[PATCH v2 11/20] rbtree: adjust node color in __rb_erase_color() only when necessary

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

In __rb_erase_color(), we were always setting a node to black after
exiting the main loop.  And in one case, after fixing up the tree to
satisfy all rbtree invariants, we were setting the current node to root
just to guarantee a loop exit, at which point the root would be set to
black.  However this is not necessary, as the root of an rbtree is already
known to be black.  The only case where the color flip is required is when
we exit the loop due to the current node being red, and it's easiest to
just do the flip at that point instead of doing it after the loop.

[adrian.hunter@intel.com: perf tools: fix build for another rbtree.c change]
Signed-off-by: Michel Lespinasse <walken@google.com>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Acked-by: David Woodhouse <David.Woodhouse@intel.com>
Cc: Rik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Daniel Santos <daniel.santos@pobox.com>
Cc: Jens Axboe <axboe@kernel.dk>
Cc: "Eric W. Biederman" <ebiederm@xmission.com>
Signed-off-by: Adrian Hunter <adrian.hunter@intel.com>
Cc: Alexander Shishkin <alexander.shishkin@intel.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
[Linux commit d6ff1273928ebf15466a85b7e1810cd00e72998b]

Ported only rbtree.c to Xen.

Signed-off-by: Praveen Kumar <kpraveen.lkml@gmail.com>
---
 xen/common/rbtree.c | 22 ++++++++++++++++------
 1 file changed, 16 insertions(+), 6 deletions(-)

diff --git a/xen/common/rbtree.c b/xen/common/rbtree.c
index d44fa22df5..2d5da9ea28 100644
--- a/xen/common/rbtree.c
+++ b/xen/common/rbtree.c
@@ -261,10 +261,24 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
 {
     struct rb_node *other;
 
-    while ((!node || rb_is_black(node)) && node != root->rb_node)
+    while (true)
     {
-        if (parent->rb_left == node)
+        /*
+         * Loop invariant: all leaf paths going through node have a
+         * black node count that is 1 lower than other leaf paths.
+         *
+         * If node is red, we can flip it to black to adjust.
+         * If node is the root, all leaf paths go through it.
+         * Otherwise, we need to adjust the tree through color flips
+         * and tree rotations as per one of the 4 cases below.
+         */
+        if (node && rb_is_red(node))
         {
+            rb_set_black(node);
+            break;
+        } else if (!parent) {
+            break;
+        } else if (parent->rb_left == node) {
             other = parent->rb_right;
             if (rb_is_red(other))
             {
@@ -293,7 +307,6 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
                 rb_set_black(parent);
                 rb_set_black(other->rb_right);
                 __rb_rotate_left(parent, root);
-                node = root->rb_node;
                 break;
             }
         }
@@ -327,13 +340,10 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
                 rb_set_black(parent);
                 rb_set_black(other->rb_left);
                 __rb_rotate_right(parent, root);
-                node = root->rb_node;
                 break;
             }
         }
     }
-    if (node)
-        rb_set_black(node);
 }
 
 void rb_erase(struct rb_node *node, struct rb_root *root)
-- 
2.12.0


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