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Rev | Author | Line No. | Line |
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4103 | Serge | 1 | /* |
2 | Red Black Trees |
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3 | (C) 1999 Andrea Arcangeli |
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4 | (C) 2002 David Woodhouse |
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5 | (C) 2012 Michel Lespinasse |
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6 | |||
7 | This program is free software; you can redistribute it and/or modify |
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8 | it under the terms of the GNU General Public License as published by |
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9 | the Free Software Foundation; either version 2 of the License, or |
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10 | (at your option) any later version. |
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11 | |||
12 | This program is distributed in the hope that it will be useful, |
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13 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 | GNU General Public License for more details. |
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16 | |||
17 | You should have received a copy of the GNU General Public License |
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18 | along with this program; if not, write to the Free Software |
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19 | Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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20 | |||
21 | linux/lib/rbtree.c |
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22 | */ |
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23 | |||
24 | #include |
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25 | #include |
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26 | |||
27 | /* |
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28 | * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree |
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29 | * |
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30 | * 1) A node is either red or black |
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31 | * 2) The root is black |
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32 | * 3) All leaves (NULL) are black |
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33 | * 4) Both children of every red node are black |
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34 | * 5) Every simple path from root to leaves contains the same number |
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35 | * of black nodes. |
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36 | * |
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37 | * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two |
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38 | * consecutive red nodes in a path and every red node is therefore followed by |
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39 | * a black. So if B is the number of black nodes on every simple path (as per |
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40 | * 5), then the longest possible path due to 4 is 2B. |
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41 | * |
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42 | * We shall indicate color with case, where black nodes are uppercase and red |
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43 | * nodes will be lowercase. Unknown color nodes shall be drawn as red within |
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44 | * parentheses and have some accompanying text comment. |
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45 | */ |
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46 | |||
6934 | serge | 47 | /* |
48 | * Notes on lockless lookups: |
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49 | * |
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50 | * All stores to the tree structure (rb_left and rb_right) must be done using |
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51 | * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the |
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52 | * tree structure as seen in program order. |
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53 | * |
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54 | * These two requirements will allow lockless iteration of the tree -- not |
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55 | * correct iteration mind you, tree rotations are not atomic so a lookup might |
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56 | * miss entire subtrees. |
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57 | * |
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58 | * But they do guarantee that any such traversal will only see valid elements |
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59 | * and that it will indeed complete -- does not get stuck in a loop. |
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60 | * |
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61 | * It also guarantees that if the lookup returns an element it is the 'correct' |
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62 | * one. But not returning an element does _NOT_ mean it's not present. |
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63 | * |
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64 | * NOTE: |
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65 | * |
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66 | * Stores to __rb_parent_color are not important for simple lookups so those |
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67 | * are left undone as of now. Nor did I check for loops involving parent |
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68 | * pointers. |
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69 | */ |
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70 | |||
4103 | Serge | 71 | static inline void rb_set_black(struct rb_node *rb) |
72 | { |
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73 | rb->__rb_parent_color |= RB_BLACK; |
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74 | } |
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75 | |||
76 | static inline struct rb_node *rb_red_parent(struct rb_node *red) |
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77 | { |
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78 | return (struct rb_node *)red->__rb_parent_color; |
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79 | } |
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80 | |||
81 | /* |
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82 | * Helper function for rotations: |
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83 | * - old's parent and color get assigned to new |
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84 | * - old gets assigned new as a parent and 'color' as a color. |
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85 | */ |
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86 | static inline void |
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87 | __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, |
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88 | struct rb_root *root, int color) |
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89 | { |
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90 | struct rb_node *parent = rb_parent(old); |
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91 | new->__rb_parent_color = old->__rb_parent_color; |
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92 | rb_set_parent_color(old, new, color); |
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93 | __rb_change_child(old, new, parent, root); |
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94 | } |
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95 | |||
96 | static __always_inline void |
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97 | __rb_insert(struct rb_node *node, struct rb_root *root, |
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98 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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99 | { |
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100 | struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; |
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101 | |||
102 | while (true) { |
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103 | /* |
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104 | * Loop invariant: node is red |
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105 | * |
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106 | * If there is a black parent, we are done. |
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107 | * Otherwise, take some corrective action as we don't |
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108 | * want a red root or two consecutive red nodes. |
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109 | */ |
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110 | if (!parent) { |
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111 | rb_set_parent_color(node, NULL, RB_BLACK); |
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112 | break; |
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113 | } else if (rb_is_black(parent)) |
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114 | break; |
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115 | |||
116 | gparent = rb_red_parent(parent); |
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117 | |||
118 | tmp = gparent->rb_right; |
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119 | if (parent != tmp) { /* parent == gparent->rb_left */ |
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120 | if (tmp && rb_is_red(tmp)) { |
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121 | /* |
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122 | * Case 1 - color flips |
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123 | * |
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124 | * G g |
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125 | * / \ / \ |
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126 | * p u --> P U |
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127 | * / / |
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5270 | serge | 128 | * n n |
4103 | Serge | 129 | * |
130 | * However, since g's parent might be red, and |
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131 | * 4) does not allow this, we need to recurse |
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132 | * at g. |
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133 | */ |
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134 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
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135 | rb_set_parent_color(parent, gparent, RB_BLACK); |
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136 | node = gparent; |
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137 | parent = rb_parent(node); |
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138 | rb_set_parent_color(node, parent, RB_RED); |
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139 | continue; |
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140 | } |
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141 | |||
142 | tmp = parent->rb_right; |
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143 | if (node == tmp) { |
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144 | /* |
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145 | * Case 2 - left rotate at parent |
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146 | * |
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147 | * G G |
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148 | * / \ / \ |
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149 | * p U --> n U |
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150 | * \ / |
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151 | * n p |
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152 | * |
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153 | * This still leaves us in violation of 4), the |
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154 | * continuation into Case 3 will fix that. |
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155 | */ |
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6934 | serge | 156 | tmp = node->rb_left; |
157 | WRITE_ONCE(parent->rb_right, tmp); |
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158 | WRITE_ONCE(node->rb_left, parent); |
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4103 | Serge | 159 | if (tmp) |
160 | rb_set_parent_color(tmp, parent, |
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161 | RB_BLACK); |
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162 | rb_set_parent_color(parent, node, RB_RED); |
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163 | augment_rotate(parent, node); |
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164 | parent = node; |
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165 | tmp = node->rb_right; |
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166 | } |
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167 | |||
168 | /* |
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169 | * Case 3 - right rotate at gparent |
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170 | * |
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171 | * G P |
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172 | * / \ / \ |
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173 | * p U --> n g |
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174 | * / \ |
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175 | * n U |
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176 | */ |
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6934 | serge | 177 | WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */ |
178 | WRITE_ONCE(parent->rb_right, gparent); |
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4103 | Serge | 179 | if (tmp) |
180 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
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181 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); |
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182 | augment_rotate(gparent, parent); |
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183 | break; |
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184 | } else { |
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185 | tmp = gparent->rb_left; |
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186 | if (tmp && rb_is_red(tmp)) { |
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187 | /* Case 1 - color flips */ |
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188 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
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189 | rb_set_parent_color(parent, gparent, RB_BLACK); |
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190 | node = gparent; |
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191 | parent = rb_parent(node); |
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192 | rb_set_parent_color(node, parent, RB_RED); |
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193 | continue; |
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194 | } |
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195 | |||
196 | tmp = parent->rb_left; |
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197 | if (node == tmp) { |
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198 | /* Case 2 - right rotate at parent */ |
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6934 | serge | 199 | tmp = node->rb_right; |
200 | WRITE_ONCE(parent->rb_left, tmp); |
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201 | WRITE_ONCE(node->rb_right, parent); |
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4103 | Serge | 202 | if (tmp) |
203 | rb_set_parent_color(tmp, parent, |
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204 | RB_BLACK); |
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205 | rb_set_parent_color(parent, node, RB_RED); |
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206 | augment_rotate(parent, node); |
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207 | parent = node; |
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208 | tmp = node->rb_left; |
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209 | } |
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210 | |||
211 | /* Case 3 - left rotate at gparent */ |
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6934 | serge | 212 | WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */ |
213 | WRITE_ONCE(parent->rb_left, gparent); |
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4103 | Serge | 214 | if (tmp) |
215 | rb_set_parent_color(tmp, gparent, RB_BLACK); |
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216 | __rb_rotate_set_parents(gparent, parent, root, RB_RED); |
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217 | augment_rotate(gparent, parent); |
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218 | break; |
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219 | } |
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220 | } |
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221 | } |
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222 | |||
223 | /* |
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224 | * Inline version for rb_erase() use - we want to be able to inline |
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225 | * and eliminate the dummy_rotate callback there |
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226 | */ |
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227 | static __always_inline void |
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228 | ____rb_erase_color(struct rb_node *parent, struct rb_root *root, |
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229 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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230 | { |
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231 | struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; |
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232 | |||
233 | while (true) { |
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234 | /* |
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235 | * Loop invariants: |
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236 | * - node is black (or NULL on first iteration) |
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237 | * - node is not the root (parent is not NULL) |
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238 | * - All leaf paths going through parent and node have a |
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239 | * black node count that is 1 lower than other leaf paths. |
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240 | */ |
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241 | sibling = parent->rb_right; |
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242 | if (node != sibling) { /* node == parent->rb_left */ |
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243 | if (rb_is_red(sibling)) { |
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244 | /* |
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245 | * Case 1 - left rotate at parent |
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246 | * |
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247 | * P S |
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248 | * / \ / \ |
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249 | * N s --> p Sr |
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250 | * / \ / \ |
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251 | * Sl Sr N Sl |
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252 | */ |
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6934 | serge | 253 | tmp1 = sibling->rb_left; |
254 | WRITE_ONCE(parent->rb_right, tmp1); |
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255 | WRITE_ONCE(sibling->rb_left, parent); |
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4103 | Serge | 256 | rb_set_parent_color(tmp1, parent, RB_BLACK); |
257 | __rb_rotate_set_parents(parent, sibling, root, |
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258 | RB_RED); |
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259 | augment_rotate(parent, sibling); |
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260 | sibling = tmp1; |
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261 | } |
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262 | tmp1 = sibling->rb_right; |
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263 | if (!tmp1 || rb_is_black(tmp1)) { |
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264 | tmp2 = sibling->rb_left; |
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265 | if (!tmp2 || rb_is_black(tmp2)) { |
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266 | /* |
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267 | * Case 2 - sibling color flip |
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268 | * (p could be either color here) |
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269 | * |
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270 | * (p) (p) |
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271 | * / \ / \ |
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272 | * N S --> N s |
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273 | * / \ / \ |
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274 | * Sl Sr Sl Sr |
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275 | * |
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276 | * This leaves us violating 5) which |
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277 | * can be fixed by flipping p to black |
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278 | * if it was red, or by recursing at p. |
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279 | * p is red when coming from Case 1. |
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280 | */ |
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281 | rb_set_parent_color(sibling, parent, |
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282 | RB_RED); |
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283 | if (rb_is_red(parent)) |
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284 | rb_set_black(parent); |
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285 | else { |
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286 | node = parent; |
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287 | parent = rb_parent(node); |
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288 | if (parent) |
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289 | continue; |
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290 | } |
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291 | break; |
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292 | } |
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293 | /* |
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294 | * Case 3 - right rotate at sibling |
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295 | * (p could be either color here) |
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296 | * |
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297 | * (p) (p) |
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298 | * / \ / \ |
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299 | * N S --> N Sl |
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300 | * / \ \ |
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301 | * sl Sr s |
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302 | * \ |
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303 | * Sr |
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304 | */ |
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6934 | serge | 305 | tmp1 = tmp2->rb_right; |
306 | WRITE_ONCE(sibling->rb_left, tmp1); |
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307 | WRITE_ONCE(tmp2->rb_right, sibling); |
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308 | WRITE_ONCE(parent->rb_right, tmp2); |
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4103 | Serge | 309 | if (tmp1) |
310 | rb_set_parent_color(tmp1, sibling, |
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311 | RB_BLACK); |
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312 | augment_rotate(sibling, tmp2); |
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313 | tmp1 = sibling; |
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314 | sibling = tmp2; |
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315 | } |
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316 | /* |
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317 | * Case 4 - left rotate at parent + color flips |
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318 | * (p and sl could be either color here. |
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319 | * After rotation, p becomes black, s acquires |
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320 | * p's color, and sl keeps its color) |
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321 | * |
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322 | * (p) (s) |
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323 | * / \ / \ |
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324 | * N S --> P Sr |
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325 | * / \ / \ |
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326 | * (sl) sr N (sl) |
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327 | */ |
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6934 | serge | 328 | tmp2 = sibling->rb_left; |
329 | WRITE_ONCE(parent->rb_right, tmp2); |
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330 | WRITE_ONCE(sibling->rb_left, parent); |
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4103 | Serge | 331 | rb_set_parent_color(tmp1, sibling, RB_BLACK); |
332 | if (tmp2) |
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333 | rb_set_parent(tmp2, parent); |
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334 | __rb_rotate_set_parents(parent, sibling, root, |
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335 | RB_BLACK); |
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336 | augment_rotate(parent, sibling); |
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337 | break; |
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338 | } else { |
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339 | sibling = parent->rb_left; |
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340 | if (rb_is_red(sibling)) { |
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341 | /* Case 1 - right rotate at parent */ |
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6934 | serge | 342 | tmp1 = sibling->rb_right; |
343 | WRITE_ONCE(parent->rb_left, tmp1); |
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344 | WRITE_ONCE(sibling->rb_right, parent); |
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4103 | Serge | 345 | rb_set_parent_color(tmp1, parent, RB_BLACK); |
346 | __rb_rotate_set_parents(parent, sibling, root, |
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347 | RB_RED); |
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348 | augment_rotate(parent, sibling); |
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349 | sibling = tmp1; |
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350 | } |
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351 | tmp1 = sibling->rb_left; |
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352 | if (!tmp1 || rb_is_black(tmp1)) { |
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353 | tmp2 = sibling->rb_right; |
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354 | if (!tmp2 || rb_is_black(tmp2)) { |
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355 | /* Case 2 - sibling color flip */ |
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356 | rb_set_parent_color(sibling, parent, |
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357 | RB_RED); |
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358 | if (rb_is_red(parent)) |
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359 | rb_set_black(parent); |
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360 | else { |
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361 | node = parent; |
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362 | parent = rb_parent(node); |
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363 | if (parent) |
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364 | continue; |
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365 | } |
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366 | break; |
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367 | } |
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368 | /* Case 3 - right rotate at sibling */ |
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6934 | serge | 369 | tmp1 = tmp2->rb_left; |
370 | WRITE_ONCE(sibling->rb_right, tmp1); |
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371 | WRITE_ONCE(tmp2->rb_left, sibling); |
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372 | WRITE_ONCE(parent->rb_left, tmp2); |
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4103 | Serge | 373 | if (tmp1) |
374 | rb_set_parent_color(tmp1, sibling, |
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375 | RB_BLACK); |
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376 | augment_rotate(sibling, tmp2); |
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377 | tmp1 = sibling; |
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378 | sibling = tmp2; |
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379 | } |
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380 | /* Case 4 - left rotate at parent + color flips */ |
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6934 | serge | 381 | tmp2 = sibling->rb_right; |
382 | WRITE_ONCE(parent->rb_left, tmp2); |
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383 | WRITE_ONCE(sibling->rb_right, parent); |
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4103 | Serge | 384 | rb_set_parent_color(tmp1, sibling, RB_BLACK); |
385 | if (tmp2) |
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386 | rb_set_parent(tmp2, parent); |
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387 | __rb_rotate_set_parents(parent, sibling, root, |
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388 | RB_BLACK); |
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389 | augment_rotate(parent, sibling); |
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390 | break; |
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391 | } |
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392 | } |
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393 | } |
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394 | |||
395 | /* Non-inline version for rb_erase_augmented() use */ |
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396 | void __rb_erase_color(struct rb_node *parent, struct rb_root *root, |
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397 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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398 | { |
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399 | ____rb_erase_color(parent, root, augment_rotate); |
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400 | } |
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401 | EXPORT_SYMBOL(__rb_erase_color); |
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402 | |||
403 | /* |
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404 | * Non-augmented rbtree manipulation functions. |
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405 | * |
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406 | * We use dummy augmented callbacks here, and have the compiler optimize them |
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407 | * out of the rb_insert_color() and rb_erase() function definitions. |
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408 | */ |
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409 | |||
410 | static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} |
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411 | static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} |
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412 | static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} |
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413 | |||
414 | static const struct rb_augment_callbacks dummy_callbacks = { |
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415 | dummy_propagate, dummy_copy, dummy_rotate |
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416 | }; |
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417 | |||
418 | void rb_insert_color(struct rb_node *node, struct rb_root *root) |
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419 | { |
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420 | __rb_insert(node, root, dummy_rotate); |
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421 | } |
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422 | EXPORT_SYMBOL(rb_insert_color); |
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423 | |||
424 | void rb_erase(struct rb_node *node, struct rb_root *root) |
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425 | { |
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426 | struct rb_node *rebalance; |
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427 | rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); |
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428 | if (rebalance) |
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429 | ____rb_erase_color(rebalance, root, dummy_rotate); |
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430 | } |
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431 | EXPORT_SYMBOL(rb_erase); |
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432 | |||
433 | /* |
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434 | * Augmented rbtree manipulation functions. |
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435 | * |
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436 | * This instantiates the same __always_inline functions as in the non-augmented |
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437 | * case, but this time with user-defined callbacks. |
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438 | */ |
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439 | |||
440 | void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, |
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441 | void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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442 | { |
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443 | __rb_insert(node, root, augment_rotate); |
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444 | } |
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445 | EXPORT_SYMBOL(__rb_insert_augmented); |
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446 | |||
447 | /* |
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448 | * This function returns the first node (in sort order) of the tree. |
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449 | */ |
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450 | struct rb_node *rb_first(const struct rb_root *root) |
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451 | { |
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452 | struct rb_node *n; |
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453 | |||
454 | n = root->rb_node; |
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455 | if (!n) |
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456 | return NULL; |
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457 | while (n->rb_left) |
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458 | n = n->rb_left; |
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459 | return n; |
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460 | } |
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461 | EXPORT_SYMBOL(rb_first); |
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462 | |||
463 | struct rb_node *rb_last(const struct rb_root *root) |
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464 | { |
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465 | struct rb_node *n; |
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466 | |||
467 | n = root->rb_node; |
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468 | if (!n) |
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469 | return NULL; |
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470 | while (n->rb_right) |
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471 | n = n->rb_right; |
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472 | return n; |
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473 | } |
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474 | EXPORT_SYMBOL(rb_last); |
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475 | |||
476 | struct rb_node *rb_next(const struct rb_node *node) |
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477 | { |
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478 | struct rb_node *parent; |
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479 | |||
480 | if (RB_EMPTY_NODE(node)) |
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481 | return NULL; |
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482 | |||
483 | /* |
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484 | * If we have a right-hand child, go down and then left as far |
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485 | * as we can. |
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486 | */ |
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487 | if (node->rb_right) { |
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488 | node = node->rb_right; |
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489 | while (node->rb_left) |
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490 | node=node->rb_left; |
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491 | return (struct rb_node *)node; |
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492 | } |
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493 | |||
494 | /* |
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495 | * No right-hand children. Everything down and left is smaller than us, |
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496 | * so any 'next' node must be in the general direction of our parent. |
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497 | * Go up the tree; any time the ancestor is a right-hand child of its |
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498 | * parent, keep going up. First time it's a left-hand child of its |
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499 | * parent, said parent is our 'next' node. |
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500 | */ |
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501 | while ((parent = rb_parent(node)) && node == parent->rb_right) |
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502 | node = parent; |
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503 | |||
504 | return parent; |
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505 | } |
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506 | EXPORT_SYMBOL(rb_next); |
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507 | |||
508 | struct rb_node *rb_prev(const struct rb_node *node) |
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509 | { |
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510 | struct rb_node *parent; |
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511 | |||
512 | if (RB_EMPTY_NODE(node)) |
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513 | return NULL; |
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514 | |||
515 | /* |
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516 | * If we have a left-hand child, go down and then right as far |
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517 | * as we can. |
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518 | */ |
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519 | if (node->rb_left) { |
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520 | node = node->rb_left; |
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521 | while (node->rb_right) |
||
522 | node=node->rb_right; |
||
523 | return (struct rb_node *)node; |
||
524 | } |
||
525 | |||
526 | /* |
||
527 | * No left-hand children. Go up till we find an ancestor which |
||
528 | * is a right-hand child of its parent. |
||
529 | */ |
||
530 | while ((parent = rb_parent(node)) && node == parent->rb_left) |
||
531 | node = parent; |
||
532 | |||
533 | return parent; |
||
534 | } |
||
535 | EXPORT_SYMBOL(rb_prev); |
||
536 | |||
537 | void rb_replace_node(struct rb_node *victim, struct rb_node *new, |
||
538 | struct rb_root *root) |
||
539 | { |
||
540 | struct rb_node *parent = rb_parent(victim); |
||
541 | |||
542 | /* Set the surrounding nodes to point to the replacement */ |
||
543 | __rb_change_child(victim, new, parent, root); |
||
544 | if (victim->rb_left) |
||
545 | rb_set_parent(victim->rb_left, new); |
||
546 | if (victim->rb_right) |
||
547 | rb_set_parent(victim->rb_right, new); |
||
548 | |||
549 | /* Copy the pointers/colour from the victim to the replacement */ |
||
550 | *new = *victim; |
||
551 | } |
||
552 | EXPORT_SYMBOL(rb_replace_node); |
||
553 | |||
554 | static struct rb_node *rb_left_deepest_node(const struct rb_node *node) |
||
555 | { |
||
556 | for (;;) { |
||
557 | if (node->rb_left) |
||
558 | node = node->rb_left; |
||
559 | else if (node->rb_right) |
||
560 | node = node->rb_right; |
||
561 | else |
||
562 | return (struct rb_node *)node; |
||
563 | } |
||
564 | } |
||
565 | |||
566 | struct rb_node *rb_next_postorder(const struct rb_node *node) |
||
567 | { |
||
568 | const struct rb_node *parent; |
||
569 | if (!node) |
||
570 | return NULL; |
||
571 | parent = rb_parent(node); |
||
572 | |||
573 | /* If we're sitting on node, we've already seen our children */ |
||
574 | if (parent && node == parent->rb_left && parent->rb_right) { |
||
575 | /* If we are the parent's left node, go to the parent's right |
||
576 | * node then all the way down to the left */ |
||
577 | return rb_left_deepest_node(parent->rb_right); |
||
578 | } else |
||
579 | /* Otherwise we are the parent's right node, and the parent |
||
580 | * should be next */ |
||
581 | return (struct rb_node *)parent; |
||
582 | } |
||
583 | EXPORT_SYMBOL(rb_next_postorder); |
||
584 | |||
585 | struct rb_node *rb_first_postorder(const struct rb_root *root) |
||
586 | { |
||
587 | if (!root->rb_node) |
||
588 | return NULL; |
||
589 | |||
590 | return rb_left_deepest_node(root->rb_node); |
||
591 | } |
||
592 | EXPORT_SYMBOL(rb_first_postorder); |