[PATCH v2] platform/chrome: sensorhub: Implement quickselect for median calculation

[Kuan-Wei Chiu]

The cros_ec_sensor_ring_median function currently uses an inefficient
sorting algorithm (> O(n)) to find the median of an array. This patch
replaces the sorting approach with the quickselect algorithm, which
achieves an average time complexity of O(n).

The algorithm employs the median-of-three rule to select the pivot,
mitigating worst-case scenarios and reducing the expected number of
necessary comparisons. This strategy enhances the algorithm's
efficiency and ensures a more balanced partitioning.

In the worst case, the runtime of quickselect could regress to O(n^2).
To address this, alternative algorithms like median-of-medians that
can guarantee O(n) even in the worst case. However, due to higher
overhead and increased complexity of implementation, quickselect
remains a pragmatic choice for our use case.

Signed-off-by: Kuan-Wei Chiu <visitorckw@xxxxxxxxx>
---
v1 -> v2:
 * Separate patch series into two patches.
 * Modify the microbenchmark[1] to set n=64 and run 10000 repeated times.
 * Enhance coding style and comments.

[1]:
static void init_array(s64 *arr, size_t length, s64 seed)
{
	for (int i = 0; i < length; i++) {
		seed = (seed * 725861) % 6599;
		arr[i] = seed;
	}
}

static int quickselect_test(void)
{
	s64 *arr;
	s64 median_old, median_new;
	ktime_t start, end;
	s64 delta, time_old = 0, time_new = 0;
	const size_t array_length = 64;
	const size_t round = 10000;

	arr = kmalloc(array_length * sizeof(s64), GFP_KERNEL);
	if (!arr)
		return -ENOMEM;

	for(size_t i = 0; i < round; i++) {
		init_array(arr, array_length, i + 1);
		start = ktime_get();
		median_old = cros_ec_sensor_ring_median(arr, array_length);
		end = ktime_get();
		delta = ktime_us_delta(end, start);
		time_old += delta;

		init_array(arr, array_length, i + 1);
		start = ktime_get();
		median_new = cros_ec_sensor_ring_median_new(arr, array_length);
		end = ktime_get();
		delta = ktime_us_delta(end, start);
		time_new += delta;

		if(median_old != median_new)
			return 1;
	}

	printk(KERN_ALERT "Total time of original function: %lld\n", time_old);
	printk(KERN_ALERT "Total time of new function: %lld\n", time_new);

	kfree(arr);

	/* return 0 on success */
	return 0;
}

/* Result:
 * Total time of original function: 157561
 * Total time of new function: 1480
 */

 .../platform/chrome/cros_ec_sensorhub_ring.c  | 62 ++++++++++++++-----
 1 file changed, 45 insertions(+), 17 deletions(-)

diff --git a/drivers/platform/chrome/cros_ec_sensorhub_ring.c b/drivers/platform/chrome/cros_ec_sensorhub_ring.c
index 9e17f7483ca0..1205219515d6 100644
--- a/drivers/platform/chrome/cros_ec_sensorhub_ring.c
+++ b/drivers/platform/chrome/cros_ec_sensorhub_ring.c
@@ -133,33 +133,61 @@ int cros_ec_sensorhub_ring_fifo_enable(struct cros_ec_sensorhub *sensorhub,
 	return ret;
 }
 
-static int cros_ec_sensor_ring_median_cmp(const void *pv1, const void *pv2)
+static void cros_ec_sensor_ring_median_swap(s64 *a, s64 *b)
 {
-	s64 v1 = *(s64 *)pv1;
-	s64 v2 = *(s64 *)pv2;
-
-	if (v1 > v2)
-		return 1;
-	else if (v1 < v2)
-		return -1;
-	else
-		return 0;
+	s64 tmp = *a;
+	*a = *b;
+	*b = tmp;
 }
 
 /*
  * cros_ec_sensor_ring_median: Gets median of an array of numbers
  *
- * For now it's implemented using an inefficient > O(n) sort then return
- * the middle element. A more optimal method would be something like
- * quickselect, but given that n = 64 we can probably live with it in the
- * name of clarity.
+ * It's implemented using the quickselect algorithm, which achieves an
+ * average time complexity of O(n) the middle element. In the worst case,
+ * the runtime of quickselect could regress to O(n^2). To mitigate this,
+ * algorithms like median-of-medians exist, which can guarantee O(n) even
+ * in the worst case. However, these algorithms come with a higher
+ * overhead and are more complex to implement, making quickselect a
+ * pragmatic choice for our use case.
  *
- * Warning: the input array gets modified (sorted)!
+ * Warning: the input array gets modified!
  */
 static s64 cros_ec_sensor_ring_median(s64 *array, size_t length)
 {
-	sort(array, length, sizeof(s64), cros_ec_sensor_ring_median_cmp, NULL);
-	return array[length / 2];
+	int lo = 0;
+	int hi = length - 1;
+
+	while (lo <= hi) {
+		int mid = lo + (hi - lo) / 2;
+		int pivot, i;
+
+		if (array[lo] > array[mid])
+			cros_ec_sensor_ring_median_swap(&array[lo], &array[mid]);
+		if (array[lo] > array[hi])
+			cros_ec_sensor_ring_median_swap(&array[lo], &array[hi]);
+		if (array[mid] < array[hi])
+			cros_ec_sensor_ring_median_swap(&array[mid], &array[hi]);
+
+		pivot = array[hi];
+		i = lo - 1;
+
+		for (int j = lo; j < hi; j++)
+			if (array[j] < pivot)
+				cros_ec_sensor_ring_median_swap(&array[++i], &array[j]);
+
+		/* The pivot's index corresponds to i+1. */
+		cros_ec_sensor_ring_median_swap(&array[i + 1], &array[hi]);
+		if (i + 1 == length / 2)
+			return array[i + 1];
+		if (i + 1 > length / 2)
+			hi = i;
+		else
+			lo = i + 2;
+	}
+
+	/* Should never reach here. */
+	return -1;
 }
 
 /*
-- 
2.25.1