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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/20240701205639.117194-1-visitorckw@gmail.com [1]
Link: https://lore.kernel.org/lkml/20241203202228.1274403-1-visitorckw@gmail.com [2]
Link: https://lore.kernel.org/lkml/20241209134226.1939163-1-visitorckw@gmail.com [3]
Link: https://lore.kernel.org/lkml/20241209145728.1975311-1-visitorckw@gmail.com [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/20250106170104.3137845-1-visitorckw@gmail.com
Link: https://lore.kernel.org/lkml/20240701205639.117194-1-visitorckw@gmail.com [1]
Link: https://lore.kernel.org/lkml/20241203202228.1274403-1-visitorckw@gmail.com [2]
Link: https://lore.kernel.org/lkml/20241209134226.1939163-1-visitorckw@gmail.com [3]
Link: https://lore.kernel.org/lkml/20241209145728.1975311-1-visitorckw@gmail.com [4]
Link: https://lkml.kernel.org/r/20250106170104.3137845-2-visitorckw@gmail.com
Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
Cc: Ching-Chun (Jim) Huang <jserv@ccns.ncku.edu.tw>
Cc: <chuang@cs.nycu.edu.tw>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>

authored by

Kuan-Wei Chiu and committed by
Andrew Morton
4e0a15f8 bb2de9b0

+7
+7
lib/sort.c
··· 200 200 * copy (e.g. fix up pointers or auxiliary data), but the built-in swap 201 201 * avoids a slow retpoline and so is significantly faster. 202 202 * 203 + * The comparison function must adhere to specific mathematical 204 + * properties to ensure correct and stable sorting: 205 + * - Antisymmetry: cmp_func(a, b) must return the opposite sign of 206 + * cmp_func(b, a). 207 + * - Transitivity: if cmp_func(a, b) <= 0 and cmp_func(b, c) <= 0, then 208 + * cmp_func(a, c) <= 0. 209 + * 203 210 * Sorting time is O(n log n) both on average and worst-case. While 204 211 * quicksort is slightly faster on average, it suffers from exploitable 205 212 * O(n*n) worst-case behavior and extra memory requirements that make