lib min_heap: optimize number of comparisons in min_heapify()

Optimize the min_heapify() function, resulting in a significant reduction
of approximately 50% in the number of comparisons for large random inputs,
while maintaining identical results.

The current implementation performs two comparisons per level to identify
the minimum among three elements. In contrast, the proposed bottom-up
variation uses only one comparison per level to assess two children until
reaching the leaves. Then, it sifts up until the correct position is
determined.

Typically, the process of sifting down proceeds to the leaf level,
resulting in O(1) secondary comparisons instead of log2(n). This
optimization significantly reduces the number of costly indirect function
calls and improves overall performance.

Link: https://lkml.kernel.org/r/20240110081213.2289636-3-visitorckw@gmail.com
Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
Acked-by: Ian Rogers <irogers@google.com>
Cc: Adrian Hunter <adrian.hunter@intel.com>
Cc: Alexander Shishkin <alexander.shishkin@linux.intel.com>
Cc: Arnaldo Carvalho de Melo <acme@kernel.org>
Cc: Ingo Molnar <mingo@redhat.com>
Cc: Jiri Olsa <jolsa@kernel.org>
Cc: Mark Rutland <mark.rutland@arm.com>
Cc: Namhyung Kim <namhyung@kernel.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>

lib min_heap: optimize number of calls to min_heapify()

Patch series "lib min_heap: Min heap optimizations".

The purpose of this patch series is to enhance the existing min heap
implementation. The optimization focuses on both the heap construction
process and the number of comparisons made during the heapify operation.


This patch (of 2):

Improve the heap construction process by reducing unnecessary heapify
operations. Specifically, adjust the starting condition from n / 2 to n /
2 - 1 in the loop that iterates over all non-leaf elements.

Link: https://lkml.kernel.org/r/20240110081213.2289636-1-visitorckw@gmail.com
Link: https://lkml.kernel.org/r/20240110081213.2289636-2-visitorckw@gmail.com
Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
Acked-by: Ian Rogers <irogers@google.com>
Cc: Adrian Hunter <adrian.hunter@intel.com>
Cc: Alexander Shishkin <alexander.shishkin@linux.intel.com>
Cc: Arnaldo Carvalho de Melo <acme@kernel.org>
Cc: Ingo Molnar <mingo@redhat.com>
Cc: Jiri Olsa <jolsa@kernel.org>
Cc: Mark Rutland <mark.rutland@arm.com>
Cc: Namhyung Kim <namhyung@kernel.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>

lib: Introduce generic min-heap

Supports push, pop and converting an array into a heap. If the sense of
the compare function is inverted then it can provide a max-heap.

Based-on-work-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Signed-off-by: Ian Rogers <irogers@google.com>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Signed-off-by: Ingo Molnar <mingo@kernel.org>
Link: https://lkml.kernel.org/r/20200214075133.181299-3-irogers@google.com