Implement and use an Interval Tree for the MultiRangeList (#2641)

* Implement and use an Interval Tree for the MultiRangeList

* Feedback

* Address Feedback

* Missed this somehow

Ryujinx.Common/Collections/IntervalTree.cs

@@ -0,0 +1,815 @@
+using System;
+using System.Collections;
+using System.Collections.Generic;
+using System.Diagnostics.CodeAnalysis;
+using System.Linq;
+
+namespace Ryujinx.Common.Collections
+{
+    /// <summary>
+    /// An Augmented Interval Tree based off of the "TreeDictionary"'s Red-Black Tree. Allows fast overlap checking of ranges.
+    /// </summary>
+    /// <typeparam name="K">Key</typeparam>
+    /// <typeparam name="V">Value</typeparam>
+    public class IntervalTree<K, V> where K : IComparable<K>
+    {
+        private const int ArrayGrowthSize = 32;
+
+        private const bool Black = true;
+        private const bool Red = false;
+        private IntervalTreeNode<K, V> _root = null;
+        private int _count = 0;
+
+        public int Count => _count;
+
+        public IntervalTree() { }
+
+        #region Public Methods
+
+        /// <summary>
+        /// Gets the values of the interval whose key is <paramref name="key"/>.
+        /// </summary>
+        /// <param name="key">Key of the node value to get</param>
+        /// <param name="overlaps">Overlaps array to place results in</param>
+        /// <returns>Number of values found</returns>
+        /// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
+        public int Get(K key, ref V[] overlaps)
+        {
+            if (key == null)
+            {
+                throw new ArgumentNullException(nameof(key));
+            }
+
+            IntervalTreeNode<K, V> node = GetNode(key);
+
+            if (node == null)
+            {
+                return 0;
+            }
+
+            if (node.Values.Count > overlaps.Length)
+            {
+                Array.Resize(ref overlaps, node.Values.Count);
+            }
+
+            int overlapsCount = 0;
+            foreach (RangeNode<K, V> value in node.Values)
+            {
+                overlaps[overlapsCount++] = value.Value;
+            }
+
+            return overlapsCount;
+        }
+
+        /// <summary>
+        /// Returns the values of the intervals whose start and end keys overlap the given range.
+        /// </summary>
+        /// <param name="start">Start of the range</param>
+        /// <param name="end">End of the range</param>
+        /// <param name="overlaps">Overlaps array to place results in</param>
+        /// <param name="overlapCount">Index to start writing results into the array. Defaults to 0</param>
+        /// <returns>Number of values found</returns>
+        /// <exception cref="ArgumentNullException"><paramref name="start"/> or <paramref name="end"/> is null</exception>
+        public int Get(K start, K end, ref V[] overlaps, int overlapCount = 0)
+        {
+            if (start == null)
+            {
+                throw new ArgumentNullException(nameof(start));
+            }
+
+            if (end == null)
+            {
+                throw new ArgumentNullException(nameof(end));
+            }
+
+            GetValues(_root, start, end, ref overlaps, ref overlapCount);
+
+            return overlapCount;
+        }
+
+        /// <summary>
+        /// Adds a new interval into the tree whose start is <paramref name="start"/>, end is <paramref name="end"/> and value is <paramref name="value"/>.
+        /// </summary>
+        /// <param name="start">Start of the range to add</param>
+        /// <param name="end">End of the range to insert</param>
+        /// <param name="value">Value to add</param>
+        /// <exception cref="ArgumentNullException"><paramref name="start"/>, <paramref name="end"/> or <paramref name="value"/> are null</exception>
+        public void Add(K start, K end, V value)
+        {
+            if (start == null)
+            {
+                throw new ArgumentNullException(nameof(start));
+            }
+
+            if (end == null)
+            {
+                throw new ArgumentNullException(nameof(end));
+            }
+
+            if (value == null)
+            {
+                throw new ArgumentNullException(nameof(value));
+            }
+
+            Insert(start, end, value);
+        }
+
+        /// <summary>
+        /// Removes the given <paramref name="value"/> from the tree, searching for it with <paramref name="key"/>.
+        /// </summary>
+        /// <param name="key">Key of the node to remove</param>
+        /// <param name="value">Value to remove</param>
+        /// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
+        /// <returns>Number of deleted values</returns>
+        public int Remove(K key, V value)
+        {
+            if (key == null)
+            {
+                throw new ArgumentNullException(nameof(key));
+            }
+
+            int removed = Delete(key, value);
+
+            _count -= removed;
+
+            return removed;
+        }
+
+        /// <summary>
+        /// Adds all the nodes in the dictionary into <paramref name="list"/>.
+        /// </summary>
+        /// <returns>A list of all RangeNodes sorted by Key Order</returns>
+        public List<RangeNode<K, V>> AsList()
+        {
+            List<RangeNode<K, V>> list = new List<RangeNode<K, V>>();
+
+            AddToList(_root, list);
+
+            return list;
+        }
+
+        #endregion
+
+        #region Private Methods (BST)
+
+        /// <summary>
+        /// Adds all RangeNodes that are children of or contained within <paramref name="node"/> into <paramref name="list"/>, in Key Order.
+        /// </summary>
+        /// <param name="node">The node to search for RangeNodes within</param>
+        /// <param name="list">The list to add RangeNodes to</param>
+        private void AddToList(IntervalTreeNode<K, V> node, List<RangeNode<K, V>> list)
+        {
+            if (node == null)
+            {
+                return;
+            }
+
+            AddToList(node.Left, list);
+
+            list.AddRange(node.Values);
+
+            AddToList(node.Right, list);
+        }
+
+        /// <summary>
+        /// Retrieve the node reference whose key is <paramref name="key"/>, or null if no such node exists.
+        /// </summary>
+        /// <param name="key">Key of the node to get</param>
+        /// <returns>Node reference in the tree</returns>
+        /// <exception cref="ArgumentNullException"><paramref name="key"/> is null</exception>
+        private IntervalTreeNode<K, V> GetNode(K key)
+        {
+            if (key == null)
+            {
+                throw new ArgumentNullException(nameof(key));
+            }
+
+            IntervalTreeNode<K, V> node = _root;
+            while (node != null)
+            {
+                int cmp = key.CompareTo(node.Start);
+                if (cmp < 0)
+                {
+                    node = node.Left;
+                }
+                else if (cmp > 0)
+                {
+                    node = node.Right;
+                }
+                else
+                {
+                    return node;
+                }
+            }
+            return null;
+        }
+
+        /// <summary>
+        /// Retrieve all values that overlap the given start and end keys.
+        /// </summary>
+        /// <param name="start">Start of the range</param>
+        /// <param name="end">End of the range</param>
+        /// <param name="overlaps">Overlaps array to place results in</param>
+        /// <param name="overlapCount">Overlaps count to update</param>
+        private void GetValues(IntervalTreeNode<K, V> node, K start, K end, ref V[] overlaps, ref int overlapCount)
+        {   
+            if (node == null || start.CompareTo(node.Max) >= 0)
+            {
+                return;
+            }
+
+            GetValues(node.Left, start, end, ref overlaps, ref overlapCount);
+
+            bool endsOnRight = end.CompareTo(node.Start) > 0;
+            if (endsOnRight)
+            {
+                if (start.CompareTo(node.End) < 0)
+                {
+                    // Contains this node. Add overlaps to list.
+                    foreach (RangeNode<K,V> overlap in node.Values)
+                    {
+                        if (start.CompareTo(overlap.End) < 0)
+                        {
+                            if (overlaps.Length >= overlapCount)
+                            {
+                                Array.Resize(ref overlaps, overlapCount + ArrayGrowthSize);
+                            }
+
+                            overlaps[overlapCount++] = overlap.Value;
+                        }
+                    }
+                }
+
+                GetValues(node.Right, start, end, ref overlaps, ref overlapCount);
+            }
+        }
+
+        /// <summary>
+        /// Inserts a new node into the tree with a given <paramref name="start"/>, <paramref name="end"/> and <paramref name="value"/>.
+        /// </summary>
+        /// <param name="start">Start of the range to insert</param>
+        /// <param name="end">End of the range to insert</param>
+        /// <param name="value">Value to insert</param>
+        private void Insert(K start, K end, V value)
+        {
+            IntervalTreeNode<K, V> newNode = BSTInsert(start, end, value);
+            RestoreBalanceAfterInsertion(newNode);
+        }
+
+        /// <summary>
+        /// Propagate an increase in max value starting at the given node, heading up the tree.
+        /// This should only be called if the max increases - not for rebalancing or removals.
+        /// </summary>
+        /// <param name="node">The node to start propagating from</param>
+        private void PropagateIncrease(IntervalTreeNode<K, V> node)
+        {
+            K max = node.Max;
+            IntervalTreeNode<K, V> ptr = node;
+
+            while ((ptr = ptr.Parent) != null)
+            {
+                if (max.CompareTo(ptr.Max) > 0)
+                {
+                    ptr.Max = max;
+                }
+                else
+                {
+                    break;
+                }
+            }
+        }
+
+        /// <summary>
+        /// Propagate recalculating max value starting at the given node, heading up the tree.
+        /// This fully recalculates the max value from all children when there is potential for it to decrease.
+        /// </summary>
+        /// <param name="node">The node to start propagating from</param>
+        private void PropagateFull(IntervalTreeNode<K, V> node)
+        {
+            IntervalTreeNode<K, V> ptr = node;
+
+            do
+            {
+                K max = ptr.End;
+
+                if (ptr.Left != null && ptr.Left.Max.CompareTo(max) > 0)
+                {
+                    max = ptr.Left.Max;
+                }
+
+                if (ptr.Right != null && ptr.Right.Max.CompareTo(max) > 0)
+                {
+                    max = ptr.Right.Max;
+                }
+
+                ptr.Max = max;
+            } while ((ptr = ptr.Parent) != null);
+        }
+
+        /// <summary>
+        /// Insertion Mechanism for the interval tree. Similar to a BST insert, with the start of the range as the key.
+        /// Iterates the tree starting from the root and inserts a new node where all children in the left subtree are less than <paramref name="start"/>, and all children in the right subtree are greater than <paramref name="start"/>.
+        /// Each node can contain multiple values, and has an end address which is the maximum of all those values.
+        /// Post insertion, the "max" value of the node and all parents are updated.
+        /// </summary>
+        /// <param name="start">Start of the range to insert</param>
+        /// <param name="end">End of the range to insert</param>
+        /// <param name="value">Value to insert</param>
+        /// <returns>The inserted Node</returns>
+        private IntervalTreeNode<K, V> BSTInsert(K start, K end, V value)
+        {
+            IntervalTreeNode<K, V> parent = null;
+            IntervalTreeNode<K, V> node = _root;
+
+            while (node != null)
+            {
+                parent = node;
+                int cmp = start.CompareTo(node.Start);
+                if (cmp < 0)
+                {
+                    node = node.Left;
+                }
+                else if (cmp > 0)
+                {
+                    node = node.Right;
+                }
+                else
+                {
+                    node.Values.Add(new RangeNode<K, V>(start, end, value));
+
+                    if (end.CompareTo(node.End) > 0)
+                    {
+                        node.End = end;
+                        if (end.CompareTo(node.Max) > 0)
+                        {
+                            node.Max = end;
+                            PropagateIncrease(node);
+                        }
+                    }
+
+                    _count++;
+                    return node;
+                }
+            }
+            IntervalTreeNode<K, V> newNode = new IntervalTreeNode<K, V>(start, end, value, parent);
+            if (newNode.Parent == null)
+            {
+                _root = newNode;
+            }
+            else if (start.CompareTo(parent.Start) < 0)
+            {
+                parent.Left = newNode;
+            }
+            else
+            {
+                parent.Right = newNode;
+            }
+
+            PropagateIncrease(newNode);
+            _count++;
+            return newNode;
+        }
+
+        /// <summary>
+        /// Removes instances of <paramref name="value"> from the dictionary after searching for it with <paramref name="key">.
+        /// </summary>
+        /// <param name="key">Key to search for</param>
+        /// <param name="value">Value to delete</param>
+        /// <returns>Number of deleted values</returns>
+        private int Delete(K key, V value)
+        {
+            IntervalTreeNode<K, V> nodeToDelete = GetNode(key);
+
+            if (nodeToDelete == null)
+            {
+                return 0;
+            }
+
+            int removed = nodeToDelete.Values.RemoveAll(node => node.Value.Equals(value));
+
+            if (nodeToDelete.Values.Count > 0)
+            {
+                if (removed > 0)
+                {
+                    nodeToDelete.End = nodeToDelete.Values.Max(node => node.End);
+
+                    // Recalculate max from children and new end.
+                    PropagateFull(nodeToDelete);
+                }
+
+                return removed;
+            }
+
+            IntervalTreeNode<K, V> replacementNode;
+
+            if (LeftOf(nodeToDelete) == null || RightOf(nodeToDelete) == null)
+            {
+                replacementNode = nodeToDelete;
+            }
+            else
+            {
+                replacementNode = PredecessorOf(nodeToDelete);
+            }
+
+            IntervalTreeNode<K, V> tmp = LeftOf(replacementNode) ?? RightOf(replacementNode);
+
+            if (tmp != null)
+            {
+                tmp.Parent = ParentOf(replacementNode);
+            }
+
+            if (ParentOf(replacementNode) == null)
+            {
+                _root = tmp;
+            }
+            else if (replacementNode == LeftOf(ParentOf(replacementNode)))
+            {
+                ParentOf(replacementNode).Left = tmp;
+            }
+            else
+            {
+                ParentOf(replacementNode).Right = tmp;
+            }
+
+            if (replacementNode != nodeToDelete)
+            {
+                nodeToDelete.Start = replacementNode.Start;
+                nodeToDelete.Values = replacementNode.Values;
+                nodeToDelete.End = replacementNode.End;
+                nodeToDelete.Max = replacementNode.Max;
+            }
+
+            PropagateFull(replacementNode);
+
+            if (tmp != null && ColorOf(replacementNode) == Black)
+            {
+                RestoreBalanceAfterRemoval(tmp);
+            }
+
+            return removed;
+        }
+
+        /// <summary>
+        /// Returns the node with the largest key where <paramref name="node"/> is considered the root node.
+        /// </summary>
+        /// <param name="node">Root Node</param>
+        /// <returns>Node with the maximum key in the tree of <paramref name="node"/></returns>
+        private static IntervalTreeNode<K, V> Maximum(IntervalTreeNode<K, V> node)
+        {
+            IntervalTreeNode<K, V> tmp = node;
+            while (tmp.Right != null)
+            {
+                tmp = tmp.Right;
+            }
+
+            return tmp;
+        }
+
+        /// <summary>
+        /// Finds the node whose key is immediately less than <paramref name="node"/>.
+        /// </summary>
+        /// <param name="node">Node to find the predecessor of</param>
+        /// <returns>Predecessor of <paramref name="node"/></returns>
+        private static IntervalTreeNode<K, V> PredecessorOf(IntervalTreeNode<K, V> node)
+        {
+            if (node.Left != null)
+            {
+                return Maximum(node.Left);
+            }
+            IntervalTreeNode<K, V> parent = node.Parent;
+            while (parent != null && node == parent.Left)
+            {
+                node = parent;
+                parent = parent.Parent;
+            }
+            return parent;
+        }
+        #endregion
+
+        #region Private Methods (RBL)
+        private void RestoreBalanceAfterRemoval(IntervalTreeNode<K, V> balanceNode)
+        {
+            IntervalTreeNode<K, V> ptr = balanceNode;
+
+            while (ptr != _root && ColorOf(ptr) == Black)
+            {
+                if (ptr == LeftOf(ParentOf(ptr)))
+                {
+                    IntervalTreeNode<K, V> sibling = RightOf(ParentOf(ptr));
+
+                    if (ColorOf(sibling) == Red)
+                    {
+                        SetColor(sibling, Black);
+                        SetColor(ParentOf(ptr), Red);
+                        RotateLeft(ParentOf(ptr));
+                        sibling = RightOf(ParentOf(ptr));
+                    }
+                    if (ColorOf(LeftOf(sibling)) == Black && ColorOf(RightOf(sibling)) == Black)
+                    {
+                        SetColor(sibling, Red);
+                        ptr = ParentOf(ptr);
+                    }
+                    else
+                    {
+                        if (ColorOf(RightOf(sibling)) == Black)
+                        {
+                            SetColor(LeftOf(sibling), Black);
+                            SetColor(sibling, Red);
+                            RotateRight(sibling);
+                            sibling = RightOf(ParentOf(ptr));
+                        }
+                        SetColor(sibling, ColorOf(ParentOf(ptr)));
+                        SetColor(ParentOf(ptr), Black);
+                        SetColor(RightOf(sibling), Black);
+                        RotateLeft(ParentOf(ptr));
+                        ptr = _root;
+                    }
+                }
+                else
+                {
+                    IntervalTreeNode<K, V> sibling = LeftOf(ParentOf(ptr));
+
+                    if (ColorOf(sibling) == Red)
+                    {
+                        SetColor(sibling, Black);
+                        SetColor(ParentOf(ptr), Red);
+                        RotateRight(ParentOf(ptr));
+                        sibling = LeftOf(ParentOf(ptr));
+                    }
+                    if (ColorOf(RightOf(sibling)) == Black && ColorOf(LeftOf(sibling)) == Black)
+                    {
+                        SetColor(sibling, Red);
+                        ptr = ParentOf(ptr);
+                    }
+                    else
+                    {
+                        if (ColorOf(LeftOf(sibling)) == Black)
+                        {
+                            SetColor(RightOf(sibling), Black);
+                            SetColor(sibling, Red);
+                            RotateLeft(sibling);
+                            sibling = LeftOf(ParentOf(ptr));
+                        }
+                        SetColor(sibling, ColorOf(ParentOf(ptr)));
+                        SetColor(ParentOf(ptr), Black);
+                        SetColor(LeftOf(sibling), Black);
+                        RotateRight(ParentOf(ptr));
+                        ptr = _root;
+                    }
+                }
+            }
+            SetColor(ptr, Black);
+        }
+
+        private void RestoreBalanceAfterInsertion(IntervalTreeNode<K, V> balanceNode)
+        {
+            SetColor(balanceNode, Red);
+            while (balanceNode != null && balanceNode != _root && ColorOf(ParentOf(balanceNode)) == Red)
+            {
+                if (ParentOf(balanceNode) == LeftOf(ParentOf(ParentOf(balanceNode))))
+                {
+                    IntervalTreeNode<K, V> sibling = RightOf(ParentOf(ParentOf(balanceNode)));
+
+                    if (ColorOf(sibling) == Red)
+                    {
+                        SetColor(ParentOf(balanceNode), Black);
+                        SetColor(sibling, Black);
+                        SetColor(ParentOf(ParentOf(balanceNode)), Red);
+                        balanceNode = ParentOf(ParentOf(balanceNode));
+                    }
+                    else
+                    {
+                        if (balanceNode == RightOf(ParentOf(balanceNode)))
+                        {
+                            balanceNode = ParentOf(balanceNode);
+                            RotateLeft(balanceNode);
+                        }
+                        SetColor(ParentOf(balanceNode), Black);
+                        SetColor(ParentOf(ParentOf(balanceNode)), Red);
+                        RotateRight(ParentOf(ParentOf(balanceNode)));
+                    }
+                }
+                else
+                {
+                    IntervalTreeNode<K, V> sibling = LeftOf(ParentOf(ParentOf(balanceNode)));
+
+                    if (ColorOf(sibling) == Red)
+                    {
+                        SetColor(ParentOf(balanceNode), Black);
+                        SetColor(sibling, Black);
+                        SetColor(ParentOf(ParentOf(balanceNode)), Red);
+                        balanceNode = ParentOf(ParentOf(balanceNode));
+                    }
+                    else
+                    {
+                        if (balanceNode == LeftOf(ParentOf(balanceNode)))
+                        {
+                            balanceNode = ParentOf(balanceNode);
+                            RotateRight(balanceNode);
+                        }
+                        SetColor(ParentOf(balanceNode), Black);
+                        SetColor(ParentOf(ParentOf(balanceNode)), Red);
+                        RotateLeft(ParentOf(ParentOf(balanceNode)));
+                    }
+                }
+            }
+            SetColor(_root, Black);
+        }
+
+        private void RotateLeft(IntervalTreeNode<K, V> node)
+        {
+            if (node != null)
+            {
+                IntervalTreeNode<K, V> right = RightOf(node);
+                node.Right = LeftOf(right);
+                if (node.Right != null)
+                {
+                    node.Right.Parent = node; 
+                }
+                IntervalTreeNode<K, V> nodeParent = ParentOf(node);
+                right.Parent = nodeParent;
+                if (nodeParent == null)
+                {
+                    _root = right;
+                }
+                else if (node == LeftOf(nodeParent))
+                {
+                    nodeParent.Left = right;
+                }
+                else
+                {
+                    nodeParent.Right = right; 
+                }
+                right.Left = node;
+                node.Parent = right;
+
+                PropagateFull(node);
+            }
+        }
+
+        private void RotateRight(IntervalTreeNode<K, V> node)
+        {
+            if (node != null)
+            {
+                IntervalTreeNode<K, V> left = LeftOf(node);
+                node.Left = RightOf(left);
+                if (node.Left != null)
+                {
+                    node.Left.Parent = node;
+                }
+                IntervalTreeNode<K, V> nodeParent = ParentOf(node);
+                left.Parent = nodeParent;
+                if (nodeParent == null)
+                {
+                    _root = left;
+                }
+                else if (node == RightOf(nodeParent))
+                {
+                    nodeParent.Right = left;
+                }
+                else
+                {
+                    nodeParent.Left = left;
+                }
+                left.Right = node;
+                node.Parent = left;
+
+                PropagateFull(node);
+            }
+        }
+        #endregion
+
+        #region Safety-Methods
+
+        // These methods save memory by allowing us to forego sentinel nil nodes, as well as serve as protection against NullReferenceExceptions.
+
+        /// <summary>
+        /// Returns the color of <paramref name="node"/>, or Black if it is null.
+        /// </summary>
+        /// <param name="node">Node</param>
+        /// <returns>The boolean color of <paramref name="node"/>, or black if null</returns>
+        private static bool ColorOf(IntervalTreeNode<K, V> node)
+        {
+            return node == null || node.Color;
+        }
+
+        /// <summary>
+        /// Sets the color of <paramref name="node"/> node to <paramref name="color"/>.
+        /// <br></br>
+        /// This method does nothing if <paramref name="node"/> is null.
+        /// </summary>
+        /// <param name="node">Node to set the color of</param>
+        /// <param name="color">Color (Boolean)</param>
+        private static void SetColor(IntervalTreeNode<K, V> node, bool color)
+        {
+            if (node != null)
+            {
+                node.Color = color;
+            }
+        }
+
+        /// <summary>
+        /// This method returns the left node of <paramref name="node"/>, or null if <paramref name="node"/> is null.
+        /// </summary>
+        /// <param name="node">Node to retrieve the left child from</param>
+        /// <returns>Left child of <paramref name="node"/></returns>
+        private static IntervalTreeNode<K, V> LeftOf(IntervalTreeNode<K, V> node)
+        {
+            return node?.Left;
+        }
+
+        /// <summary>
+        /// This method returns the right node of <paramref name="node"/>, or null if <paramref name="node"/> is null.
+        /// </summary>
+        /// <param name="node">Node to retrieve the right child from</param>
+        /// <returns>Right child of <paramref name="node"/></returns>
+        private static IntervalTreeNode<K, V> RightOf(IntervalTreeNode<K, V> node)
+        {
+            return node?.Right;
+        }
+
+        /// <summary>
+        /// Returns the parent node of <paramref name="node"/>, or null if <paramref name="node"/> is null.
+        /// </summary>
+        /// <param name="node">Node to retrieve the parent from</param>
+        /// <returns>Parent of <paramref name="node"/></returns>
+        private static IntervalTreeNode<K, V> ParentOf(IntervalTreeNode<K, V> node)
+        {
+            return node?.Parent;
+        }
+        #endregion
+
+        public bool ContainsKey(K key)
+        {
+            if (key == null)
+            {
+                throw new ArgumentNullException(nameof(key));
+            }
+            return GetNode(key) != null;
+        }
+
+        public void Clear()
+        {
+            _root = null;
+            _count = 0;
+        }
+    }
+
+    /// <summary>
+    /// Represents a value and its start and end keys.
+    /// </summary>
+    /// <typeparam name="K"></typeparam>
+    /// <typeparam name="V"></typeparam>
+    public readonly struct RangeNode<K, V>
+    {
+        public readonly K Start;
+        public readonly K End;
+        public readonly V Value;
+
+        public RangeNode(K start, K end, V value)
+        {
+            Start = start;
+            End = end;
+            Value = value;
+        }
+    }
+
+    /// <summary>
+    /// Represents a node in the IntervalTree which contains start and end keys of type K, and a value of generic type V.
+    /// </summary>
+    /// <typeparam name="K">Key type of the node</typeparam>
+    /// <typeparam name="V">Value type of the node</typeparam>
+    internal class IntervalTreeNode<K, V>
+    {
+        internal bool Color = true;
+        internal IntervalTreeNode<K, V> Left = null;
+        internal IntervalTreeNode<K, V> Right = null;
+        internal IntervalTreeNode<K, V> Parent = null;
+
+        /// <summary>
+        /// The start of the range.
+        /// </summary>
+        internal K Start;
+
+        /// <summary>
+        /// The end of the range - maximum of all in the Values list.
+        /// </summary>
+        internal K End;
+
+        /// <summary>
+        /// The maximum end value of this node and all its children.
+        /// </summary>
+        internal K Max;
+
+        internal List<RangeNode<K, V>> Values;
+
+        public IntervalTreeNode(K start, K end, V value, IntervalTreeNode<K, V> parent)
+        {
+            this.Start = start;
+            this.End = end;
+            this.Max = end;
+            this.Values = new List<RangeNode<K, V>> { new RangeNode<K, V>(start, end, value) };
+            this.Parent = parent;
+        }
+    }
+}

Ryujinx.Common/Collections/TreeDictionary.cs

@@ -182,38 +182,40 @@ namespace Ryujinx.Common.Collections
 
         /// <summary>
         /// Adds all the nodes in the dictionary into <paramref name="list"/>.
-        /// <br></br>
-        /// The nodes will be added in Sorted by Key Order.
         /// </summary>
+        /// <returns>A list of all KeyValuePairs sorted by Key Order</returns>
         public List<KeyValuePair<K, V>> AsList()
         {
             List<KeyValuePair<K, V>> list = new List<KeyValuePair<K, V>>();
 
-            Queue<Node<K, V>> nodes = new Queue<Node<K, V>>();
-
-            if (this._root != null)
-            {
-                nodes.Enqueue(this._root);
-            }
-            while (nodes.Count > 0)
-            {
-                Node<K, V> node = nodes.Dequeue();
-                list.Add(new KeyValuePair<K, V>(node.Key, node.Value));
-                if (node.Left != null)
-                {
-                    nodes.Enqueue(node.Left);
-                }
-                if (node.Right != null)
-                {
-                    nodes.Enqueue(node.Right);
-                }
-            }
+            AddToList(_root, list);
 
             return list;
         }
+
         #endregion
+
         #region Private Methods (BST)
 
+        /// <summary>
+        /// Adds all nodes that are children of or contained within <paramref name="node"/> into <paramref name="list"/>, in Key Order.
+        /// </summary>
+        /// <param name="node">The node to search for nodes within</param>
+        /// <param name="list">The list to add node to</param>
+        private void AddToList(Node<K, V> node, List<KeyValuePair<K, V>> list)
+        {
+            if (node == null)
+            {
+                return;
+            }
+
+            AddToList(node.Left, list);
+
+            list.Add(new KeyValuePair<K, V>(node.Key, node.Value));
+
+            AddToList(node.Right, list);
+        }
+
         /// <summary>
         /// Retrieve the node reference whose key is <paramref name="key"/>, or null if no such node exists.
         /// </summary>
@@ -373,13 +375,8 @@ namespace Ryujinx.Common.Collections
         /// </summary>
         /// <param name="node">Root Node</param>
         /// <returns>Node with the maximum key in the tree of <paramref name="node"/></returns>
-        /// <exception cref="ArgumentNullException"><paramref name="node"/> is null</exception>
         private static Node<K, V> Maximum(Node<K, V> node)
         {
-            if (node == null)
-            {
-                throw new ArgumentNullException(nameof(node));
-            }
             Node<K, V> tmp = node;
             while (tmp.Right != null)
             {
@@ -519,7 +516,7 @@ namespace Ryujinx.Common.Collections
         }
 
         /// <summary>
-        /// Finds the node with the key immediately greater than <paramref name="node"/>.Key.
+        /// Finds the node with the key is immediately greater than <paramref name="node"/>.
         /// </summary>
         /// <param name="node">Node to find the successor of</param>
         /// <returns>Successor of <paramref name="node"/></returns>
@@ -539,7 +536,7 @@ namespace Ryujinx.Common.Collections
         }
 
         /// <summary>
-        /// Finds the node whose key immediately less than <paramref name="node"/>.Key.
+        /// Finds the node whose key is immediately less than <paramref name="node"/>.
         /// </summary>
         /// <param name="node">Node to find the predecessor of</param>
         /// <returns>Predecessor of <paramref name="node"/></returns>
@@ -557,7 +554,9 @@ namespace Ryujinx.Common.Collections
             }
             return parent;
         }
+
         #endregion
+
         #region Private Methods (RBL)
 
         private void RestoreBalanceAfterRemoval(Node<K, V> balanceNode)
@@ -748,7 +747,7 @@ namespace Ryujinx.Common.Collections
 
         #region Safety-Methods
 
-        // These methods save memory by allowing us to forego sentinel nil nodes, as well as serve as protection against nullpointerexceptions.
+        // These methods save memory by allowing us to forego sentinel nil nodes, as well as serve as protection against NullReferenceExceptions.
 
         /// <summary>
         /// Returns the color of <paramref name="node"/>, or Black if it is null.

Ryujinx.Memory/Range/MultiRangeList.cs

@@ -1,27 +1,21 @@
-using System;
+using Ryujinx.Common.Collections;
 using System.Collections;
 using System.Collections.Generic;
 
 namespace Ryujinx.Memory.Range
 {
-    /// <summary>
-    /// Sorted list of ranges that supports binary search.
-    /// </summary>
-    /// <typeparam name="T">Type of the range.</typeparam>
     public class MultiRangeList<T> : IEnumerable<T> where T : IMultiRangeItem
     {
-        private const int ArrayGrowthSize = 32;
+        private readonly IntervalTree<ulong, T> _items;
 
-        private readonly List<T> _items;
-
-        public int Count => _items.Count;
+        public int Count { get; private set; }
 
         /// <summary>
         /// Creates a new range list.
         /// </summary>
         public MultiRangeList()
         {
-            _items = new List<T>();
+            _items = new IntervalTree<ulong, T>();
         }
 
         /// <summary>
@@ -30,14 +24,15 @@ namespace Ryujinx.Memory.Range
         /// <param name="item">The item to be added</param>
         public void Add(T item)
         {
-            int index = BinarySearch(item.BaseAddress);
+            MultiRange range = item.Range;
 
-            if (index < 0)
+            for (int i = 0; i < range.Count; i++)
             {
-                index = ~index;
+                var subrange = range.GetSubRange(i);
+                _items.Add(subrange.Address, subrange.EndAddress, item);
             }
 
-            _items.Insert(index, item);
+            Count++;
         }
 
         /// <summary>
@@ -47,34 +42,23 @@ namespace Ryujinx.Memory.Range
         /// <returns>True if the item was removed, or false if it was not found</returns>
         public bool Remove(T item)
         {
-            int index = BinarySearch(item.BaseAddress);
+            MultiRange range = item.Range;
 
-            if (index >= 0)
+            int removed = 0;
+
+            for (int i = 0; i < range.Count; i++)
             {
-                while (index > 0 && _items[index - 1].BaseAddress == item.BaseAddress)
-                {
-                    index--;
-                }
-
-                while (index < _items.Count)
-                {
-                    if (_items[index].Equals(item))
-                    {
-                        _items.RemoveAt(index);
-
-                        return true;
-                    }
-
-                    if (_items[index].BaseAddress > item.BaseAddress)
-                    {
-                        break;
-                    }
-
-                    index++;
-                }
+                var subrange = range.GetSubRange(i);
+                removed += _items.Remove(subrange.Address, item);
             }
 
-            return false;
+            if (removed > 0)
+            {
+                // All deleted intervals are for the same item - the one we removed.
+                Count--;
+            }
+
+            return removed > 0;
         }
 
         /// <summary>
@@ -97,22 +81,47 @@ namespace Ryujinx.Memory.Range
         /// <returns>The number of overlapping items found</returns>
         public int FindOverlaps(MultiRange range, ref T[] output)
         {
-            int outputIndex = 0;
+            int overlapCount = 0;
 
-            foreach (T item in _items)
+            for (int i = 0; i < range.Count; i++)
             {
-                if (item.Range.OverlapsWith(range))
-                {
-                    if (outputIndex == output.Length)
-                    {
-                        Array.Resize(ref output, outputIndex + ArrayGrowthSize);
-                    }
-
-                    output[outputIndex++] = item;
-                }
+                var subrange = range.GetSubRange(i);
+                overlapCount = _items.Get(subrange.Address, subrange.EndAddress, ref output, overlapCount);
             }
 
-            return outputIndex;
+            // Remove any duplicates, caused by items having multiple sub range nodes in the tree.
+            if (overlapCount > 1)
+            {
+                int insertPtr = 0;
+                for (int i = 0; i < overlapCount; i++)
+                {
+                    T item = output[i];
+                    bool duplicate = false;
+
+                    for (int j = insertPtr - 1; j >= 0; j--)
+                    {
+                        if (item.Equals(output[j]))
+                        {
+                            duplicate = true;
+                            break;
+                        }
+                    }
+
+                    if (!duplicate)
+                    {
+                        if (insertPtr != i)
+                        {
+                            output[insertPtr] = item;
+                        }
+
+                        insertPtr++;
+                    }
+                }
+
+                overlapCount = insertPtr;
+            }
+
+            return overlapCount;
         }
 
         /// <summary>
@@ -123,82 +132,50 @@ namespace Ryujinx.Memory.Range
         /// <returns>The number of matches found</returns>
         public int FindOverlaps(ulong baseAddress, ref T[] output)
         {
-            int index = BinarySearch(baseAddress);
+            int count = _items.Get(baseAddress, ref output);
 
-            int outputIndex = 0;
-
-            if (index >= 0)
+            // Only output items with matching base address
+            int insertPtr = 0;
+            for (int i = 0; i < count; i++)
             {
-                while (index > 0 && _items[index - 1].BaseAddress == baseAddress)
+                if (output[i].BaseAddress == baseAddress)
                 {
-                    index--;
-                }
-
-                while (index < _items.Count)
-                {
-                    T overlap = _items[index++];
-
-                    if (overlap.BaseAddress != baseAddress)
+                    if (i != insertPtr)
                     {
-                        break;
+                        output[insertPtr] = output[i];
                     }
 
-                    if (outputIndex == output.Length)
-                    {
-                        Array.Resize(ref output, outputIndex + ArrayGrowthSize);
-                    }
-
-                    output[outputIndex++] = overlap;
+                    insertPtr++;
                 }
             }
 
-            return outputIndex;
+            return insertPtr;
         }
 
-        /// <summary>
-        /// Performs binary search on the internal list of items.
-        /// </summary>
-        /// <param name="address">Address to find</param>
-        /// <returns>List index of the item, or complement index of nearest item with lower value on the list</returns>
-        private int BinarySearch(ulong address)
+        private List<T> GetList()
         {
-            int left = 0;
-            int right = _items.Count - 1;
+            var items = _items.AsList();
+            var result = new List<T>();
 
-            while (left <= right)
+            foreach (RangeNode<ulong, T> item in items)
             {
-                int range = right - left;
-
-                int middle = left + (range >> 1);
-
-                T item = _items[middle];
-
-                if (item.BaseAddress == address)
+                if (item.Start == item.Value.BaseAddress)
                 {
-                    return middle;
-                }
-
-                if (address < item.BaseAddress)
-                {
-                    right = middle - 1;
-                }
-                else
-                {
-                    left = middle + 1;
+                    result.Add(item.Value);
                 }
             }
 
-            return ~left;
+            return result;
         }
 
         public IEnumerator<T> GetEnumerator()
         {
-            return _items.GetEnumerator();
+            return GetList().GetEnumerator();
         }
 
         IEnumerator IEnumerable.GetEnumerator()
         {
-            return _items.GetEnumerator();
+            return GetList().GetEnumerator();
         }
     }
-}
+}