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new 690ae987 NUMBERS-206: Add selection for int arrays
690ae987 is described below
commit 690ae98726ebde34288a9a1dddf31633d821be63
Author: Alex Herbert <aherb...@apache.org>
AuthorDate: Mon Jun 17 17:27:42 2024 +0100
NUMBERS-206: Add selection for int arrays
---
.../apache/commons/numbers/arrays/QuickSelect.java | 1261 ++++++++++++++++++++
.../apache/commons/numbers/arrays/Selection.java | 76 ++
.../org/apache/commons/numbers/arrays/Sorting.java | 228 ++++
.../commons/numbers/arrays/SelectionTest.java | 817 +++++++++++++
.../apache/commons/numbers/arrays/SortingTest.java | 340 +++++-
.../examples/jmh/arrays/SelectionPerformance.java | 120 +-
.../checkstyle/checkstyle-suppressions.xml | 1 +
7 files changed, 2828 insertions(+), 15 deletions(-)
diff --git
a/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/QuickSelect.java
b/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/QuickSelect.java
index f0b90795..f5ca7e48 100644
---
a/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/QuickSelect.java
+++
b/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/QuickSelect.java
@@ -1464,6 +1464,1267 @@ final class QuickSelect {
return lower;
}
+ /**
+ * Partition the elements between {@code ka} and {@code kb} using a heap
select
+ * algorithm. It is assumed {@code left <= ka <= kb <= right}.
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param ka Lower index to select.
+ * @param kb Upper index to select.
+ */
+ static void heapSelect(int[] a, int left, int right, int ka, int kb) {
+ if (right <= left) {
+ return;
+ }
+ // Use the smallest heap
+ if (kb - left < right - ka) {
+ heapSelectLeft(a, left, right, ka, kb);
+ } else {
+ heapSelectRight(a, left, right, ka, kb);
+ }
+ }
+
+ /**
+ * Partition the elements between {@code ka} and {@code kb} using a heap
select
+ * algorithm. It is assumed {@code left <= ka <= kb <= right}.
+ *
+ * <p>For best performance this should be called with {@code k} in the
lower
+ * half of the range.
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param ka Lower index to select.
+ * @param kb Upper index to select.
+ */
+ static void heapSelectLeft(int[] a, int left, int right, int ka, int kb) {
+ // Create a max heap in-place in [left, k], rooted at a[left] = max
+ // |l|-max-heap-|k|--------------|
+ // Build the heap using Floyd's heap-construction algorithm for heap
size n.
+ // Start at parent of the last element in the heap (k),
+ // i.e. start = parent(n-1) : parent(c) = floor((c - 1) / 2) : c = k -
left
+ int end = kb + 1;
+ for (int p = left + ((kb - left - 1) >> 1); p >= left; p--) {
+ maxHeapSiftDown(a, a[p], p, left, end);
+ }
+ // Scan the remaining data and insert
+ // Mitigate worst case performance on descending data by backward sweep
+ int max = a[left];
+ for (int i = right + 1; --i > kb;) {
+ final int v = a[i];
+ if (v < max) {
+ a[i] = max;
+ maxHeapSiftDown(a, v, left, left, end);
+ max = a[left];
+ }
+ }
+ // Partition [ka, kb]
+ // |l|-max-heap-|k|--------------|
+ // | <-swap-> | then sift down reduced size heap
+ // Avoid sifting heap of size 1
+ final int last = Math.max(left, ka - 1);
+ while (--end > last) {
+ maxHeapSiftDown(a, a[end], left, left, end);
+ a[end] = max;
+ max = a[left];
+ }
+ }
+
+ /**
+ * Sift the element down the max heap.
+ *
+ * <p>Assumes {@code root <= p < end}, i.e. the max heap is above root.
+ *
+ * @param a Heap data.
+ * @param v Value to sift.
+ * @param p Start position.
+ * @param root Root of the heap.
+ * @param end End of the heap (exclusive).
+ */
+ private static void maxHeapSiftDown(int[] a, int v, int p, int root, int
end) {
+ // child2 = root + 2 * (parent - root) + 2
+ // = 2 * parent - root + 2
+ while (true) {
+ // Right child
+ int c = (p << 1) - root + 2;
+ if (c > end) {
+ // No left child
+ break;
+ }
+ // Use the left child if right doesn't exist, or it is greater
+ if (c == end || a[c] < a[c - 1]) {
+ --c;
+ }
+ if (v >= a[c]) {
+ // Parent greater than largest child - done
+ break;
+ }
+ // Swap and descend
+ a[p] = a[c];
+ p = c;
+ }
+ a[p] = v;
+ }
+
+ /**
+ * Partition the elements between {@code ka} and {@code kb} using a heap
select
+ * algorithm. It is assumed {@code left <= ka <= kb <= right}.
+ *
+ * <p>For best performance this should be called with {@code k} in the
upper
+ * half of the range.
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param ka Lower index to select.
+ * @param kb Upper index to select.
+ */
+ static void heapSelectRight(int[] a, int left, int right, int ka, int kb) {
+ // Create a min heap in-place in [k, right], rooted at a[right] = min
+ // |--------------|k|-min-heap-|r|
+ // Build the heap using Floyd's heap-construction algorithm for heap
size n.
+ // Start at parent of the last element in the heap (k),
+ // i.e. start = parent(n-1) : parent(c) = floor((c - 1) / 2) : c =
right - k
+ int end = ka - 1;
+ for (int p = right - ((right - ka - 1) >> 1); p <= right; p++) {
+ minHeapSiftDown(a, a[p], p, right, end);
+ }
+ // Scan the remaining data and insert
+ // Mitigate worst case performance on descending data by backward sweep
+ int min = a[right];
+ for (int i = left - 1; ++i < ka;) {
+ final int v = a[i];
+ if (v > min) {
+ a[i] = min;
+ minHeapSiftDown(a, v, right, right, end);
+ min = a[right];
+ }
+ }
+ // Partition [ka, kb]
+ // |--------------|k|-min-heap-|r|
+ // | <-swap-> | then sift down reduced size heap
+ // Avoid sifting heap of size 1
+ final int last = Math.min(right, kb + 1);
+ while (++end < last) {
+ minHeapSiftDown(a, a[end], right, right, end);
+ a[end] = min;
+ min = a[right];
+ }
+ }
+
+ /**
+ * Sift the element down the min heap.
+ *
+ * <p>Assumes {@code root >= p > end}, i.e. the max heap is below root.
+ *
+ * @param a Heap data.
+ * @param v Value to sift.
+ * @param p Start position.
+ * @param root Root of the heap.
+ * @param end End of the heap (exclusive).
+ */
+ private static void minHeapSiftDown(int[] a, int v, int p, int root, int
end) {
+ // child2 = root - 2 * (root - parent) - 2
+ // = 2 * parent - root - 2
+ while (true) {
+ // Right child
+ int c = (p << 1) - root - 2;
+ if (c < end) {
+ // No left child
+ break;
+ }
+ // Use the left child if right doesn't exist, or it is less
+ if (c == end || a[c] > a[c + 1]) {
+ ++c;
+ }
+ if (v <= a[c]) {
+ // Parent less than smallest child - done
+ break;
+ }
+ // Swap and descend
+ a[p] = a[c];
+ p = c;
+ }
+ a[p] = v;
+ }
+
+ /**
+ * Partition the elements between {@code ka} and {@code kb} using a sort
select
+ * algorithm. It is assumed {@code left <= ka <= kb <= right}.
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param ka Lower index to select.
+ * @param kb Upper index to select.
+ */
+ static void sortSelect(int[] a, int left, int right, int ka, int kb) {
+ // Combine the test for right <= left with
+ // avoiding the overhead of sort select on tiny data.
+ if (right - left <= MIN_SORTSELECT_SIZE) {
+ Sorting.sort(a, left, right);
+ return;
+ }
+ // Sort the smallest side
+ if (kb - left < right - ka) {
+ sortSelectLeft(a, left, right, kb);
+ } else {
+ sortSelectRight(a, left, right, ka);
+ }
+ }
+
+ /**
+ * Partition the minimum {@code n} elements below {@code k} where
+ * {@code n = k - left + 1}. Uses an insertion sort algorithm.
+ *
+ * <p>Works with any {@code k} in the range {@code left <= k <= right}
+ * and performs a full sort of the range below {@code k}.
+ *
+ * <p>For best performance this should be called with
+ * {@code k - left < right - k}, i.e.
+ * to partition a value in the lower half of the range.
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param k Index to select.
+ */
+ static void sortSelectLeft(int[] a, int left, int right, int k) {
+ // Sort
+ for (int i = left; ++i <= k;) {
+ final int v = a[i];
+ // Move preceding higher elements above (if required)
+ if (v < a[i - 1]) {
+ int j = i;
+ while (--j >= left && v < a[j]) {
+ a[j + 1] = a[j];
+ }
+ a[j + 1] = v;
+ }
+ }
+ // Scan the remaining data and insert
+ // Mitigate worst case performance on descending data by backward sweep
+ int m = a[k];
+ for (int i = right + 1; --i > k;) {
+ final int v = a[i];
+ if (v < m) {
+ a[i] = m;
+ int j = k;
+ while (--j >= left && v < a[j]) {
+ a[j + 1] = a[j];
+ }
+ a[j + 1] = v;
+ m = a[k];
+ }
+ }
+ }
+
+ /**
+ * Partition the maximum {@code n} elements above {@code k} where
+ * {@code n = right - k + 1}. Uses an insertion sort algorithm.
+ *
+ * <p>Works with any {@code k} in the range {@code left <= k <= right}
+ * and can be used to perform a full sort of the range above {@code k}.
+ *
+ * <p>For best performance this should be called with
+ * {@code k - left > right - k}, i.e.
+ * to partition a value in the upper half of the range.
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param k Index to select.
+ */
+ static void sortSelectRight(int[] a, int left, int right, int k) {
+ // Sort
+ for (int i = right; --i >= k;) {
+ final int v = a[i];
+ // Move succeeding lower elements below (if required)
+ if (v > a[i + 1]) {
+ int j = i;
+ while (++j <= right && v > a[j]) {
+ a[j - 1] = a[j];
+ }
+ a[j - 1] = v;
+ }
+ }
+ // Scan the remaining data and insert
+ // Mitigate worst case performance on descending data by backward sweep
+ int m = a[k];
+ for (int i = left - 1; ++i < k;) {
+ final int v = a[i];
+ if (v > m) {
+ a[i] = m;
+ int j = k;
+ while (++j <= right && v > a[j]) {
+ a[j - 1] = a[j];
+ }
+ a[j - 1] = v;
+ m = a[k];
+ }
+ }
+ }
+
+ /**
+ * Partition the array such that index {@code k} corresponds to its
correctly
+ * sorted value in the equivalent fully sorted array.
+ *
+ * <p>Assumes {@code k} is a valid index into [left, right].
+ *
+ * @param a Values.
+ * @param left Lower bound of data (inclusive).
+ * @param right Upper bound of data (inclusive).
+ * @param k Index.
+ */
+ static void select(int[] a, int left, int right, int k) {
+ quickSelectAdaptive(a, left, right, k, k, new int[1],
MODE_FR_SAMPLING);
+ }
+
+ /**
+ * Partition the array such that indices {@code k} correspond to their
correctly
+ * sorted value in the equivalent fully sorted array.
+ *
+ * <p>The count of the number of used indices is returned. If the keys are
sorted in-place,
+ * the count is returned as a negative.
+ *
+ * @param a Values.
+ * @param left Lower bound of data (inclusive).
+ * @param right Upper bound of data (inclusive).
+ * @param k Indices (may be destructively modified).
+ * @param n Count of indices.
+ * @throws IndexOutOfBoundsException if any index {@code k} is not within
the
+ * sub-range {@code [left, right]}
+ */
+ static void select(int[] a, int left, int right, int[] k, int n) {
+ if (n == 1) {
+ quickSelectAdaptive(a, left, right, k[0], k[0], new int[1],
MODE_FR_SAMPLING);
+ return;
+ }
+
+ // Interval creation validates the indices are in [left, right]
+ final UpdatingInterval keys =
IndexSupport.createUpdatingInterval(left, right, k, n);
+
+ // Note: If the keys are not separated then they are effectively a
single key.
+ // Any split of keys separated by the sort select size
+ // will be finished on the next iteration.
+ final int k1 = keys.left();
+ final int kn = keys.right();
+ if (kn - k1 < DP_SORTSELECT_SIZE) {
+ quickSelectAdaptive(a, left, right, k1, kn, new int[1],
MODE_FR_SAMPLING);
+ } else {
+ // Dual-pivot mode with small range sort length configured using
index density
+ dualPivotQuickSelect(a, left, right, keys, dualPivotFlags(left,
right, k1, kn));
+ }
+ }
+
+ /**
+ * Partition the array such that indices {@code k} correspond to their
+ * correctly sorted value in the equivalent fully sorted array.
+ *
+ * <p>For all indices {@code [ka, kb]} and any index {@code i}:
+ *
+ * <pre>{@code
+ * data[i < ka] <= data[ka] <= data[kb] <= data[kb < i]
+ * }</pre>
+ *
+ * <p>This function accepts indices {@code [ka, kb]} that define the
+ * range of indices to partition. It is expected that the range is small.
+ *
+ * <p>The {@code flags} are used to control the sampling mode and adaption
of
+ * the index within the sample.
+ *
+ * <p>Returns the bounds containing {@code [ka, kb]}. These may be
lower/higher
+ * than the keys if equal values are present in the data.
+ *
+ * @param a Values.
+ * @param left Lower bound of data (inclusive, assumed to be strictly
positive).
+ * @param right Upper bound of data (inclusive, assumed to be strictly
positive).
+ * @param ka First key of interest.
+ * @param kb Last key of interest.
+ * @param bounds Upper bound of the range containing {@code [ka, kb]}
(inclusive).
+ * @param flags Adaption flags.
+ * @return Lower bound of the range containing {@code [ka, kb]}
(inclusive).
+ */
+ static int quickSelectAdaptive(int[] a, int left, int right, int ka, int
kb,
+ int[] bounds, int flags) {
+ int l = left;
+ int r = right;
+ int m = flags;
+ while (true) {
+ // Select when ka and kb are close to the same end
+ // |l|-----|ka|kkkkkkkk|kb|------|r|
+ if (Math.min(kb - l, r - ka) < LINEAR_SORTSELECT_SIZE) {
+ sortSelect(a, l, r, ka, kb);
+ bounds[0] = kb;
+ return ka;
+ }
+
+ // Only target ka; kb is assumed to be close
+ int p0;
+ final int n = r - l;
+ // f in [0, 1]
+ final double f = (double) (ka - l) / n;
+ // Record the larger margin (start at 1/4) to create the estimated
size.
+ // step L R
+ // far left 1/12 1/3 (use 1/4 + 1/32 + 1/64 ~ 0.328)
+ // left 1/6 1/4
+ // middle 2/9 2/9 (use 1/4 - 1/32 ~ 0.219)
+ int margin = n >> 2;
+ if (m < MODE_SAMPLING && r - l > FR_SAMPLING_SIZE) {
+ // Floyd-Rivest sample step uses the same margins
+ p0 = sampleStep(a, l, r, ka, bounds);
+ if (f <= STEP_FAR_LEFT || f >= STEP_FAR_RIGHT) {
+ margin += (n >> 5) + (n >> 6);
+ } else if (f > STEP_LEFT && f < STEP_RIGHT) {
+ margin -= n >> 5;
+ }
+ } else if (f <= STEP_LEFT) {
+ if (f <= STEP_FAR_LEFT) {
+ margin += (n >> 5) + (n >> 6);
+ p0 = repeatedStepFarLeft(a, l, r, ka, bounds, m);
+ } else {
+ p0 = repeatedStepLeft(a, l, r, ka, bounds, m);
+ }
+ } else if (f >= STEP_RIGHT) {
+ if (f >= STEP_FAR_RIGHT) {
+ margin += (n >> 5) + (n >> 6);
+ p0 = repeatedStepFarRight(a, l, r, ka, bounds, m);
+ } else {
+ p0 = repeatedStepRight(a, l, r, ka, bounds, m);
+ }
+ } else {
+ margin -= n >> 5;
+ p0 = repeatedStep(a, l, r, ka, bounds, m);
+ }
+
+ // Note: Here we expect [ka, kb] to be small and splitting is
unlikely.
+ // p0 p1
+ // |l|--|ka|kkkk|kb|--|P|-------------------|r|
+ // |l|----------------|P|--|ka|kkk|kb|------|r|
+ // |l|-----------|ka|k|P|k|kb|--------------|r|
+ final int p1 = bounds[0];
+ if (kb < p0) {
+ // Entirely on left side
+ r = p0 - 1;
+ } else if (ka > p1) {
+ // Entirely on right side
+ l = p1 + 1;
+ } else {
+ // Pivot splits [ka, kb]. Expect ends to be close to the pivot
and finish.
+ // Here we set the bounds for use after median-of-medians
pivot selection.
+ // In the event there are many equal values this allows
collecting those
+ // known to be equal together when moving around the medians
sample.
+ if (kb > p1) {
+ sortSelectLeft(a, p1 + 1, r, kb);
+ bounds[0] = kb;
+ }
+ if (ka < p0) {
+ sortSelectRight(a, l, p0 - 1, ka);
+ p0 = ka;
+ }
+ return p0;
+ }
+ // Update mode based on target partition size
+ if (r - l > n - margin) {
+ m++;
+ }
+ }
+ }
+
+ /**
+ * Partition an array slice around a pivot. Partitioning exchanges array
elements such
+ * that all elements smaller than pivot are before it and all elements
larger than
+ * pivot are after it.
+ *
+ * <p>Partitions a Floyd-Rivest sample around a pivot offset so that the
input {@code k} will
+ * fall in the smaller partition when the entire range is partitioned.
+ *
+ * <p>Assumes the range {@code r - l} is large.
+ *
+ * @param a Data array.
+ * @param l Lower bound (inclusive).
+ * @param r Upper bound (inclusive).
+ * @param k Target index.
+ * @param upper Upper bound (inclusive) of the pivot range.
+ * @return Lower bound (inclusive) of the pivot range.
+ */
+ private static int sampleStep(int[] a, int l, int r, int k, int[] upper) {
+ // Floyd-Rivest: use SELECT recursively on a sample of size S to get
an estimate
+ // for the (k-l+1)-th smallest element into a[k], biased slightly so
that the
+ // (k-l+1)-th element is expected to lie in the smaller set after
partitioning.
+ final int n = r - l + 1;
+ final int ith = k - l + 1;
+ final double z = Math.log(n);
+ // sample size = 0.5 * n^(2/3)
+ final double s = 0.5 * Math.exp(0.6666666666666666 * z);
+ final double sd = 0.5 * Math.sqrt(z * s * (n - s) / n) *
Integer.signum(ith - (n >> 1));
+ final int ll = Math.max(l, (int) (k - ith * s / n + sd));
+ final int rr = Math.min(r, (int) (k + (n - ith) * s / n + sd));
+ // Sample recursion restarts from [ll, rr]
+ final int p = quickSelectAdaptive(a, ll, rr, k, k, upper,
MODE_FR_SAMPLING);
+ return expandPartition(a, l, r, ll, rr, p, upper[0], upper);
+ }
+
+ /**
+ * Partition an array slice around a pivot. Partitioning exchanges array
elements such
+ * that all elements smaller than pivot are before it and all elements
larger than
+ * pivot are after it.
+ *
+ * <p>Assumes the range {@code r - l >= 8}; the caller is responsible for
selection on a smaller
+ * range. If using a 12th-tile for sampling then assumes {@code r - l >=
11}.
+ *
+ * <p>Uses the Chen and Dumitrescu repeated step
median-of-medians-of-medians algorithm
+ * with the median of 3 then median of 3; the final sample is placed in the
+ * 5th 9th-tile; the pivot chosen from the sample is adaptive using the
input {@code k}.
+ *
+ * <p>Given a pivot in the middle of the sample this has margins of 2/9
and 2/9.
+ *
+ * @param a Data array.
+ * @param l Lower bound (inclusive).
+ * @param r Upper bound (inclusive).
+ * @param k Target index.
+ * @param upper Upper bound (inclusive) of the pivot range.
+ * @param flags Control flags.
+ * @return Lower bound (inclusive) of the pivot range.
+ */
+ private static int repeatedStep(int[] a, int l, int r, int k, int[] upper,
int flags) {
+ // Adapted from Alexandrescu (2016), algorithm 8.
+ int fp;
+ int s;
+ int p;
+ if (flags <= MODE_SAMPLING) {
+ // Median into a 12th-tile
+ fp = (r - l + 1) / 12;
+ // Position the sample around the target k
+ s = k - mapDistance(k - l, l, r, fp);
+ p = k;
+ } else {
+ // i in tertile [3f':6f')
+ fp = (r - l + 1) / 9;
+ final int f3 = 3 * fp;
+ final int end = l + (f3 << 1);
+ for (int i = l + f3; i < end; i++) {
+ Sorting.sort3(a, i - f3, i, i + f3);
+ }
+ // 5th 9th-tile: [4f':5f')
+ s = l + (fp << 2);
+ // No adaption uses the middle to enforce strict margins
+ p = s + (flags == MODE_ADAPTION ? mapDistance(k - l, l, r, fp) :
(fp >>> 1));
+ }
+ final int e = s + fp - 1;
+ for (int i = s; i <= e; i++) {
+ Sorting.sort3(a, i - fp, i, i + fp);
+ }
+ p = quickSelectAdaptive(a, s, e, p, p, upper, MODE_FR_SAMPLING);
+ return expandPartition(a, l, r, s, e, p, upper[0], upper);
+ }
+
+ /**
+ * Partition an array slice around a pivot. Partitioning exchanges array
elements such
+ * that all elements smaller than pivot are before it and all elements
larger than
+ * pivot are after it.
+ *
+ * <p>Assumes the range {@code r - l >= 11}; the caller is responsible for
selection on a smaller
+ * range.
+ *
+ * <p>Uses the Chen and Dumitrescu repeated step
median-of-medians-of-medians algorithm
+ * with the lower median of 4 then either median of 3 with the final
sample placed in the
+ * 5th 12th-tile, or min of 3 with the final sample in the 4th 12th-tile;
+ * the pivot chosen from the sample is adaptive using the input {@code k}.
+ *
+ * <p>Given a pivot in the middle of the sample this has margins of 1/6
and 1/4.
+ *
+ * @param a Data array.
+ * @param l Lower bound (inclusive).
+ * @param r Upper bound (inclusive).
+ * @param k Target index.
+ * @param upper Upper bound (inclusive) of the pivot range.
+ * @param flags Control flags.
+ * @return Lower bound (inclusive) of the pivot range.
+ */
+ private static int repeatedStepLeft(int[] a, int l, int r, int k, int[]
upper, int flags) {
+ // Adapted from Alexandrescu (2016), algorithm 9.
+ int fp;
+ int s;
+ int p;
+ if (flags <= MODE_SAMPLING) {
+ // Median into a 12th-tile
+ fp = (r - l + 1) / 12;
+ // Position the sample around the target k
+ // Avoid bounds error due to rounding as (k-l)/(r-l) -> 1/12
+ s = Math.max(k - mapDistance(k - l, l, r, fp), l + fp);
+ p = k;
+ } else {
+ // i in 2nd quartile
+ final int f = (r - l + 1) >> 2;
+ final int f2 = f + f;
+ final int end = l + f2;
+ for (int i = l + f; i < end; i++) {
+ Sorting.lowerMedian4(a, i - f, i, i + f, i + f2);
+ }
+ // i in 5th 12th-tile
+ fp = f / 3;
+ s = l + f + fp;
+ // No adaption uses the middle to enforce strict margins
+ p = s + (flags == MODE_ADAPTION ? mapDistance(k - l, l, r, fp) :
(fp >>> 1));
+ }
+ final int e = s + fp - 1;
+ for (int i = s; i <= e; i++) {
+ Sorting.sort3(a, i - fp, i, i + fp);
+ }
+ p = quickSelectAdaptive(a, s, e, p, p, upper, MODE_FR_SAMPLING);
+ return expandPartition(a, l, r, s, e, p, upper[0], upper);
+ }
+
+ /**
+ * Partition an array slice around a pivot. Partitioning exchanges array
elements such
+ * that all elements smaller than pivot are before it and all elements
larger than
+ * pivot are after it.
+ *
+ * <p>Assumes the range {@code r - l >= 11}; the caller is responsible for
selection on a smaller
+ * range.
+ *
+ * <p>Uses the Chen and Dumitrescu repeated step
median-of-medians-of-medians algorithm
+ * with the upper median of 4 then either median of 3 with the final
sample placed in the
+ * 8th 12th-tile, or max of 3 with the final sample in the 9th 12th-tile;
+ * the pivot chosen from the sample is adaptive using the input {@code k}.
+ *
+ * <p>Given a pivot in the middle of the sample this has margins of 1/4
and 1/6.
+ *
+ * @param a Data array.
+ * @param l Lower bound (inclusive).
+ * @param r Upper bound (inclusive).
+ * @param k Target index.
+ * @param upper Upper bound (inclusive) of the pivot range.
+ * @param flags Control flags.
+ * @return Lower bound (inclusive) of the pivot range.
+ */
+ private static int repeatedStepRight(int[] a, int l, int r, int k, int[]
upper, int flags) {
+ // Mirror image repeatedStepLeft using upper median into 3rd quartile
+ int fp;
+ int e;
+ int p;
+ if (flags <= MODE_SAMPLING) {
+ // Median into a 12th-tile
+ fp = (r - l + 1) / 12;
+ // Position the sample around the target k
+ // Avoid bounds error due to rounding as (r-k)/(r-l) -> 11/12
+ e = Math.min(k + mapDistance(r - k, l, r, fp), r - fp);
+ p = k;
+ } else {
+ // i in 3rd quartile
+ final int f = (r - l + 1) >> 2;
+ final int f2 = f + f;
+ final int end = r - f2;
+ for (int i = r - f; i > end; i--) {
+ Sorting.upperMedian4(a, i - f2, i - f, i, i + f);
+ }
+ // i in 8th 12th-tile
+ fp = f / 3;
+ e = r - f - fp;
+ // No adaption uses the middle to enforce strict margins
+ p = e - (flags == MODE_ADAPTION ? mapDistance(r - k, l, r, fp) :
(fp >>> 1));
+ }
+ final int s = e - fp + 1;
+ for (int i = s; i <= e; i++) {
+ Sorting.sort3(a, i - fp, i, i + fp);
+ }
+ p = quickSelectAdaptive(a, s, e, p, p, upper, MODE_FR_SAMPLING);
+ return expandPartition(a, l, r, s, e, p, upper[0], upper);
+ }
+
+ /**
+ * Partition an array slice around a pivot. Partitioning exchanges array
elements such
+ * that all elements smaller than pivot are before it and all elements
larger than
+ * pivot are after it.
+ *
+ * <p>Assumes the range {@code r - l >= 11}; the caller is responsible for
selection on a smaller
+ * range.
+ *
+ * <p>Uses the Chen and Dumitrescu repeated step
median-of-medians-of-medians algorithm
+ * with the minimum of 4 then median of 3; the final sample is placed in
the
+ * 2nd 12th-tile; the pivot chosen from the sample is adaptive using the
input {@code k}.
+ *
+ * <p>Given a pivot in the middle of the sample this has margins of 1/12
and 1/3.
+ *
+ * @param a Data array.
+ * @param l Lower bound (inclusive).
+ * @param r Upper bound (inclusive).
+ * @param k Target index.
+ * @param upper Upper bound (inclusive) of the pivot range.
+ * @param flags Control flags.
+ * @return Lower bound (inclusive) of the pivot range.
+ */
+ private static int repeatedStepFarLeft(int[] a, int l, int r, int k, int[]
upper, int flags) {
+ // Far step has been changed from the Alexandrescu (2016) step of
lower-median-of-4, min-of-3
+ // into the 4th 12th-tile to a min-of-4, median-of-3 into the 2nd
12th-tile.
+ // The differences are:
+ // - The upper margin when not sampling is 8/24 vs. 9/24; the lower
margin remains at 1/12.
+ // - The position of the sample is closer to the expected location of
k < |A| / 12.
+ // - Sampling mode uses a median-of-3 with adaptive k, matching the
other step methods.
+ // A min-of-3 sample can create a pivot too small if used with
adaption of k leaving
+ // k in the larger parition and a wasted iteration.
+ // - Adaption is adjusted to force use of the lower margin when not
sampling.
+ int fp;
+ int s;
+ int p;
+ if (flags <= MODE_SAMPLING) {
+ // 2nd 12th-tile
+ fp = (r - l + 1) / 12;
+ s = l + fp;
+ // Use adaption
+ p = s + mapDistance(k - l, l, r, fp);
+ } else {
+ // i in 2nd quartile; min into i-f (1st quartile)
+ final int f = (r - l + 1) >> 2;
+ final int f2 = f + f;
+ final int end = l + f2;
+ for (int i = l + f; i < end; i++) {
+ if (a[i + f] < a[i - f]) {
+ final int u = a[i + f];
+ a[i + f] = a[i - f];
+ a[i - f] = u;
+ }
+ if (a[i + f2] < a[i]) {
+ final int v = a[i + f2];
+ a[i + f2] = a[i];
+ a[i] = v;
+ }
+ if (a[i] < a[i - f]) {
+ final int u = a[i];
+ a[i] = a[i - f];
+ a[i - f] = u;
+ }
+ }
+ // 2nd 12th-tile
+ fp = f / 3;
+ s = l + fp;
+ // Lower margin has 2(d+1) elements; d == (position in sample) - s
+ // Force k into the lower margin
+ p = s + ((k - l) >>> 1);
+ }
+ final int e = s + fp - 1;
+ for (int i = s; i <= e; i++) {
+ Sorting.sort3(a, i - fp, i, i + fp);
+ }
+ p = quickSelectAdaptive(a, s, e, p, p, upper, MODE_FR_SAMPLING);
+ return expandPartition(a, l, r, s, e, p, upper[0], upper);
+ }
+
+ /**
+ * Partition an array slice around a pivot. Partitioning exchanges array
elements such
+ * that all elements smaller than pivot are before it and all elements
larger than
+ * pivot are after it.
+ *
+ * <p>Assumes the range {@code r - l >= 11}; the caller is responsible for
selection on a smaller
+ * range.
+ *
+ * <p>Uses the Chen and Dumitrescu repeated step
median-of-medians-of-medians algorithm
+ * with the maximum of 4 then median of 3; the final sample is placed in
the
+ * 11th 12th-tile; the pivot chosen from the sample is adaptive using the
input {@code k}.
+ *
+ * <p>Given a pivot in the middle of the sample this has margins of 1/3
and 1/12.
+ *
+ * @param a Data array.
+ * @param l Lower bound (inclusive).
+ * @param r Upper bound (inclusive).
+ * @param k Target index.
+ * @param upper Upper bound (inclusive) of the pivot range.
+ * @param flags Control flags.
+ * @return Lower bound (inclusive) of the pivot range.
+ */
+ private static int repeatedStepFarRight(int[] a, int l, int r, int k,
int[] upper, int flags) {
+ // Mirror image repeatedStepFarLeft
+ int fp;
+ int e;
+ int p;
+ if (flags <= MODE_SAMPLING) {
+ // 11th 12th-tile
+ fp = (r - l + 1) / 12;
+ e = r - fp;
+ // Use adaption
+ p = e - mapDistance(r - k, l, r, fp);
+ } else {
+ // i in 3rd quartile; max into i+f (4th quartile)
+ final int f = (r - l + 1) >> 2;
+ final int f2 = f + f;
+ final int end = r - f2;
+ for (int i = r - f; i > end; i--) {
+ if (a[i - f] > a[i + f]) {
+ final int u = a[i - f];
+ a[i - f] = a[i + f];
+ a[i + f] = u;
+ }
+ if (a[i - f2] > a[i]) {
+ final int v = a[i - f2];
+ a[i - f2] = a[i];
+ a[i] = v;
+ }
+ if (a[i] > a[i + f]) {
+ final int u = a[i];
+ a[i] = a[i + f];
+ a[i + f] = u;
+ }
+ }
+ // 11th 12th-tile
+ fp = f / 3;
+ e = r - fp;
+ // Upper margin has 2(d+1) elements; d == e - (position in sample)
+ // Force k into the upper margin
+ p = e - ((r - k) >>> 1);
+ }
+ final int s = e - fp + 1;
+ for (int i = s; i <= e; i++) {
+ Sorting.sort3(a, i - fp, i, i + fp);
+ }
+ p = quickSelectAdaptive(a, s, e, p, p, upper, MODE_FR_SAMPLING);
+ return expandPartition(a, l, r, s, e, p, upper[0], upper);
+ }
+
+ /**
+ * Expand a partition around a single pivot. Partitioning exchanges array
+ * elements such that all elements smaller than pivot are before it and all
+ * elements larger than pivot are after it. The central region is already
+ * partitioned.
+ *
+ * <pre>{@code
+ * |l |s |p0 p1| e| r|
+ * | ??? | <P | ==P | >P | ??? |
+ * }</pre>
+ *
+ * <p>This requires that {@code start != end}. However it handles
+ * {@code left == start} and/or {@code end == right}.
+ *
+ * @param a Data array.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param start Start of the partition range (inclusive).
+ * @param end End of the partitioned range (inclusive).
+ * @param pivot0 Lower pivot location (inclusive).
+ * @param pivot1 Upper pivot location (inclusive).
+ * @param upper Upper bound (inclusive) of the pivot range [k1].
+ * @return Lower bound (inclusive) of the pivot range [k0].
+ */
+ // package-private for testing
+ static int expandPartition(int[] a, int left, int right, int start, int
end,
+ int pivot0, int pivot1, int[] upper) {
+ // 3-way partition of the data using a pivot value into
+ // less-than, equal or greater-than.
+ // Based on Sedgewick's Bentley-McIroy partitioning: always swap i<->j
then
+ // check for equal to the pivot and move again.
+ //
+ // Move sentinels from start and end to left and right. Scan towards
the
+ // sentinels until >=,<=. Swap then move == to the pivot region.
+ // <-i j->
+ // |l | | |p0 p1| | | r|
+ // |>=| ??? | < | == | > | ??? |<=|
+ //
+ // When either i or j reach the edge perform finishing loop.
+ // Finish loop for a[j] <= v replaces j with p1+1, optionally moves
value
+ // to p0 for < and updates the pivot range p1 (and optionally p0):
+ // j->
+ // |l |p0 p1| | | r|
+ // | < | == | > | ??? |<=|
+
+ final int v = a[pivot0];
+ // Use start/end as sentinels (requires start != end)
+ int vi = a[start];
+ int vj = a[end];
+ a[start] = a[left];
+ a[end] = a[right];
+ a[left] = vj;
+ a[right] = vi;
+
+ int i = start + 1;
+ int j = end - 1;
+
+ // Positioned for pre-in/decrement to write to pivot region
+ int p0 = pivot0 == start ? i : pivot0;
+ int p1 = pivot1 == end ? j : pivot1;
+
+ while (true) {
+ do {
+ --i;
+ } while (a[i] < v);
+ do {
+ ++j;
+ } while (a[j] > v);
+ vj = a[i];
+ vi = a[j];
+ a[i] = vi;
+ a[j] = vj;
+ // Move the equal values to pivot region
+ if (vi == v) {
+ a[i] = a[--p0];
+ a[p0] = v;
+ }
+ if (vj == v) {
+ a[j] = a[++p1];
+ a[p1] = v;
+ }
+ // Termination check and finishing loops.
+ // Note: This works even if pivot region is zero length (p1 ==
p0-1 due to
+ // length 1 pivot region at either start/end) because we
pre-inc/decrement
+ // one side and post-inc/decrement the other side.
+ if (i == left) {
+ while (j < right) {
+ do {
+ ++j;
+ } while (a[j] > v);
+ final int w = a[j];
+ // Move upper bound of pivot region
+ a[j] = a[++p1];
+ a[p1] = v;
+ // Move lower bound of pivot region
+ if (w != v) {
+ a[p0] = w;
+ p0++;
+ }
+ }
+ break;
+ }
+ if (j == right) {
+ while (i > left) {
+ do {
+ --i;
+ } while (a[i] < v);
+ final int w = a[i];
+ // Move lower bound of pivot region
+ a[i] = a[--p0];
+ a[p0] = v;
+ // Move upper bound of pivot region
+ if (w != v) {
+ a[p1] = w;
+ p1--;
+ }
+ }
+ break;
+ }
+ }
+
+ upper[0] = p1;
+ return p0;
+ }
+
+ /**
+ * Partition the array such that indices {@code k} correspond to their
+ * correctly sorted value in the equivalent fully sorted array.
+ *
+ * <p>For all indices {@code k} and any index {@code i}:
+ *
+ * <pre>{@code
+ * data[i < k] <= data[k] <= data[k < i]
+ * }</pre>
+ *
+ * <p>This function accepts a {@link UpdatingInterval} of indices {@code
k} that define the
+ * range of indices to partition. The {@link UpdatingInterval} can be
narrowed or split as
+ * partitioning divides the range.
+ *
+ * <p>Uses an introselect variant. The quickselect is a dual-pivot
quicksort
+ * partition method by Vladimir Yaroslavskiy; the fall-back on poor
convergence of
+ * the quickselect is a heapselect.
+ *
+ * <p>The {@code flags} contain the the current recursion count and the
configured
+ * length threshold for {@code r - l} to perform sort select. The count is
in the upper
+ * bits and the threshold is in the lower bits.
+ *
+ * @param a Values.
+ * @param left Lower bound of data (inclusive, assumed to be strictly
positive).
+ * @param right Upper bound of data (inclusive, assumed to be strictly
positive).
+ * @param k Interval of indices to partition (ordered).
+ * @param flags Control flags.
+ */
+ // package-private for testing
+ static void dualPivotQuickSelect(int[] a, int left, int right,
UpdatingInterval k, int flags) {
+ // If partitioning splits the interval then recursion is used for the
left-most side(s)
+ // and the right-most side remains within this function. If
partitioning does
+ // not split the interval then it remains within this function.
+ int l = left;
+ int r = right;
+ int f = flags;
+ int ka = k.left();
+ int kb = k.right();
+ final int[] upper = {0, 0, 0};
+ while (true) {
+ // Select when ka and kb are close to the same end,
+ // or the entire range is small
+ // |l|-----|ka|--------|kb|------|r|
+ final int n = r - l;
+ if (Math.min(kb - l, r - ka) < DP_SORTSELECT_SIZE ||
+ n < (f & SORTSELECT_MASK)) {
+ sortSelect(a, l, r, ka, kb);
+ return;
+ }
+ if (kb - ka < DP_SORTSELECT_SIZE) {
+ // Switch to single-pivot mode with Floyd-Rivest sub-sampling
+ quickSelectAdaptive(a, l, r, ka, kb, upper, MODE_FR_SAMPLING);
+ return;
+ }
+ if (f < 0) {
+ // Excess recursion, switch to heap select
+ heapSelect(a, l, r, ka, kb);
+ return;
+ }
+
+ // Dual-pivot partitioning
+ final int p0 = partition(a, l, r, upper);
+ final int p1 = upper[0];
+
+ // Recursion to max depth
+ // Note: Here we possibly branch left, middle and right with
multiple keys.
+ // It is possible that the partition has split the keys
+ // and the recursion proceeds with a reduced set in each region.
+ // p0 p1 p2 p3
+ // |l|--|ka|--k----k--|P|------k--|kb|----|P|----|r|
+ // kb | ka
+ f += RECURSION_INCREMENT;
+ // Recurse left side if required
+ if (ka < p0) {
+ if (kb <= p1) {
+ // Entirely on left side
+ r = p0 - 1;
+ if (r < kb) {
+ kb = k.updateRight(r);
+ }
+ continue;
+ }
+ dualPivotQuickSelect(a, l, p0 - 1, k.splitLeft(p0, p1), f);
+ // Here we must process middle and/or right
+ ka = k.left();
+ } else if (kb <= p1) {
+ // No middle/right side
+ return;
+ } else if (ka <= p1) {
+ // Advance lower bound
+ ka = k.updateLeft(p1 + 1);
+ }
+ // Recurse middle if required
+ final int p2 = upper[1];
+ final int p3 = upper[2];
+ if (ka < p2) {
+ l = p1 + 1;
+ if (kb <= p3) {
+ // Entirely in middle
+ r = p2 - 1;
+ if (r < kb) {
+ kb = k.updateRight(r);
+ }
+ continue;
+ }
+ dualPivotQuickSelect(a, l, p2 - 1, k.splitLeft(p2, p3), f);
+ ka = k.left();
+ } else if (kb <= p3) {
+ // No right side
+ return;
+ } else if (ka <= p3) {
+ ka = k.updateLeft(p3 + 1);
+ }
+ // Continue right
+ l = p3 + 1;
+ }
+ }
+
+ /**
+ * Partition an array slice around 2 pivots. Partitioning exchanges array
elements
+ * such that all elements smaller than pivot are before it and all
elements larger
+ * than pivot are after it.
+ *
+ * <p>This method returns 4 points describing the pivot ranges of equal
values.
+ *
+ * <pre>{@code
+ * |k0 k1| |k2 k3|
+ * | <P | ==P1 | <P1 && <P2 | ==P2 | >P |
+ * }</pre>
+ *
+ * <ul>
+ * <li>k0: lower pivot1 point
+ * <li>k1: upper pivot1 point (inclusive)
+ * <li>k2: lower pivot2 point
+ * <li>k3: upper pivot2 point (inclusive)
+ * </ul>
+ *
+ * <p>Bounds are set so {@code i < k0}, {@code i > k3} and {@code k1 < i <
k2} are
+ * unsorted. When the range {@code [k0, k3]} contains fully sorted
elements the result
+ * is set to {@code k1 = k3; k2 == k0}. This can occur if
+ * {@code P1 == P2} or there are zero or one value between the pivots
+ * {@code P1 < v < P2}. Any sort/partition of ranges [left, k0-1], [k1+1,
k2-1] and
+ * [k3+1, right] must check the length is {@code > 1}.
+ *
+ * @param a Data array.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param bounds Points [k1, k2, k3].
+ * @return Lower bound (inclusive) of the pivot range [k0].
+ */
+ private static int partition(int[] a, int left, int right, int[] bounds) {
+ // Pick 2 pivots from 5 approximately uniform through the range.
+ // Spacing is ~ 1/7 made using shifts. Other strategies are equal or
much
+ // worse. 1/7 = 5/35 ~ 1/8 + 1/64 : 0.1429 ~ 0.1406
+ // Ensure the value is above zero to choose different points!
+ final int n = right - left;
+ final int step = 1 + (n >>> 3) + (n >>> 6);
+ final int i3 = left + (n >>> 1);
+ final int i2 = i3 - step;
+ final int i1 = i2 - step;
+ final int i4 = i3 + step;
+ final int i5 = i4 + step;
+ Sorting.sort5(a, i1, i2, i3, i4, i5);
+
+ // Partition data using pivots P1 and P2 into less-than, greater-than
or between.
+ // Pivot values P1 & P2 are placed at the end. If P1 < P2, P2 acts as
a sentinel.
+ // k traverses the unknown region ??? and values moved if less-than or
+ // greater-than:
+ //
+ // left less k great right
+ // |P1| <P1 | P1 <= & <= P2 | ??? | >P2 |P2|
+ //
+ // <P1 (left, lt)
+ // P1 <= & <= P2 [lt, k)
+ // >P2 (gt, right)
+ //
+ // At the end pivots are swapped back to behind the less and great
pointers.
+ //
+ // | <P1 |P1| P1<= & <= P2 |P2| >P2 |
+
+ // Swap ends to the pivot locations.
+ final int v1 = a[i2];
+ a[i2] = a[left];
+ a[left] = v1;
+ final int v2 = a[i4];
+ a[i4] = a[right];
+ a[right] = v2;
+
+ // pointers
+ int less = left;
+ int great = right;
+
+ // Fast-forward ascending / descending runs to reduce swaps.
+ // Cannot overrun as end pivots (v1 <= v2) act as sentinels.
+ do {
+ ++less;
+ } while (a[less] < v1);
+ do {
+ --great;
+ } while (a[great] > v2);
+
+ // a[less - 1] < P1 : a[great + 1] > P2
+ // unvisited in [less, great]
+ SORTING:
+ for (int k = less - 1; ++k <= great;) {
+ final int v = a[k];
+ if (v < v1) {
+ // swap(a, k, less++)
+ a[k] = a[less];
+ a[less] = v;
+ less++;
+ } else if (v > v2) {
+ // while k < great and a[great] > v2:
+ // great--
+ while (a[great] > v2) {
+ if (great-- == k) {
+ // Done
+ break SORTING;
+ }
+ }
+ // swap(a, k, great--)
+ // if a[k] < v1:
+ // swap(a, k, less++)
+ final int w = a[great];
+ a[great] = v;
+ great--;
+ // delay a[k] = w
+ if (w < v1) {
+ a[k] = a[less];
+ a[less] = w;
+ less++;
+ } else {
+ a[k] = w;
+ }
+ }
+ }
+
+ // Change to inclusive ends : a[less] < P1 : a[great] > P2
+ less--;
+ great++;
+ // Move the pivots to correct locations
+ a[left] = a[less];
+ a[less] = v1;
+ a[right] = a[great];
+ a[great] = v2;
+
+ // Record the pivot locations
+ final int lower = less;
+ bounds[2] = great;
+
+ // equal elements
+ // Original paper: If middle partition is bigger than a threshold
+ // then check for equal elements.
+
+ // Note: This is extra work. When performing partitioning the region
of interest
+ // may be entirely above or below the central region and this can be
skipped.
+
+ // Here we look for equal elements if the centre is more than 5/8 the
length.
+ // 5/8 = 1/2 + 1/8. Pivots must be different.
+ if ((great - less) > (n >>> 1) + (n >>> 3) && v1 != v2) {
+
+ // Fast-forward to reduce swaps. Changes inclusive ends to
exclusive ends.
+ // Since v1 != v2 these act as sentinels to prevent overrun.
+ do {
+ ++less;
+ } while (a[less] == v1);
+ do {
+ --great;
+ } while (a[great] == v2);
+
+ // This copies the logic in the sorting loop using == comparisons
+ EQUAL:
+ for (int k = less - 1; ++k <= great;) {
+ final int v = a[k];
+ if (v == v1) {
+ a[k] = a[less];
+ a[less] = v;
+ less++;
+ } else if (v == v2) {
+ while (a[great] == v2) {
+ if (great-- == k) {
+ // Done
+ break EQUAL;
+ }
+ }
+ final int w = a[great];
+ a[great] = v;
+ great--;
+ if (w == v1) {
+ a[k] = a[less];
+ a[less] = w;
+ less++;
+ } else {
+ a[k] = w;
+ }
+ }
+ }
+
+ // Change to inclusive ends
+ less--;
+ great++;
+ }
+
+ // Between pivots in (less, great)
+ if (v1 != v2 && less < great - 1) {
+ // Record the pivot end points
+ bounds[0] = less;
+ bounds[1] = great;
+ } else {
+ // No unsorted internal region (set k1 = k3; k2 = k0)
+ bounds[0] = bounds[2];
+ bounds[1] = lower;
+ }
+
+ return lower;
+ }
+
/**
* Map the distance from the edge of {@code [l, r]} to a new distance in
{@code [0, n)}.
*
diff --git
a/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Selection.java
b/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Selection.java
index 60c7d73f..21c7dfcf 100644
---
a/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Selection.java
+++
b/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Selection.java
@@ -331,4 +331,80 @@ public final class Selection {
}
}
}
+
+ /**
+ * Partition the array such that index {@code k} corresponds to its
correctly
+ * sorted value in the equivalent fully sorted array.
+ *
+ * @param a Values.
+ * @param k Index.
+ * @throws IndexOutOfBoundsException if index {@code k} is not within the
+ * sub-range {@code [0, a.length)}
+ */
+ public static void select(int[] a, int k) {
+ IndexSupport.checkIndex(0, a.length, k);
+ if (a.length <= 1) {
+ return;
+ }
+ QuickSelect.select(a, 0, a.length - 1, k);
+ }
+
+ /**
+ * Partition the array such that indices {@code k} correspond to their
correctly
+ * sorted value in the equivalent fully sorted array.
+ *
+ * @param a Values.
+ * @param k Indices (may be destructively modified).
+ * @throws IndexOutOfBoundsException if any index {@code k} is not within
the
+ * sub-range {@code [0, a.length)}
+ */
+ public static void select(int[] a, int[] k) {
+ IndexSupport.checkIndices(0, a.length, k);
+ if (k.length == 0 || a.length <= 1) {
+ return;
+ }
+ QuickSelect.select(a, 0, a.length - 1, k, k.length);
+ }
+
+ /**
+ * Partition the array such that index {@code k} corresponds to its
correctly
+ * sorted value in the equivalent fully sorted array.
+ *
+ * @param a Values.
+ * @param fromIndex Index of the first element (inclusive).
+ * @param toIndex Index of the last element (exclusive).
+ * @param k Index.
+ * @throws IndexOutOfBoundsException if the sub-range {@code [fromIndex,
toIndex)} is out of
+ * bounds of range {@code [0, a.length)}; or if index {@code k} is not
within the
+ * sub-range {@code [fromIndex, toIndex)}
+ */
+ public static void select(int[] a, int fromIndex, int toIndex, int k) {
+ IndexSupport.checkFromToIndex(fromIndex, toIndex, a.length);
+ IndexSupport.checkIndex(fromIndex, toIndex, k);
+ if (toIndex - fromIndex <= 1) {
+ return;
+ }
+ QuickSelect.select(a, fromIndex, toIndex - 1, k);
+ }
+
+ /**
+ * Partition the array such that indices {@code k} correspond to their
correctly
+ * sorted value in the equivalent fully sorted array.
+ *
+ * @param a Values.
+ * @param fromIndex Index of the first element (inclusive).
+ * @param toIndex Index of the last element (exclusive).
+ * @param k Indices (may be destructively modified).
+ * @throws IndexOutOfBoundsException if the sub-range {@code [fromIndex,
toIndex)} is out of
+ * bounds of range {@code [0, a.length)}; or if any index {@code k} is not
within the
+ * sub-range {@code [fromIndex, toIndex)}
+ */
+ public static void select(int[] a, int fromIndex, int toIndex, int[] k) {
+ IndexSupport.checkFromToIndex(fromIndex, toIndex, a.length);
+ IndexSupport.checkIndices(fromIndex, toIndex, k);
+ if (k.length == 0 || toIndex - fromIndex <= 1) {
+ return;
+ }
+ QuickSelect.select(a, fromIndex, toIndex - 1, k, k.length);
+ }
}
diff --git
a/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Sorting.java
b/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Sorting.java
index 114c7477..cf35c4a0 100644
---
a/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Sorting.java
+++
b/commons-numbers-arrays/src/main/java/org/apache/commons/numbers/arrays/Sorting.java
@@ -264,6 +264,234 @@ final class Sorting {
}
}
+ /**
+ * Sorts an array using an insertion sort.
+ *
+ * @param x Data array.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ */
+ static void sort(int[] x, int left, int right) {
+ for (int i = left; ++i <= right;) {
+ final int v = x[i];
+ // Move preceding higher elements above (if required)
+ if (v < x[i - 1]) {
+ int j = i;
+ while (--j >= left && v < x[j]) {
+ x[j + 1] = x[j];
+ }
+ x[j + 1] = v;
+ }
+ }
+ }
+
+ /**
+ * Sorts the elements at the given distinct indices in an array.
+ *
+ * @param x Data array.
+ * @param a Index.
+ * @param b Index.
+ * @param c Index.
+ */
+ static void sort3(int[] x, int a, int b, int c) {
+ // Decision tree avoiding swaps:
+ // Order [(0,2)]
+ // Move point 1 above point 2 or below point 0
+ final int u = x[a];
+ final int v = x[b];
+ final int w = x[c];
+ if (w < u) {
+ if (v < w) {
+ x[a] = v;
+ x[b] = w;
+ x[c] = u;
+ return;
+ }
+ if (u < v) {
+ x[a] = w;
+ x[b] = u;
+ x[c] = v;
+ return;
+ }
+ // w < v < u
+ x[a] = w;
+ x[c] = u;
+ return;
+ }
+ if (v < u) {
+ // v < u < w
+ x[a] = v;
+ x[b] = u;
+ return;
+ }
+ if (w < v) {
+ // u < w < v
+ x[b] = w;
+ x[c] = v;
+ }
+ // u < v < w
+ }
+
+ /**
+ * Sorts the elements at the given distinct indices in an array.
+ *
+ * @param x Data array.
+ * @param a Index.
+ * @param b Index.
+ * @param c Index.
+ * @param d Index.
+ * @param e Index.
+ */
+ static void sort5(int[] x, int a, int b, int c, int d, int e) {
+ // Uses an optimal sorting network from Knuth's Art of Computer
Programming.
+ // 9 comparisons.
+ // Order pairs:
+ // [(0,3),(1,4)]
+ // [(0,2),(1,3)]
+ // [(0,1),(2,4)]
+ // [(1,2),(3,4)]
+ // [(2,3)]
+ if (x[e] < x[b]) {
+ final int u = x[e];
+ x[e] = x[b];
+ x[b] = u;
+ }
+ if (x[d] < x[a]) {
+ final int v = x[d];
+ x[d] = x[a];
+ x[a] = v;
+ }
+
+ if (x[d] < x[b]) {
+ final int u = x[d];
+ x[d] = x[b];
+ x[b] = u;
+ }
+ if (x[c] < x[a]) {
+ final int v = x[c];
+ x[c] = x[a];
+ x[a] = v;
+ }
+
+ if (x[e] < x[c]) {
+ final int u = x[e];
+ x[e] = x[c];
+ x[c] = u;
+ }
+ if (x[b] < x[a]) {
+ final int v = x[b];
+ x[b] = x[a];
+ x[a] = v;
+ }
+
+ if (x[e] < x[d]) {
+ final int u = x[e];
+ x[e] = x[d];
+ x[d] = u;
+ }
+ if (x[c] < x[b]) {
+ final int v = x[c];
+ x[c] = x[b];
+ x[b] = v;
+ }
+
+ if (x[d] < x[c]) {
+ final int u = x[d];
+ x[d] = x[c];
+ x[c] = u;
+ }
+ }
+
+ /**
+ * Place the lower median of 4 elements in {@code b}; the smaller element
in
+ * {@code a}; and the larger two elements in {@code c, d}.
+ *
+ * @param x Values
+ * @param a Index.
+ * @param b Index.
+ * @param c Index.
+ * @param d Index.
+ */
+ static void lowerMedian4(int[] x, int a, int b, int c, int d) {
+ // 3 to 5 comparisons
+ if (x[d] < x[b]) {
+ final int u = x[d];
+ x[d] = x[b];
+ x[b] = u;
+ }
+ if (x[c] < x[a]) {
+ final int v = x[c];
+ x[c] = x[a];
+ x[a] = v;
+ }
+ // a--c
+ // b--d
+ if (x[c] < x[b]) {
+ final int u = x[c];
+ x[c] = x[b];
+ x[b] = u;
+ } else if (x[b] < x[a]) {
+ // a--c
+ // b--d
+ final int xb = x[a];
+ x[a] = x[b];
+ x[b] = xb;
+ // b--c
+ // a--d
+ if (x[d] < xb) {
+ x[b] = x[d];
+ // Move a pair to maintain the sorted order
+ x[d] = x[c];
+ x[c] = xb;
+ }
+ }
+ }
+
+ /**
+ * Place the upper median of 4 elements in {@code c}; the smaller two
elements in
+ * {@code a,b}; and the larger element in {@code d}.
+ *
+ * @param x Values
+ * @param a Index.
+ * @param b Index.
+ * @param c Index.
+ * @param d Index.
+ */
+ static void upperMedian4(int[] x, int a, int b, int c, int d) {
+ // 3 to 5 comparisons
+ if (x[d] < x[b]) {
+ final int u = x[d];
+ x[d] = x[b];
+ x[b] = u;
+ }
+ if (x[c] < x[a]) {
+ final int v = x[c];
+ x[c] = x[a];
+ x[a] = v;
+ }
+ // a--c
+ // b--d
+ if (x[b] > x[c]) {
+ final int u = x[c];
+ x[c] = x[b];
+ x[b] = u;
+ } else if (x[c] > x[d]) {
+ // a--c
+ // b--d
+ final int xc = x[d];
+ x[d] = x[c];
+ x[c] = xc;
+ // a--d
+ // b--c
+ if (x[a] > xc) {
+ x[c] = x[a];
+ // Move a pair to maintain the sorted order
+ x[a] = x[b];
+ x[b] = xc;
+ }
+ }
+ }
+
/**
* Sort the unique indices in-place to the start of the array. The number
of
* unique indices is returned.
diff --git
a/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SelectionTest.java
b/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SelectionTest.java
index 43118b92..efc5d346 100644
---
a/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SelectionTest.java
+++
b/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SelectionTest.java
@@ -988,6 +988,823 @@ class SelectionTest {
return builder.build();
}
+ /**
+ * Partition function. Used to test different implementations.
+ */
+ private interface IntRangePartitionFunction {
+ /**
+ * Partition the array such that range of indices {@code [ka, kb]}
correspond to
+ * their correctly sorted value in the equivalent fully sorted array.
For all
+ * indices {@code k} and any index {@code i}:
+ *
+ * <pre>{@code
+ * data[i < k] <= data[k] <= data[k < i]
+ * }</pre>
+ *
+ * @param a Data array to use to find out the K<sup>th</sup> value.
+ * @param left Lower bound (inclusive).
+ * @param right Upper bound (inclusive).
+ * @param ka Lower index to select.
+ * @param kb Upper index to select.
+ */
+ void partition(int[] a, int left, int right, int ka, int kb);
+ }
+
+ /**
+ * Partition function. Used to test different implementations.
+ */
+ private interface IntPartitionFunction {
+ /**
+ * Partition the array such that indices {@code k} correspond to their
correctly
+ * sorted value in the equivalent fully sorted array. For all indices
{@code k}
+ * and any index {@code i}:
+ *
+ * <pre>{@code
+ * data[i < k] <= data[k] <= data[k < i]
+ * }</pre>
+ *
+ * <p>This method allows variable length indices using a count of the
indices to
+ * process.
+ *
+ * @param a Values.
+ * @param k Indices.
+ * @param n Count of indices.
+ */
+ void partition(int[] a, int[] k, int n);
+ }
+
+ /**
+ * Return a sorted copy of the {@code values}.
+ *
+ * @param values Values.
+ * @return the copy
+ */
+ private static int[] sort(int[] values) {
+ final int[] sorted = values.clone();
+ Arrays.sort(sorted);
+ return sorted;
+ }
+
+ /**
+ * Return a copy of the {@code values} sorted in the range {@code [from,
to]}.
+ *
+ * @param values Values.
+ * @param from From (inclusive).
+ * @param to To (inclusive).
+ * @return the copy
+ */
+ private static int[] sort(int[] values, int from, int to) {
+ final int[] sorted = values.clone();
+ Arrays.sort(sorted, from, to + 1);
+ return sorted;
+ }
+
+ /**
+ * Shuffles the entries of the given array.
+ *
+ * @param rng Source of randomness.
+ * @param array Array whose entries will be shuffled (in-place).
+ * @return Shuffled input array.
+ */
+ // TODO - replace with Commons RNG 1.6: o.a.c.rng.sampling.ArraySampler
+ private static int[] shuffle(UniformRandomProvider rng, int[] array) {
+ for (int i = array.length; i > 1; i--) {
+ swap(array, i - 1, rng.nextInt(i));
+ }
+ return array;
+ }
+
+ /**
+ * Swaps the two specified elements in the array.
+ *
+ * @param array Array.
+ * @param i First index.
+ * @param j Second index.
+ */
+ private static void swap(int[] array, int i, int j) {
+ final int tmp = array[i];
+ array[i] = array[j];
+ array[j] = tmp;
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntHeapSelect", "testIntSelectMinMax",
"testIntSelectMinMax2"})
+ void testIntHeapSelectLeft(int[] values, int from, int to) {
+ final int[] sorted = sort(values, from, to);
+
+ final int[] x = values.clone();
+ final IntRangePartitionFunction fun = QuickSelect::heapSelectLeft;
+
+ for (int k = from; k <= to; k++) {
+ assertPartitionRange(sorted, fun, x.clone(), from, to, k, k);
+ if (k > from) {
+ // Sort an extra 1
+ assertPartitionRange(sorted, fun, x.clone(), from, to, k - 1,
k);
+ if (k > from + 1) {
+ // Sort all
+ // Test clipping with k < from
+ assertPartitionRange(sorted, fun, x.clone(), from, to,
from - 23, k);
+ }
+ }
+ }
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntHeapSelect", "testIntSelectMinMax",
"testIntSelectMinMax2"})
+ void testIntHeapSelectRight(int[] values, int from, int to) {
+ final int[] sorted = sort(values, from, to);
+
+ final int[] x = values.clone();
+ final IntRangePartitionFunction fun = QuickSelect::heapSelectRight;
+
+ for (int k = from; k <= to; k++) {
+ assertPartitionRange(sorted, fun, x.clone(), from, to, k, k);
+ if (k < to) {
+ // Sort an extra 1
+ assertPartitionRange(sorted, fun, x.clone(), from, to, k, k +
1);
+ if (k < to - 1) {
+ // Sort all
+ // Test clipping with k > to
+ assertPartitionRange(sorted, fun, x.clone(), from, to, k,
to + 23);
+ }
+ }
+ }
+ }
+
+ static Stream<Arguments> testIntHeapSelect() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ builder.add(Arguments.of(new int[] {1}, 0, 0));
+ builder.add(Arguments.of(new int[] {3, 2, 1}, 1, 1));
+ builder.add(Arguments.of(new int[] {2, 1}, 0, 1));
+ builder.add(Arguments.of(new int[] {4, 3, 2, 1}, 1, 2));
+ builder.add(Arguments.of(new int[] {-2, 0, -1, -1, 2}, 0, 4));
+ builder.add(Arguments.of(new int[] {-2, 0, -1, -1, 2}, 0, 2));
+ builder.add(Arguments.of(new int[] {2, 0, -1, -1, -2}, 0, 4));
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 1,
6));
+ return builder.build();
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntHeapSelectRange"})
+ void testIntHeapSelectRange(int[] values, int from, int to, int k1, int
k2) {
+ assertPartitionRange(sort(values, from, to),
+ QuickSelect::heapSelect, values, from, to, k1, k2);
+ }
+
+ static Stream<Arguments> testIntHeapSelectRange() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 0, 7,
1, 2));
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 0, 7,
2, 2));
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 0, 7,
5, 7));
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 0, 7,
1, 6));
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 0, 7,
0, 3));
+ builder.add(Arguments.of(new int[] {-1, 2, -3, 4, -4, 3, -2, 1}, 0, 7,
4, 7));
+ return builder.build();
+ }
+
+ static Stream<Arguments> testIntSelectMinMax() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ builder.add(Arguments.of(new int[] {1, 2, 3, 4, 5}, 0, 4));
+ builder.add(Arguments.of(new int[] {5, 4, 3, 2, 1}, 0, 4));
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create();
+ for (final int size : new int[] {5, 10}) {
+ final int[] values = rng.ints(size).toArray();
+ builder.add(Arguments.of(values.clone(), 0, size - 1));
+ builder.add(Arguments.of(values.clone(), size >>> 1, size - 1));
+ builder.add(Arguments.of(values.clone(), 1, size >>> 1));
+ }
+ builder.add(Arguments.of(new int[] {-1, 0}, 0, 1));
+ builder.add(Arguments.of(new int[] {0, -1}, 0, 1));
+ builder.add(Arguments.of(new int[] {-1, -1}, 0, 1));
+ builder.add(Arguments.of(new int[] {0, 0}, 0, 1));
+ builder.add(Arguments.of(new int[] {0, -1, 0, -1}, 0, 3));
+ builder.add(Arguments.of(new int[] {-1, 0, -1, 0}, 0, 3));
+ builder.add(Arguments.of(new int[] {0, -1, -1, 0}, 0, 3));
+ builder.add(Arguments.of(new int[] {-1, 0, 0, -1}, 0, 3));
+ return builder.build();
+ }
+
+ static Stream<Arguments> testIntSelectMinMax2() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ final int[] values = {-1, 0, 2};
+ final int x = -123;
+ final int y = 42;
+ for (final int a : values) {
+ for (final int b : values) {
+ builder.add(Arguments.of(new int[] {a, b}, 0, 1));
+ builder.add(Arguments.of(new int[] {x, a, b, y}, 1, 2));
+ for (final int c : values) {
+ builder.add(Arguments.of(new int[] {a, b, c}, 0, 2));
+ builder.add(Arguments.of(new int[] {x, a, b, c, y}, 1, 3));
+ for (final int d : values) {
+ builder.add(Arguments.of(new int[] {a, b, c, d}, 0,
3));
+ builder.add(Arguments.of(new int[] {x, a, b, c, d, y},
1, 4));
+ }
+ }
+ }
+ }
+ builder.add(Arguments.of(new int[] {-1, -1, -1, 4, 3, 2, 1, y}, 3, 6));
+ builder.add(Arguments.of(new int[] {1, 2, 3, 4, 5}, 0, 4));
+ builder.add(Arguments.of(new int[] {5, 4, 3, 2, 1}, 0, 4));
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create();
+ for (final int size : new int[] {5, 10}) {
+ final int[] a = rng.ints(size).toArray();
+ builder.add(Arguments.of(a.clone(), 0, size - 1));
+ builder.add(Arguments.of(a.clone(), size >>> 1, size - 1));
+ builder.add(Arguments.of(a.clone(), 1, size >>> 1));
+ }
+ builder.add(Arguments.of(new int[] {-0, 1}, 0, 1));
+ builder.add(Arguments.of(new int[] {1, -0}, 0, 1));
+ builder.add(Arguments.of(new int[] {-0, -0}, 0, 1));
+ builder.add(Arguments.of(new int[] {1, 1}, 0, 1));
+ builder.add(Arguments.of(new int[] {1, -0, 1, -0}, 0, 3));
+ builder.add(Arguments.of(new int[] {-0, 1, -0, 1}, 0, 3));
+ builder.add(Arguments.of(new int[] {1, -0, -0, 1}, 0, 3));
+ builder.add(Arguments.of(new int[] {-0, 1, 1, -0}, 0, 3));
+ return builder.build();
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntHeapSelect", "testIntSelectMinMax",
"testIntSelectMinMax2"})
+ void testIntSortSelectLeft(int[] values, int from, int to) {
+ final int[] sorted = sort(values, from, to);
+
+ final int[] x = values.clone();
+ final IntRangePartitionFunction fun = (a, l, r, ka, kb) ->
+ QuickSelect.sortSelectLeft(a, l, r, kb);
+
+ for (int k = from; k <= to; k++) {
+ assertPartitionRange(sorted, fun, x.clone(), from, to, from, k);
+ }
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntHeapSelect", "testIntSelectMinMax",
"testIntSelectMinMax2"})
+ void testIntSortSelectRight(int[] values, int from, int to) {
+ final int[] sorted = sort(values, from, to);
+
+ final int[] x = values.clone();
+ final IntRangePartitionFunction fun = (a, l, r, ka, kb) ->
+ QuickSelect.sortSelectRight(a, l, r, ka);
+
+ for (int k = from; k <= to; k++) {
+ assertPartitionRange(sorted, fun, x.clone(), from, to, k, to);
+ }
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntHeapSelectRange"})
+ void testIntSortSelectRange(int[] values, int from, int to, int k1, int
k2) {
+ assertPartitionRange(sort(values, from, to),
+ QuickSelect::sortSelect, values, from, to, k1, k2);
+ }
+
+ /**
+ * Assert the function correctly partitions the range.
+ *
+ * @param sorted Expected sort result.
+ * @param fun Partition function.
+ * @param values Values.
+ * @param from From (inclusive).
+ * @param to To (inclusive).
+ * @param ka Lower index to select.
+ * @param kb Upper index to select.
+ */
+ private static void assertPartitionRange(int[] sorted,
+ IntRangePartitionFunction fun,
+ int[] values, int from, int to, int ka, int kb) {
+ Arrays.sort(sorted, from, to + 1);
+ fun.partition(values, from, to, ka, kb);
+ // Clip
+ ka = ka < from ? from : ka;
+ kb = kb > to ? to : kb;
+ for (int i = ka; i <= kb; i++) {
+ final int index = i;
+ Assertions.assertEquals(sorted[i], values[i], () -> "index: " +
index);
+ }
+ // Check the data is the same
+ Arrays.sort(values, from, to + 1);
+ Assertions.assertArrayEquals(sorted, values, "Data destroyed");
+ }
+
+ @ParameterizedTest
+ @MethodSource
+ void testIntSelectThrows(int[] values, int[] indices, int from, int to) {
+ final int[] x = values.clone();
+ final int[] k = indices.clone();
+ if (from == IGNORE_FROM) {
+ Assertions.assertThrows(IndexOutOfBoundsException.class, () ->
Selection.select(values, indices));
+ } else {
+ Assertions.assertThrows(IndexOutOfBoundsException.class, () ->
Selection.select(values, from, to, indices));
+ }
+ Assertions.assertArrayEquals(x, values, "Data modified");
+ Assertions.assertArrayEquals(k, indices, "Indices modified");
+ if (k.length != 1) {
+ return;
+ }
+ if (from == IGNORE_FROM) {
+ Assertions.assertThrows(IndexOutOfBoundsException.class, () ->
Selection.select(values, k[0]));
+ } else {
+ Assertions.assertThrows(IndexOutOfBoundsException.class, () ->
Selection.select(values, from, to, k[0]));
+ }
+ Assertions.assertArrayEquals(x, values, "Data modified for single k");
+ }
+
+ static Stream<Arguments> testIntSelectThrows() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ final int[] a = {1, 2, 3, -123, 0, -1};
+ // Invalid range
+ builder.add(Arguments.of(a.clone(), new int[] {0}, 0, a.length + 1));
+ builder.add(Arguments.of(a.clone(), new int[] {0}, -1, a.length));
+ builder.add(Arguments.of(a.clone(), new int[] {0}, 0, 0));
+ builder.add(Arguments.of(a.clone(), new int[] {0}, a.length, 0));
+ builder.add(Arguments.of(a.clone(), new int[] {1}, 3, 1));
+ // Single k
+ // Full length
+ builder.add(Arguments.of(a.clone(), new int[] {-1}, IGNORE_FROM, 0));
+ builder.add(Arguments.of(a.clone(), new int[] {10}, IGNORE_FROM, 0));
+ // Range
+ builder.add(Arguments.of(a.clone(), new int[] {-1}, 0, 5));
+ builder.add(Arguments.of(a.clone(), new int[] {1}, 2, 5));
+ builder.add(Arguments.of(a.clone(), new int[] {10}, 2, 5));
+ // Multiple k, some invalid
+ // Full length
+ builder.add(Arguments.of(a.clone(), new int[] {0, -1, 1, 2},
IGNORE_FROM, 0));
+ builder.add(Arguments.of(a.clone(), new int[] {0, 2, 3, 10},
IGNORE_FROM, 0));
+ // Range
+ builder.add(Arguments.of(a.clone(), new int[] {0, -1, 1, 2}, 0, 5));
+ builder.add(Arguments.of(a.clone(), new int[] {2, 3, 1}, 2, 5));
+ builder.add(Arguments.of(a.clone(), new int[] {2, 10, 3}, 2, 5));
+ return builder.build();
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntQuickSelectAdaptiveFRSampling(int[] values, int[] indices) {
+ assertQuickSelectAdaptive(values, indices,
QuickSelect.MODE_FR_SAMPLING);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntQuickSelectAdaptiveSampling(int[] values, int[] indices) {
+ assertQuickSelectAdaptive(values, indices, QuickSelect.MODE_SAMPLING);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntQuickSelectAdaptiveAdaption(int[] values, int[] indices) {
+ assertQuickSelectAdaptive(values, indices, QuickSelect.MODE_ADAPTION);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntQuickSelectAdaptiveStrict(int[] values, int[] indices) {
+ assertQuickSelectAdaptive(values, indices, QuickSelect.MODE_STRICT);
+ }
+
+ private static void assertQuickSelectAdaptive(int[] values, int[] indices,
int mode) {
+ Assumptions.assumeTrue(indices.length == 1 ||
+ (indices.length == 2 && Math.abs(indices[1] - indices[0]) < 10));
+ final int k1 = Math.min(indices[0], indices[indices.length - 1]);
+ final int kn = Math.max(indices[0], indices[indices.length - 1]);
+ assertPartition(values, indices, (a, k, n) ->
+ QuickSelect.quickSelectAdaptive(a, 0, a.length - 1, k1, kn, new
int[1], mode), true);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntDualPivotQuickSelectMaxRecursion(int[] values, int[] indices) {
+ assertPartition(values, indices, (a, k, n) -> {
+ final int right = a.length - 1;
+ if (right < 1 || k.length == 0) {
+ return;
+ }
+ QuickSelect.dualPivotQuickSelect(a, 0, right,
+ IndexSupport.createUpdatingInterval(0, right, k, k.length),
+ QuickSelect.dualPivotFlags(2, 5));
+ }, false);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntSelect(int[] values, int[] indices) {
+ assertPartition(values, indices, (a, k, n) -> {
+ int[] b = a;
+ if (n == 1) {
+ b = a.clone();
+ Selection.select(b, k[0]);
+ }
+ Selection.select(a, Arrays.copyOf(k, n));
+ if (n == 1) {
+ Assertions.assertArrayEquals(a, b, "single k mismatch");
+ }
+ }, false);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntPartition", "testIntPartitionBigData"})
+ void testIntSelectRange(int[] values, int[] indices) {
+ assertPartition(values, indices, (a, k, n) -> {
+ int[] b = a;
+ if (n == 1) {
+ b = a.clone();
+ Selection.select(b, 0, b.length, k[0]);
+ }
+ Selection.select(a, 0, a.length, Arrays.copyOf(k, n));
+ if (n == 1) {
+ Assertions.assertArrayEquals(a, b, "single k mismatch");
+ }
+ }, false);
+ }
+
+ static void assertPartition(int[] values, int[] indices,
IntPartitionFunction function,
+ boolean sortedRange) {
+ final int[] data = values.clone();
+ final int[] sorted = sort(values);
+ // Indices may be destructively modified
+ function.partition(data, indices.clone(), indices.length);
+ if (indices.length == 0) {
+ return;
+ }
+ for (final int k : indices) {
+ Assertions.assertEquals(sorted[k], data[k], () -> "k[" + k + "]");
+ }
+ // Check partial ordering
+ Arrays.sort(indices);
+ int i = 0;
+ for (final int k : indices) {
+ final int value = sorted[k];
+ while (i < k) {
+ final int j = i;
+ Assertions.assertTrue(Integer.compare(data[i], value) <= 0,
+ () -> j + " < " + k + " : " + data[j] + " < " + value);
+ i++;
+ }
+ }
+ final int k = indices[indices.length - 1];
+ final int value = sorted[k];
+ while (i < data.length) {
+ final int j = i;
+ Assertions.assertTrue(Integer.compare(data[i], value) >= 0,
+ () -> k + " < " + j);
+ i++;
+ }
+ if (sortedRange) {
+ final int[] a = Arrays.copyOfRange(sorted, indices[0], k + 1);
+ final int[] b = Arrays.copyOfRange(data, indices[0], k + 1);
+ Assertions.assertArrayEquals(a, b, "Entire range of indices is not
sorted");
+ }
+ Arrays.sort(data);
+ Assertions.assertArrayEquals(sorted, data, "Data destroyed");
+ }
+
+ static Stream<Arguments> testIntPartition() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ UniformRandomProvider rng = RandomSource.XO_SHI_RO_128_PP.create(123);
+ // Sizes above and below the threshold for partitioning.
+ // The largest size should trigger single-pivot sub-sampling for pivot
selection.
+ for (final int size : new int[] {5, 47, SU + 10}) {
+ final int halfSize = size >>> 1;
+ final int from = -halfSize;
+ final int to = -halfSize + size;
+ final int[] values = IntStream.range(from, to).toArray();
+ final int[] zeros = values.clone();
+ final int quarterSize = size >>> 2;
+ Arrays.fill(zeros, quarterSize, halfSize + quarterSize, 0);
+ for (final int k : new int[] {1, 2, 3, size}) {
+ for (int i = 0; i < 15; i++) {
+ // Note: Duplicate indices do not matter
+ final int[] indices = rng.ints(k, 0, size).toArray();
+ builder.add(Arguments.of(
+ shuffle(rng, values.clone()),
+ indices.clone()));
+ builder.add(Arguments.of(
+ shuffle(rng, zeros.clone()),
+ indices.clone()));
+ }
+ }
+ // Test sequential processing by creating potential ranges
+ // after an initial low point. This should be high enough
+ // so any range analysis that joins indices will leave the initial
+ // index as a single point.
+ final int limit = 50;
+ if (size > limit) {
+ for (int i = 0; i < 10; i++) {
+ final int[] indices = rng.ints(size - limit, limit,
size).toArray();
+ // This sets a low index
+ indices[rng.nextInt(indices.length)] = rng.nextInt(0,
limit >>> 1);
+ builder.add(Arguments.of(
+ shuffle(rng, values.clone()),
+ indices.clone()));
+ }
+ }
+ // min; max; min/max
+ builder.add(Arguments.of(values.clone(), new int[] {0}));
+ builder.add(Arguments.of(values.clone(), new int[] {size - 1}));
+ builder.add(Arguments.of(values.clone(), new int[] {0, size - 1}));
+ builder.add(Arguments.of(zeros.clone(), new int[] {0}));
+ builder.add(Arguments.of(zeros.clone(), new int[] {size - 1}));
+ builder.add(Arguments.of(zeros.clone(), new int[] {0, size - 1}));
+ }
+ final int value = Integer.MIN_VALUE;
+ builder.add(Arguments.of(new int[] {}, new int[0]));
+ builder.add(Arguments.of(new int[] {value}, new int[] {0}));
+ builder.add(Arguments.of(new int[] {0, value}, new int[] {1}));
+ builder.add(Arguments.of(new int[] {value, value, value}, new int[]
{2}));
+ builder.add(Arguments.of(new int[] {value, 0, 0, value}, new int[]
{3}));
+ builder.add(Arguments.of(new int[] {value, 0, 0, value}, new int[] {1,
2}));
+ builder.add(Arguments.of(new int[] {value, 0, 1, 0, value}, new int[]
{1, 3}));
+ builder.add(Arguments.of(new int[] {value, 0, 0}, new int[] {0, 2}));
+ builder.add(Arguments.of(new int[] {value, 123, 0, -456, 0, value},
new int[] {0, 1, 3}));
+ // Dual-pivot with a large middle region (> 5 / 8) requires equal
elements loop
+ final int n = 128;
+ final int[] x = IntStream.range(0, n).toArray();
+ // Put equal elements in the central region:
+ // 2/16 6/16 10/16 14/16
+ // | <P1 | P1 | P1< & < P2 | P2 | >P2 |
+ final int sixteenth = n / 16;
+ final int i2 = 2 * sixteenth;
+ final int i6 = 6 * sixteenth;
+ final int p1 = x[i2];
+ final int p2 = x[n - i2];
+ // Lots of values equal to the pivots
+ Arrays.fill(x, i2, i6, p1);
+ Arrays.fill(x, n - i6, n - i2, p2);
+ // Equal value in between the pivots
+ Arrays.fill(x, i6, n - i6, (p1 + p2) / 2);
+ // Shuffle this and partition in the middle.
+ // Also partition with the pivots in P1 and P2 using thirds.
+ final int third = (int) (n / 3.0);
+ // Use a fix seed to ensure we hit coverage with only 5 loops.
+ rng = RandomSource.XO_SHI_RO_128_PP.create(-8111061151820577011L);
+ for (int i = 0; i < 5; i++) {
+ builder.add(Arguments.of(shuffle(rng, x.clone()), new int[] {n >>
1}));
+ builder.add(Arguments.of(shuffle(rng, x.clone()),
+ new int[] {third, 2 * third}));
+ }
+ // A single value smaller/greater than the pivot at the
left/right/both ends
+ Arrays.fill(x, 1);
+ for (int i = 0; i <= 2; i++) {
+ for (int j = 0; j <= 2; j++) {
+ x[n - 1] = i;
+ x[0] = j;
+ builder.add(Arguments.of(x.clone(), new int[] {50}));
+ }
+ }
+ // Reverse data. Makes it simple to detect failed range selection.
+ final int[] a = IntStream.range(0, 50).toArray();
+ for (int i = -1, j = a.length; ++i < --j;) {
+ final int v = a[i];
+ a[i] = a[j];
+ a[j] = v;
+ }
+ builder.add(Arguments.of(a, new int[] {1, 1}));
+ builder.add(Arguments.of(a, new int[] {1, 2}));
+ builder.add(Arguments.of(a, new int[] {10, 12}));
+ builder.add(Arguments.of(a, new int[] {10, 42}));
+ builder.add(Arguments.of(a, new int[] {1, 48}));
+ builder.add(Arguments.of(a, new int[] {48, 49}));
+ return builder.build();
+ }
+
+ static Stream<Arguments> testIntPartitionBigData() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create(123);
+ // Sizes above the threshold (1200) for recursive partitioning
+ for (final int size : new int[] {1000, 5000, 10000}) {
+ final int[] a = IntStream.range(0, size).toArray();
+ // With repeat elements
+ final int[] b = rng.ints(size, 0, size >> 3).toArray();
+ for (int i = 0; i < 15; i++) {
+ builder.add(Arguments.of(
+ shuffle(rng, a.clone()),
+ new int[] {rng.nextInt(size)}));
+ builder.add(Arguments.of(b.clone(),
+ new int[] {rng.nextInt(size)}));
+ }
+ }
+ // Hit Floyd-Rivest sub-sampling conditions.
+ // Close to edge but outside edge select size.
+ final int n = 7000;
+ final int[] x = IntStream.range(0, n).toArray();
+ builder.add(Arguments.of(x.clone(), new int[] {20}));
+ builder.add(Arguments.of(x.clone(), new int[] {n - 1 - 20}));
+ // Constant value when using FR partitioning
+ Arrays.fill(x, 123);
+ builder.add(Arguments.of(x, new int[] {x.length >>> 1}));
+ return builder.build();
+ }
+
+ @ParameterizedTest
+ @MethodSource
+ void testIntExpandPartition(int[] values, int start, int end, int pivot0,
int pivot1) {
+ final int[] upper = new int[1];
+ final int[] sorted = sort(values);
+ final int v = values[pivot0];
+ final int p0 = QuickSelect.expandPartition(values, 0, values.length -
1, start, end, pivot0, pivot1, upper);
+ final int p1 = upper[0];
+ for (int i = 0; i < p0; i++) {
+ final int index = i;
+ Assertions.assertTrue(values[i] < v,
+ () -> String.format("[%d] : %s < %s", index, values[index],
v));
+ }
+ for (int i = p0; i <= p1; i++) {
+ final int index = i;
+ Assertions.assertEquals(v, values[i],
+ () -> String.format("[%d] : %s == %s", index, values[index],
v));
+ }
+ for (int i = p1 + 1; i < values.length; i++) {
+ final int index = i;
+ Assertions.assertTrue(values[i] > v,
+ () -> String.format("[%d] : %s > %s", index, values[index],
v));
+ }
+ Arrays.sort(values);
+ Assertions.assertArrayEquals(sorted, values, "Data destroyed");
+ }
+
+ static Stream<Arguments> testIntExpandPartition() {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ // Create data:
+ // |l |start |p0 p1| end| r|
+ // | ??? | < | == | > | ??? |
+ // Arguments: data, start, end, pivot0, pivot1
+
+ // Create the data with unique values 42 and 0 either side of
+ // [start, end] (e.g. region ???). These are permuted for -1 and 10
+ // to create cases that may or not have to swap elements.
+
+ // Single pivot
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 3, 4, 0}, 1,
4, 2, 2);
+ // Pivot range
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 2, 3, 0}, 1,
4, 2, 3);
+ // Single pivot at start/end
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 3, 4, 0}, 1,
4, 1, 1);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 3, 4, 0}, 1,
4, 4, 4);
+ // Pivot range at start/end
+ addExpandPartitionArguments(builder, new int[] {42, 1, 1, 2, 3, 0}, 1,
4, 1, 2);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 3, 3, 0}, 1,
4, 3, 4);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 2, 2, 0}, 1,
4, 2, 4);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 1, 1, 2, 0}, 1,
4, 1, 3);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 1, 1, 1, 0}, 1,
4, 1, 4);
+
+ // Single pivot at left/right
+ addExpandPartitionArguments(builder, new int[] {1, 2, 3, 4, 0}, 0, 3,
0, 0);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 3, 4}, 1, 4,
4, 4);
+ // Pivot range at left/right
+ addExpandPartitionArguments(builder, new int[] {1, 1, 2, 3, 4, 0}, 0,
4, 0, 1);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 3, 4, 4}, 1,
5, 4, 5);
+ addExpandPartitionArguments(builder, new int[] {1, 1, 1, 1, 2, 0}, 0,
4, 0, 3);
+ addExpandPartitionArguments(builder, new int[] {42, 3, 4, 4, 4, 4}, 1,
5, 2, 5);
+ addExpandPartitionArguments(builder, new int[] {1, 1, 1, 1, 1, 0}, 0,
4, 0, 4);
+ addExpandPartitionArguments(builder, new int[] {42, 4, 4, 4, 4, 4}, 1,
5, 1, 5);
+
+ // Minimum range: [start, end] == length 2
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 0}, 1, 2, 1,
1);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2, 0}, 1, 2, 2,
2);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 1, 0}, 1, 2, 1,
2);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2}, 1, 2, 1, 1);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 2}, 1, 2, 2, 2);
+ addExpandPartitionArguments(builder, new int[] {42, 1, 1}, 1, 2, 1, 2);
+ addExpandPartitionArguments(builder, new int[] {1, 2, 0}, 0, 1, 0, 0);
+ addExpandPartitionArguments(builder, new int[] {1, 2, 0}, 0, 1, 1, 1);
+ addExpandPartitionArguments(builder, new int[] {1, 1, 0}, 0, 1, 0, 1);
+ addExpandPartitionArguments(builder, new int[] {1, 2}, 0, 1, 0, 0);
+ addExpandPartitionArguments(builder, new int[] {1, 2}, 0, 1, 1, 1);
+ addExpandPartitionArguments(builder, new int[] {1, 1}, 0, 1, 0, 1);
+
+ return builder.build();
+ }
+
+ private static void addExpandPartitionArguments(Stream.Builder<Arguments>
builder,
+ int[] a, int start, int end, int pivot0, int pivot1) {
+ builder.add(Arguments.of(a.clone(), start, end, pivot0, pivot1));
+ final int[] b = a.clone();
+ if (replace(a, 42, -1)) {
+ builder.add(Arguments.of(a.clone(), start, end, pivot0, pivot1));
+ if (replace(a, 0, 10)) {
+ builder.add(Arguments.of(a, start, end, pivot0, pivot1));
+ }
+ }
+ if (replace(b, 0, 10)) {
+ builder.add(Arguments.of(b, start, end, pivot0, pivot1));
+ }
+ }
+
+ private static boolean replace(int[] a, int x, int y) {
+ boolean updated = false;
+ for (int i = 0; i < a.length; i++) {
+ if (a[i] == x) {
+ a[i] = y;
+ updated = true;
+ }
+ }
+ return updated;
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort"})
+ void testIntSortUsingHeapSelect(int[] values) {
+ Assumptions.assumeTrue(values.length > 0);
+ assertSort(values, x -> {
+ final int right = x.length - 1;
+ // heapSelect is robust to right <= left
+ QuickSelect.heapSelect(x, 0, right, 0, right);
+ });
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort"})
+ void testIntSortUsingHeapSelectLeft(int[] values) {
+ Assumptions.assumeTrue(values.length > 0);
+ assertSort(values, x -> {
+ final int right = x.length - 1;
+ if (right < 1) {
+ return;
+ }
+ QuickSelect.heapSelectLeft(x, 0, right, 0, right);
+ });
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort"})
+ void testIntSortUsingHeapSelectRight(int[] values) {
+ Assumptions.assumeTrue(values.length > 0);
+ assertSort(values, x -> {
+ final int right = x.length - 1;
+ if (right < 1) {
+ return;
+ }
+ QuickSelect.heapSelectRight(x, 0, right, 0, right);
+ });
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort"})
+ void testIntSortUsingSelection(int[] values) {
+ // This tests that the select function performs
+ // a full sort when the interval is saturated
+ assertSort(values, a -> {
+ final int right = a.length - 1;
+ if (right < 1) {
+ return;
+ }
+ QuickSelect.dualPivotQuickSelect(a, 0, right, new RangeInterval(0,
right),
+
QuickSelect.dualPivotFlags(QuickSelect.dualPivotMaxDepth(right), 20));
+ });
+ }
+
+ private static void assertSort(int[] values, Consumer<int[]> function) {
+ final int[] data = values.clone();
+ final int[] sorted = sort(values);
+ function.accept(data);
+ Assertions.assertArrayEquals(sorted, data);
+ }
+
+ static Stream<int[]> testIntSort() {
+ final Stream.Builder<int[]> builder = Stream.builder();
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create(123);
+ // Sizes above and below the threshold for partitioning
+ for (final int size : new int[] {5, 50}) {
+ int[] a = new int[size];
+ Arrays.fill(a, 123);
+ builder.add(a.clone());
+ for (int ii = 0; ii < size; ii++) {
+ a[ii] = ii;
+ }
+ builder.add(a.clone());
+ for (int ii = 0; ii < size; ii++) {
+ a[ii] = size - ii;
+ }
+ builder.add(a.clone());
+ for (int i = 0; i < 5; i++) {
+ a = rng.ints(size).toArray();
+ builder.add(a.clone());
+ final int j = rng.nextInt(size);
+ final int k = rng.nextInt(size);
+ a[j] = 0;
+ a[k] = 0;
+ builder.add(a.clone());
+ for (int z = 0; z < size; z++) {
+ a[z] = rng.nextBoolean() ? 0 : 1;
+ }
+ builder.add(a.clone());
+ a[j] = -rng.nextInt();
+ a[k] = rng.nextInt();
+ builder.add(a.clone());
+ }
+ }
+ final int value = Integer.MIN_VALUE;
+ builder.add(new int[] {});
+ builder.add(new int[] {value});
+ builder.add(new int[] {0, value});
+ builder.add(new int[] {value, value, value});
+ builder.add(new int[] {value, 0, 0, value});
+ builder.add(new int[] {value, 0, 0});
+ builder.add(new int[] {value, 0, 1, 0});
+ builder.add(new int[] {value, 123, 0, 456, 0, value});
+ return builder.build();
+ }
+
@Test
void testDualPivotMaxDepth() {
// Reasonable behaviour at small x
diff --git
a/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SortingTest.java
b/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SortingTest.java
index 310947a5..83bdd708 100644
---
a/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SortingTest.java
+++
b/commons-numbers-arrays/src/test/java/org/apache/commons/numbers/arrays/SortingTest.java
@@ -155,7 +155,7 @@ class SortingTest {
}
builder.add(a);
for (int i = 0; i < 5; i++) {
- builder.add(rng.doubles(size).toArray().clone());
+ builder.add(rng.doubles(size).toArray());
}
}
return builder.build();
@@ -365,6 +365,334 @@ class SortingTest {
return builder.build();
}
+ private static double[] extractIndices(double[] values, int[] indices) {
+ final double[] data = new double[indices.length];
+ for (int i = 0; i < indices.length; i++) {
+ data[i] = values[indices[i]];
+ }
+ return data;
+ }
+
+ // int[]
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort"})
+ void testIntInsertionSort(int[] values) {
+ assertSort(values, x -> Sorting.sort(x, 0, x.length - 1));
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort", "testIntSort3"})
+ void testIntSort3(int[] values) {
+ final int[] data = Arrays.copyOf(values, 3);
+ assertSort(data, x -> Sorting.sort3(x, 0, 1, 2));
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort", "testIntSort5"})
+ void testIntSort5(int[] values) {
+ final int[] data = Arrays.copyOf(values, 5);
+ assertSort(data, x -> Sorting.sort5(x, 0, 1, 2, 3, 4));
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort3Internal"})
+ void testIntSort3Internal(int[] values, int[] indices) {
+ final int a = indices[0];
+ final int b = indices[1];
+ final int c = indices[2];
+ assertSortInternal(values, x -> Sorting.sort3(x, a, b, c), indices);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort5Internal"})
+ void testIntSort5Internal(int[] values, int[] indices) {
+ final int a = indices[0];
+ final int b = indices[1];
+ final int c = indices[2];
+ final int d = indices[3];
+ final int e = indices[4];
+ assertSortInternal(values, x -> Sorting.sort5(x, a, b, c, d, e),
indices);
+ }
+
+ /**
+ * Assert that the sort {@code function} computes the same result as
+ * {@link Arrays#sort(int[])}.
+ *
+ * @param values Data.
+ * @param function Sort function.
+ */
+ private static void assertSort(int[] values, Consumer<int[]> function) {
+ final int[] expected = values.clone();
+ Arrays.sort(expected);
+ final int[] actual = values.clone();
+ function.accept(actual);
+ Assertions.assertArrayEquals(expected, actual, "Invalid sort");
+ }
+
+ /**
+ * Assert that the sort {@code function} computes the same result as
+ * {@link Arrays#sort(int[])} run on the provided {@code indices}.
+ *
+ * @param values Data.
+ * @param function Sort function.
+ * @param indices Indices.
+ */
+ private static void assertSortInternal(int[] values, Consumer<int[]>
function, int... indices) {
+ Assertions.assertFalse(containsDuplicates(indices), () -> "Duplicate
indices: " + Arrays.toString(indices));
+ // Pick out the data to sort
+ final int[] expected = extractIndices(values, indices);
+ Arrays.sort(expected);
+ final int[] data = values.clone();
+ function.accept(data);
+ // Pick out the data that was sorted
+ final int[] actual = extractIndices(data, indices);
+ Assertions.assertArrayEquals(expected, actual, "Invalid sort");
+ // Check outside the sorted indices
+ OUTSIDE: for (int i = 0; i < values.length; i++) {
+ for (final int ignore : indices) {
+ if (i == ignore) {
+ continue OUTSIDE;
+ }
+ }
+ Assertions.assertEquals(values[i], data[i]);
+ }
+ }
+
+ static Stream<int[]> testIntSort() {
+ final Stream.Builder<int[]> builder = Stream.builder();
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create();
+ for (final int size : new int[] {10, 15}) {
+ int[] a = new int[size];
+ Arrays.fill(a, 123);
+ builder.add(a.clone());
+ for (int ii = 0; ii < size; ii++) {
+ a[ii] = ii;
+ }
+ builder.add(a.clone());
+ for (int ii = 0; ii < size; ii++) {
+ a[ii] = size - ii;
+ }
+ builder.add(a);
+ for (int i = 0; i < 5; i++) {
+ builder.add(rng.ints(size).toArray());
+ }
+ }
+ return builder.build();
+ }
+
+ static Stream<int[]> testIntSort3() {
+ // Permutations is 3! = 6
+ final int x = 335;
+ final int y = 123;
+ final int z = -999;
+ final int[][] a = {
+ {x, y, z},
+ {x, z, y},
+ {z, x, y},
+ {y, x, z},
+ {y, z, x},
+ {z, y, x},
+ };
+ return Arrays.stream(a);
+ }
+
+ static Stream<int[]> testIntSort5() {
+ final Stream.Builder<int[]> builder = Stream.builder();
+ final int[] a = new int[5];
+ // Permutations is 5! = 120
+ final int shift = 42;
+ for (int i = 0; i < 5; i++) {
+ a[0] = i + shift;
+ for (int j = 0; j < 5; j++) {
+ if (j == i) {
+ continue;
+ }
+ a[1] = j + shift;
+ for (int k = 0; k < 5; k++) {
+ if (k == j || k == i) {
+ continue;
+ }
+ a[2] = k + shift;
+ for (int l = 0; l < 5; l++) {
+ if (l == k || l == j || l == i) {
+ continue;
+ }
+ a[3] = l + shift;
+ for (int m = 0; m < 5; m++) {
+ if (m == l || m == k || m == j || m == i) {
+ continue;
+ }
+ a[3] = m + shift;
+ builder.add(a.clone());
+ }
+ }
+ }
+ }
+ }
+ return builder.build();
+ }
+
+ static Stream<Arguments> testIntSort3Internal() {
+ return testIntSortInternal(3);
+ }
+
+ static Stream<Arguments> testIntSort5Internal() {
+ return testIntSortInternal(5);
+ }
+
+ static Stream<Arguments> testIntSortInternal(int k) {
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create();
+ for (final int size : new int[] {k, 2 * k, 4 * k}) {
+ final PermutationSampler s = new PermutationSampler(rng, size, k);
+ for (int i = k * k; i-- >= 0;) {
+ final int[] a = rng.ints(size).toArray();
+ final int[] indices = s.sample();
+ builder.add(Arguments.of(a, indices));
+ }
+ }
+ return builder.build();
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort4Internal"})
+ void testIntLowerMedian4Internal(int[] values, int[] indices) {
+ final int a = indices[0];
+ final int b = indices[1];
+ final int c = indices[2];
+ final int d = indices[3];
+ assertMedian(values, x -> {
+ Sorting.lowerMedian4(x, a, b, c, d);
+ return b;
+ }, true, false, indices);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort4Internal"})
+ void testIntUpperMedian4Internal(int[] values, int[] indices) {
+ final int a = indices[0];
+ final int b = indices[1];
+ final int c = indices[2];
+ final int d = indices[3];
+ assertMedian(values, x -> {
+ Sorting.upperMedian4(x, a, b, c, d);
+ return c;
+ }, false, false, indices);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort4"})
+ void testIntLowerMedian4(int[] a) {
+ // This method computes in place
+ assertMedian(a, x -> {
+ Sorting.lowerMedian4(x, 0, 1, 2, 3);
+ return 1;
+ }, true, true, 0, 1, 2, 3);
+ }
+
+ @ParameterizedTest
+ @MethodSource(value = {"testIntSort4"})
+ void testIntUpperMedian4(int[] a) {
+ // This method computes in place
+ assertMedian(a, x -> {
+ Sorting.upperMedian4(x, 0, 1, 2, 3);
+ return 2;
+ }, false, true, 0, 1, 2, 3);
+ }
+
+ /**
+ * Assert that the median {@code function} computes the same result as
+ * {@link Arrays#sort(int[])} run on the provided {@code indices}.
+ *
+ * @param values Data.
+ * @param function Sort function.
+ * @param lower For even lengths use the lower median; else the upper
median.
+ * @param stable If true then no swaps should be made on the second pass.
+ * @param indices Indices.
+ */
+ private static void assertMedian(int[] values, ToIntFunction<int[]>
function,
+ boolean lower, boolean stable, int... indices) {
+ Assertions.assertFalse(containsDuplicates(indices), () -> "Duplicate
indices: " + Arrays.toString(indices));
+ // Pick out the data to sort
+ final int[] expected = extractIndices(values, indices);
+ Arrays.sort(expected);
+ final int[] data = values.clone();
+ final int m = function.applyAsInt(data);
+ Assertions.assertEquals(expected[(lower ? -1 : 0) + (expected.length
>>> 1)], data[m]);
+ // Check outside the sorted indices
+ OUTSIDE: for (int i = 0; i < values.length; i++) {
+ for (final int ignore : indices) {
+ if (i == ignore) {
+ continue OUTSIDE;
+ }
+ }
+ Assertions.assertEquals(values[i], data[i]);
+ }
+ // This is not a strict requirement but check that no swaps occur on a
second pass
+ if (stable) {
+ final int[] x = data.clone();
+ final int m2 = function.applyAsInt(data);
+ Assertions.assertEquals(m, m2);
+ Assertions.assertArrayEquals(x, data);
+ }
+ }
+
+
+ static Stream<int[]> testIntSort4() {
+ final Stream.Builder<int[]> builder = Stream.builder();
+ final int[] a = new int[4];
+ // Permutations is 4! = 24
+ final int shift = 42;
+ for (int i = 0; i < 4; i++) {
+ a[0] = i + shift;
+ for (int j = 0; j < 4; j++) {
+ if (j == i) {
+ continue;
+ }
+ a[1] = j + shift;
+ for (int k = 0; k < 4; k++) {
+ if (k == j || k == i) {
+ continue;
+ }
+ a[2] = k + shift;
+ for (int l = 0; l < 4; l++) {
+ if (l == k || l == j || l == i) {
+ continue;
+ }
+ a[3] = l + shift;
+ builder.add(a.clone());
+ }
+ }
+ }
+ }
+ return builder.build();
+ }
+
+ static Stream<Arguments> testIntSort4Internal() {
+ final int k = 4;
+ final Stream.Builder<Arguments> builder = Stream.builder();
+ final UniformRandomProvider rng =
RandomSource.XO_SHI_RO_128_PP.create();
+ for (final int size : new int[] {k, 2 * k, 4 * k}) {
+ int[] a = rng.ints(size).toArray();
+ final PermutationSampler s = new PermutationSampler(rng, size, k);
+ for (int i = k * k; i-- >= 0;) {
+ a = rng.ints(size).toArray();
+ final int[] indices = s.sample();
+ builder.add(Arguments.of(a, indices));
+ }
+ }
+ return builder.build();
+ }
+
+ private static int[] extractIndices(int[] values, int[] indices) {
+ final int[] data = new int[indices.length];
+ for (int i = 0; i < indices.length; i++) {
+ data[i] = values[indices[i]];
+ }
+ return data;
+ }
+
// Sorting unique indices
@ParameterizedTest
@@ -451,16 +779,6 @@ class SortingTest {
return builder.build();
}
- // Helper methods
-
- private static double[] extractIndices(double[] values, int[] indices) {
- final double[] data = new double[indices.length];
- for (int i = 0; i < indices.length; i++) {
- data[i] = values[indices[i]];
- }
- return data;
- }
-
private static boolean containsDuplicates(int[] indices) {
for (int i = 0; i < indices.length; i++) {
for (int j = 0; j < i; j++) {
diff --git
a/commons-numbers-examples/examples-jmh/src/main/java/org/apache/commons/numbers/examples/jmh/arrays/SelectionPerformance.java
b/commons-numbers-examples/examples-jmh/src/main/java/org/apache/commons/numbers/examples/jmh/arrays/SelectionPerformance.java
index ade2484e..d2ac0557 100644
---
a/commons-numbers-examples/examples-jmh/src/main/java/org/apache/commons/numbers/examples/jmh/arrays/SelectionPerformance.java
+++
b/commons-numbers-examples/examples-jmh/src/main/java/org/apache/commons/numbers/examples/jmh/arrays/SelectionPerformance.java
@@ -52,7 +52,7 @@ import org.openjdk.jmh.annotations.Warmup;
import org.openjdk.jmh.infra.Blackhole;
/**
- * Executes a benchmark of the selection of indices from {@code double} array
data.
+ * Executes a benchmark of the selection of indices from array data.
*/
@BenchmarkMode(Mode.AverageTime)
@OutputTimeUnit(TimeUnit.NANOSECONDS)
@@ -456,6 +456,18 @@ public class SelectionPerformance {
return getDataSample(order[index]);
}
+ /**
+ * Gets the sample for the given {@code index}.
+ *
+ * <p>This is returned in a randomized order per iteration.
+ *
+ * @param index Index.
+ * @return the data sample
+ */
+ public int[] getIntData(int index) {
+ return getIntDataSample(order[index]);
+ }
+
/**
* Gets the sample for the given {@code index}.
*
@@ -471,6 +483,22 @@ public class SelectionPerformance {
return x;
}
+ /**
+ * Gets the sample for the given {@code index}.
+ *
+ * @param index Index.
+ * @return the data sample
+ */
+ protected int[] getIntDataSample(int index) {
+ // For parity with other methods do not use data.clone()
+ final int[] a = data[index];
+ final int[] x = new int[a.length];
+ for (int i = -1; ++i < a.length;) {
+ x[i] = a[i];
+ }
+ return x;
+ }
+
/**
* Gets the sample size for the given {@code index}.
*
@@ -1247,6 +1275,12 @@ public class SelectionPerformance {
return super.getDataSample(order[index] / repeats);
}
+ /** {@inheritDoc} */
+ @Override
+ public int[] getIntData(int index) {
+ return super.getIntDataSample(order[index] / repeats);
+ }
+
/**
* Gets the indices for the given {@code index}.
*
@@ -2251,10 +2285,10 @@ public class SelectionPerformance {
}
/**
- * Source of a k-th selector function.
+ * Source of a k-th selector function for {@code double} data.
*/
@State(Scope.Benchmark)
- public static class KFunctionSource {
+ public static class DoubleKFunctionSource {
/** Name of the source. */
@Param({SORT + JDK, SPH,
SP, BM, SBM,
@@ -2469,6 +2503,66 @@ public class SelectionPerformance {
}
}
+ /**
+ * Source of a k-th selector function for {@code int} data.
+ */
+ @State(Scope.Benchmark)
+ public static class IntKFunctionSource {
+ /** Name of the source. */
+ @Param({SORT + JDK, SELECT})
+ private String name;
+
+ /** The action. */
+ private BiFunction<int[], int[], int[]> function;
+
+ /**
+ * @return the function
+ */
+ public BiFunction<int[], int[], int[]> getFunction() {
+ return function;
+ }
+
+ /**
+ * Create the function.
+ */
+ @Setup
+ public void setup() {
+ Objects.requireNonNull(name);
+ // Note: Always clone the indices
+ if (name.equals(BASELINE)) {
+ function = (data, indices) -> extractIndices(data,
indices.clone());
+ } else if (name.startsWith(SORT)) {
+ function = (data, indices) -> {
+ Arrays.sort(data);
+ return extractIndices(data, indices.clone());
+ };
+ } else if (name.startsWith(SELECT)) {
+ function = (data, indices) -> {
+ Selection.select(data, indices.clone());
+ return extractIndices(data, indices);
+ };
+ }
+ if (function == null) {
+ throw new IllegalStateException("Unknown int selector
function: " + name);
+ }
+ }
+
+ /**
+ * Extract the data at the specified indices.
+ *
+ * @param data Data.
+ * @param indices Indices.
+ * @return the data
+ */
+ private static int[] extractIndices(int[] data, int[] indices) {
+ final int[] x = new int[indices.length];
+ for (int i = 0; i < indices.length; i++) {
+ x[i] = data[indices[i]];
+ }
+ return x;
+ }
+ }
+
/**
* Source of a function that pre-processes NaN and signed zeros (-0.0).
*
@@ -2978,7 +3072,7 @@ public class SelectionPerformance {
* @param bh Data sink.
*/
@Benchmark
- public void partition(KFunctionSource function, KSource source, Blackhole
bh) {
+ public void doublePartition(DoubleKFunctionSource function, KSource
source, Blackhole bh) {
final int size = source.size();
final BiFunction<double[], int[], double[]> fun =
function.getFunction();
for (int j = -1; ++j < size;) {
@@ -2988,6 +3082,24 @@ public class SelectionPerformance {
}
}
+ /**
+ * Benchmark partitioning using k partition indices on {@code int} data.
+ *
+ * @param function Source of the function.
+ * @param source Source of the data.
+ * @param bh Data sink.
+ */
+ @Benchmark
+ public void intPartition(IntKFunctionSource function, KSource source,
Blackhole bh) {
+ final int size = source.size();
+ final BiFunction<int[], int[], int[]> fun = function.getFunction();
+ for (int j = -1; ++j < size;) {
+ // Note: This uses the indices without cloning. This is because
some
+ // functions do not destructively modify the data.
+ bh.consume(fun.apply(source.getIntData(j), source.getIndices(j)));
+ }
+ }
+
/**
* Benchmark partitioning of an interval of indices a set distance from
the edge.
* This is used to benchmark the switch from quickselect partitioning to
edgeselect.
diff --git a/src/main/resources/checkstyle/checkstyle-suppressions.xml
b/src/main/resources/checkstyle/checkstyle-suppressions.xml
index c8072ef8..54189b1f 100644
--- a/src/main/resources/checkstyle/checkstyle-suppressions.xml
+++ b/src/main/resources/checkstyle/checkstyle-suppressions.xml
@@ -71,6 +71,7 @@
<suppress checks="MethodLength" files=".*[/\\]BoostBetaTest.java" />
<suppress checks="UnnecessaryParentheses"
files=".*[/\\]gamma[/\\]BoostGammaTest.java" />
<suppress checks="ParameterNumber" files=".*[/\\]DDTest\.java" />
+ <suppress checks="FileLength" files=".*[/\\]arrays[/\\]SelectionTest.java" />
<suppress checks="UnnecessaryParentheses"
files=".*[/\\]arrays[/\\]SelectionTest.java" />
<suppress checks="FileLength"
files=".*[/\\]jmh[/\\]arrays[/\\]PartitionTest.java" />
<suppress checks="UnnecessaryParentheses"
files=".*[/\\]jmh[/\\]arrays[/\\]PartitionTest.java" />
