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/*
* Copyright (c) 2009, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
package com.sun.marlin;
import java.util.Arrays;
/**
* This class implements powerful and fully optimized versions, both
* sequential and parallel, of the Dual-Pivot Quicksort algorithm by
* Vladimir Yaroslavskiy, Jon Bentley and Josh Bloch. This algorithm
* offers O(n log(n)) performance on all data sets, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
*
* There are also additional algorithms, invoked from the Dual-Pivot
* Quicksort, such as mixed insertion sort, merging of runs and heap
* sort, counting sort and parallel merge sort.
*
* @author Vladimir Yaroslavskiy
* @author Jon Bentley
* @author Josh Bloch
* @author Doug Lea
*
* @version 2018.08.18
*
* @since 1.7 * 14
*/
public final class DualPivotQuicksort20191112Ext {
private static final boolean FAST_ISORT = true;
/*
From OpenJDK14 source code:
8226297: Dual-pivot quicksort improvements
Reviewed-by: dl, lbourges
Contributed-by: Vladimir Yaroslavskiy
Tue, 12 Nov 2019 13:49:40 -0800
*/
/**
* Prevents instantiation.
*/
private DualPivotQuicksort20191112Ext() {
}
/**
* Max array size to use mixed insertion sort.
*/
private static final int MAX_MIXED_INSERTION_SORT_SIZE = 65;
/**
* Max array size to use insertion sort.
*/
private static final int MAX_INSERTION_SORT_SIZE = 44;
/**
* Min array size to try merging of runs.
*/
private static final int MIN_TRY_MERGE_SIZE = 4 << 10;
/**
* Min size of the first run to continue with scanning.
*/
private static final int MIN_FIRST_RUN_SIZE = 16;
/**
* Min factor for the first runs to continue scanning.
*/
private static final int MIN_FIRST_RUNS_FACTOR = 7;
/**
* Max capacity of the index array for tracking runs.
*/
/* private */ static final int MAX_RUN_CAPACITY = 5 << 10;
/**
* Threshold of mixed insertion sort is incremented by this value.
*/
private static final int DELTA = 3 << 1;
/**
* Max recursive partitioning depth before using heap sort.
*/
private static final int MAX_RECURSION_DEPTH = 64 * DELTA;
/**
* Sorts the specified range of the array.
*
* @param sorter sorter context
* @param a the array to be sorted
* @param auxA auxiliary storage for the array to be sorted
* @param b the secondary array to be ordered
* @param auxB auxiliary storage for the permutation array to be handled
* @param low the index of the first element, inclusive, to be sorted
* @param high the index of the last element, exclusive, to be sorted
*/
static void sort(DPQSSorterContext sorter, int[] a, int[] auxA, int[] b, int[] auxB, int low, int high) {
/*
* LBO Shortcut: Invoke insertion sort on the leftmost part.
*/
if (FAST_ISORT && ((high - low) <= MAX_INSERTION_SORT_SIZE)) {
insertionSort(a, b, low, high);
return;
}
sorter.initBuffers(high, auxA, auxB);
sort(sorter, a, b, 0, low, high);
}
/**
* Sorts the specified array using the Dual-Pivot Quicksort and/or
* other sorts in special-cases, possibly with parallel partitions.
*
* @param sorter sorter context
* @param a the array to be sorted
* @param b the secondary array to be ordered
* @param bits the combination of recursion depth and bit flag, where
* the right bit "0" indicates that array is the leftmost part
* @param low the index of the first element, inclusive, to be sorted
* @param high the index of the last element, exclusive, to be sorted
*/
private static void sort(DPQSSorterContext sorter, int[] a, int[] b, int bits, int low, int high) {
while (true) {
int end = high - 1, size = high - low;
/*
* Run mixed insertion sort on small non-leftmost parts.
*/
if (size < MAX_MIXED_INSERTION_SORT_SIZE + bits && (bits & 1) > 0) {
mixedInsertionSort(a, b, low, high - 3 * ((size >> 5) << 3), high);
return;
}
/*
* Invoke insertion sort on small leftmost part.
*/
if (size < MAX_INSERTION_SORT_SIZE) {
insertionSort(a, b, low, high);
return;
}
/*
* Check if the whole array or large non-leftmost
* parts are nearly sorted and then merge runs.
*/
if ((bits == 0 || size > MIN_TRY_MERGE_SIZE && (bits & 1) > 0)
&& tryMergeRuns(sorter, a, b, low, size)) {
return;
}
/*
* Switch to heap sort if execution
* time is becoming quadratic.
*/
if ((bits += DELTA) > MAX_RECURSION_DEPTH) {
heapSort(a, b, low, high);
return;
}
/*
* Use an inexpensive approximation of the golden ratio
* to select five sample elements and determine pivots.
*/
int step = (size >> 3) * 3 + 3;
/*
* Five elements around (and including) the central element
* will be used for pivot selection as described below. The
* unequal choice of spacing these elements was empirically
* determined to work well on a wide variety of inputs.
*/
int e1 = low + step;
int e5 = end - step;
int e3 = (e1 + e5) >>> 1;
int e2 = (e1 + e3) >>> 1;
int e4 = (e3 + e5) >>> 1;
int a3 = a[e3];
/*
* Sort these elements in place by the combination
* of 4-element sorting network and insertion sort.
*
* 5 ------o-----------o------------
* | |
* 4 ------|-----o-----o-----o------
* | | |
* 2 ------o-----|-----o-----o------
* | |
* 1 ------------o-----o------------
*/
if (a[e5] < a[e2]) { int t = a[e5]; a[e5] = a[e2]; a[e2] = t; }
if (a[e4] < a[e1]) { int t = a[e4]; a[e4] = a[e1]; a[e1] = t; }
if (a[e5] < a[e4]) { int t = a[e5]; a[e5] = a[e4]; a[e4] = t; }
if (a[e2] < a[e1]) { int t = a[e2]; a[e2] = a[e1]; a[e1] = t; }
if (a[e4] < a[e2]) { int t = a[e4]; a[e4] = a[e2]; a[e2] = t; }
if (a3 < a[e2]) {
if (a3 < a[e1]) {
a[e3] = a[e2]; a[e2] = a[e1]; a[e1] = a3;
} else {
a[e3] = a[e2]; a[e2] = a3;
}
} else if (a3 > a[e4]) {
if (a3 > a[e5]) {
a[e3] = a[e4]; a[e4] = a[e5]; a[e5] = a3;
} else {
a[e3] = a[e4]; a[e4] = a3;
}
}
// Pointers
int lower = low; // The index of the last element of the left part
int upper = end; // The index of the first element of the right part
/*
* Partitioning with 2 pivots in case of different elements.
*/
if (a[e1] < a[e2] && a[e2] < a[e3] && a[e3] < a[e4] && a[e4] < a[e5]) {
/*
* Use the first and fifth of the five sorted elements as
* the pivots. These values are inexpensive approximation
* of tertiles. Note, that pivot1 < pivot2.
*/
int pivotA1 = a[e1];
int pivotA2 = a[e5];
int pivotB1 = b[e1];
int pivotB2 = b[e5];
/*
* The first and the last elements to be sorted are moved
* to the locations formerly occupied by the pivots. When
* partitioning is completed, the pivots are swapped back
* into their final positions, and excluded from the next
* subsequent sorting.
*/
a[e1] = a[lower];
a[e5] = a[upper];
b[e1] = b[lower];
b[e5] = b[upper];
/*
* Skip elements, which are less or greater than the pivots.
*/
while (a[++lower] < pivotA1);
while (a[--upper] > pivotA2);
/*
* Backward 3-interval partitioning
*
* left part central part right part
* +------------------------------------------------------------+
* | < pivot1 | ? | pivot1 <= && <= pivot2 | > pivot2 |
* +------------------------------------------------------------+
* ^ ^ ^
* | | |
* lower k upper
*
* Invariants:
*
* all in (low, lower] < pivot1
* pivot1 <= all in (k, upper) <= pivot2
* all in [upper, end) > pivot2
*
* Pointer k is the last index of ?-part
*/
for (int unused = --lower, k = ++upper; --k > lower; ) {
int ak = a[k];
int bk = b[k];
if (ak < pivotA1) { // Move a[k] to the left side
while (lower < k) {
if (a[++lower] >= pivotA1) {
if (a[lower] > pivotA2) {
a[k] = a[--upper];
a[upper] = a[lower];
b[k] = b[ upper];
b[upper] = b[lower];
} else {
a[k] = a[lower];
b[k] = b[lower];
}
a[lower] = ak;
b[lower] = bk;
break;
}
}
} else if (ak > pivotA2) { // Move a[k] to the right side
a[k] = a[--upper];
a[upper] = ak;
b[k] = b[ upper];
b[upper] = bk;
}
}
/*
* Swap the pivots into their final positions.
*/
a[low] = a[lower]; a[lower] = pivotA1;
a[end] = a[upper]; a[upper] = pivotA2;
b[low] = b[lower]; b[lower] = pivotB1;
b[end] = b[upper]; b[upper] = pivotB2;
/*
* Sort non-left parts recursively (possibly in parallel),
* excluding known pivots.
*/
sort(sorter, a, b, bits | 1, lower + 1, upper);
sort(sorter, a, b, bits | 1, upper + 1, high);
} else { // Use single pivot in case of many equal elements
/*
* Use the third of the five sorted elements as the pivot.
* This value is inexpensive approximation of the median.
*/
int pivotA = a[e3];
int pivotB = b[e3];
/*
* The first element to be sorted is moved to the
* location formerly occupied by the pivot. After
* completion of partitioning the pivot is swapped
* back into its final position, and excluded from
* the next subsequent sorting.
*/
a[e3] = a[lower];
b[e3] = b[lower];
/*
* Traditional 3-way (Dutch National Flag) partitioning
*
* left part central part right part
* +------------------------------------------------------+
* | < pivot | ? | == pivot | > pivot |
* +------------------------------------------------------+
* ^ ^ ^
* | | |
* lower k upper
*
* Invariants:
*
* all in (low, lower] < pivot
* all in (k, upper) == pivot
* all in [upper, end] > pivot
*
* Pointer k is the last index of ?-part
*/
for (int k = ++upper; --k > lower; ) {
int ak = a[k];
if (ak != pivotA) {
a[k] = pivotA;
int bk = b[k];
if (ak < pivotA) { // Move a[k] to the left side
while (a[++lower] < pivotA);
if (a[lower] > pivotA) {
a[k] = a[--upper];
a[upper] = a[lower];
b[k] = b[ upper];
b[upper] = b[lower];
} else {
a[k] = a[lower];
b[k] = b[lower];
}
a[lower] = ak;
b[lower] = bk;
} else { // ak > pivot - Move a[k] to the right side
a[k] = a[--upper];
a[upper] = ak;
b[k] = b[ upper];
b[upper] = bk;
}
}
}
/*
* Swap the pivot into its final position.
*/
a[low] = a[lower]; a[lower] = pivotA;
b[low] = b[lower]; b[lower] = pivotB;
/*
* Sort the right part (possibly in parallel), excluding
* known pivot. All elements from the central part are
* equal and therefore already sorted.
*/
sort(sorter, a, b, bits | 1, upper, high);
}
high = lower; // Iterate along the left part
}
}
/**
* Sorts the specified range of the array using mixed insertion sort.
*
* Mixed insertion sort is combination of simple insertion sort,
* pin insertion sort and pair insertion sort.
*
* In the context of Dual-Pivot Quicksort, the pivot element
* from the left part plays the role of sentinel, because it
* is less than any elements from the given part. Therefore,
* expensive check of the left range can be skipped on each
* iteration unless it is the leftmost call.
*
* @param a the array to be sorted
* @param b the secondary array to be ordered
* @param low the index of the first element, inclusive, to be sorted
* @param end the index of the last element for simple insertion sort
* @param high the index of the last element, exclusive, to be sorted
*/
private static void mixedInsertionSort(int[] a, int[] b, int low, int end, int high) {
if (end == high) {
/*
* Invoke simple insertion sort on tiny array.
*/
for (int i; ++low < end; ) {
int ai = a[i = low];
if (ai < a[i - 1]) {
int bi = b[i];
while (ai < a[--i]) {
a[i + 1] = a[i];
b[i + 1] = b[i];
}
a[i + 1] = ai;
b[i + 1] = bi;
}
}
} else {
/*
* Start with pin insertion sort on small part.
*
* Pin insertion sort is extended simple insertion sort.
* The main idea of this sort is to put elements larger
* than an element called pin to the end of array (the
* proper area for such elements). It avoids expensive
* movements of these elements through the whole array.
*/
int pin = a[end];
for (int i, p = high; ++low < end; ) {
int ai = a[i = low];
int bi = b[i];
if (ai < a[i - 1]) { // Small element
/*
* Insert small element into sorted part.
*/
a[i] = a[i - 1];
b[i] = b[--i];
while (ai < a[--i]) {
a[i + 1] = a[i];
b[i + 1] = b[i];
}
a[i + 1] = ai;
b[i + 1] = bi;
} else if (p > i && ai > pin) { // Large element
/*
* Find element smaller than pin.
*/
while (a[--p] > pin);
/*
* Swap it with large element.
*/
if (p > i) {
ai = a[p];
a[p] = a[i];
bi = b[p];
b[p] = b[i];
}
/*
* Insert small element into sorted part.
*/
while (ai < a[--i]) {
a[i + 1] = a[i];
b[i + 1] = b[i];
}
a[i + 1] = ai;
b[i + 1] = bi;
}
}
/*
* Continue with pair insertion sort on remain part.
*/
for (int i; low < high; ++low) {
int a1 = a[i = low], a2 = a[++low];
int b1 = b[i], b2 = b[ low];
/*
* Insert two elements per iteration: at first, insert the
* larger element and then insert the smaller element, but
* from the position where the larger element was inserted.
*/
if (a1 > a2) {
while (a1 < a[--i]) {
a[i + 2] = a[i];
b[i + 2] = b[i];
}
a[++i + 1] = a1;
b[ i + 1] = b1;
while (a2 < a[--i]) {
a[i + 1] = a[i];
b[i + 1] = b[i];
}
a[i + 1] = a2;
b[i + 1] = b2;
} else if (a1 < a[i - 1]) {
while (a2 < a[--i]) {
a[i + 2] = a[i];
b[i + 2] = b[i];
}
a[++i + 1] = a2;
b[ i + 1] = b2;
while (a1 < a[--i]) {
a[i + 1] = a[i];
b[i + 1] = b[i];
}
a[i + 1] = a1;
b[i + 1] = b1;
}
}
}
}
/**
* Sorts the specified range of the array using insertion sort.
*
* @param a the array to be sorted
* @param b the secondary array to be ordered
* @param low the index of the first element, inclusive, to be sorted
* @param high the index of the last element, exclusive, to be sorted
*/
static void insertionSort(int[] a, int[] b, int low, int high) {
for (int i, k = low; ++k < high; ) {
int ai = a[i = k];
if (ai < a[i - 1]) {
int bi = b[i];
while (--i >= low && ai < a[i]) {
a[i + 1] = a[i];
b[i + 1] = b[i];
}
a[i + 1] = ai;
b[i + 1] = bi;
}
}
}
/**
* Sorts the specified range of the array using heap sort.
*
* @param a the array to be sorted
* @param b the secondary array to be ordered
* @param low the index of the first element, inclusive, to be sorted
* @param high the index of the last element, exclusive, to be sorted
*/
private static void heapSort(int[] a, int[] b, int low, int high) {
for (int k = (low + high) >>> 1; k > low; ) {
pushDown(a, b, --k, a[k], b[k], low, high);
}
while (--high > low) {
int maxA = a[low];
int maxB = b[low];
pushDown(a, b, low, a[high], b[high], low, high);
a[high] = maxA;
b[high] = maxB;
}
}
/**
* Pushes specified element down during heap sort.
*
* @param a the array to be sorted
* @param b the secondary array to be ordered
* @param p the start index
* @param valueA the given element in a
* @param valueB the given element in b
* @param low the index of the first element, inclusive, to be sorted
* @param high the index of the last element, exclusive, to be sorted
*/
private static void pushDown(int[] a, int[] b, int p, int valueA, int valueB, int low, int high) {
for (int k;; a[p] = a[k], b[p] = b[p = k]) {
k = (p << 1) - low + 2; // Index of the right child
if (k > high) {
break;
}
if (k == high || a[k] < a[k - 1]) {
--k;
}
if (a[k] <= valueA) {
break;
}
}
a[p] = valueA;
b[p] = valueB;
}
/**
* Tries to sort the specified range of the array.
*
* @param sorter sorter context
* @param a the array to be sorted
* @param b the secondary array to be ordered
* @param low the index of the first element to be sorted
* @param size the array size
* @return true if finally sorted, false otherwise
*/
private static boolean tryMergeRuns(DPQSSorterContext sorter, int[] a, int[] b, int low, int size) {
/*
* The run array is constructed only if initial runs are
* long enough to continue, run[i] then holds start index
* of the i-th sequence of elements in non-descending order.
*/
int[] run = null;
int high = low + size;
int count = 1, last = low;
/*
* Identify all possible runs.
*/
for (int k = low + 1; k < high; ) {
/*
* Find the end index of the current run.
*/
if (a[k - 1] < a[k]) {
// Identify ascending sequence
while (++k < high && a[k - 1] <= a[k]);
} else if (a[k - 1] > a[k]) {
// Identify descending sequence
while (++k < high && a[k - 1] >= a[k]);
// Reverse into ascending order
for (int i = last - 1, j = k, t; ++i < --j && a[i] > a[j]; ) {
t = a[i]; a[i] = a[j]; a[j] = t;
t = b[i]; b[i] = b[j]; b[j] = t;
}
} else { // Identify constant sequence
for (int ak = a[k]; ++k < high && ak == a[k]; );
if (k < high) {
continue;
}
}
/*
* Check special cases.
*/
if (sorter.runInit || run == null) {
sorter.runInit = false; // LBO
if (k == high) {
/*
* The array is monotonous sequence,
* and therefore already sorted.
*/
return true;
}
if (k - low < MIN_FIRST_RUN_SIZE) {
/*
* The first run is too small
* to proceed with scanning.
*/
return false;
}
// System.out.println("alloc run");
// run = new int[((size >> 10) | 0x7F) & 0x3FF];
run = sorter.run; // LBO: prealloc
run[0] = low;
} else if (a[last - 1] > a[last]) {
if (count > (k - low) >> MIN_FIRST_RUNS_FACTOR) {
/*
* The first runs are not long
* enough to continue scanning.
*/
return false;
}
if (++count == MAX_RUN_CAPACITY) {
/*
* Array is not highly structured.
*/
return false;
}
if (false && count == run.length) {
/*
* Increase capacity of index array.
*/
// System.out.println("alloc run (resize)");
run = Arrays.copyOf(run, count << 1);
}
}
run[count] = (last = k);
// fix ALMOST_CONTIGUOUS ie consecutive (ascending / descending runs)
if (k < high - 1) {
k++; // LBO
}
}
/*
* Merge runs of highly structured array.
*/
if (count > 1) {
int[] auxA = sorter.auxA;
int[] auxB = sorter.auxB;
int offset = low;
// LBO: prealloc
if ((auxA.length < size || auxB.length < size)) {
// System.out.println("alloc aux: "+size);
auxA = new int[size];
auxB = new int[size];
}
mergeRuns(a, auxA, b, auxB, offset, 1, run, 0, count);
}
return true;
}
/**
* Merges the specified runs.
*
* @param srcA the source array for the array to be sorted (a)
* @param dstA the temporary buffer used in merging (a)
* @param srcB the source array for the secondary array to be ordered (b)
* @param offset the start index in the source, inclusive
* @param dstB the temporary buffer used in merging (b)
* @param aim specifies merging: to source ( > 0), buffer ( < 0) or any ( == 0)
* @param run the start indexes of the runs, inclusive
* @param lo the start index of the first run, inclusive
* @param hi the start index of the last run, inclusive
* @return the destination where runs are merged
*/
private static int[] mergeRuns(int[] srcA, int[] dstA, int[] srcB, int[] dstB, int offset,
int aim, int[] run, int lo, int hi) {
if (hi - lo == 1) {
if (aim >= 0) {
return srcA;
}
for (int i = run[hi], j = i - offset, low = run[lo]; i > low;
--j, --i, dstA[j] = srcA[i], dstB[j] = srcB[i]
);
return dstA;
}
/*
* Split into approximately equal parts.
*/
int mi = lo, rmi = (run[lo] + run[hi]) >>> 1;
while (run[++mi + 1] <= rmi);
/*
* Merge the left and right parts.
*/
int[] a1, a2;
a1 = mergeRuns(srcA, dstA, srcB, dstB, offset, -aim, run, lo, mi);
a2 = mergeRuns(srcA, dstA, srcB, dstB, offset, 0, run, mi, hi);
int[] b1, b2;
b1 = a1 == srcA ? srcB : dstB;
b2 = a2 == srcA ? srcB : dstB;
int[] resA = a1 == srcA ? dstA : srcA;
int[] resB = a1 == srcA ? dstB : srcB;
int k = a1 == srcA ? run[lo] - offset : run[lo];
int lo1 = a1 == dstA ? run[lo] - offset : run[lo];
int hi1 = a1 == dstA ? run[mi] - offset : run[mi];
int lo2 = a2 == dstA ? run[mi] - offset : run[mi];
int hi2 = a2 == dstA ? run[hi] - offset : run[hi];
mergeParts(resA, resB, k, a1, b1, lo1, hi1, a2, b2, lo2, hi2);
return resA;
}
/**
* Merges the sorted parts.
*
* @param dstA the destination where parts are merged (a)
* @param dstB the destination where parts are merged (b)
* @param k the start index of the destination, inclusive
* @param a1 the first part (a)
* @param b1 the first part (b)
* @param lo1 the start index of the first part, inclusive
* @param hi1 the end index of the first part, exclusive
* @param a2 the second part (a)
* @param b2 the second part (b)
* @param lo2 the start index of the second part, inclusive
* @param hi2 the end index of the second part, exclusive
*/
private static void mergeParts(int[] dstA, int[] dstB, int k,
int[] a1, int[] b1, int lo1, int hi1, int[] a2, int[] b2, int lo2, int hi2) {
// ...
/*
* Merge small parts sequentially.
*/
while (lo1 < hi1 && lo2 < hi2) {
if (a1[lo1] < a2[lo2]) {
dstA[k] = a1[lo1];
dstB[k] = b1[lo1];
k++; lo1++;
} else {
dstA[k] = a2[lo2];
dstB[k] = b2[lo2];
k++; lo2++;
}
}
if (dstA != a1 || k < lo1) {
while (lo1 < hi1) {
dstA[k] = a1[lo1];
dstB[k] = b1[lo1];
k++; lo1++;
}
}
if (dstA != a2 || k < lo2) {
while (lo2 < hi2) {
dstA[k] = a2[lo2];
dstB[k] = b2[lo2];
k++; lo2++;
}
}
}
}
