void rbtree_insert(volatile rbtree_t *tree,rbtree_node_t *node){
rbtree_node_t **root,*temp,*sentinel;
root = (rbtree_node_t **)&tree -> root;
sentinel = tree -> sentinel;
if(*root == sentinel){
node -> parent = NULL;
node -> left = sentinel;
node -> right = sentinel;
rbt_black(node);
*root = node;
return;
}
tree -> insert(*root,node,sentinel);
/*re_balance tree*/
while(node != *root && rbt_is_red(node -> parent)){
if(node -> parent == node -> parent -> parent -> left){
temp = node -> parent -> parent -> right;
if(rbt_is_red(temp)){
rbt_black(node -> parent);
rbt_black(temp);
rbt_red(node -> parent -> parent);
node = node -> parent -> parent;
}else{
if(node == node -> parent -> right){
node = node -> parent;
rbtree_left_rotate(root,sentinel,node);
}
rbt_black(node -> parent);
rbt_red(node -> parent -> parent);
rbtree_right_rotate(root,sentinel,node -> parent -> parent);
}
}else{
temp = node -> parent -> parent -> left;
if(rbt_is_red(temp)){
rbt_black(node -> parent);
rbt_black(temp);
rbt_red(node -> parent -> parent);
node = node -> parent -> parent;
}else{
if(node == node -> parent -> left){
node = node -> parent;
rbtree_right_rotate(root,sentinel,node);
}
rbt_black(node -> parent);
rbt_red(node -> parent -> parent);
rbtree_left_rotate(root,sentinel,node -> parent -> parent);
}
}
}
rbt_black(*root);
}
void rbtree_init(ezRBTree *tree, ezRBTreeNode *sentinel, rbTreeNodeCompare node_cmp_proc)
{
/* a sentinel must be black */
rbt_black(sentinel);
sentinel->parent = NULL;
sentinel->left = NULL;
sentinel->right = NULL;
tree->root = sentinel;
tree->sentinel = sentinel;
tree->node_cmp_proc = node_cmp_proc;
}
void
rbtree_delete( rbtree_t *tree , rbtree_node_t *node )
{
uint_t red;
rbtree_node_t **root,*sentinel,*subst,*temp,*w;
/* a binary tree delete */
root = (rbtree_node_t **) &tree->root;
sentinel = tree->sentinel;
if (node->left == sentinel)
{
temp = node->right;
subst = node;
}
else if (node->right == sentinel)
{
temp = node->left;
subst = node;
}
else
{
subst = rbtree_min( node->right , sentinel );
if (subst->left != sentinel)
{
temp = subst->left;
}
else
{
temp = subst->right;
}
}
if (subst == *root)
{
*root = temp;
rbt_black( temp );
/* DEBUG stuff */
node->left = NULL;
node->right = NULL;
node->parent = NULL;
node->key = 0;
return;
}
red = rbt_is_red(subst);
if (subst == subst->parent->left)
{
subst->parent->left = temp;
}
else
{
subst->parent->right = temp;
}
if (subst == node)
{
temp->parent = subst->parent;
}
else
{
if (subst->parent == node)
{
temp->parent = subst;
}
else
{
temp->parent = subst->parent;
}
subst->left = node->left;
subst->right = node->right;
subst->parent = node->parent;
rbt_copy_color( subst , node );
if (node == *root)
{
*root = subst;
}
else
{
if (node == node->parent->left)
{
node->parent->left = subst;
}
else
{
node->parent->right = subst;
}
}
if (subst->left != sentinel)
{
subst->left->parent = subst;
}
if (subst->right != sentinel)
{
subst->right->parent = subst;
}
}
/* DEBUG stuff */
node->left = NULL;
node->right = NULL;
node->parent = NULL;
node->key = 0;
if (red)
{
return;
}
/* a delete fixup */
while (temp != *root && rbt_is_black(temp) )
{
if (temp == temp->parent->left)
{
w = temp->parent->right;
if (rbt_is_red(w) )
{
rbt_black( w );
rbt_red( temp->parent );
rbtree_left_rotate( root , sentinel , temp->parent );
w = temp->parent->right;
}
if (rbt_is_black(w->left) && rbt_is_black(w->right) )
{
rbt_red( w );
temp = temp->parent;
}
else
{
if (rbt_is_black(w->right) )
{
rbt_black( w->left );
rbt_red( w );
rbtree_right_rotate( root , sentinel , w );
w = temp->parent->right;
}
rbt_copy_color( w , temp->parent );
rbt_black( temp->parent );
rbt_black( w->right );
rbtree_left_rotate( root , sentinel , temp->parent );
temp = *root;
}
}
else
{
w = temp->parent->left;
if (rbt_is_red(w) )
{
rbt_black( w );
rbt_red( temp->parent );
rbtree_right_rotate( root , sentinel , temp->parent );
w = temp->parent->left;
}
if (rbt_is_black(w->left) && rbt_is_black(w->right) )
{
rbt_red( w );
temp = temp->parent;
}
else
{
if (rbt_is_black(w->left) )
{
rbt_black( w->right );
rbt_red( w );
rbtree_left_rotate( root , sentinel , w );
w = temp->parent->left;
}
rbt_copy_color( w , temp->parent );
rbt_black( temp->parent );
rbt_black( w->left );
rbtree_right_rotate( root , sentinel , temp->parent );
temp = *root;
}
}
}
rbt_black( temp );
}
#include "dryad_rbt.h"
_(logic \bool mutable_rbt(RBTNode * x) = x != NULL ==> \mutable(x) && \writable(x))
_(dryad)
int rbt_find_smallest(RBTNode * x)
_(requires x != NULL && rbt(x))
_(ensures x != NULL && rbt(x))
_(ensures rbt_reach(x) == \old(rbt_reach(x)))
_(ensures rbt_keys(x) == \old(rbt_keys(x)))
_(ensures rbt_bh(x) == \old(rbt_bh(x)))
_(ensures rbt_black(x) == \old(rbt_black(x)))
_(ensures \intset_in(\result, rbt_keys(x)))
_(ensures \intset_le_one1(\result, rbt_keys(x)))
{
_(assume mutable_rbt(x))
if (x->left == NULL) {
return x->key;
} else {
int r = rbt_find_smallest(x->left);
return r;
}
}
void rbtree_insert(ezRBTree *tree, ezRBTreeNode *node) {
ezRBTreeNode **root, *temp, *sentinel;
/* a binary tree insert */
root = (ezRBTreeNode **) &tree->root;
sentinel = tree->sentinel;
if (*root == sentinel) {
node->parent = NULL;
node->left = sentinel;
node->right = sentinel;
rbt_black(node);
*root = node;
return;
}
default_rbtree_insert_value(tree, *root, node, sentinel);
/* re-balance tree */
while (node != *root && rbt_is_red(node->parent)) {
if (node->parent == node->parent->parent->left) {
temp = node->parent->parent->right;
if (rbt_is_red(temp)) {
rbt_black(node->parent);
rbt_black(temp);
rbt_red(node->parent->parent);
node = node->parent->parent;
} else {
if (node == node->parent->right) {
node = node->parent;
rbtree_left_rotate(root, sentinel, node);
}
rbt_black(node->parent);
rbt_red(node->parent->parent);
rbtree_right_rotate(root, sentinel, node->parent->parent);
}
} else {
temp = node->parent->parent->left;
if (rbt_is_red(temp)) {
rbt_black(node->parent);
rbt_black(temp);
rbt_red(node->parent->parent);
node = node->parent->parent;
} else {
if (node == node->parent->left) {
node = node->parent;
rbtree_right_rotate(root, sentinel, node);
}
rbt_black(node->parent);
rbt_red(node->parent->parent);
rbtree_left_rotate(root, sentinel, node->parent->parent);
}
}
}
rbt_black(*root);
}