/*
* Copyright 2009 Sun Microsystems, Inc. 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. Sun designates this
* particular file as subject to the "Classpath" exception as provided
* by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
* CA 95054 USA or visit www.sun.com if you need additional information or
* have any questions.
*/
package java.util;
/**
* This class implements the Dual-Pivot Quicksort algorithm by
* Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. The algorithm
* offers O(n log(n)) performance on many data sets that cause other
* quicksorts to degrade to quadratic performance, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
*
* @author Vladimir Yaroslavskiy
* @author Jon Bentley
* @author Josh Bloch
*
* @version 2009.11.09 m765.827.v8
*/
final class DualPivotQuicksort {
// Suppresses default constructor
private DualPivotQuicksort() {}
/*
* Tuning Parameters.
*/
/**
* If the length of an array to be sorted is less than this
* constant, insertion sort is used in preference to Quicksort.
*/
private static final int INSERTION_SORT_THRESHOLD = 32;
/**
* If the length of a byte array to be sorted is greater than
* this constant, counting sort is used in preference to Quicksort.
*/
private static final int COUNTING_SORT_THRESHOLD_FOR_BYTE = 128;
/**
* If the length of a short or char array to be sorted is greater
* than this constant, counting sort is used in preference to Quicksort.
*/
private static final int COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR = 32768;
/*
* Sorting methods for the seven primitive types.
*/
/**
* Sorts the specified array into ascending numerical order.
*
* @param a the array to be sorted
*/
public static void sort(int[] a) {
doSort(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(int[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
doSort(a, fromIndex, toIndex - 1);
}
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the
* {@code right} index is inclusive, and it does no range checking on
* {@code left} or {@code right}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(int[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
int ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(int[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { int t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { int t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { int t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { int t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { int t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { int t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { int t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { int t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { int t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
int pivot1 = a[e2]; a[e2] = a[left];
int pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
int ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
int ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Sorts the specified array into ascending numerical order.
*
* @param a the array to be sorted
*/
public static void sort(long[] a) {
doSort(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(long[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
doSort(a, fromIndex, toIndex - 1);
}
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the
* {@code right} index is inclusive, and it does no range checking on
* {@code left} or {@code right}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(long[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
long ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(long[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { long t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { long t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { long t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { long t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { long t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { long t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { long t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { long t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { long t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
long pivot1 = a[e2]; a[e2] = a[left];
long pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
long ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
long ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Sorts the specified array into ascending numerical order.
*
* @param a the array to be sorted
*/
public static void sort(short[] a) {
doSort(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(short[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
doSort(a, fromIndex, toIndex - 1);
}
/** The number of distinct short values. */
private static final int NUM_SHORT_VALUES = 1 << 16;
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the
* {@code right} index is inclusive, and it does no range checking on
* {@code left} or {@code right}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(short[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
short ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
// Use counting sort on huge arrays
int[] count = new int[NUM_SHORT_VALUES];
for (int i = left; i <= right; i++) {
count[a[i] - Short.MIN_VALUE]++;
}
for (int i = 0, k = left; i < count.length && k <= right; i++) {
short value = (short) (i + Short.MIN_VALUE);
for (int s = count[i]; s > 0; s--) {
a[k++] = value;
}
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(short[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { short t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { short t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { short t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { short t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { short t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { short t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { short t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { short t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { short t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
short pivot1 = a[e2]; a[e2] = a[left];
short pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
short ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
short ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Sorts the specified array into ascending numerical order.
*
* @param a the array to be sorted
*/
public static void sort(char[] a) {
doSort(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(char[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
doSort(a, fromIndex, toIndex - 1);
}
/** The number of distinct char values. */
private static final int NUM_CHAR_VALUES = 1 << 16;
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the
* {@code right} index is inclusive, and it does no range checking on
* {@code left} or {@code right}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(char[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
char ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else if (right-left+1 > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
// Use counting sort on huge arrays
int[] count = new int[NUM_CHAR_VALUES];
for (int i = left; i <= right; i++) {
count[a[i]]++;
}
for (int i = 0, k = left; i < count.length && k <= right; i++) {
for (int s = count[i]; s > 0; s--) {
a[k++] = (char) i;
}
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(char[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { char t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { char t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { char t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { char t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { char t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { char t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { char t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { char t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { char t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
char pivot1 = a[e2]; a[e2] = a[left];
char pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
char ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
char ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Sorts the specified array into ascending numerical order.
*
* @param a the array to be sorted
*/
public static void sort(byte[] a) {
doSort(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(byte[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
doSort(a, fromIndex, toIndex - 1);
}
/** The number of distinct byte values. */
private static final int NUM_BYTE_VALUES = 1 << 8;
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in that the
* {@code right} index is inclusive, and it does no range checking on
* {@code left} or {@code right}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(byte[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
byte ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else if (right - left + 1 > COUNTING_SORT_THRESHOLD_FOR_BYTE) {
// Use counting sort on huge arrays
int[] count = new int[NUM_BYTE_VALUES];
for (int i = left; i <= right; i++) {
count[a[i] - Byte.MIN_VALUE]++;
}
for (int i = 0, k = left; i < count.length && k <= right; i++) {
byte value = (byte) (i + Byte.MIN_VALUE);
for (int s = count[i]; s > 0; s--) {
a[k++] = value;
}
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(byte[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { byte t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { byte t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { byte t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { byte t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { byte t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { byte t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { byte t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { byte t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { byte t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
byte pivot1 = a[e2]; a[e2] = a[left];
byte pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
byte ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
byte ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Sorts the specified array into ascending numerical order.
*
* The {@code <} relation does not provide a total order on all float
* values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
* value compares neither less than, greater than, nor equal to any value,
* even itself. This method uses the total order imposed by the method
* {@link Float#compareTo}: {@code -0.0f} is treated as less than value
* {@code 0.0f} and {@code Float.NaN} is considered greater than any
* other value and all {@code Float.NaN} values are considered equal.
*
* @param a the array to be sorted
*/
public static void sort(float[] a) {
sortNegZeroAndNaN(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
*
The {@code <} relation does not provide a total order on all float
* values: {@code -0.0f == 0.0f} is {@code true} and a {@code Float.NaN}
* value compares neither less than, greater than, nor equal to any value,
* even itself. This method uses the total order imposed by the method
* {@link Float#compareTo}: {@code -0.0f} is treated as less than value
* {@code 0.0f} and {@code Float.NaN} is considered greater than any
* other value and all {@code Float.NaN} values are considered equal.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(float[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
sortNegZeroAndNaN(a, fromIndex, toIndex - 1);
}
/**
* Sorts the specified range of the array into ascending order. The
* sort is done in three phases to avoid expensive comparisons in the
* inner loop. The comparisons would be expensive due to anomalies
* associated with negative zero {@code -0.0f} and {@code Float.NaN}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void sortNegZeroAndNaN(float[] a, int left, int right) {
/*
* Phase 1: Count negative zeros and move NaNs to end of array
*/
final int NEGATIVE_ZERO = Float.floatToIntBits(-0.0f);
int numNegativeZeros = 0;
int n = right;
for (int k = left; k <= n; k++) {
float ak = a[k];
if (ak == 0.0f && NEGATIVE_ZERO == Float.floatToIntBits(ak)) {
a[k] = 0.0f;
numNegativeZeros++;
} else if (ak != ak) { // i.e., ak is NaN
a[k--] = a[n];
a[n--] = Float.NaN;
}
}
/*
* Phase 2: Sort everything except NaNs (which are already in place)
*/
doSort(a, left, n);
/*
* Phase 3: Turn positive zeros back into negative zeros as appropriate
*/
if (numNegativeZeros == 0) {
return;
}
// Find first zero element
int zeroIndex = findAnyZero(a, left, n);
for (int i = zeroIndex - 1; i >= left && a[i] == 0.0f; i--) {
zeroIndex = i;
}
// Turn the right number of positive zeros back into negative zeros
for (int i = zeroIndex, m = zeroIndex + numNegativeZeros; i < m; i++) {
a[i] = -0.0f;
}
}
/**
* Returns the index of some zero element in the specified range via
* binary search. The range is assumed to be sorted, and must contain
* at least one zero.
*
* @param a the array to be searched
* @param low the index of the first element, inclusive, to be searched
* @param high the index of the last element, inclusive, to be searched
*/
private static int findAnyZero(float[] a, int low, int high) {
while (true) {
int middle = (low + high) >>> 1;
float middleValue = a[middle];
if (middleValue < 0.0f) {
low = middle + 1;
} else if (middleValue > 0.0f) {
high = middle - 1;
} else { // middleValue == 0.0f
return middle;
}
}
}
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in three ways:
* {@code right} index is inclusive, it does no range checking on
* {@code left} or {@code right}, and it does not handle negative
* zeros or NaNs in the array.
*
* @param a the array to be sorted, which must not contain -0.0f or NaN
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(float[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
float ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(float[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { float t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { float t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { float t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { float t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { float t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { float t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { float t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { float t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { float t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
float pivot1 = a[e2]; a[e2] = a[left];
float pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
float ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
float ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Sorts the specified array into ascending numerical order.
*
*
The {@code <} relation does not provide a total order on all double
* values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
* value compares neither less than, greater than, nor equal to any value,
* even itself. This method uses the total order imposed by the method
* {@link Double#compareTo}: {@code -0.0d} is treated as less than value
* {@code 0.0d} and {@code Double.NaN} is considered greater than any
* other value and all {@code Double.NaN} values are considered equal.
*
* @param a the array to be sorted
*/
public static void sort(double[] a) {
sortNegZeroAndNaN(a, 0, a.length - 1);
}
/**
* Sorts the specified range of the array into ascending order. The range
* to be sorted extends from the index {@code fromIndex}, inclusive, to
* the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* the range to be sorted is empty.
*
*
The {@code <} relation does not provide a total order on all double
* values: {@code -0.0d == 0.0d} is {@code true} and a {@code Double.NaN}
* value compares neither less than, greater than, nor equal to any value,
* even itself. This method uses the total order imposed by the method
* {@link Double#compareTo}: {@code -0.0d} is treated as less than value
* {@code 0.0d} and {@code Double.NaN} is considered greater than any
* other value and all {@code Double.NaN} values are considered equal.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusive, to be sorted
* @param toIndex the index of the last element, exclusive, to be sorted
* @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws ArrayIndexOutOfBoundsException
* if {@code fromIndex < 0} or {@code toIndex > a.length}
*/
public static void sort(double[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex);
sortNegZeroAndNaN(a, fromIndex, toIndex - 1);
}
/**
* Sorts the specified range of the array into ascending order. The
* sort is done in three phases to avoid expensive comparisons in the
* inner loop. The comparisons would be expensive due to anomalies
* associated with negative zero {@code -0.0d} and {@code Double.NaN}.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void sortNegZeroAndNaN(double[] a, int left, int right) {
/*
* Phase 1: Count negative zeros and move NaNs to end of array
*/
final long NEGATIVE_ZERO = Double.doubleToLongBits(-0.0d);
int numNegativeZeros = 0;
int n = right;
for (int k = left; k <= n; k++) {
double ak = a[k];
if (ak == 0.0d && NEGATIVE_ZERO == Double.doubleToLongBits(ak)) {
a[k] = 0.0d;
numNegativeZeros++;
} else if (ak != ak) { // i.e., ak is NaN
a[k--] = a[n];
a[n--] = Double.NaN;
}
}
/*
* Phase 2: Sort everything except NaNs (which are already in place)
*/
doSort(a, left, n);
/*
* Phase 3: Turn positive zeros back into negative zeros as appropriate
*/
if (numNegativeZeros == 0) {
return;
}
// Find first zero element
int zeroIndex = findAnyZero(a, left, n);
for (int i = zeroIndex - 1; i >= left && a[i] == 0.0d; i--) {
zeroIndex = i;
}
// Turn the right number of positive zeros back into negative zeros
for (int i = zeroIndex, m = zeroIndex + numNegativeZeros; i < m; i++) {
a[i] = -0.0d;
}
}
/**
* Returns the index of some zero element in the specified range via
* binary search. The range is assumed to be sorted, and must contain
* at least one zero.
*
* @param a the array to be searched
* @param low the index of the first element, inclusive, to be searched
* @param high the index of the last element, inclusive, to be searched
*/
private static int findAnyZero(double[] a, int low, int high) {
while (true) {
int middle = (low + high) >>> 1;
double middleValue = a[middle];
if (middleValue < 0.0d) {
low = middle + 1;
} else if (middleValue > 0.0d) {
high = middle - 1;
} else { // middleValue == 0.0d
return middle;
}
}
}
/**
* Sorts the specified range of the array into ascending order. This
* method differs from the public {@code sort} method in three ways:
* {@code right} index is inclusive, it does no range checking on
* {@code left} or {@code right}, and it does not handle negative
* zeros or NaNs in the array.
*
* @param a the array to be sorted, which must not contain -0.0d and NaN
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void doSort(double[] a, int left, int right) {
// Use insertion sort on tiny arrays
if (right - left + 1 < INSERTION_SORT_THRESHOLD) {
for (int k = left + 1; k <= right; k++) {
double ak = a[k];
int j;
for (j = k - 1; j >= left && ak < a[j]; j--) {
a[j + 1] = a[j];
}
a[j + 1] = ak;
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/**
* Sorts the specified range of the array into ascending order by the
* Dual-Pivot Quicksort algorithm.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusive, to be sorted
* @param right the index of the last element, inclusive, to be sorted
*/
private static void dualPivotQuicksort(double[] a, int left, int right) {
// Compute indices of five evenly spaced elements
int sixth = (right - left + 1) / 6;
int e1 = left + sixth;
int e5 = right - sixth;
int e3 = (left + right) >>> 1; // The midpoint
int e4 = e3 + sixth;
int e2 = e3 - sixth;
// Sort these elements in place using a 5-element sorting network
if (a[e1] > a[e2]) { double t = a[e1]; a[e1] = a[e2]; a[e2] = t; }
if (a[e4] > a[e5]) { double t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
if (a[e1] > a[e3]) { double t = a[e1]; a[e1] = a[e3]; a[e3] = t; }
if (a[e2] > a[e3]) { double t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e1] > a[e4]) { double t = a[e1]; a[e1] = a[e4]; a[e4] = t; }
if (a[e3] > a[e4]) { double t = a[e3]; a[e3] = a[e4]; a[e4] = t; }
if (a[e2] > a[e5]) { double t = a[e2]; a[e2] = a[e5]; a[e5] = t; }
if (a[e2] > a[e3]) { double t = a[e2]; a[e2] = a[e3]; a[e3] = t; }
if (a[e4] > a[e5]) { double t = a[e4]; a[e4] = a[e5]; a[e5] = t; }
/*
* Use the second and fourth of the five sorted elements as pivots.
* These values are inexpensive approximations of the first and
* second terciles of the array. Note that pivot1 <= pivot2.
*
* The pivots are stored in local variables, and the first and
* the last of the sorted elements are moved to the locations
* formerly occupied by the pivots. When partitioning is complete,
* the pivots are swapped back into their final positions, and
* excluded from subsequent sorting.
*/
double pivot1 = a[e2]; a[e2] = a[left];
double pivot2 = a[e4]; a[e4] = a[right];
/*
* Partitioning
*
* left part center part right part
* ------------------------------------------------------------
* [ < pivot1 | pivot1 <= && <= pivot2 | ? | > pivot2 ]
* ------------------------------------------------------------
* ^ ^ ^
* | | |
* less k great
*/
// Pointers
int less = left + 1; // The index of first element of center part
int great = right - 1; // The index before first element of right part
boolean pivotsDiffer = pivot1 != pivot2;
if (pivotsDiffer) {
/*
* Invariants:
* all in (left, less) < pivot1
* pivot1 <= all in [less, k) <= pivot2
* all in (great, right) > pivot2
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
double ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else if (ak > pivot2) {
while (a[great] > pivot2 && k < great) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
} else { // Pivots are equal
/*
* Partition degenerates to the traditional 3-way
* (or "Dutch National Flag") partition:
*
* left part center part right part
* -------------------------------------------------
* [ < pivot | == pivot | ? | > pivot ]
* -------------------------------------------------
*
* ^ ^ ^
* | | |
* less k great
*
* Invariants:
*
* all in (left, less) < pivot
* all in [less, k) == pivot
* all in (great, right) > pivot
*
* Pointer k is the first index of ?-part
*/
for (int k = less; k <= great; k++) {
double ak = a[k];
if (ak == pivot1) {
continue;
}
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
} else {
while (a[great] > pivot1) {
great--;
}
a[k] = a[great];
a[great--] = ak;
ak = a[k];
if (ak < pivot1) {
a[k] = a[less];
a[less++] = ak;
}
}
}
}
// Swap pivots into their final positions
a[left] = a[less - 1]; a[less - 1] = pivot1;
a[right] = a[great + 1]; a[great + 1] = pivot2;
// Sort left and right parts recursively, excluding known pivot values
doSort(a, left, less - 2);
doSort(a, great + 2, right);
/*
* If pivot1 == pivot2, all elements from center
* part are equal and, therefore, already sorted
*/
if (!pivotsDiffer) {
return;
}
/*
* If center part is too large (comprises > 5/6 of
* the array), swap internal pivot values to ends
*/
if (less < e1 && e5 < great) {
while (a[less] == pivot1) {
less++;
}
for (int k = less + 1; k <= great; k++) {
if (a[k] == pivot1) {
a[k] = a[less];
a[less++] = pivot1;
}
}
while (a[great] == pivot2) {
great--;
}
for (int k = great - 1; k >= less; k--) {
if (a[k] == pivot2) {
a[k] = a[great];
a[great--] = pivot2;
}
}
}
// Sort center part recursively, excluding known pivot values
doSort(a, less, great);
}
/**
* Checks that {@code fromIndex} and {@code toIndex} are in
* the range and throws an appropriate exception, if they aren't.
*/
private static void rangeCheck(int length, int fromIndex, int toIndex) {
if (fromIndex > toIndex) {
throw new IllegalArgumentException(
"fromIndex(" + fromIndex + ") > toIndex(" + toIndex + ")");
}
if (fromIndex < 0) {
throw new ArrayIndexOutOfBoundsException(fromIndex);
}
if (toIndex > length) {
throw new ArrayIndexOutOfBoundsException(toIndex);
}
}
}