[nasm:debug-macros] rbtree: implement a "threaded LLRB tree"
nasm-bot for H. Peter Anvin (Intel)
hpa at zytor.com
Thu Jul 9 17:51:03 PDT 2020
Commit-ID: 110e5046c910541c7e020bbb660a06d40b40f8c4
Gitweb: http://repo.or.cz/w/nasm.git?a=commitdiff;h=110e5046c910541c7e020bbb660a06d40b40f8c4
Author: H. Peter Anvin (Intel) <hpa at zytor.com>
AuthorDate: Mon, 29 Jun 2020 23:23:51 -0700
Committer: H. Peter Anvin (Intel) <hpa at zytor.com>
CommitDate: Wed, 8 Jul 2020 09:18:22 -0700
rbtree: implement a "threaded LLRB tree"
Change the left-leaning red-black (LLRB) trees into left-leaning
threaded red-black trees. Instead of NULL pointers at leaf nodes, use
the otherwise unused field as a pointer to the lexical predecessor
(left) or successor (right). This allows fast previous/next
interator operation without needing to keep track of the root of the
tree at all times.
The additional metadata that needs to be kept can be done for "free"
simply by changing "bool red" into a flag field.
Signed-off-by: H. Peter Anvin (Intel) <hpa at zytor.com>
---
include/rbtree.h | 49 ++++++++++---
nasmlib/rbtree.c | 212 ++++++++++++++++++++++++++++++++++++++++++-------------
2 files changed, 204 insertions(+), 57 deletions(-)
diff --git a/include/rbtree.h b/include/rbtree.h
index f0ffb914..8ccd129c 100644
--- a/include/rbtree.h
+++ b/include/rbtree.h
@@ -1,6 +1,6 @@
/* ----------------------------------------------------------------------- *
- *
- * Copyright 1996-2009 The NASM Authors - All Rights Reserved
+ *
+ * Copyright 1996-2020 The NASM Authors - All Rights Reserved
* See the file AUTHORS included with the NASM distribution for
* the specific copyright holders.
*
@@ -14,7 +14,7 @@
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.
- *
+ *
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
@@ -36,16 +36,47 @@
#include "compiler.h"
-/* This structure should be embedded in a larger data structure;
- the final output from rb_search() can then be converted back
- to the larger data structure via container_of(). */
+/*
+ * This structure should be embedded in a larger data structure;
+ * the final output from rb_search() can then be converted back
+ * to the larger data structure via container_of().
+ *
+ * An empty tree is simply represented by a NULL pointer.
+ */
+
+/* Note: the values of these flags is significant */
+enum rbtree_node_flags {
+ RBTREE_NODE_BLACK = 1, /* Node color is black */
+ RBTREE_NODE_PRED = 2, /* Left pointer is an uplink */
+ RBTREE_NODE_SUCC = 4 /* Right pointer is an uplink */
+};
+
struct rbtree {
uint64_t key;
- struct rbtree *left, *right;
- bool red;
+ struct rbtree_metadata {
+ struct rbtree *left, *right;
+ enum rbtree_node_flags flags;
+ } m;
};
+/*
+ * Add a node to a tree. Returns the new root pointer.
+ * The key value in the structure needs to be preinitialized;
+ * the rest of the structure should be zero.
+ */
struct rbtree *rb_insert(struct rbtree *, struct rbtree *);
-struct rbtree *rb_search(struct rbtree *, uint64_t);
+
+/*
+ * Find a node in the tree corresponding to the key immediately
+ * <= the passed-in key value.
+ */
+struct rbtree *rb_search(const struct rbtree *, uint64_t);
+
+/*
+ * Return the immediately previous or next node in key order.
+ * Returns NULL if this node is the end of the
+ */
+struct rbtree *rb_prev(const struct rbtree *);
+struct rbtree *rb_next(const struct rbtree *);
#endif /* NASM_RBTREE_H */
diff --git a/nasmlib/rbtree.c b/nasmlib/rbtree.c
index 5af6067d..8b74c0c4 100644
--- a/nasmlib/rbtree.c
+++ b/nasmlib/rbtree.c
@@ -1,6 +1,6 @@
/* ----------------------------------------------------------------------- *
- *
- * Copyright 1996-2009 The NASM Authors - All Rights Reserved
+ *
+ * Copyright 1996-2020 The NASM Authors - All Rights Reserved
* See the file AUTHORS included with the NASM distribution for
* the specific copyright holders.
*
@@ -14,7 +14,7 @@
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials provided
* with the distribution.
- *
+ *
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
@@ -34,86 +34,202 @@
/*
* rbtree.c
*
- * Simple implementation of a left-leaning red-black tree with 64-bit
- * integer keys. The search operation will return the highest node <=
- * the key; only search and insert are supported, but additional
- * standard llrbtree operations can be coded up at will.
+ * Simple implementation of a "left-leaning threaded red-black tree"
+ * with 64-bit integer keys. The search operation will return the
+ * highest node <= the key; only search and insert are supported, but
+ * additional standard llrbtree operations can be coded up at will.
*
* See http://www.cs.princeton.edu/~rs/talks/LLRB/RedBlack.pdf for
* information about left-leaning red-black trees.
+ *
+ * The "threaded" part means that left and right pointers that would
+ * otherwise be NULL are pointers to the in-order predecessor or
+ * successor node. The only pointers that are NULL are the very left-
+ * and rightmost, for which no corresponding side node exists.
+ *
+ * This, among other things, allows for efficient predecessor and
+ * successor operations without requiring dedicated space for a parent
+ * pointer.
+ *
+ * This implementation is robust for identical key values; such keys
+ * will not have their insertion order preserved, and after insertion
+ * of unrelated keys a lookup may return a different node for the
+ * duplicated key, but the prev/next operations will always enumerate
+ * all entries.
+ *
+ * The NULL pointers at the end are considered predecessor/successor
+ * pointers, so if the corresponding flags are clear it is always safe
+ * to access the pointed-to object without an explicit NULL pointer
+ * check.
*/
#include "rbtree.h"
+#include "nasmlib.h"
-struct rbtree *rb_search(struct rbtree *tree, uint64_t key)
+struct rbtree *rb_search(const struct rbtree *tree, uint64_t key)
{
- struct rbtree *best = NULL;
-
- while (tree) {
- if (tree->key == key)
- return tree;
- else if (tree->key > key)
- tree = tree->left;
- else {
- best = tree;
- tree = tree->right;
+ const struct rbtree *best = NULL;
+
+ if (tree) {
+ while (true) {
+ if (tree->key > key) {
+ if (tree->m.flags & RBTREE_NODE_PRED)
+ break;
+ tree = tree->m.left;
+ } else {
+ best = tree;
+ if (tree->key == key || (tree->m.flags & RBTREE_NODE_SUCC))
+ break;
+ tree = tree->m.right;
+ }
}
}
- return best;
+ return (struct rbtree *)best;
+}
+
+/* Reds two left in a row? */
+static inline bool is_red_left_left(struct rbtree *h)
+{
+ return !(h->m.flags & RBTREE_NODE_PRED) &&
+ !(h->m.left->m.flags & (RBTREE_NODE_BLACK|RBTREE_NODE_PRED)) &&
+ !(h->m.left->m.left->m.flags & RBTREE_NODE_BLACK);
}
-static bool is_red(struct rbtree *h)
+/* Node to the right is red? */
+static inline bool is_red_right(struct rbtree *h)
{
- return h && h->red;
+ return !(h->m.flags & RBTREE_NODE_SUCC) &&
+ !(h->m.right->m.flags & RBTREE_NODE_BLACK);
}
-static struct rbtree *rotate_left(struct rbtree *h)
+/* Both the left and right hand nodes are red? */
+static inline bool is_red_both(struct rbtree *h)
{
- struct rbtree *x = h->right;
- h->right = x->left;
- x->left = h;
- x->red = x->left->red;
- x->left->red = true;
+ return !(h->m.flags & (RBTREE_NODE_PRED|RBTREE_NODE_SUCC))
+ && !(h->m.left->m.flags & h->m.right->m.flags & RBTREE_NODE_BLACK);
+}
+
+static inline struct rbtree *rotate_left(struct rbtree *h)
+{
+ struct rbtree *x = h->m.right;
+ enum rbtree_node_flags hf = h->m.flags;
+ enum rbtree_node_flags xf = x->m.flags;
+
+ if (xf & RBTREE_NODE_PRED) {
+ h->m.right = x;
+ h->m.flags = (hf & RBTREE_NODE_PRED) | RBTREE_NODE_SUCC;
+ } else {
+ h->m.right = x->m.left;
+ h->m.flags = hf & RBTREE_NODE_PRED;
+ }
+ x->m.flags = (hf & RBTREE_NODE_BLACK) | (xf & RBTREE_NODE_SUCC);
+ x->m.left = h;
+
return x;
}
-static struct rbtree *rotate_right(struct rbtree *h)
+static inline struct rbtree *rotate_right(struct rbtree *h)
{
- struct rbtree *x = h->left;
- h->left = x->right;
- x->right = h;
- x->red = x->right->red;
- x->right->red = true;
+ struct rbtree *x = h->m.left;
+ enum rbtree_node_flags hf = h->m.flags;
+ enum rbtree_node_flags xf = x->m.flags;
+
+ if (xf & RBTREE_NODE_SUCC) {
+ h->m.left = x;
+ h->m.flags = (hf & RBTREE_NODE_SUCC) | RBTREE_NODE_PRED;
+ } else {
+ h->m.left = x->m.right;
+ h->m.flags = hf & RBTREE_NODE_SUCC;
+ }
+ x->m.flags = (hf & RBTREE_NODE_BLACK) | (xf & RBTREE_NODE_PRED);
+ x->m.right = h;
+
return x;
}
-static void color_flip(struct rbtree *h)
+static inline void color_flip(struct rbtree *h)
{
- h->red = !h->red;
- h->left->red = !h->left->red;
- h->right->red = !h->right->red;
+ h->m.flags ^= RBTREE_NODE_BLACK;
+ h->m.left->m.flags ^= RBTREE_NODE_BLACK;
+ h->m.right->m.flags ^= RBTREE_NODE_BLACK;
}
+static struct rbtree *
+_rb_insert(struct rbtree *tree, struct rbtree *node);
+
struct rbtree *rb_insert(struct rbtree *tree, struct rbtree *node)
{
- if (!tree) {
- node->red = true;
- return node;
- }
+ /* Initialize node as if it was the sole member of the tree */
+
+ nasm_zero(node->m);
+ node->m.flags = RBTREE_NODE_PRED|RBTREE_NODE_SUCC;
+
+ if (unlikely(!tree))
+ return node;
+
+ return _rb_insert(tree, node);
+}
- if (is_red(tree->left) && is_red(tree->right))
+static struct rbtree *
+_rb_insert(struct rbtree *tree, struct rbtree *node)
+{
+ /* Recursive part of the algorithm */
+
+ /* Red on both sides? */
+ if (is_red_both(tree))
color_flip(tree);
- if (node->key < tree->key)
- tree->left = rb_insert(tree->left, node);
- else
- tree->right = rb_insert(tree->right, node);
+ if (node->key < tree->key) {
+ node->m.right = tree; /* Potential successor */
+ if (tree->m.flags & RBTREE_NODE_PRED) {
+ node->m.left = tree->m.left;
+ tree->m.flags &= ~RBTREE_NODE_PRED;
+ tree->m.left = node;
+ } else {
+ tree->m.left = _rb_insert(tree->m.left, node);
+ }
+ } else {
+ node->m.left = tree; /* Potential predecessor */
+ if (tree->m.flags & RBTREE_NODE_SUCC) {
+ node->m.right = tree->m.right;
+ tree->m.flags &= ~RBTREE_NODE_SUCC;
+ tree->m.right = node;
+ } else {
+ tree->m.right = _rb_insert(tree->m.right, node);
+ }
+ }
- if (is_red(tree->right))
+ if (is_red_right(tree))
tree = rotate_left(tree);
- if (is_red(tree->left) && is_red(tree->left->left))
+ if (is_red_left_left(tree))
tree = rotate_right(tree);
return tree;
}
+
+struct rbtree *rb_prev(const struct rbtree *node)
+{
+ struct rbtree *np = node->m.left;
+
+ if (node->m.flags & RBTREE_NODE_PRED)
+ return np;
+
+ while (!(np->m.flags & RBTREE_NODE_SUCC))
+ np = np->m.right;
+
+ return np;
+}
+
+struct rbtree *rb_next(const struct rbtree *node)
+{
+ struct rbtree *np = node->m.right;
+
+ if (node->m.flags & RBTREE_NODE_SUCC)
+ return np;
+
+ while (!(np->m.flags & RBTREE_NODE_PRED))
+ np = np->m.left;
+
+ return np;
+}
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