[Resend][PATCH 16/17] rbtree: low level optimizations in rb_erase()

[Praveen Kumar <kpraveen.lkml@gmail.com>]

Various minor optimizations in rb_erase():
- Avoid multiple loading of node->__rb_parent_color when computing parent
  and color information (possibly not in close sequence, as there might
  be further branches in the algorithm)
- In the 1-child subcase of case 1, copy the __rb_parent_color field from
  the erased node to the child instead of recomputing it from the desired
  parent and color
- When searching for the erased node's successor, differentiate between
  cases 2 and 3 based on whether any left links were followed. This avoids
  a condition later down.
- In case 3, keep a pointer to the erased node's right child so we don't
  have to refetch it later to adjust its parent.
- In the no-childs subcase of cases 2 and 3, place the rebalance assigment
  last so that the compiler can remove the following if(rebalance) test.

Also, added some comments to illustrate cases 2 and 3.

commit 4f035ad67f4633c233cb3642711d49b4efc9c82d from Linux tree

Signed-off-by: Praveen Kumar <kpraveen.lkml@gmail.com>
---
 xen/common/rbtree.c | 102 ++++++++++++++++++++++++++++++++++------------------
 1 file changed, 67 insertions(+), 35 deletions(-)

diff --git a/xen/common/rbtree.c b/xen/common/rbtree.c
index 6e37e960ab..83b4892f54 100644
--- a/xen/common/rbtree.c
+++ b/xen/common/rbtree.c
@@ -46,9 +46,14 @@
 #define    RB_RED    0
 #define    RB_BLACK  1
 
-#define rb_color(r)     ((r)->__rb_parent_color & 1)
-#define rb_is_red(r)    (!rb_color(r))
-#define rb_is_black(r)  rb_color(r)
+#define __rb_parent(pc)    ((struct rb_node *)(pc & ~3))
+
+#define __rb_color(pc)     ((pc) & 1)
+#define __rb_is_black(pc)  __rb_color(pc)
+#define __rb_is_red(pc)    (!__rb_color(pc))
+#define rb_color(rb)       __rb_color((rb)->__rb_parent_color)
+#define rb_is_red(rb)      __rb_is_red((rb)->__rb_parent_color)
+#define rb_is_black(rb)    __rb_is_black((rb)->__rb_parent_color)
 
 static inline void rb_set_black(struct rb_node *rb)
 {
@@ -387,6 +392,7 @@ void rb_erase(struct rb_node *node, struct rb_root *root)
 {
     struct rb_node *child = node->rb_right, *tmp = node->rb_left;
     struct rb_node *parent, *rebalance;
+    unsigned long pc;
 
     if (!tmp)
     {
@@ -398,53 +404,79 @@ void rb_erase(struct rb_node *node, struct rb_root *root)
          * so as to bypass __rb_erase_color() later on.
          */
 
-        parent = rb_parent(node);
+        pc = node->__rb_parent_color;
+        parent = __rb_parent(pc);
         __rb_change_child(node, child, parent, root);
         if (child)
         {
-            rb_set_parent_color(child, parent, RB_BLACK);
+            child->__rb_parent_color = pc;
             rebalance = NULL;
-        } else {
-            rebalance = rb_is_black(node) ? parent : NULL;
-        }
+        } else
+            rebalance = __rb_is_black(pc) ? parent : NULL;
     } else if (!child) {
         /* Still case 1, but this time the child is node->rb_left */
-        parent = rb_parent(node);
+        tmp->__rb_parent_color = pc = node->__rb_parent_color;
+        parent = __rb_parent(pc);
         __rb_change_child(node, tmp, parent, root);
-        rb_set_parent_color(tmp, parent, RB_BLACK);
         rebalance = NULL;
     } else {
-        struct rb_node *old = node, *left;
-
-        node = child;
-        while ((left = node->rb_left) != NULL)
-            node = left;
-
-        __rb_change_child(old, node, rb_parent(old), root);
-
-        child = node->rb_right;
-        parent = rb_parent(node);
-
-        if (parent == old) {
-            parent = node;
+        struct rb_node *successor = child, *child2;
+        tmp = child->rb_left;
+        if (!tmp)
+        {
+            /*
+             * Case 2: node's successor is its right child
+             *
+             *    (n)          (s)
+             *    / \          / \
+             *  (x) (s)  ->  (x) (c)
+             *        \
+             *        (c)
+             */
+            parent = child;
+            child2 = child->rb_right;
         } else {
-            parent->rb_left = child;
-
-            node->rb_right = old->rb_right;
-            rb_set_parent(old->rb_right, node);
+            /*
+             * Case 3: node's successor is leftmost under
+             * node's right child subtree
+             *
+             *    (n)          (s)
+             *    / \          / \
+             *  (x) (y)  ->  (x) (y)
+             *      /            /
+             *    (p)          (p)
+             *    /            /
+             *  (s)          (c)
+             *    \
+             *    (c)
+             */
+            do
+            {
+                parent = successor;
+                successor = tmp;
+                tmp = tmp->rb_left;
+            } while (tmp);
+            parent->rb_left = child2 = successor->rb_right;
+            successor->rb_right = child;
+            rb_set_parent(child, successor);
         }
 
-        if (child) {
-            rb_set_parent_color(child, parent, RB_BLACK);
+        successor->rb_left = tmp = node->rb_left;
+        rb_set_parent(tmp, successor);
+
+        pc = node->__rb_parent_color;
+        tmp = __rb_parent(pc);
+        __rb_change_child(node, successor, tmp, root);
+        if (child2)
+        {
+            successor->__rb_parent_color = pc;
+            rb_set_parent_color(child2, parent, RB_BLACK);
             rebalance = NULL;
         } else {
-            rebalance = rb_is_black(node) ? parent : NULL;
+            unsigned long pc2 = successor->__rb_parent_color;
+            successor->__rb_parent_color = pc;
+            rebalance = __rb_is_black(pc2) ? parent : NULL;
         }
-
-        node->__rb_parent_color = old->__rb_parent_color;
-        node->rb_left = old->rb_left;
-
-        rb_set_parent(old->rb_left, node);
     }
 
     if (rebalance)
-- 
2.12.0


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