lib/sort: clarify comparison function requirements in sort_r()

Patch series "lib: clarify comparison function requirements", v2.

Add a detailed explanation in the sort_r/list_sort kernel doc comment
specifying that the comparison function must satisfy antisymmetry and
transitivity.  These properties are essential for the sorting algorithm to
produce correct results.

Issues have arisen in the past [1][2][3][4] where comparison functions
violated the transitivity property, causing sorting algorithms to fail to
correctly order elements.  While these requirements may seem
straightforward, they are commonly misunderstood or overlooked, leading to
bugs.  Highlighting these properties in the documentation will help
prevent such mistakes in the future.

Link: https://lore.kernel.org/lkml/[email protected] [1]
Link: https://lore.kernel.org/lkml/[email protected] [2]
Link: https://lore.kernel.org/lkml/[email protected] [3]
Link: https://lore.kernel.org/lkml/[email protected] [4]


This patch (of 2):

Add a detailed explanation in the sort_r() kernel doc comment specifying
that the comparison function must satisfy antisymmetry and transitivity. 
These properties are essential for the sorting algorithm to produce
correct results.

Issues have arisen in the past [1][2][3][4] where comparison functions
violated the transitivity property, causing sorting algorithms to fail to
correctly order elements.  While these requirements may seem
straightforward, they are commonly misunderstood or overlooked, leading to
bugs.  Highlighting these properties in the documentation will help
prevent such mistakes in the future.

Link: https://lkml.kernel.org/r/[email protected]
Link: https://lore.kernel.org/lkml/[email protected] [1]
Link: https://lore.kernel.org/lkml/[email protected] [2]
Link: https://lore.kernel.org/lkml/[email protected] [3]
Link: https://lore.kernel.org/lkml/[email protected] [4]
Link: https://lkml.kernel.org/r/[email protected]
Signed-off-by: Kuan-Wei Chiu <[email protected]>
Cc: Ching-Chun (Jim) Huang <[email protected]>
Cc: <[email protected]>
Signed-off-by: Andrew Morton <[email protected]>

lib/sort.c

@@ -200,6 +200,13 @@ static size_t parent(size_t i, unsigned int lsbit, size_t size)
  * copy (e.g. fix up pointers or auxiliary data), but the built-in swap
  * avoids a slow retpoline and so is significantly faster.
  *
+ * The comparison function must adhere to specific mathematical
+ * properties to ensure correct and stable sorting:
+ * - Antisymmetry: cmp_func(a, b) must return the opposite sign of
+ * cmp_func(b, a).
+ * - Transitivity: if cmp_func(a, b) <= 0 and cmp_func(b, c) <= 0, then
+ * cmp_func(a, c) <= 0.
+ *
  * Sorting time is O(n log n) both on average and worst-case. While
  * quicksort is slightly faster on average, it suffers from exploitable
  * O(n*n) worst-case behavior and extra memory requirements that make