Initial version.

src/nxt_rbtree.c

@@ -0,0 +1,515 @@
+
+/*
+ * Copyright (C) Igor Sysoev
+ * Copyright (C) NGINX, Inc.
+ */
+
+#include <nxt_main.h>
+
+
+/*
+ * The red-black tree code is based on the algorithm described in
+ * the "Introduction to Algorithms" by Cormen, Leiserson and Rivest.
+ */
+
+
+static void nxt_rbtree_insert_fixup(nxt_rbtree_node_t *node);
+static void nxt_rbtree_delete_fixup(nxt_rbtree_t *tree,
+    nxt_rbtree_node_t *node);
+nxt_inline void nxt_rbtree_left_rotate(nxt_rbtree_node_t *node);
+nxt_inline void nxt_rbtree_right_rotate(nxt_rbtree_node_t *node);
+nxt_inline void nxt_rbtree_parent_relink(nxt_rbtree_node_t *subst,
+    nxt_rbtree_node_t *node);
+
+
+#define NXT_RBTREE_BLACK  0
+#define NXT_RBTREE_RED    1
+
+
+#define nxt_rbtree_set_callback_type(tree, type)                              \
+    (tree)->sentinel.spare = type
+
+#define nxt_rbtree_has_insertion_callback(tree)                               \
+    ((tree)->sentinel.spare != 0)
+
+#define nxt_rbtree_comparison_callback(tree)                                  \
+    ((nxt_rbtree_compare_t) (tree)->sentinel.right)
+
+
+void
+nxt_rbtree_init(nxt_rbtree_t *tree, nxt_rbtree_compare_t compare,
+    nxt_rbtree_insert_t insert)
+{
+    void        *callback;
+    nxt_bool_t  insertion;
+
+    /*
+     * The sentinel is used as a leaf node sentinel and as a tree root
+     * sentinel: it is a parent of a root node and the root node is
+     * the left child of the sentinel.  Combining two sentinels in one
+     * entry and the fact that the sentinel's left child is a root node
+     * simplifies nxt_rbtree_node_successor() and eliminates explicit
+     * root node test before or inside nxt_rbtree_min().
+     */
+
+    /* The root is empty. */
+    tree->sentinel.left = &tree->sentinel;
+
+    /*
+     * The sentinel's right child is never used so either insertion
+     * or comparison callback can be safely stored here.
+     */
+    insertion = (insert != NULL);
+    nxt_rbtree_set_callback_type(tree, insertion);
+    callback = insertion ? (void *) insert : (void *) compare;
+    tree->sentinel.right = callback;
+
+    /* The root and leaf sentinel must be black. */
+    tree->sentinel.color = NXT_RBTREE_BLACK;
+}
+
+
+void
+nxt_rbtree_insert(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
+{
+    void                  *callback;
+    nxt_rbtree_node_t     *node, *new_node, *sentinel, **child;
+    nxt_rbtree_insert_t   insert;
+    nxt_rbtree_compare_t  compare;
+
+    new_node = (nxt_rbtree_node_t *) part;
+
+    node = nxt_rbtree_root(tree);
+    sentinel = nxt_rbtree_sentinel(tree);
+
+    new_node->left = sentinel;
+    new_node->right = sentinel;
+    new_node->color = NXT_RBTREE_RED;
+
+    callback = tree->sentinel.right;
+
+    if (nxt_rbtree_has_insertion_callback(tree)) {
+        insert = (nxt_rbtree_insert_t) callback;
+
+        insert(node, new_node, sentinel);
+
+    } else {
+        compare = (nxt_rbtree_compare_t) callback;
+
+        child = &nxt_rbtree_root(tree);
+
+        while (*child != sentinel) {
+            node = *child;
+
+            nxt_prefetch(node->left);
+            nxt_prefetch(node->right);
+
+            child = (compare(new_node, node) < 0) ? &node->left : &node->right;
+        }
+
+        *child = new_node;
+
+        new_node->parent = node;
+    }
+
+    nxt_rbtree_insert_fixup(new_node);
+
+    node = nxt_rbtree_root(tree);
+    node->color = NXT_RBTREE_BLACK;
+}
+
+
+static void
+nxt_rbtree_insert_fixup(nxt_rbtree_node_t *node)
+{
+    nxt_rbtree_node_t  *parent, *grandparent, *uncle;
+
+    /*
+     * Prefetching parent nodes does not help here because they are
+     * already traversed during insertion.
+     */
+
+    for ( ;; ) {
+        parent = node->parent;
+
+        /*
+         * Testing whether a node is a tree root is not required here since
+         * a root node's parent is the sentinel and it is always black.
+         */
+        if (parent->color == NXT_RBTREE_BLACK) {
+            return;
+        }
+
+        grandparent = parent->parent;
+
+        if (parent == grandparent->left) {
+            uncle = grandparent->right;
+
+            if (uncle->color == NXT_RBTREE_BLACK) {
+
+                if (node == parent->right) {
+                    node = parent;
+                    nxt_rbtree_left_rotate(node);
+                }
+
+                parent = node->parent;
+                parent->color = NXT_RBTREE_BLACK;
+
+                grandparent = parent->parent;
+                grandparent->color = NXT_RBTREE_RED;
+                nxt_rbtree_right_rotate(grandparent);
+
+                continue;
+            }
+
+        } else {
+            uncle = grandparent->left;
+
+            if (uncle->color == NXT_RBTREE_BLACK) {
+
+                if (node == parent->left) {
+                    node = parent;
+                    nxt_rbtree_right_rotate(node);
+                }
+
+                parent = node->parent;
+                parent->color = NXT_RBTREE_BLACK;
+
+                grandparent = parent->parent;
+                grandparent->color = NXT_RBTREE_RED;
+                nxt_rbtree_left_rotate(grandparent);
+
+                continue;
+            }
+        }
+
+        uncle->color = NXT_RBTREE_BLACK;
+        parent->color = NXT_RBTREE_BLACK;
+        grandparent->color = NXT_RBTREE_RED;
+
+        node = grandparent;
+    }
+}
+
+
+nxt_rbtree_node_t *
+nxt_rbtree_find(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
+{
+    nxt_int_t             n;
+    nxt_rbtree_node_t     *node, *next, *sentinel;
+    nxt_rbtree_compare_t  compare;
+
+    node = (nxt_rbtree_node_t *) part;
+
+    next = nxt_rbtree_root(tree);
+    sentinel = nxt_rbtree_sentinel(tree);
+    compare = nxt_rbtree_comparison_callback(tree);
+
+    while (next != sentinel) {
+        nxt_prefetch(next->left);
+        nxt_prefetch(next->right);
+
+        n = compare(node, next);
+
+        if (n < 0) {
+            next = next->left;
+
+        } else if (n > 0) {
+            next = next->right;
+
+        } else {
+            return next;
+        }
+    }
+
+    return NULL;
+}
+
+
+nxt_rbtree_node_t *
+nxt_rbtree_find_less_or_equal(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
+{
+    nxt_int_t             n;
+    nxt_rbtree_node_t     *node, *retval, *next, *sentinel;
+    nxt_rbtree_compare_t  compare;
+
+    node = (nxt_rbtree_node_t *) part;
+
+    retval = NULL;
+    next = nxt_rbtree_root(tree);
+    sentinel = nxt_rbtree_sentinel(tree);
+    compare = nxt_rbtree_comparison_callback(tree);
+
+    while (next != sentinel) {
+        nxt_prefetch(next->left);
+        nxt_prefetch(next->right);
+
+        n = compare(node, next);
+
+        if (n < 0) {
+            next = next->left;
+
+        } else if (n > 0) {
+            retval = next;
+            next = next->right;
+
+        } else {
+            /* Exact match. */
+            return next;
+        }
+    }
+
+    return retval;
+}
+
+
+nxt_rbtree_node_t *
+nxt_rbtree_find_greater_or_equal(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
+{
+    nxt_int_t             n;
+    nxt_rbtree_node_t     *node, *retval, *next, *sentinel;
+    nxt_rbtree_compare_t  compare;
+
+    node = (nxt_rbtree_node_t *) part;
+
+    retval = NULL;
+    next = nxt_rbtree_root(tree);
+    sentinel = nxt_rbtree_sentinel(tree);
+    compare = nxt_rbtree_comparison_callback(tree);
+
+    while (next != sentinel) {
+        nxt_prefetch(next->left);
+        nxt_prefetch(next->right);
+
+        n = compare(node, next);
+
+        if (n < 0) {
+            retval = next;
+            next = next->left;
+
+        } else if (n > 0) {
+            next = next->right;
+
+        } else {
+            /* Exact match. */
+            return next;
+        }
+    }
+
+    return retval;
+}
+
+
+void
+nxt_rbtree_delete(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
+{
+    nxt_uint_t         color;
+    nxt_rbtree_node_t  *node, *sentinel, *subst, *child;
+
+    node = (nxt_rbtree_node_t *) part;
+
+    subst = node;
+    sentinel = nxt_rbtree_sentinel(tree);
+
+    if (node->left == sentinel) {
+        child = node->right;
+
+    } else if (node->right == sentinel) {
+        child = node->left;
+
+    } else {
+        subst = nxt_rbtree_branch_min(tree, node->right);
+        child = subst->right;
+    }
+
+    nxt_rbtree_parent_relink(child, subst);
+
+    color = subst->color;
+
+    if (subst != node) {
+        /* Move the subst node to the deleted node position in the tree. */
+
+        subst->color = node->color;
+
+        subst->left = node->left;
+        subst->left->parent = subst;
+
+        subst->right = node->right;
+        subst->right->parent = subst;
+
+        nxt_rbtree_parent_relink(subst, node);
+    }
+
+#if (NXT_DEBUG)
+    node->left = NULL;
+    node->right = NULL;
+    node->parent = NULL;
+#endif
+
+    if (color == NXT_RBTREE_BLACK) {
+        nxt_rbtree_delete_fixup(tree, child);
+    }
+}
+
+
+static void
+nxt_rbtree_delete_fixup(nxt_rbtree_t *tree, nxt_rbtree_node_t *node)
+{
+    nxt_rbtree_node_t  *parent, *sibling;
+
+    while (node != nxt_rbtree_root(tree) && node->color == NXT_RBTREE_BLACK) {
+        /*
+         * Prefetching parent nodes does not help here according
+         * to microbenchmarks.
+         */
+
+        parent = node->parent;
+
+        if (node == parent->left) {
+            sibling = parent->right;
+
+            if (sibling->color != NXT_RBTREE_BLACK) {
+
+                sibling->color = NXT_RBTREE_BLACK;
+                parent->color = NXT_RBTREE_RED;
+
+                nxt_rbtree_left_rotate(parent);
+
+                sibling = parent->right;
+            }
+
+            if (sibling->right->color == NXT_RBTREE_BLACK) {
+
+                sibling->color = NXT_RBTREE_RED;
+
+                if (sibling->left->color == NXT_RBTREE_BLACK) {
+                    node = parent;
+                    continue;
+                }
+
+                sibling->left->color = NXT_RBTREE_BLACK;
+
+                nxt_rbtree_right_rotate(sibling);
+                /*
+                 * If the node is the leaf sentinel then the right
+                 * rotate above changes its parent so a sibling below
+                 * becames the leaf sentinel as well and this causes
+                 * segmentation fault.  This is the reason why usual
+                 * red-black tree implementations with a leaf sentinel
+                 * which does not require to test leaf nodes at all
+                 * nevertheless test the leaf sentinel in the left and
+                 * right rotate procedures.  Since according to the
+                 * algorithm node->parent must not be changed by both
+                 * the left and right rotates above, it can be cached
+                 * in a local variable.  This not only eliminates the
+                 * sentinel test in nxt_rbtree_parent_relink() but also
+                 * decreases the code size because C forces to reload
+                 * non-restrict pointers.
+                 */
+                sibling = parent->right;
+            }
+
+            sibling->color = parent->color;
+            parent->color = NXT_RBTREE_BLACK;
+            sibling->right->color = NXT_RBTREE_BLACK;
+
+            nxt_rbtree_left_rotate(parent);
+
+            break;
+
+        } else {
+            sibling = parent->left;
+
+            if (sibling->color != NXT_RBTREE_BLACK) {
+
+                sibling->color = NXT_RBTREE_BLACK;
+                parent->color = NXT_RBTREE_RED;
+
+                nxt_rbtree_right_rotate(parent);
+
+                sibling = parent->left;
+            }
+
+            if (sibling->left->color == NXT_RBTREE_BLACK) {
+
+                sibling->color = NXT_RBTREE_RED;
+
+                if (sibling->right->color == NXT_RBTREE_BLACK) {
+                    node = parent;
+                    continue;
+                }
+
+                sibling->right->color = NXT_RBTREE_BLACK;
+
+                nxt_rbtree_left_rotate(sibling);
+
+                /* See the comment in the symmetric branch above. */
+                sibling = parent->left;
+            }
+
+            sibling->color = parent->color;
+            parent->color = NXT_RBTREE_BLACK;
+            sibling->left->color = NXT_RBTREE_BLACK;
+
+            nxt_rbtree_right_rotate(parent);
+
+            break;
+        }
+    }
+
+    node->color = NXT_RBTREE_BLACK;
+}
+
+
+nxt_inline void
+nxt_rbtree_left_rotate(nxt_rbtree_node_t *node)
+{
+    nxt_rbtree_node_t  *child;
+
+    child = node->right;
+    node->right = child->left;
+    child->left->parent = node;
+    child->left = node;
+
+    nxt_rbtree_parent_relink(child, node);
+
+    node->parent = child;
+}
+
+
+nxt_inline void
+nxt_rbtree_right_rotate(nxt_rbtree_node_t *node)
+{
+    nxt_rbtree_node_t  *child;
+
+    child = node->left;
+    node->left = child->right;
+    child->right->parent = node;
+    child->right = node;
+
+    nxt_rbtree_parent_relink(child, node);
+
+    node->parent = child;
+}
+
+
+/* Relink a parent from the node to the subst node. */
+
+nxt_inline void
+nxt_rbtree_parent_relink(nxt_rbtree_node_t *subst, nxt_rbtree_node_t *node)
+{
+    nxt_rbtree_node_t  *parent, **link;
+
+    parent = node->parent;
+    /*
+     * The leaf sentinel's parent can be safely changed here.
+     * See the comment in nxt_rbtree_delete_fixup() for details.
+     */
+    subst->parent = parent;
+    /*
+     * If the node's parent is the root sentinel it is safely changed
+     * because the root sentinel's left child is the tree root.
+     */
+    link = (node == parent->left) ? &parent->left : &parent->right;
+    *link = subst;
+}