10Sigor@sysoev.ru
20Sigor@sysoev.ru /*
30Sigor@sysoev.ru * Copyright (C) Igor Sysoev
40Sigor@sysoev.ru * Copyright (C) NGINX, Inc.
50Sigor@sysoev.ru */
60Sigor@sysoev.ru
70Sigor@sysoev.ru #include <nxt_main.h>
80Sigor@sysoev.ru
90Sigor@sysoev.ru
100Sigor@sysoev.ru /*
110Sigor@sysoev.ru * The red-black tree code is based on the algorithm described in
120Sigor@sysoev.ru * the "Introduction to Algorithms" by Cormen, Leiserson and Rivest.
130Sigor@sysoev.ru */
140Sigor@sysoev.ru
150Sigor@sysoev.ru
160Sigor@sysoev.ru static void nxt_rbtree_insert_fixup(nxt_rbtree_node_t *node);
170Sigor@sysoev.ru static void nxt_rbtree_delete_fixup(nxt_rbtree_t *tree,
180Sigor@sysoev.ru nxt_rbtree_node_t *node);
190Sigor@sysoev.ru nxt_inline void nxt_rbtree_left_rotate(nxt_rbtree_node_t *node);
200Sigor@sysoev.ru nxt_inline void nxt_rbtree_right_rotate(nxt_rbtree_node_t *node);
210Sigor@sysoev.ru nxt_inline void nxt_rbtree_parent_relink(nxt_rbtree_node_t *subst,
220Sigor@sysoev.ru nxt_rbtree_node_t *node);
230Sigor@sysoev.ru
240Sigor@sysoev.ru
250Sigor@sysoev.ru #define NXT_RBTREE_BLACK 0
260Sigor@sysoev.ru #define NXT_RBTREE_RED 1
270Sigor@sysoev.ru
280Sigor@sysoev.ru
290Sigor@sysoev.ru #define nxt_rbtree_comparison_callback(tree) \
300Sigor@sysoev.ru ((nxt_rbtree_compare_t) (tree)->sentinel.right)
310Sigor@sysoev.ru
320Sigor@sysoev.ru
330Sigor@sysoev.ru void
nxt_rbtree_init(nxt_rbtree_t * tree,nxt_rbtree_compare_t compare)345Sigor@sysoev.ru nxt_rbtree_init(nxt_rbtree_t *tree, nxt_rbtree_compare_t compare)
350Sigor@sysoev.ru {
360Sigor@sysoev.ru /*
370Sigor@sysoev.ru * The sentinel is used as a leaf node sentinel and as a tree root
380Sigor@sysoev.ru * sentinel: it is a parent of a root node and the root node is
390Sigor@sysoev.ru * the left child of the sentinel. Combining two sentinels in one
400Sigor@sysoev.ru * entry and the fact that the sentinel's left child is a root node
410Sigor@sysoev.ru * simplifies nxt_rbtree_node_successor() and eliminates explicit
420Sigor@sysoev.ru * root node test before or inside nxt_rbtree_min().
430Sigor@sysoev.ru */
440Sigor@sysoev.ru
450Sigor@sysoev.ru /* The root is empty. */
460Sigor@sysoev.ru tree->sentinel.left = &tree->sentinel;
470Sigor@sysoev.ru
480Sigor@sysoev.ru /*
495Sigor@sysoev.ru * The sentinel's right child is never used so
505Sigor@sysoev.ru * comparison callback can be safely stored here.
510Sigor@sysoev.ru */
525Sigor@sysoev.ru tree->sentinel.right = (void *) compare;
530Sigor@sysoev.ru
540Sigor@sysoev.ru /* The root and leaf sentinel must be black. */
550Sigor@sysoev.ru tree->sentinel.color = NXT_RBTREE_BLACK;
560Sigor@sysoev.ru }
570Sigor@sysoev.ru
580Sigor@sysoev.ru
590Sigor@sysoev.ru void
nxt_rbtree_insert(nxt_rbtree_t * tree,nxt_rbtree_part_t * part)600Sigor@sysoev.ru nxt_rbtree_insert(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
610Sigor@sysoev.ru {
620Sigor@sysoev.ru nxt_rbtree_node_t *node, *new_node, *sentinel, **child;
630Sigor@sysoev.ru nxt_rbtree_compare_t compare;
640Sigor@sysoev.ru
650Sigor@sysoev.ru new_node = (nxt_rbtree_node_t *) part;
660Sigor@sysoev.ru
670Sigor@sysoev.ru node = nxt_rbtree_root(tree);
680Sigor@sysoev.ru sentinel = nxt_rbtree_sentinel(tree);
690Sigor@sysoev.ru
700Sigor@sysoev.ru new_node->left = sentinel;
710Sigor@sysoev.ru new_node->right = sentinel;
720Sigor@sysoev.ru new_node->color = NXT_RBTREE_RED;
730Sigor@sysoev.ru
745Sigor@sysoev.ru compare = (nxt_rbtree_compare_t) tree->sentinel.right;
755Sigor@sysoev.ru child = &nxt_rbtree_root(tree);
760Sigor@sysoev.ru
775Sigor@sysoev.ru while (*child != sentinel) {
785Sigor@sysoev.ru node = *child;
790Sigor@sysoev.ru
805Sigor@sysoev.ru nxt_prefetch(node->left);
815Sigor@sysoev.ru nxt_prefetch(node->right);
820Sigor@sysoev.ru
835Sigor@sysoev.ru child = (compare(new_node, node) < 0) ? &node->left : &node->right;
845Sigor@sysoev.ru }
850Sigor@sysoev.ru
865Sigor@sysoev.ru *child = new_node;
875Sigor@sysoev.ru new_node->parent = node;
880Sigor@sysoev.ru
890Sigor@sysoev.ru nxt_rbtree_insert_fixup(new_node);
900Sigor@sysoev.ru
910Sigor@sysoev.ru node = nxt_rbtree_root(tree);
920Sigor@sysoev.ru node->color = NXT_RBTREE_BLACK;
930Sigor@sysoev.ru }
940Sigor@sysoev.ru
950Sigor@sysoev.ru
960Sigor@sysoev.ru static void
nxt_rbtree_insert_fixup(nxt_rbtree_node_t * node)970Sigor@sysoev.ru nxt_rbtree_insert_fixup(nxt_rbtree_node_t *node)
980Sigor@sysoev.ru {
990Sigor@sysoev.ru nxt_rbtree_node_t *parent, *grandparent, *uncle;
1000Sigor@sysoev.ru
1010Sigor@sysoev.ru /*
1020Sigor@sysoev.ru * Prefetching parent nodes does not help here because they are
1030Sigor@sysoev.ru * already traversed during insertion.
1040Sigor@sysoev.ru */
1050Sigor@sysoev.ru
1060Sigor@sysoev.ru for ( ;; ) {
1070Sigor@sysoev.ru parent = node->parent;
1080Sigor@sysoev.ru
1090Sigor@sysoev.ru /*
1100Sigor@sysoev.ru * Testing whether a node is a tree root is not required here since
1110Sigor@sysoev.ru * a root node's parent is the sentinel and it is always black.
1120Sigor@sysoev.ru */
1130Sigor@sysoev.ru if (parent->color == NXT_RBTREE_BLACK) {
1140Sigor@sysoev.ru return;
1150Sigor@sysoev.ru }
1160Sigor@sysoev.ru
1170Sigor@sysoev.ru grandparent = parent->parent;
1180Sigor@sysoev.ru
1190Sigor@sysoev.ru if (parent == grandparent->left) {
1200Sigor@sysoev.ru uncle = grandparent->right;
1210Sigor@sysoev.ru
1220Sigor@sysoev.ru if (uncle->color == NXT_RBTREE_BLACK) {
1230Sigor@sysoev.ru
1240Sigor@sysoev.ru if (node == parent->right) {
1250Sigor@sysoev.ru node = parent;
1260Sigor@sysoev.ru nxt_rbtree_left_rotate(node);
1270Sigor@sysoev.ru }
1280Sigor@sysoev.ru
12948Sigor@sysoev.ru /*
13048Sigor@sysoev.ru * nxt_rbtree_left_rotate() swaps parent and
13148Sigor@sysoev.ru * child whilst keeps grandparent the same.
13248Sigor@sysoev.ru */
1330Sigor@sysoev.ru parent = node->parent;
1340Sigor@sysoev.ru
13548Sigor@sysoev.ru parent->color = NXT_RBTREE_BLACK;
1360Sigor@sysoev.ru grandparent->color = NXT_RBTREE_RED;
13748Sigor@sysoev.ru
1380Sigor@sysoev.ru nxt_rbtree_right_rotate(grandparent);
1395Sigor@sysoev.ru /*
1405Sigor@sysoev.ru * nxt_rbtree_right_rotate() does not change node->parent
1415Sigor@sysoev.ru * color which is now black, so testing color is not required
1425Sigor@sysoev.ru * to return from function.
1435Sigor@sysoev.ru */
1445Sigor@sysoev.ru return;
1450Sigor@sysoev.ru }
1460Sigor@sysoev.ru
1470Sigor@sysoev.ru } else {
1480Sigor@sysoev.ru uncle = grandparent->left;
1490Sigor@sysoev.ru
1500Sigor@sysoev.ru if (uncle->color == NXT_RBTREE_BLACK) {
1510Sigor@sysoev.ru
1520Sigor@sysoev.ru if (node == parent->left) {
1530Sigor@sysoev.ru node = parent;
1540Sigor@sysoev.ru nxt_rbtree_right_rotate(node);
1550Sigor@sysoev.ru }
1560Sigor@sysoev.ru
15748Sigor@sysoev.ru /* See the comment in the symmetric branch above. */
1580Sigor@sysoev.ru parent = node->parent;
1590Sigor@sysoev.ru
16048Sigor@sysoev.ru parent->color = NXT_RBTREE_BLACK;
1610Sigor@sysoev.ru grandparent->color = NXT_RBTREE_RED;
16248Sigor@sysoev.ru
1630Sigor@sysoev.ru nxt_rbtree_left_rotate(grandparent);
1640Sigor@sysoev.ru
1655Sigor@sysoev.ru /* See the comment in the symmetric branch above. */
1665Sigor@sysoev.ru return;
1670Sigor@sysoev.ru }
1680Sigor@sysoev.ru }
1690Sigor@sysoev.ru
1700Sigor@sysoev.ru uncle->color = NXT_RBTREE_BLACK;
1710Sigor@sysoev.ru parent->color = NXT_RBTREE_BLACK;
1720Sigor@sysoev.ru grandparent->color = NXT_RBTREE_RED;
1730Sigor@sysoev.ru
1740Sigor@sysoev.ru node = grandparent;
1750Sigor@sysoev.ru }
1760Sigor@sysoev.ru }
1770Sigor@sysoev.ru
1780Sigor@sysoev.ru
1790Sigor@sysoev.ru nxt_rbtree_node_t *
nxt_rbtree_find(nxt_rbtree_t * tree,nxt_rbtree_part_t * part)1800Sigor@sysoev.ru nxt_rbtree_find(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
1810Sigor@sysoev.ru {
1825Sigor@sysoev.ru intptr_t n;
1830Sigor@sysoev.ru nxt_rbtree_node_t *node, *next, *sentinel;
1840Sigor@sysoev.ru nxt_rbtree_compare_t compare;
1850Sigor@sysoev.ru
1860Sigor@sysoev.ru node = (nxt_rbtree_node_t *) part;
1870Sigor@sysoev.ru
1880Sigor@sysoev.ru next = nxt_rbtree_root(tree);
1890Sigor@sysoev.ru sentinel = nxt_rbtree_sentinel(tree);
1900Sigor@sysoev.ru compare = nxt_rbtree_comparison_callback(tree);
1910Sigor@sysoev.ru
1920Sigor@sysoev.ru while (next != sentinel) {
1930Sigor@sysoev.ru nxt_prefetch(next->left);
1940Sigor@sysoev.ru nxt_prefetch(next->right);
1950Sigor@sysoev.ru
1960Sigor@sysoev.ru n = compare(node, next);
1970Sigor@sysoev.ru
1980Sigor@sysoev.ru if (n < 0) {
1990Sigor@sysoev.ru next = next->left;
2000Sigor@sysoev.ru
2010Sigor@sysoev.ru } else if (n > 0) {
2020Sigor@sysoev.ru next = next->right;
2030Sigor@sysoev.ru
2040Sigor@sysoev.ru } else {
2050Sigor@sysoev.ru return next;
2060Sigor@sysoev.ru }
2070Sigor@sysoev.ru }
2080Sigor@sysoev.ru
2090Sigor@sysoev.ru return NULL;
2100Sigor@sysoev.ru }
2110Sigor@sysoev.ru
2120Sigor@sysoev.ru
2130Sigor@sysoev.ru nxt_rbtree_node_t *
nxt_rbtree_find_less_or_equal(nxt_rbtree_t * tree,nxt_rbtree_part_t * part)2140Sigor@sysoev.ru nxt_rbtree_find_less_or_equal(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
2150Sigor@sysoev.ru {
2165Sigor@sysoev.ru intptr_t n;
2170Sigor@sysoev.ru nxt_rbtree_node_t *node, *retval, *next, *sentinel;
2180Sigor@sysoev.ru nxt_rbtree_compare_t compare;
2190Sigor@sysoev.ru
2200Sigor@sysoev.ru node = (nxt_rbtree_node_t *) part;
2210Sigor@sysoev.ru
2220Sigor@sysoev.ru retval = NULL;
2230Sigor@sysoev.ru next = nxt_rbtree_root(tree);
2240Sigor@sysoev.ru sentinel = nxt_rbtree_sentinel(tree);
2250Sigor@sysoev.ru compare = nxt_rbtree_comparison_callback(tree);
2260Sigor@sysoev.ru
2270Sigor@sysoev.ru while (next != sentinel) {
2280Sigor@sysoev.ru nxt_prefetch(next->left);
2290Sigor@sysoev.ru nxt_prefetch(next->right);
2300Sigor@sysoev.ru
2310Sigor@sysoev.ru n = compare(node, next);
2320Sigor@sysoev.ru
2330Sigor@sysoev.ru if (n < 0) {
2340Sigor@sysoev.ru next = next->left;
2350Sigor@sysoev.ru
2360Sigor@sysoev.ru } else if (n > 0) {
2370Sigor@sysoev.ru retval = next;
2380Sigor@sysoev.ru next = next->right;
2390Sigor@sysoev.ru
2400Sigor@sysoev.ru } else {
2410Sigor@sysoev.ru /* Exact match. */
2420Sigor@sysoev.ru return next;
2430Sigor@sysoev.ru }
2440Sigor@sysoev.ru }
2450Sigor@sysoev.ru
2460Sigor@sysoev.ru return retval;
2470Sigor@sysoev.ru }
2480Sigor@sysoev.ru
2490Sigor@sysoev.ru
2500Sigor@sysoev.ru nxt_rbtree_node_t *
nxt_rbtree_find_greater_or_equal(nxt_rbtree_t * tree,nxt_rbtree_part_t * part)2510Sigor@sysoev.ru nxt_rbtree_find_greater_or_equal(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
2520Sigor@sysoev.ru {
2535Sigor@sysoev.ru intptr_t n;
2540Sigor@sysoev.ru nxt_rbtree_node_t *node, *retval, *next, *sentinel;
2550Sigor@sysoev.ru nxt_rbtree_compare_t compare;
2560Sigor@sysoev.ru
2570Sigor@sysoev.ru node = (nxt_rbtree_node_t *) part;
2580Sigor@sysoev.ru
2590Sigor@sysoev.ru retval = NULL;
2600Sigor@sysoev.ru next = nxt_rbtree_root(tree);
2610Sigor@sysoev.ru sentinel = nxt_rbtree_sentinel(tree);
2620Sigor@sysoev.ru compare = nxt_rbtree_comparison_callback(tree);
2630Sigor@sysoev.ru
2640Sigor@sysoev.ru while (next != sentinel) {
2650Sigor@sysoev.ru nxt_prefetch(next->left);
2660Sigor@sysoev.ru nxt_prefetch(next->right);
2670Sigor@sysoev.ru
2680Sigor@sysoev.ru n = compare(node, next);
2690Sigor@sysoev.ru
2700Sigor@sysoev.ru if (n < 0) {
2710Sigor@sysoev.ru retval = next;
2720Sigor@sysoev.ru next = next->left;
2730Sigor@sysoev.ru
2740Sigor@sysoev.ru } else if (n > 0) {
2750Sigor@sysoev.ru next = next->right;
2760Sigor@sysoev.ru
2770Sigor@sysoev.ru } else {
2780Sigor@sysoev.ru /* Exact match. */
2790Sigor@sysoev.ru return next;
2800Sigor@sysoev.ru }
2810Sigor@sysoev.ru }
2820Sigor@sysoev.ru
2830Sigor@sysoev.ru return retval;
2840Sigor@sysoev.ru }
2850Sigor@sysoev.ru
2860Sigor@sysoev.ru
2870Sigor@sysoev.ru void
nxt_rbtree_delete(nxt_rbtree_t * tree,nxt_rbtree_part_t * part)2880Sigor@sysoev.ru nxt_rbtree_delete(nxt_rbtree_t *tree, nxt_rbtree_part_t *part)
2890Sigor@sysoev.ru {
2905Sigor@sysoev.ru uint8_t color;
2910Sigor@sysoev.ru nxt_rbtree_node_t *node, *sentinel, *subst, *child;
2920Sigor@sysoev.ru
2930Sigor@sysoev.ru node = (nxt_rbtree_node_t *) part;
2940Sigor@sysoev.ru
2950Sigor@sysoev.ru subst = node;
2960Sigor@sysoev.ru sentinel = nxt_rbtree_sentinel(tree);
2970Sigor@sysoev.ru
2980Sigor@sysoev.ru if (node->left == sentinel) {
2990Sigor@sysoev.ru child = node->right;
3000Sigor@sysoev.ru
3010Sigor@sysoev.ru } else if (node->right == sentinel) {
3020Sigor@sysoev.ru child = node->left;
3030Sigor@sysoev.ru
3040Sigor@sysoev.ru } else {
3050Sigor@sysoev.ru subst = nxt_rbtree_branch_min(tree, node->right);
3060Sigor@sysoev.ru child = subst->right;
3070Sigor@sysoev.ru }
3080Sigor@sysoev.ru
3090Sigor@sysoev.ru nxt_rbtree_parent_relink(child, subst);
3100Sigor@sysoev.ru
3110Sigor@sysoev.ru color = subst->color;
3120Sigor@sysoev.ru
3130Sigor@sysoev.ru if (subst != node) {
3140Sigor@sysoev.ru /* Move the subst node to the deleted node position in the tree. */
3150Sigor@sysoev.ru
3160Sigor@sysoev.ru subst->color = node->color;
3170Sigor@sysoev.ru
3180Sigor@sysoev.ru subst->left = node->left;
3190Sigor@sysoev.ru subst->left->parent = subst;
3200Sigor@sysoev.ru
3210Sigor@sysoev.ru subst->right = node->right;
3220Sigor@sysoev.ru subst->right->parent = subst;
3230Sigor@sysoev.ru
3240Sigor@sysoev.ru nxt_rbtree_parent_relink(subst, node);
3250Sigor@sysoev.ru }
3260Sigor@sysoev.ru
3270Sigor@sysoev.ru #if (NXT_DEBUG)
3280Sigor@sysoev.ru node->left = NULL;
3290Sigor@sysoev.ru node->right = NULL;
3300Sigor@sysoev.ru node->parent = NULL;
3310Sigor@sysoev.ru #endif
3320Sigor@sysoev.ru
3330Sigor@sysoev.ru if (color == NXT_RBTREE_BLACK) {
3340Sigor@sysoev.ru nxt_rbtree_delete_fixup(tree, child);
3350Sigor@sysoev.ru }
3360Sigor@sysoev.ru }
3370Sigor@sysoev.ru
3380Sigor@sysoev.ru
3390Sigor@sysoev.ru static void
nxt_rbtree_delete_fixup(nxt_rbtree_t * tree,nxt_rbtree_node_t * node)3400Sigor@sysoev.ru nxt_rbtree_delete_fixup(nxt_rbtree_t *tree, nxt_rbtree_node_t *node)
3410Sigor@sysoev.ru {
3420Sigor@sysoev.ru nxt_rbtree_node_t *parent, *sibling;
3430Sigor@sysoev.ru
3440Sigor@sysoev.ru while (node != nxt_rbtree_root(tree) && node->color == NXT_RBTREE_BLACK) {
3450Sigor@sysoev.ru /*
3460Sigor@sysoev.ru * Prefetching parent nodes does not help here according
3470Sigor@sysoev.ru * to microbenchmarks.
3480Sigor@sysoev.ru */
3490Sigor@sysoev.ru
3500Sigor@sysoev.ru parent = node->parent;
3510Sigor@sysoev.ru
3520Sigor@sysoev.ru if (node == parent->left) {
3530Sigor@sysoev.ru sibling = parent->right;
3540Sigor@sysoev.ru
3550Sigor@sysoev.ru if (sibling->color != NXT_RBTREE_BLACK) {
3560Sigor@sysoev.ru
3570Sigor@sysoev.ru sibling->color = NXT_RBTREE_BLACK;
3580Sigor@sysoev.ru parent->color = NXT_RBTREE_RED;
3590Sigor@sysoev.ru
3600Sigor@sysoev.ru nxt_rbtree_left_rotate(parent);
3610Sigor@sysoev.ru
3620Sigor@sysoev.ru sibling = parent->right;
3630Sigor@sysoev.ru }
3640Sigor@sysoev.ru
3650Sigor@sysoev.ru if (sibling->right->color == NXT_RBTREE_BLACK) {
3660Sigor@sysoev.ru
3670Sigor@sysoev.ru sibling->color = NXT_RBTREE_RED;
3680Sigor@sysoev.ru
3690Sigor@sysoev.ru if (sibling->left->color == NXT_RBTREE_BLACK) {
3700Sigor@sysoev.ru node = parent;
3710Sigor@sysoev.ru continue;
3720Sigor@sysoev.ru }
3730Sigor@sysoev.ru
3740Sigor@sysoev.ru sibling->left->color = NXT_RBTREE_BLACK;
3750Sigor@sysoev.ru
3760Sigor@sysoev.ru nxt_rbtree_right_rotate(sibling);
3770Sigor@sysoev.ru /*
3780Sigor@sysoev.ru * If the node is the leaf sentinel then the right
3790Sigor@sysoev.ru * rotate above changes its parent so a sibling below
3800Sigor@sysoev.ru * becames the leaf sentinel as well and this causes
3810Sigor@sysoev.ru * segmentation fault. This is the reason why usual
3820Sigor@sysoev.ru * red-black tree implementations with a leaf sentinel
3830Sigor@sysoev.ru * which does not require to test leaf nodes at all
3840Sigor@sysoev.ru * nevertheless test the leaf sentinel in the left and
3850Sigor@sysoev.ru * right rotate procedures. Since according to the
3860Sigor@sysoev.ru * algorithm node->parent must not be changed by both
3870Sigor@sysoev.ru * the left and right rotates above, it can be cached
3880Sigor@sysoev.ru * in a local variable. This not only eliminates the
3890Sigor@sysoev.ru * sentinel test in nxt_rbtree_parent_relink() but also
3900Sigor@sysoev.ru * decreases the code size because C forces to reload
3910Sigor@sysoev.ru * non-restrict pointers.
3920Sigor@sysoev.ru */
3930Sigor@sysoev.ru sibling = parent->right;
3940Sigor@sysoev.ru }
3950Sigor@sysoev.ru
3960Sigor@sysoev.ru sibling->color = parent->color;
3970Sigor@sysoev.ru parent->color = NXT_RBTREE_BLACK;
3980Sigor@sysoev.ru sibling->right->color = NXT_RBTREE_BLACK;
3990Sigor@sysoev.ru
4000Sigor@sysoev.ru nxt_rbtree_left_rotate(parent);
4010Sigor@sysoev.ru
402*50Sigor@sysoev.ru return;
4030Sigor@sysoev.ru
4040Sigor@sysoev.ru } else {
4050Sigor@sysoev.ru sibling = parent->left;
4060Sigor@sysoev.ru
4070Sigor@sysoev.ru if (sibling->color != NXT_RBTREE_BLACK) {
4080Sigor@sysoev.ru
4090Sigor@sysoev.ru sibling->color = NXT_RBTREE_BLACK;
4100Sigor@sysoev.ru parent->color = NXT_RBTREE_RED;
4110Sigor@sysoev.ru
4120Sigor@sysoev.ru nxt_rbtree_right_rotate(parent);
4130Sigor@sysoev.ru
4140Sigor@sysoev.ru sibling = parent->left;
4150Sigor@sysoev.ru }
4160Sigor@sysoev.ru
4170Sigor@sysoev.ru if (sibling->left->color == NXT_RBTREE_BLACK) {
4180Sigor@sysoev.ru
4190Sigor@sysoev.ru sibling->color = NXT_RBTREE_RED;
4200Sigor@sysoev.ru
4210Sigor@sysoev.ru if (sibling->right->color == NXT_RBTREE_BLACK) {
4220Sigor@sysoev.ru node = parent;
4230Sigor@sysoev.ru continue;
4240Sigor@sysoev.ru }
4250Sigor@sysoev.ru
4260Sigor@sysoev.ru sibling->right->color = NXT_RBTREE_BLACK;
4270Sigor@sysoev.ru
4280Sigor@sysoev.ru nxt_rbtree_left_rotate(sibling);
4290Sigor@sysoev.ru
4300Sigor@sysoev.ru /* See the comment in the symmetric branch above. */
4310Sigor@sysoev.ru sibling = parent->left;
4320Sigor@sysoev.ru }
4330Sigor@sysoev.ru
4340Sigor@sysoev.ru sibling->color = parent->color;
4350Sigor@sysoev.ru parent->color = NXT_RBTREE_BLACK;
4360Sigor@sysoev.ru sibling->left->color = NXT_RBTREE_BLACK;
4370Sigor@sysoev.ru
4380Sigor@sysoev.ru nxt_rbtree_right_rotate(parent);
4390Sigor@sysoev.ru
440*50Sigor@sysoev.ru return;
4410Sigor@sysoev.ru }
4420Sigor@sysoev.ru }
4430Sigor@sysoev.ru
4440Sigor@sysoev.ru node->color = NXT_RBTREE_BLACK;
4450Sigor@sysoev.ru }
4460Sigor@sysoev.ru
4470Sigor@sysoev.ru
4480Sigor@sysoev.ru nxt_inline void
nxt_rbtree_left_rotate(nxt_rbtree_node_t * node)4490Sigor@sysoev.ru nxt_rbtree_left_rotate(nxt_rbtree_node_t *node)
4500Sigor@sysoev.ru {
4510Sigor@sysoev.ru nxt_rbtree_node_t *child;
4520Sigor@sysoev.ru
4530Sigor@sysoev.ru child = node->right;
4540Sigor@sysoev.ru node->right = child->left;
4550Sigor@sysoev.ru child->left->parent = node;
4560Sigor@sysoev.ru child->left = node;
4570Sigor@sysoev.ru
4580Sigor@sysoev.ru nxt_rbtree_parent_relink(child, node);
4590Sigor@sysoev.ru
4600Sigor@sysoev.ru node->parent = child;
4610Sigor@sysoev.ru }
4620Sigor@sysoev.ru
4630Sigor@sysoev.ru
4640Sigor@sysoev.ru nxt_inline void
nxt_rbtree_right_rotate(nxt_rbtree_node_t * node)4650Sigor@sysoev.ru nxt_rbtree_right_rotate(nxt_rbtree_node_t *node)
4660Sigor@sysoev.ru {
4670Sigor@sysoev.ru nxt_rbtree_node_t *child;
4680Sigor@sysoev.ru
4690Sigor@sysoev.ru child = node->left;
4700Sigor@sysoev.ru node->left = child->right;
4710Sigor@sysoev.ru child->right->parent = node;
4720Sigor@sysoev.ru child->right = node;
4730Sigor@sysoev.ru
4740Sigor@sysoev.ru nxt_rbtree_parent_relink(child, node);
4750Sigor@sysoev.ru
4760Sigor@sysoev.ru node->parent = child;
4770Sigor@sysoev.ru }
4780Sigor@sysoev.ru
4790Sigor@sysoev.ru
4800Sigor@sysoev.ru /* Relink a parent from the node to the subst node. */
4810Sigor@sysoev.ru
4820Sigor@sysoev.ru nxt_inline void
nxt_rbtree_parent_relink(nxt_rbtree_node_t * subst,nxt_rbtree_node_t * node)4830Sigor@sysoev.ru nxt_rbtree_parent_relink(nxt_rbtree_node_t *subst, nxt_rbtree_node_t *node)
4840Sigor@sysoev.ru {
4850Sigor@sysoev.ru nxt_rbtree_node_t *parent, **link;
4860Sigor@sysoev.ru
4870Sigor@sysoev.ru parent = node->parent;
4880Sigor@sysoev.ru /*
4890Sigor@sysoev.ru * The leaf sentinel's parent can be safely changed here.
4900Sigor@sysoev.ru * See the comment in nxt_rbtree_delete_fixup() for details.
4910Sigor@sysoev.ru */
4920Sigor@sysoev.ru subst->parent = parent;
4930Sigor@sysoev.ru /*
4940Sigor@sysoev.ru * If the node's parent is the root sentinel it is safely changed
4950Sigor@sysoev.ru * because the root sentinel's left child is the tree root.
4960Sigor@sysoev.ru */
4970Sigor@sysoev.ru link = (node == parent->left) ? &parent->left : &parent->right;
4980Sigor@sysoev.ru *link = subst;
4990Sigor@sysoev.ru }
50023Sigor@sysoev.ru
50123Sigor@sysoev.ru
50223Sigor@sysoev.ru nxt_rbtree_node_t *
nxt_rbtree_destroy_next(nxt_rbtree_t * tree,nxt_rbtree_node_t ** next)50323Sigor@sysoev.ru nxt_rbtree_destroy_next(nxt_rbtree_t *tree, nxt_rbtree_node_t **next)
50423Sigor@sysoev.ru {
50523Sigor@sysoev.ru nxt_rbtree_node_t *node, *subst, *parent, *sentinel;
50623Sigor@sysoev.ru
50723Sigor@sysoev.ru sentinel = nxt_rbtree_sentinel(tree);
50823Sigor@sysoev.ru
50923Sigor@sysoev.ru /* Find the leftmost node. */
51023Sigor@sysoev.ru for (node = *next; node->left != sentinel; node = node->left);
51123Sigor@sysoev.ru
51223Sigor@sysoev.ru /* Replace the leftmost node with its right child. */
51323Sigor@sysoev.ru subst = node->right;
51423Sigor@sysoev.ru parent = node->parent;
51523Sigor@sysoev.ru
51623Sigor@sysoev.ru parent->left = subst;
51723Sigor@sysoev.ru subst->parent = parent;
51823Sigor@sysoev.ru
51923Sigor@sysoev.ru /*
52023Sigor@sysoev.ru * The right child is used as the next start node. If the right child
52123Sigor@sysoev.ru * is the sentinel then parent of the leftmost node is used as the next
52223Sigor@sysoev.ru * start node. The parent of the root node is the sentinel so after
52323Sigor@sysoev.ru * the single root node will be replaced with the sentinel, the next
52423Sigor@sysoev.ru * start node will be equal to the sentinel and iteration will stop.
52523Sigor@sysoev.ru */
52623Sigor@sysoev.ru if (subst == sentinel) {
52723Sigor@sysoev.ru subst = parent;
52823Sigor@sysoev.ru }
52923Sigor@sysoev.ru
53023Sigor@sysoev.ru *next = subst;
53123Sigor@sysoev.ru
53223Sigor@sysoev.ru return node;
53323Sigor@sysoev.ru }
534