes.NextPrimeGreaterThan(input).Should().Be(nextPrime);
+        }
+
+        // This test method replicates the hash table sizes that will be computed by ConcurrentDictionary
+        // on earlier versions of .NET before prime numbers are used.
+        // 277 is prime
+        // 557 is prime
+        // 1117 is prime
+        // 2237 is prime
+        // 4477 has factors 11, 37, 121, 407
+        // 8957 has factors 13, 53, 169, 689
+        // 17917 has factors 19, 23, 41, 437, 779, 943
+        // 35837 is prime
+        // 71677 has factors 229, 313
+        // 143357 is prime
+        // 286717 has factors 163, 1759
+        // 573437 is prime
+        // 1146877 is prime
+        // 2293757 is prime
+        // 4587517 has factors 11, 103, 1133, 4049, 44539, 417047
+        // 9175037 is prime
+        // 18350077 has factors 701, 26177
+        // 36700157 has factors 13, 23, 299, 122743, 1595659, 2823089
+        // 73400317 has factors 4999, 14683
+        // 146800637 is prime
+        // 293601277 has factors 6113, 48029
+        // 587202557 has factors 1877, 312841
+        // 1174405117 has factors 10687, 109891
+        [Fact(Skip="Not a functional test")]
+        public void ComputeHashTableSizes()
+        {
+            // 137 gives a good balance of primes for smaller sizes, and few factors for larger sizes.
+            // Other good candidates: 131, 151, 163, 211
+            int size = 137;
+            for (int i = 0; i < 23; i++)
+            {
+                int nextSize = NextTableSize(size);
+                this.testOutputHelper.WriteLine($"{nextSize} {GetFactorsString(nextSize)}");
+                size = nextSize;
+            }
+        }
+
+        // Replicates .NET framework ConcurrentDictionary resize logic:
+        // https://github.com/microsoft/referencesource/blob/51cf7850defa8a17d815b4700b67116e3fa283c2/mscorlib/system/collections/Concurrent/ConcurrentDictionary.cs#L1828C29-L1828C29
+        private static int NextTableSize(int initial)
+        {
+            // Double the size of the buckets table and add one, so that we have an odd integer.
+            int newLength = initial * 2 + 1;
+
+            // Now, we only need to check odd integers, and find the first that is not divisible
+            // by 3, 5 or 7.
+            while (newLength % 3 == 0 || newLength % 5 == 0 || newLength % 7 == 0)
+            {
+                newLength += 2;
+            }
+
+            return newLength;
+        }
+
+        private static string GetFactorsString(int nextSize)
+        {
+            var factors = Factor(nextSize);
+
+            factors.Remove(1);
+            factors.Remove(nextSize);
+            factors.Sort();
+
+            if (factors.Count == 0)
+            {
+                return "is prime";
+            }
+
+            return $"has factors {string.Join(", ", factors)}";
+        }
+
+        // https://stackoverflow.com/questions/239865/best-way-to-find-all-factors-of-a-given-number
+        private static List<int> Factor(int number)
+        {
+            var factors = new List<int>();
+            int max = (int)Math.Sqrt(number);  // Round down
+
+            for (int factor = 1; factor <= max; ++factor) // Test from 1 to the square root, or the int below it, inclusive.
+            {
+                if (number % factor == 0)
+                {
+                    factors.Add(factor);
+                    if (factor != number / factor) // Don't add the square root twice!  Thanks Jon
+                        factors.Add(number / factor);
+                }
+            }
+
+            return factors;
+        }
+    }
+}

BitFaster.Caching/HashTablePrimes.cs

@@ -0,0 +1,46 @@
+using System;
+
+namespace BitFaster.Caching
+{
+    // Using the capacity passed into the cache ctor to initialize the ConcurrentDictionary has 2 problems:
+    //
+    // 1. By allocating up front, we eliminate resizing. However, if the capacity is very large and the cache is not used,
+    // we will waste a lot of memory.
+    // 2. On earlier versions of .NET, ConcurrentDictionary uses the capacity arg to directly initialize the hash table
+    // size. On resize, the hashtable is grown to 2x + 1 while avoiding factors of 3, 5, or 7 (but not larger). On
+    // newer versions of.NET, both initial size and resize is based the next prime number larger than capacity. Collisions
+    // are reduced when hash table size is prime. Hence the change to use primes in all cases in newer versions of the
+    // framework.
+    //
+    // To mitigate this, we adopt a simple scheme: find the next prime larger than the capacity arg, up to 137. If the
+    // capacity is greater than 137, just set the initial size to 137, thereby bounding initial memory consumption for
+    // large caches.
+    // 
+    // - Older.NET implementations: For smaller caches, we fix size at the next largest prime. For larger tables, we now
+    // start out with a larger prime (avoiding all factors up to 137, not just 3, 5 and 7). Above 137, some sizes will be
+    // prime and others have relatively few factors.The complete list is given as a comment in the unit test code.
+    // - Newer.NET implementations: as above for smaller caches. For larger caches, the resize will use successively larger
+    // primes.The duplicate prime computation added is only during construction and is effectively a no-op.
+    internal class HashTablePrimes
+    {
+#if NETSTANDARD2_0
+        internal static int[] Primes = new int[] {
+#else
+        internal static ReadOnlySpan<int> Primes => new int[] {
+#endif
+            7, 11, 17, 23, 29, 37, 47, 59, 71, 89, 107, 131
+        };
+        internal static int NextPrimeGreaterThan(int min)
+        {
+            foreach (int prime in Primes)
+            {
+                if (prime > min)
+                {
+                    return prime;
+                }
+            }
+
+            return 137;
+        }
+    }
+}

BitFaster.Caching/Lfu/ConcurrentLfu.cs

@@ -90,7 +90,8 @@ public ConcurrentLfu(int capacity)
         /// <param name="comparer">The equality comparer.</param>
         public ConcurrentLfu(int concurrencyLevel, int capacity, IScheduler scheduler, IEqualityComparer<K> comparer)
         {
-            this.dictionary = new ConcurrentDictionary<K, LfuNode<K, V>>(concurrencyLevel, capacity, comparer);
+            int dictionaryCapacity = HashTablePrimes.NextPrimeGreaterThan(capacity);
+            this.dictionary = new ConcurrentDictionary<K, LfuNode<K, V>>(concurrencyLevel, dictionaryCapacity, comparer);
 
             // cap concurrency at proc count * 2
             int readStripes = Math.Min(BitOps.CeilingPowerOfTwo(concurrencyLevel), BitOps.CeilingPowerOfTwo(Environment.ProcessorCount * 2));

BitFaster.Caching/Lru/ClassicLru.cs

@@ -52,7 +52,8 @@ public ClassicLru(int concurrencyLevel, int capacity, IEqualityComparer<K> compa
                 Throw.ArgNull(ExceptionArgument.comparer);
 
             this.capacity = capacity;
-            this.dictionary = new ConcurrentDictionary<K, LinkedListNode<LruItem>>(concurrencyLevel, this.capacity + 1, comparer);
+            int dictionaryCapacity = HashTablePrimes.NextPrimeGreaterThan(capacity);
+            this.dictionary = new ConcurrentDictionary<K, LinkedListNode<LruItem>>(concurrencyLevel, dictionaryCapacity, comparer);
             this.policy = new CachePolicy(new Optional<IBoundedPolicy>(this), Optional<ITimePolicy>.None());
         }
 

BitFaster.Caching/Lru/ConcurrentLruCore.cs

@@ -88,7 +88,7 @@ public ConcurrentLruCore(
             this.warmQueue = new ConcurrentQueue<I>();
             this.coldQueue = new ConcurrentQueue<I>();
 
-            int dictionaryCapacity = this.Capacity + 1;
+            int dictionaryCapacity = HashTablePrimes.NextPrimeGreaterThan(this.Capacity);
 
             this.dictionary = new ConcurrentDictionary<K, I>(concurrencyLevel, dictionaryCapacity, comparer);
             this.itemPolicy = itemPolicy;