[PATCH v2 02/10] lib min_heap: Optimize min heap by prescaling counters for better performance

Kuan-Wei Chiu
2024-10-20T04:02:32Z

Improve the efficiency of the min heap by prescaling counters,
eliminating the need to repeatedly compute 'index * element_size' when
accessing elements. By doing so, we avoid the overhead associated with
recalculating the byte offset for each heap operation.

However, with prescaling, the calculation for the parent element's
location is no longer as simple as '(i - 1) / 2'. To address this, we
copy the parent function from 'lib/sort.c', which calculates the parent
offset in a branchless manner without using any division instructions.

This optimization should result in a more efficient heap implementation
by reducing the computational overhead of finding parent and child
offsets.

Signed-off-by: Kuan-Wei Chiu <visitorckw@gmail.com>
---
Tested with test_min_heap module.

include/linux/min_heap.h | 73 +++++++++++++++++++++++++++-------------
1 file changed, 49 insertions(+), 24 deletions(-)

diff --git a/include/linux/min_heap.h b/include/linux/min_heap.h
index 0abb21173979..41b092a14238 100644
--- a/include/linux/min_heap.h
+++ b/include/linux/min_heap.h
@@ -38,6 +38,32 @@ struct min_heap_callbacks {
void (*swp)(void *lhs, void *rhs, void *args);
};

+/**
+ * parent - given the offset of the child, find the offset of the parent.
+ * @i: the offset of the heap element whose parent is sought. Non-zero.
+ * @lsbit: a precomputed 1-bit mask, equal to "size & -size"
+ * @size: size of each element
+ *
+ * In terms of array indexes, the parent of element j = @i/@size is simply
+ * (j-1)/2. But when working in byte offsets, we can't use implicit
+ * truncation of integer divides.
+ *
+ * Fortunately, we only need one bit of the quotient, not the full divide.
+ * @size has a least significant bit. That bit will be clear if @i is
+ * an even multiple of @size, and set if it's an odd multiple.
+ *
+ * Logically, we're doing "if (i & lsbit) i -= size;", but since the
+ * branch is unpredictable, it's done with a bit of clever branch-free
+ * code instead.
+ */
+__attribute_const__ __always_inline
+static size_t parent(size_t i, unsigned int lsbit, size_t size)
+{
+ i -= size;
+ i -= size & -(i & lsbit);
+ return i / 2;
+}
+
/* Initialize a min-heap. */
static __always_inline
void __min_heap_init_inline(min_heap_char *heap, void *data, int size)
@@ -78,33 +104,30 @@ static __always_inline
void __min_heap_sift_down_inline(min_heap_char *heap, int pos, size_t elem_size,
const struct min_heap_callbacks *func, void *args)
{
- void *left, *right;
+ const unsigned long lsbit = elem_size & -elem_size;
void *data = heap->data;
- void *root = data + pos * elem_size;
- int i = pos, j;
+ /* pre-scale counters for performance */
+ size_t a = pos * elem_size;
+ size_t b, c, d;
+ size_t n = heap->nr * elem_size;

/* Find the sift-down path all the way to the leaves. */
- for (;;) {
- if (i * 2 + 2 >= heap->nr)
- break;
- left = data + (i * 2 + 1) * elem_size;
- right = data + (i * 2 + 2) * elem_size;
- i = func->less(left, right, args) ? i * 2 + 1 : i * 2 + 2;
- }
+ for (b = a; c = 2 * b + elem_size, (d = c + elem_size) < n;)
+ b = func->less(data + c, data + d, args) ? c : d;

/* Special case for the last leaf with no sibling. */
- if (i * 2 + 2 == heap->nr)
- i = i * 2 + 1;
+ if (d == n)
+ b = c;

/* Backtrack to the correct location. */
- while (i != pos && func->less(root, data + i * elem_size, args))
- i = (i - 1) / 2;
+ while (b != a && func->less(data + a, data + b, args))
+ b = parent(b, lsbit, elem_size);

/* Shift the element into its correct place. */
- j = i;
- while (i != pos) {
- i = (i - 1) / 2;
- func->swp(data + i * elem_size, data + j * elem_size, args);
+ c = b;
+ while (b != a) {
+ b = parent(b, lsbit, elem_size);
+ func->swp(data + b, data + c, args);
}
}

@@ -117,15 +140,17 @@ static __always_inline
void __min_heap_sift_up_inline(min_heap_char *heap, size_t elem_size, size_t idx,
const struct min_heap_callbacks *func, void *args)
{
+ const unsigned long lsbit = elem_size & -elem_size;
void *data = heap->data;
- size_t parent;
+ /* pre-scale counters for performance */
+ size_t a = idx * elem_size, b;

- while (idx) {
- parent = (idx - 1) / 2;
- if (func->less(data + parent * elem_size, data + idx * elem_size, args))
+ while (a) {
+ b = parent(a, lsbit, elem_size);
+ if (func->less(data + b, data + a, args))
break;
- func->swp(data + parent * elem_size, data + idx * elem_size, args);
- idx = parent;
+ func->swp(data + a, data + b, args);
+ a = b;
}
}

--
2.34.1