void rb_insert_fixup(Node* &T, Node *n)
{
// 如果n的父亲是红色，则需要调整
// 如果n的父亲是黑色，则不需要调整，因为n本身是红色
while(IS_RED(PARENT(n))) {
// 根据n的叔叔节点的颜色，来决定调整方案
Node *p = IS_LEFT(PARENT(n))? RIGHT(PARENT(PARENT(n))): LEFT(PARENT(PARENT(n)));
// 如果叔叔是红色，那很简单，把爷爷的黑色转移给父亲和叔叔，爷爷刷成红色
// 这样，即满足了性质4，也没有破坏性质5及其他性质
// 但是，爷爷可能破坏了红黑性质4，则从爷爷开始继续调整（向上递归了两层）
if (IS_RED(p)) {
// 父亲刷成黑色
SET_BLACK(PARENT(n));
// 叔叔刷成黑色
SET_BLACK(p);
// 爷爷刷成红色
SET_RED(PARENT(PARENT(n)));
// 从爷爷开始继续调整
n = PARENT(PARENT(n));
continue;
}
// 如果叔叔是黑色，就复杂一点，引入旋转操作
// 如果n是左孩子，那么需要一次右旋+颜色调整即可
// 如果n是右孩子，则通过一次左旋调整成左孩子，然后按上面情况处理
if (IS_LEFT(PARENT(n))) {
// 如果n是右孩子，通过右旋调整成左孩子
if (IS_RIGHT(n)) {
n = PARENT(n);
left_rotate(T, n);
}
// 现在n是左孩子了
SET_BLACK(PARENT(n));
SET_RED(PARENT(PARENT(n)));
right_rotate(T, PARENT(PARENT(n)));
} else {
if (IS_LEFT(n)) {
n = PARENT(n);
right_rotate(T,n);
}
SET_BLACK(PARENT(n));
SET_RED(PARENT(PARENT(n)));
left_rotate(T,PARENT(PARENT(n)));
}
}
// 如果n是根节点，则把根设置为黑色
if (NIL == PARENT(n))
SET_BLACK(n);
}
static void
aoff_link_free_block(Allctr_t *allctr, Block_t *block, Uint32 flags)
{
AOFFAllctr_t *alc = (AOFFAllctr_t *) allctr;
AOFF_RBTree_t *blk = (AOFF_RBTree_t *) block;
AOFF_RBTree_t **root = ((flags & ERTS_ALCU_FLG_SBMBC)
? &alc->sbmbc_root : &alc->mbc_root);
Uint blk_sz = BLK_SZ(blk);
#ifdef HARD_DEBUG
check_tree(*root, 0);
#endif
blk->flags = 0;
blk->left = NULL;
blk->right = NULL;
blk->max_sz = blk_sz;
if (!*root) {
blk->parent = NULL;
SET_BLACK(blk);
*root = blk;
}
else {
AOFF_RBTree_t *x = *root;
while (1) {
if (x->max_sz < blk_sz) {
x->max_sz = blk_sz;
}
if (blk < x) {
if (!x->left) {
blk->parent = x;
x->left = blk;
break;
}
x = x->left;
}
else {
if (!x->right) {
blk->parent = x;
x->right = blk;
break;
}
x = x->right;
}
}
/* Insert block into size tree */
RBT_ASSERT(blk->parent);
SET_RED(blk);
if (IS_RED(blk->parent))
tree_insert_fixup(root, blk);
}
#ifdef HARD_DEBUG
check_tree(*root, 0);
#endif
}
static void
aobf_link_free_block(Allctr_t *allctr, Block_t *block)
{
BFAllctr_t *bfallctr = (BFAllctr_t *) allctr;
RBTree_t **root = &bfallctr->mbc_root;
RBTree_t *blk = (RBTree_t *) block;
Uint blk_sz = BF_BLK_SZ(blk);
blk->flags = 0;
blk->left = NULL;
blk->right = NULL;
if (!*root) {
blk->parent = NULL;
SET_BLACK(blk);
*root = blk;
}
else {
RBTree_t *x = *root;
while (1) {
Uint size;
size = BF_BLK_SZ(x);
if (blk_sz < size || (blk_sz == size && blk < x)) {
if (!x->left) {
blk->parent = x;
x->left = blk;
break;
}
x = x->left;
}
else {
if (!x->right) {
blk->parent = x;
x->right = blk;
break;
}
x = x->right;
}
}
/* Insert block into size tree */
RBT_ASSERT(blk->parent);
SET_RED(blk);
if (IS_RED(blk->parent))
tree_insert_fixup(root, blk);
}
#ifdef HARD_DEBUG
check_tree(root, 1, 0);
#endif
}
static void
set_black (GCObjectPtr ptr)
{
uint32_t cell_idx;
PageInfo *page = find_page_and_cell(ptr, &cell_idx);
if (!page)
return;
SET_BLACK(page->page_bitmap[cell_idx]);
}
Node* tree_insert(Node* &T, Interval key)
{
// 分配新节点
Node *n = malloc_node(key);
// 如果当前是空树，则n节点作为根，刷成黑色即满足红黑性质
if (NIL == T){
SET_BLACK(n);
T = n;
return n;
}
// 如果当前不是空树，则先找到插入位置
Node *p = T;
Node *q;
while(NIL != p) {
// 调整路径上节点的max值
if (MAX(p) < HIGH(key))
MAX(p) = HIGH(key);
q = p;
if (LT(key,KEY(p)))
p = LEFT(p);
else
p = RIGHT(p);
}
// 找到了插入位置，n节点的父亲为q
PARENT(n) = q;
if (LT(key, KEY(q))) {
LEFT(q) = n;
} else {
RIGHT(q) = n;
}
// 设置n节点为红色
// 这样只可能违背红黑性质4（性质4的调整应该比性质5简单）
SET_RED(n);
// 从n节点开始调整，使之符合红黑性质4
// 调整的每一步，都不会破坏其他红黑性质
rb_insert_fixup(T, n);
return n;
}
Node* tree_insert(Node* &T, int key)
{
// 分配新节点
Node *n = malloc_node(key);
// 如果当前是空树，则n节点作为根，刷成黑色即满足红黑性质
if (NIL == T){
SET_BLACK(n);
T = n;
return n;
}
// 如果当前不是空树，则先找到插入位置
Node *p = T;
Node *q;
while(NIL != p) {
// 每经过一个节点，其size加一
SIZE(p)++;
q = p;
if (key < KEY(p))
p = LEFT(p);
else
p = RIGHT(p);
}
// 找到了插入位置，n节点的父亲为q
PARENT(n) = q;
if (key < KEY(q)) {
LEFT(q) = n;
} else {
RIGHT(q) = n;
}
// 设置n节点为红色
// 这样只可能违背红黑性质4（性质4的调整应该比性质5简单）
SET_RED(n);
// 从n节点开始调整，使之符合红黑性质4
// 调整的每一步，都不会破坏其他红黑性质
rb_insert_fixup(T, n);
return n;
}
static void
bf_link_free_block(Allctr_t *allctr, Block_t *block)
{
BFAllctr_t *bfallctr = (BFAllctr_t *) allctr;
RBTree_t **root = &bfallctr->mbc_root;
RBTree_t *blk = (RBTree_t *) block;
Uint blk_sz = BF_BLK_SZ(blk);
SET_TREE_NODE(blk);
blk->flags = 0;
blk->left = NULL;
blk->right = NULL;
if (!*root) {
blk->parent = NULL;
SET_BLACK(blk);
*root = blk;
}
else {
RBTree_t *x = *root;
while (1) {
Uint size;
size = BF_BLK_SZ(x);
if (blk_sz == size) {
SET_LIST_ELEM(blk);
LIST_NEXT(blk) = LIST_NEXT(x);
LIST_PREV(blk) = x;
if (LIST_NEXT(x))
LIST_PREV(LIST_NEXT(x)) = blk;
LIST_NEXT(x) = blk;
return; /* Finnished */
}
else if (blk_sz < size) {
if (!x->left) {
blk->parent = x;
x->left = blk;
break;
}
x = x->left;
}
else {
if (!x->right) {
blk->parent = x;
x->right = blk;
break;
}
x = x->right;
}
}
RBT_ASSERT(blk->parent);
SET_RED(blk);
if (IS_RED(blk->parent))
tree_insert_fixup(root, blk);
}
SET_TREE_NODE(blk);
LIST_NEXT(blk) = NULL;
#ifdef HARD_DEBUG
check_tree(root, 0, 0);
#endif
}
/*
* The argument types of "Allctr_t *" and "Block_t *" have been
* chosen since we then can use tree_delete() as unlink_free_block
* callback function in the address order case.
*/
static void
tree_delete(Allctr_t *allctr, Block_t *del)
{
BFAllctr_t *bfallctr = (BFAllctr_t *) allctr;
Uint spliced_is_black;
RBTree_t **root = &bfallctr->mbc_root;
RBTree_t *x, *y, *z = (RBTree_t *) del;
RBTree_t null_x; /* null_x is used to get the fixup started when we
splice out a node without children. */
null_x.parent = NULL;
#ifdef HARD_DEBUG
check_tree(*root, bfallctr->address_order, 0);
#endif
/* Remove node from tree... */
/* Find node to splice out */
if (!z->left || !z->right)
y = z;
else
/* Set y to z:s successor */
for(y = z->right; y->left; y = y->left);
/* splice out y */
x = y->left ? y->left : y->right;
spliced_is_black = IS_BLACK(y);
if (x) {
x->parent = y->parent;
}
else if (!x && spliced_is_black) {
x = &null_x;
x->flags = 0;
SET_BLACK(x);
x->right = x->left = NULL;
x->parent = y->parent;
y->left = x;
}
if (!y->parent) {
RBT_ASSERT(*root == y);
*root = x;
}
else if (y == y->parent->left)
y->parent->left = x;
else {
RBT_ASSERT(y == y->parent->right);
y->parent->right = x;
}
if (y != z) {
/* We spliced out the successor of z; replace z by the successor */
replace(root, z, y);
}
if (spliced_is_black) {
/* We removed a black node which makes the resulting tree
violate the Red-Black Tree properties. Fixup tree... */
while (IS_BLACK(x) && x->parent) {
/*
* x has an "extra black" which we move up the tree
* until we reach the root or until we can get rid of it.
*
* y is the sibbling of x
*/
if (x == x->parent->left) {
y = x->parent->right;
RBT_ASSERT(y);
if (IS_RED(y)) {
RBT_ASSERT(y->right);
RBT_ASSERT(y->left);
SET_BLACK(y);
RBT_ASSERT(IS_BLACK(x->parent));
SET_RED(x->parent);
left_rotate(root, x->parent);
y = x->parent->right;
}
RBT_ASSERT(y);
RBT_ASSERT(IS_BLACK(y));
if (IS_BLACK(y->left) && IS_BLACK(y->right)) {
SET_RED(y);
x = x->parent;
}
else {
if (IS_BLACK(y->right)) {
SET_BLACK(y->left);
SET_RED(y);
right_rotate(root, y);
y = x->parent->right;
}
RBT_ASSERT(y);
if (IS_RED(x->parent)) {
SET_BLACK(x->parent);
SET_RED(y);
}
RBT_ASSERT(y->right);
SET_BLACK(y->right);
left_rotate(root, x->parent);
x = *root;
break;
}
}
else {
RBT_ASSERT(x == x->parent->right);
y = x->parent->left;
RBT_ASSERT(y);
if (IS_RED(y)) {
RBT_ASSERT(y->right);
RBT_ASSERT(y->left);
SET_BLACK(y);
RBT_ASSERT(IS_BLACK(x->parent));
SET_RED(x->parent);
right_rotate(root, x->parent);
y = x->parent->left;
}
RBT_ASSERT(y);
RBT_ASSERT(IS_BLACK(y));
if (IS_BLACK(y->right) && IS_BLACK(y->left)) {
SET_RED(y);
x = x->parent;
}
else {
if (IS_BLACK(y->left)) {
SET_BLACK(y->right);
SET_RED(y);
left_rotate(root, y);
y = x->parent->left;
}
RBT_ASSERT(y);
if (IS_RED(x->parent)) {
SET_BLACK(x->parent);
SET_RED(y);
}
RBT_ASSERT(y->left);
SET_BLACK(y->left);
right_rotate(root, x->parent);
x = *root;
break;
}
}
}
SET_BLACK(x);
if (null_x.parent) {
if (null_x.parent->left == &null_x)
null_x.parent->left = NULL;
else {
RBT_ASSERT(null_x.parent->right == &null_x);
null_x.parent->right = NULL;
}
RBT_ASSERT(!null_x.left);
RBT_ASSERT(!null_x.right);
}
else if (*root == &null_x) {
*root = NULL;
RBT_ASSERT(!null_x.left);
RBT_ASSERT(!null_x.right);
}
}
DESTROY_TREE_NODE(del);
#ifdef HARD_DEBUG
check_tree(root, bfallctr->address_order, 0);
#endif
}
static void
tree_insert_fixup(RBTree_t **root, RBTree_t *blk)
{
RBTree_t *x = blk, *y;
/*
* Rearrange the tree so that it satisfies the Red-Black Tree properties
*/
RBT_ASSERT(x != *root && IS_RED(x->parent));
do {
/*
* x and its parent are both red. Move the red pair up the tree
* until we get to the root or until we can separate them.
*/
RBT_ASSERT(IS_RED(x));
RBT_ASSERT(IS_BLACK(x->parent->parent));
RBT_ASSERT(x->parent->parent);
if (x->parent == x->parent->parent->left) {
y = x->parent->parent->right;
if (IS_RED(y)) {
SET_BLACK(y);
x = x->parent;
SET_BLACK(x);
x = x->parent;
SET_RED(x);
}
else {
if (x == x->parent->right) {
x = x->parent;
left_rotate(root, x);
}
RBT_ASSERT(x == x->parent->parent->left->left);
RBT_ASSERT(IS_RED(x));
RBT_ASSERT(IS_RED(x->parent));
RBT_ASSERT(IS_BLACK(x->parent->parent));
RBT_ASSERT(IS_BLACK(y));
SET_BLACK(x->parent);
SET_RED(x->parent->parent);
right_rotate(root, x->parent->parent);
RBT_ASSERT(x == x->parent->left);
RBT_ASSERT(IS_RED(x));
RBT_ASSERT(IS_RED(x->parent->right));
RBT_ASSERT(IS_BLACK(x->parent));
break;
}
}
else {
RBT_ASSERT(x->parent == x->parent->parent->right);
y = x->parent->parent->left;
if (IS_RED(y)) {
SET_BLACK(y);
x = x->parent;
SET_BLACK(x);
x = x->parent;
SET_RED(x);
}
else {
if (x == x->parent->left) {
x = x->parent;
right_rotate(root, x);
}
RBT_ASSERT(x == x->parent->parent->right->right);
RBT_ASSERT(IS_RED(x));
RBT_ASSERT(IS_RED(x->parent));
RBT_ASSERT(IS_BLACK(x->parent->parent));
RBT_ASSERT(IS_BLACK(y));
SET_BLACK(x->parent);
SET_RED(x->parent->parent);
left_rotate(root, x->parent->parent);
RBT_ASSERT(x == x->parent->right);
RBT_ASSERT(IS_RED(x));
RBT_ASSERT(IS_RED(x->parent->left));
RBT_ASSERT(IS_BLACK(x->parent));
break;
}
}
} while (x != *root && IS_RED(x->parent));
SET_BLACK(*root);
}
static void
rbt_insert(enum AOFFSortOrder order, AOFF_RBTree_t** root, AOFF_RBTree_t* blk)
{
Uint blk_sz = AOFF_BLK_SZ(blk);
#ifdef DEBUG
blk->flags = (order == FF_BF) ? IS_BF_FLG : 0;
#else
blk->flags = 0;
#endif
blk->left = NULL;
blk->right = NULL;
blk->max_sz = blk_sz;
if (!*root) {
blk->parent = NULL;
SET_BLACK(blk);
*root = blk;
}
else {
AOFF_RBTree_t *x = *root;
while (1) {
SWord diff;
if (x->max_sz < blk_sz) {
x->max_sz = blk_sz;
}
diff = cmp_blocks(order, blk, x);
if (diff < 0) {
if (!x->left) {
blk->parent = x;
x->left = blk;
break;
}
x = x->left;
}
else if (diff > 0) {
if (!x->right) {
blk->parent = x;
x->right = blk;
break;
}
x = x->right;
}
else {
ASSERT(order == FF_BF);
ASSERT(blk->flags & IS_BF_FLG);
ASSERT(x->flags & IS_BF_FLG);
SET_LIST_ELEM(blk);
LIST_NEXT(blk) = LIST_NEXT(x);
LIST_PREV(blk) = x;
if (LIST_NEXT(x))
LIST_PREV(LIST_NEXT(x)) = blk;
LIST_NEXT(x) = blk;
return;
}
}
/* Insert block into size tree */
RBT_ASSERT(blk->parent);
SET_RED(blk);
if (IS_RED(blk->parent))
tree_insert_fixup(root, blk);
}
if (order == FF_BF) {
SET_TREE_NODE(blk);
LIST_NEXT(blk) = NULL;
}
}
static void
rbt_delete(AOFF_RBTree_t** root, AOFF_RBTree_t* del)
{
Uint spliced_is_black;
AOFF_RBTree_t *x, *y, *z = del;
AOFF_RBTree_t null_x; /* null_x is used to get the fixup started when we
splice out a node without children. */
HARD_CHECK_IS_MEMBER(*root, del);
null_x.parent = NULL;
/* Remove node from tree... */
/* Find node to splice out */
if (!z->left || !z->right)
y = z;
else
/* Set y to z:s successor */
for(y = z->right; y->left; y = y->left);
/* splice out y */
x = y->left ? y->left : y->right;
spliced_is_black = IS_BLACK(y);
if (x) {
x->parent = y->parent;
}
else if (spliced_is_black) {
x = &null_x;
x->flags = 0;
SET_BLACK(x);
x->right = x->left = NULL;
x->max_sz = 0;
x->parent = y->parent;
y->left = x;
}
if (!y->parent) {
RBT_ASSERT(*root == y);
*root = x;
}
else {
if (y == y->parent->left) {
y->parent->left = x;
}
else {
RBT_ASSERT(y == y->parent->right);
y->parent->right = x;
}
if (y->parent != z) {
lower_max_size(y->parent, (y==z ? NULL : z));
}
}
if (y != z) {
/* We spliced out the successor of z; replace z by the successor */
ASSERT(z != &null_x);
replace(root, z, y);
lower_max_size(y, NULL);
}
if (spliced_is_black) {
/* We removed a black node which makes the resulting tree
violate the Red-Black Tree properties. Fixup tree... */
while (IS_BLACK(x) && x->parent) {
/*
* x has an "extra black" which we move up the tree
* until we reach the root or until we can get rid of it.
*
* y is the sibbling of x
*/
if (x == x->parent->left) {
y = x->parent->right;
RBT_ASSERT(y);
if (IS_RED(y)) {
RBT_ASSERT(y->right);
RBT_ASSERT(y->left);
SET_BLACK(y);
RBT_ASSERT(IS_BLACK(x->parent));
SET_RED(x->parent);
left_rotate(root, x->parent);
y = x->parent->right;
}
RBT_ASSERT(y);
RBT_ASSERT(IS_BLACK(y));
if (IS_BLACK(y->left) && IS_BLACK(y->right)) {
SET_RED(y);
x = x->parent;
}
else {
if (IS_BLACK(y->right)) {
SET_BLACK(y->left);
SET_RED(y);
right_rotate(root, y);
y = x->parent->right;
}
RBT_ASSERT(y);
if (IS_RED(x->parent)) {
SET_BLACK(x->parent);
SET_RED(y);
}
RBT_ASSERT(y->right);
SET_BLACK(y->right);
left_rotate(root, x->parent);
x = *root;
break;
}
}
else {
RBT_ASSERT(x == x->parent->right);
y = x->parent->left;
RBT_ASSERT(y);
if (IS_RED(y)) {
RBT_ASSERT(y->right);
RBT_ASSERT(y->left);
SET_BLACK(y);
RBT_ASSERT(IS_BLACK(x->parent));
SET_RED(x->parent);
right_rotate(root, x->parent);
y = x->parent->left;
}
RBT_ASSERT(y);
RBT_ASSERT(IS_BLACK(y));
if (IS_BLACK(y->right) && IS_BLACK(y->left)) {
SET_RED(y);
x = x->parent;
}
else {
if (IS_BLACK(y->left)) {
SET_BLACK(y->right);
SET_RED(y);
left_rotate(root, y);
y = x->parent->left;
}
RBT_ASSERT(y);
if (IS_RED(x->parent)) {
SET_BLACK(x->parent);
SET_RED(y);
}
RBT_ASSERT(y->left);
SET_BLACK(y->left);
right_rotate(root, x->parent);
x = *root;
break;
}
}
}
SET_BLACK(x);
if (null_x.parent) {
if (null_x.parent->left == &null_x)
null_x.parent->left = NULL;
else {
RBT_ASSERT(null_x.parent->right == &null_x);
null_x.parent->right = NULL;
}
RBT_ASSERT(!null_x.left);
RBT_ASSERT(!null_x.right);
}
else if (*root == &null_x) {
*root = NULL;
RBT_ASSERT(!null_x.left);
RBT_ASSERT(!null_x.right);
}
}
}
void rb_delete_fixup(Node* &T, Node *x)
{
while ((NIL!= x) && !IS_ROOT(x) && IS_BLACK(x)) {
if (IS_LEFT(x)) {
// w是x的右兄弟，w是下面不同处理方式的选择依据
// 总共四种处理方式：
// case 1: w是红色，两个孩子的颜色无所谓
// case 2: w是黑色，左孩子黑色，右孩子黑色
// case 3: w是黑色，左孩子红色，右孩子黑色
// case 4: w是黑色，右孩子红色，左孩子的颜色无所谓
Node *w = RIGHT(PARENT(x));
// case1: w是红色，则通过一次左旋，并刷成黑色，转成case 2、3、4
if (IS_RED(w)) {
SET_BLACK(w);
SET_RED(PARENT(x));
left_rotate(T, PARENT(x));
}
// case 2: w的两个孩子都是黑色，把w刷成红色，x的父亲取代x，向上递归处理
if (IS_BLACK(LEFT(w)) && IS_BLACK(RIGHT(w))) {
SET_RED(w);
x = PARENT(x);
continue;
}
// case 3: w的左孩子红色，右孩子黑色，把w左孩子刷成黑色，w刷成红色，做一次右旋，转成case 4
if (IS_BLACK(RIGHT(w))) {
SET_BLACK(LEFT(w));
SET_RED(w);
right_rotate(T, w);
w = PARENT(w); // 转成case 4
}
// case 4: w的右孩子为红色，把w刷成红色，w右节点刷成黑色，x父亲刷成黑色，做一次左旋，满足红黑性质，结束处理
COLOR(w) = COLOR(PARENT(x));
SET_BLACK(RIGHT(w));
SET_BLACK(PARENT(x));
left_rotate(T, PARENT(x));
x = T;
} else {
// w是x的左兄弟，w是下面不同处理方式的选择依据
// 总共四种处理方式：
// case 1: w是红色，两个孩子的颜色无所谓
// case 2: w是黑色，左孩子黑色，右孩子黑色
// case 3: w是黑色，左孩子红色，右孩子黑色
// case 4: w是黑色，右孩子红色，左孩子的颜色无所谓
Node *w = LEFT(PARENT(x));
// case1: w是红色，则通过一次右旋，并刷成黑色，转成case 2、3、4
if (IS_RED(w)) {
SET_BLACK(w);
SET_RED(PARENT(x));
right_rotate(T, PARENT(x));
}
// case 2: w的两个孩子都是黑色，把w刷成红色，x的父亲取代x，线上递归处理
if (IS_BLACK(LEFT(w)) && IS_BLACK(RIGHT(w))) {
SET_RED(w);
x = PARENT(x);
continue;
}
// case 3: w的左孩子黑色，右孩子红色，把w右孩子刷成黑色，w刷成红色，做一次左旋，转成case 4
if (IS_BLACK(LEFT(w))) {
SET_BLACK(RIGHT(w));
SET_RED(w);
left_rotate(T, w);
w = PARENT(w); // 转成case 4
}
// case 4: w的左孩子为红色，把w刷成红色，w左节点刷成黑色，x父亲刷成黑色，做一次右旋，满足红黑性质，结束处理
COLOR(w) = COLOR(PARENT(x));
SET_BLACK(LEFT(w));
SET_BLACK(PARENT(x));
right_rotate(T, PARENT(x));
x = T;
}
}
// 如果x是根节点，或为红色，则都刷成黑色，即可保持红黑树性质
SET_BLACK(x);
}
