[PATCH 7/7] platform/chrome: Implement quickselect for median calculation
From: Kuan-Wei Chiu
Date: Thu Nov 09 2023 - 13:55:35 EST
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, quickselect remains a pragmatic
choice for our use case.
Signed-off-by: Kuan-Wei Chiu <visitorckw@xxxxxxxxx>
---
.../platform/chrome/cros_ec_sensorhub_ring.c | 71 ++++++++++++++-----
1 file changed, 54 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..4ac718be38b0 100644
--- a/drivers/platform/chrome/cros_ec_sensorhub_ring.c
+++ b/drivers/platform/chrome/cros_ec_sensorhub_ring.c
@@ -133,33 +133,70 @@ 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];
+ const int k = length / 2;
+ int lo = 0;
+ int hi = length - 1;
+
+ while (lo <= hi) {
+ int mid = lo + (hi - lo) / 2;
+ int pivot, pivot_index;
+ int i = lo - 1;
+
+ /* We employ the median-of-three rule to choose the pivot, mitigating
+ * worst-case scenarios such as already sorted arrays and aiming to reduce
+ * the expected number of necessary comparisons. This strategy enhances the
+ * algorithm's performance and ensures a more balanced partitioning.
+ */
+ 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];
+
+ for (int j = lo; j < hi; j++)
+ if (array[j] < pivot)
+ cros_ec_sensor_ring_median_swap(&array[++i],
+ &array[j]);
+
+ cros_ec_sensor_ring_median_swap(&array[i + 1], &array[hi]);
+ pivot_index = i + 1;
+ if (pivot_index == k)
+ return array[pivot_index];
+ if (pivot_index > k)
+ hi = pivot_index - 1;
+ else
+ lo = pivot_index + 1;
+ }
+
+ /* Should never reach here. */
+ return -1;
}
/*
--
2.25.1