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提交 dac3d340 编写于 作者: A alanb
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6880672: Replace quicksort in java.util.Arrays with dual-pivot implementation 

Reviewed-by: jjb
Contributed-by: vladimir.yaroslavskiy@sun.com, joshua.bloch@google.com, jbentley@avaya.com
上级 5881c952
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make/java/java/FILES_java.gmk
浏览文件 @ dac3d340
...@@ -251,6 +251,7 @@ JAVA_JAVA_java = \ ...@@ -251,6 +251,7 @@ JAVA_JAVA_java = \
java/util/IdentityHashMap.java \ java/util/IdentityHashMap.java \
java/util/EnumMap.java \ java/util/EnumMap.java \
java/util/Arrays.java \ java/util/Arrays.java \
java/util/DualPivotQuicksort.java \
java/util/TimSort.java \ java/util/TimSort.java \
java/util/ComparableTimSort.java \ java/util/ComparableTimSort.java \
java/util/ConcurrentModificationException.java \ java/util/ConcurrentModificationException.java \
......
src/share/classes/java/util/Arrays.java
浏览文件 @ dac3d340
/* /*
* Copyright 1997-2008 Sun Microsystems, Inc. All Rights Reserved. * Copyright 1997-2009 Sun Microsystems, Inc. All Rights Reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
* *
* This code is free software; you can redistribute it and/or modify it * This code is free software; you can redistribute it and/or modify it
...@@ -29,1047 +29,458 @@ import java.lang.reflect.*; ...@@ -29,1047 +29,458 @@ import java.lang.reflect.*;
/** /**
* This class contains various methods for manipulating arrays (such as * This class contains various methods for manipulating arrays (such as
* sorting and searching). This class also contains a static factory * sorting and searching). This class also contains a static factory
* that allows arrays to be viewed as lists. * that allows arrays to be viewed as lists.
* *
* <p>The methods in this class all throw a <tt>NullPointerException</tt> if * <p>The methods in this class all throw a {@code NullPointerException},
* the specified array reference is null, except where noted. * if the specified array reference is null, except where noted.
* *
* <p>The documentation for the methods contained in this class includes * <p>The documentation for the methods contained in this class includes
* briefs description of the <i>implementations</i>. Such descriptions should * briefs description of the <i>implementations</i>. Such descriptions should
* be regarded as <i>implementation notes</i>, rather than parts of the * be regarded as <i>implementation notes</i>, rather than parts of the
* <i>specification</i>. Implementors should feel free to substitute other * <i>specification</i>. Implementors should feel free to substitute other
* algorithms, so long as the specification itself is adhered to. (For * algorithms, so long as the specification itself is adhered to. (For
* example, the algorithm used by <tt>sort(Object[])</tt> does not have to be * example, the algorithm used by {@code sort(Object[])} does not have to be
* a mergesort, but it does have to be <i>stable</i>.) * a MergeSort, but it does have to be <i>stable</i>.)
* *
* <p>This class is a member of the * <p>This class is a member of the
* <a href="{@docRoot}/../technotes/guides/collections/index.html"> * <a href="{@docRoot}/../technotes/guides/collections/index.html">
* Java Collections Framework</a>. * Java Collections Framework</a>.
* *
* @author Josh Bloch * @author Josh Bloch
* @author Neal Gafter * @author Neal Gafter
* @author John Rose * @author John Rose
* @since 1.2 * @since 1.2
*/ */
public class Arrays { public class Arrays {
// Suppresses default constructor, ensuring non-instantiability. // Suppresses default constructor, ensuring non-instantiability.
private Arrays() { private Arrays() {}
}
// Sorting // Sorting
/** /**
* Sorts the specified array of longs into ascending numerical order. * Sorts the specified array into ascending numerical order.
* The sorting algorithm is a tuned quicksort, adapted from Jon *
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* 1993). This algorithm offers n*log(n) performance on many data sets * offers O(n log(n)) performance on many data sets that cause other
* that cause other quicksorts to degrade to quadratic performance. * quicksorts to degrade to quadratic performance, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
*/ */
public static void sort(long[] a) { public static void sort(long[] a) {
sort1(a, 0, a.length); sort(a, 0, a.length);
} }
/** /**
* Sorts the specified range of the specified array of longs into * Sorts the specified range of the specified array into ascending order. The
* ascending numerical order. The range to be sorted extends from index * range of to be sorted extends from the index {@code fromIndex}, inclusive,
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive. * to the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.) * the range to be sorted is empty.
* *
* <p>The sorting algorithm is a tuned quicksort, adapted from Jon * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * offers O(n log(n)) performance on many data sets that cause other
* 1993). This algorithm offers n*log(n) performance on many data sets * quicksorts to degrade to quadratic performance, and is typically
* that cause other quicksorts to degrade to quadratic performance. * faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element (inclusive) to be * @param fromIndex the index of the first element, inclusively, to be sorted
* sorted * @param toIndex the index of the last element, exclusively, to be sorted
* @param toIndex the index of the last element (exclusive) to be sorted * @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt> * @throws ArrayIndexOutOfBoundsException
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or * if {@code fromIndex < 0} or {@code toIndex > a.length}
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(long[] a, int fromIndex, int toIndex) { public static void sort(long[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex); rangeCheck(a.length, fromIndex, toIndex);
sort1(a, fromIndex, toIndex-fromIndex); DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
} }
/** /**
* Sorts the specified array of ints into ascending numerical order. * Sorts the specified array into ascending numerical order.
* The sorting algorithm is a tuned quicksort, adapted from Jon *
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* 1993). This algorithm offers n*log(n) performance on many data sets * offers O(n log(n)) performance on many data sets that cause other
* that cause other quicksorts to degrade to quadratic performance. * quicksorts to degrade to quadratic performance, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
*/ */
public static void sort(int[] a) { public static void sort(int[] a) {
sort1(a, 0, a.length); sort(a, 0, a.length);
} }
/** /**
* Sorts the specified range of the specified array of ints into * Sorts the specified range of the specified array into ascending order. The
* ascending numerical order. The range to be sorted extends from index * range of to be sorted extends from the index {@code fromIndex}, inclusive,
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive. * to the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p> * the range to be sorted is empty.
* *
* The sorting algorithm is a tuned quicksort, adapted from Jon * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * offers O(n log(n)) performance on many data sets that cause other
* 1993). This algorithm offers n*log(n) performance on many data sets * quicksorts to degrade to quadratic performance, and is typically
* that cause other quicksorts to degrade to quadratic performance. * faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element (inclusive) to be * @param fromIndex the index of the first element, inclusively, to be sorted
* sorted * @param toIndex the index of the last element, exclusively, to be sorted
* @param toIndex the index of the last element (exclusive) to be sorted * @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt> * @throws ArrayIndexOutOfBoundsException
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or * if {@code fromIndex < 0} or {@code toIndex > a.length}
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(int[] a, int fromIndex, int toIndex) { public static void sort(int[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex); rangeCheck(a.length, fromIndex, toIndex);
sort1(a, fromIndex, toIndex-fromIndex); DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
} }
/** /**
* Sorts the specified array of shorts into ascending numerical order. * Sorts the specified array into ascending numerical order.
* The sorting algorithm is a tuned quicksort, adapted from Jon *
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* 1993). This algorithm offers n*log(n) performance on many data sets * offers O(n log(n)) performance on many data sets that cause other
* that cause other quicksorts to degrade to quadratic performance. * quicksorts to degrade to quadratic performance, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
*/ */
public static void sort(short[] a) { public static void sort(short[] a) {
sort1(a, 0, a.length); sort(a, 0, a.length);
} }
/** /**
* Sorts the specified range of the specified array of shorts into * Sorts the specified range of the specified array into ascending order. The
* ascending numerical order. The range to be sorted extends from index * range of to be sorted extends from the index {@code fromIndex}, inclusive,
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive. * to the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p> * the range to be sorted is empty.
* *
* The sorting algorithm is a tuned quicksort, adapted from Jon * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * offers O(n log(n)) performance on many data sets that cause other
* 1993). This algorithm offers n*log(n) performance on many data sets * quicksorts to degrade to quadratic performance, and is typically
* that cause other quicksorts to degrade to quadratic performance. * faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element (inclusive) to be * @param fromIndex the index of the first element, inclusively, to be sorted
* sorted * @param toIndex the index of the last element, exclusively, to be sorted
* @param toIndex the index of the last element (exclusive) to be sorted * @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt> * @throws ArrayIndexOutOfBoundsException
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or * if {@code fromIndex < 0} or {@code toIndex > a.length}
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(short[] a, int fromIndex, int toIndex) { public static void sort(short[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex); rangeCheck(a.length, fromIndex, toIndex);
sort1(a, fromIndex, toIndex-fromIndex); DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
} }
/** /**
* Sorts the specified array of chars into ascending numerical order. * Sorts the specified array into ascending numerical order.
* The sorting algorithm is a tuned quicksort, adapted from Jon *
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* 1993). This algorithm offers n*log(n) performance on many data sets * offers O(n log(n)) performance on many data sets that cause other
* that cause other quicksorts to degrade to quadratic performance. * quicksorts to degrade to quadratic performance, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
*/ */
public static void sort(char[] a) { public static void sort(char[] a) {
sort1(a, 0, a.length); sort(a, 0, a.length);
} }
/** /**
* Sorts the specified range of the specified array of chars into * Sorts the specified range of the specified array into ascending order. The
* ascending numerical order. The range to be sorted extends from index * range of to be sorted extends from the index {@code fromIndex}, inclusive,
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive. * to the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p> * the range to be sorted is empty.
* *
* The sorting algorithm is a tuned quicksort, adapted from Jon * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * offers O(n log(n)) performance on many data sets that cause other
* 1993). This algorithm offers n*log(n) performance on many data sets * quicksorts to degrade to quadratic performance, and is typically
* that cause other quicksorts to degrade to quadratic performance. * faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element (inclusive) to be * @param fromIndex the index of the first element, inclusively, to be sorted
* sorted * @param toIndex the index of the last element, exclusively, to be sorted
* @param toIndex the index of the last element (exclusive) to be sorted * @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt> * @throws ArrayIndexOutOfBoundsException
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or * if {@code fromIndex < 0} or {@code toIndex > a.length}
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(char[] a, int fromIndex, int toIndex) { public static void sort(char[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex); rangeCheck(a.length, fromIndex, toIndex);
sort1(a, fromIndex, toIndex-fromIndex); DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
} }
/** /**
* Sorts the specified array of bytes into ascending numerical order. * Sorts the specified array into ascending numerical order.
* The sorting algorithm is a tuned quicksort, adapted from Jon *
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* 1993). This algorithm offers n*log(n) performance on many data sets * offers O(n log(n)) performance on many data sets that cause other
* that cause other quicksorts to degrade to quadratic performance. * quicksorts to degrade to quadratic performance, and is typically
* faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
*/ */
public static void sort(byte[] a) { public static void sort(byte[] a) {
sort1(a, 0, a.length); sort(a, 0, a.length);
} }
/** /**
* Sorts the specified range of the specified array of bytes into * Sorts the specified range of the specified array into ascending order. The
* ascending numerical order. The range to be sorted extends from index * range of to be sorted extends from the index {@code fromIndex}, inclusive,
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive. * to the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)<p> * the range to be sorted is empty.
* *
* The sorting algorithm is a tuned quicksort, adapted from Jon * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * offers O(n log(n)) performance on many data sets that cause other
* 1993). This algorithm offers n*log(n) performance on many data sets * quicksorts to degrade to quadratic performance, and is typically
* that cause other quicksorts to degrade to quadratic performance. * faster than traditional (one-pivot) Quicksort implementations.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element (inclusive) to be * @param fromIndex the index of the first element, inclusively, to be sorted
* sorted * @param toIndex the index of the last element, exclusively, to be sorted
* @param toIndex the index of the last element (exclusive) to be sorted * @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt> * @throws ArrayIndexOutOfBoundsException
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or * if {@code fromIndex < 0} or {@code toIndex > a.length}
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(byte[] a, int fromIndex, int toIndex) { public static void sort(byte[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex); rangeCheck(a.length, fromIndex, toIndex);
sort1(a, fromIndex, toIndex-fromIndex); DualPivotQuicksort.sort(a, fromIndex, toIndex - 1);
} }
/** /**
* Sorts the specified array of doubles into ascending numerical order. * Sorts the specified array into ascending numerical order.
* <p>
* The <code>&lt;</code> relation does not provide a total order on
* all floating-point values; although they are distinct numbers
* <code>-0.0 == 0.0</code> is <code>true</code> and a NaN value
* compares neither less than, greater than, nor equal to any
* floating-point value, even itself. To allow the sort to
* proceed, instead of using the <code>&lt;</code> relation to
* determine ascending numerical order, this method uses the total
* order imposed by {@link Double#compareTo}. This ordering
* differs from the <code>&lt;</code> relation in that
* <code>-0.0</code> is treated as less than <code>0.0</code> and
* NaN is considered greater than any other floating-point value.
* For the purposes of sorting, all NaN values are considered
* equivalent and equal.
* <p>
* The sorting algorithm is a tuned quicksort, adapted from Jon
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
* 1993). This algorithm offers n*log(n) performance on many data sets
* that cause other quicksorts to degrade to quadratic performance.
* *
* @param a the array to be sorted * <p>The {@code <} relation does not provide a total order on
*/
public static void sort(double[] a) {
sort2(a, 0, a.length);
}
/**
* Sorts the specified range of the specified array of doubles into
* ascending numerical order. The range to be sorted extends from index
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
* <p>
* The <code>&lt;</code> relation does not provide a total order on
* all floating-point values; although they are distinct numbers * all floating-point values; although they are distinct numbers
* <code>-0.0 == 0.0</code> is <code>true</code> and a NaN value * {@code -0.0d == 0.0d} is {@code true} and a NaN value compares
* compares neither less than, greater than, nor equal to any * neither less than, greater than, nor equal to any floating-point
* floating-point value, even itself. To allow the sort to * value, even itself. To allow the sort to proceed, instead of using
* proceed, instead of using the <code>&lt;</code> relation to * the {@code <} relation to determine ascending numerical order,
* determine ascending numerical order, this method uses the total * this method uses the total order imposed by {@link Double#compareTo}.
* order imposed by {@link Double#compareTo}. This ordering * This ordering differs from the {@code <} relation in that {@code -0.0d}
* differs from the <code>&lt;</code> relation in that * is treated as less than {@code 0.0d} and NaN is considered greater than
* <code>-0.0</code> is treated as less than <code>0.0</code> and * any other floating-point value. For the purposes of sorting, all NaN
* NaN is considered greater than any other floating-point value. * values are considered equivalent and equal.
* For the purposes of sorting, all NaN values are considered *
* equivalent and equal. * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* <p> * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* The sorting algorithm is a tuned quicksort, adapted from Jon * offers O(n log(n)) performance on many data sets that cause other
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * quicksorts to degrade to quadratic performance, and is typically
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * faster than traditional (one-pivot) Quicksort implementations.
* 1993). This algorithm offers n*log(n) performance on many data sets
* that cause other quicksorts to degrade to quadratic performance.
* *
* @param a the array to be sorted * @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 <tt>fromIndex &gt; toIndex</tt>
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(double[] a, int fromIndex, int toIndex) { public static void sort(double[] a) {
rangeCheck(a.length, fromIndex, toIndex); sort(a, 0, a.length);
sort2(a, fromIndex, toIndex);
} }
/** /**
* Sorts the specified array of floats into ascending numerical order. * Sorts the specified range of the specified array into ascending order. The
* <p> * range of to be sorted extends from the index {@code fromIndex}, inclusive,
* The <code>&lt;</code> relation does not provide a total order on * to the index {@code toIndex}, exclusive. If {@code fromIndex == toIndex},
* all floating-point values; although they are distinct numbers * the range to be sorted is empty.
* <code>-0.0f == 0.0f</code> is <code>true</code> and a NaN value
* compares neither less than, greater than, nor equal to any
* floating-point value, even itself. To allow the sort to
* proceed, instead of using the <code>&lt;</code> relation to
* determine ascending numerical order, this method uses the total
* order imposed by {@link Float#compareTo}. This ordering
* differs from the <code>&lt;</code> relation in that
* <code>-0.0f</code> is treated as less than <code>0.0f</code> and
* NaN is considered greater than any other floating-point value.
* For the purposes of sorting, all NaN values are considered
* equivalent and equal.
* <p>
* The sorting algorithm is a tuned quicksort, adapted from Jon
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
* 1993). This algorithm offers n*log(n) performance on many data sets
* that cause other quicksorts to degrade to quadratic performance.
* *
* @param a the array to be sorted * <p>The {@code <} relation does not provide a total order on
*/
public static void sort(float[] a) {
sort2(a, 0, a.length);
}
/**
* Sorts the specified range of the specified array of floats into
* ascending numerical order. The range to be sorted extends from index
* <tt>fromIndex</tt>, inclusive, to index <tt>toIndex</tt>, exclusive.
* (If <tt>fromIndex==toIndex</tt>, the range to be sorted is empty.)
* <p>
* The <code>&lt;</code> relation does not provide a total order on
* all floating-point values; although they are distinct numbers * all floating-point values; although they are distinct numbers
* <code>-0.0f == 0.0f</code> is <code>true</code> and a NaN value * {@code -0.0d == 0.0d} is {@code true} and a NaN value compares
* compares neither less than, greater than, nor equal to any * neither less than, greater than, nor equal to any floating-point
* floating-point value, even itself. To allow the sort to * value, even itself. To allow the sort to proceed, instead of using
* proceed, instead of using the <code>&lt;</code> relation to * the {@code <} relation to determine ascending numerical order,
* determine ascending numerical order, this method uses the total * this method uses the total order imposed by {@link Double#compareTo}.
* order imposed by {@link Float#compareTo}. This ordering * This ordering differs from the {@code <} relation in that {@code -0.0d}
* differs from the <code>&lt;</code> relation in that * is treated as less than {@code 0.0d} and NaN is considered greater than
* <code>-0.0f</code> is treated as less than <code>0.0f</code> and * any other floating-point value. For the purposes of sorting, all NaN
* NaN is considered greater than any other floating-point value. * values are considered equivalent and equal.
* For the purposes of sorting, all NaN values are considered *
* equivalent and equal. * <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* <p> * by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm
* The sorting algorithm is a tuned quicksort, adapted from Jon * offers O(n log(n)) performance on many data sets that cause other
* L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function", * quicksorts to degrade to quadratic performance, and is typically
* Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November * faster than traditional (one-pivot) Quicksort implementations.
* 1993). This algorithm offers n*log(n) performance on many data sets
* that cause other quicksorts to degrade to quadratic performance.
* *
* @param a the array to be sorted * @param a the array to be sorted
* @param fromIndex the index of the first element (inclusive) to be * @param fromIndex the index of the first element, inclusively, to be sorted
* sorted * @param toIndex the index of the last element, exclusively, to be sorted
* @param toIndex the index of the last element (exclusive) to be sorted * @throws IllegalArgumentException if {@code fromIndex > toIndex}
* @throws IllegalArgumentException if <tt>fromIndex &gt; toIndex</tt> * @throws ArrayIndexOutOfBoundsException
* @throws ArrayIndexOutOfBoundsException if <tt>fromIndex &lt; 0</tt> or * if {@code fromIndex < 0} or {@code toIndex > a.length}
* <tt>toIndex &gt; a.length</tt>
*/ */
public static void sort(float[] a, int fromIndex, int toIndex) { public static void sort(double[] a, int fromIndex, int toIndex) {
rangeCheck(a.length, fromIndex, toIndex); rangeCheck(a.length, fromIndex, toIndex);
sort2(a, fromIndex, toIndex); sortNegZeroAndNaN(a, fromIndex, toIndex);
} }
private static void sort2(double a[], int fromIndex, int toIndex) { private static void sortNegZeroAndNaN(double[] a, int fromIndex, int toIndex) {
final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d); final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d);
/* /*
* The sort is done in three phases to avoid the expense of using * The sort is done in three phases to avoid the expense of using
* NaN and -0.0 aware comparisons during the main sort. * NaN and -0.0d aware comparisons during the main sort.
*/ *
* Preprocessing phase: move any NaN's to end of array, count the
/* * number of -0.0d's, and turn them into 0.0d's.
* Preprocessing phase: Move any NaN's to end of array, count the
* number of -0.0's, and turn them into 0.0's.
*/ */
int numNegZeros = 0; int numNegZeros = 0;
int i = fromIndex, n = toIndex; int i = fromIndex;
while(i < n) { int n = toIndex;
double temp;
while (i < n) {
if (a[i] != a[i]) { if (a[i] != a[i]) {
swap(a, i, --n); n--;
} else { temp = a[i];
if (a[i]==0 && Double.doubleToLongBits(a[i])==NEG_ZERO_BITS) { a[i] = a[n];
a[n] = temp;
}
else {
if (a[i] == 0 && Double.doubleToLongBits(a[i]) == NEG_ZERO_BITS) {
a[i] = 0.0d; a[i] = 0.0d;
numNegZeros++; numNegZeros++;
} }
i++; i++;
} }
} }
// Main sort phase: quicksort everything but the NaN's // Main sort phase: quicksort everything but the NaN's
sort1(a, fromIndex, n-fromIndex); DualPivotQuicksort.sort(a, fromIndex, n - 1);
// Postprocessing phase: change 0.0's to -0.0's as required // Postprocessing phase: change 0.0d's to -0.0d's as required
if (numNegZeros != 0) { if (numNegZeros != 0) {
int j = binarySearch0(a, fromIndex, n, 0.0d); // posn of ANY zero int j = binarySearch0(a, fromIndex, n, 0.0d); // position of ANY zero
do { do {
j--; j--;
} while (j>=fromIndex && a[j]==0.0d); }
while (j >= fromIndex && a[j] == 0.0d);
// j is now one less than the index of the FIRST zero // j is now one less than the index of the FIRST zero
for (int k=0; k<numNegZeros; k++) for (int k = 0; k < numNegZeros; k++) {
a[++j] = -0.0d; a[++j] = -0.0d;
}
} }
} }
/**
* Sorts the specified array into ascending numerical order.
*
* <p>The {@code <} relation does not provide a total order on
* all floating-point values; although they are distinct numbers
* {@code -0.0f == 0.0f} is {@code true} and a NaN value compares
* neither less than, greater than, nor equal to any floating-point
* value, even itself. To allow the sort to proceed, instead of using
* the {@code <} relation to determine ascending numerical order,
* this method uses the total order imposed by {@link Float#compareTo}.
* This ordering differs from the {@code <} relation in that {@code -0.0f}
* is treated as less than {@code 0.0f} and NaN is considered greater than
* any other floating-point value. For the purposes of sorting, all NaN
* values are considered equivalent and equal.
*
* <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This 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.
*
* @param a the array to be sorted
*/
public static void sort(float[] a) {
sort(a, 0, a.length);
}
/**
* Sorts the specified range of the specified array into ascending order. The
* range of 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.
*
* <p>The {@code <} relation does not provide a total order on
* all floating-point values; although they are distinct numbers
* {@code -0.0f == 0.0f} is {@code true} and a NaN value compares
* neither less than, greater than, nor equal to any floating-point
* value, even itself. To allow the sort to proceed, instead of using
* the {@code <} relation to determine ascending numerical order,
* this method uses the total order imposed by {@link Float#compareTo}.
* This ordering differs from the {@code <} relation in that {@code -0.0f}
* is treated as less than {@code 0.0f} and NaN is considered greater than
* any other floating-point value. For the purposes of sorting, all NaN
* values are considered equivalent and equal.
*
* <p>Implementation note: The sorting algorithm is a Dual-Pivot Quicksort,
* by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This 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.
*
* @param a the array to be sorted
* @param fromIndex the index of the first element, inclusively, to be sorted
* @param toIndex the index of the last element, exclusively, 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);
}
private static void sort2(float a[], int fromIndex, int toIndex) { private static void sortNegZeroAndNaN(float[] a, int fromIndex, int toIndex) {
final int NEG_ZERO_BITS = Float.floatToIntBits(-0.0f); final int NEG_ZERO_BITS = Float.floatToIntBits(-0.0f);
/* /*
* The sort is done in three phases to avoid the expense of using * The sort is done in three phases to avoid the expense of using
* NaN and -0.0 aware comparisons during the main sort. * NaN and -0.0f aware comparisons during the main sort.
*/ *
* Preprocessing phase: move any NaN's to end of array, count the
/* * number of -0.0f's, and turn them into 0.0f's.
* Preprocessing phase: Move any NaN's to end of array, count the
* number of -0.0's, and turn them into 0.0's.
*/ */
int numNegZeros = 0; int numNegZeros = 0;
int i = fromIndex, n = toIndex; int i = fromIndex;
while(i < n) { int n = toIndex;
float temp;
while (i < n) {
if (a[i] != a[i]) { if (a[i] != a[i]) {
swap(a, i, --n); n--;
} else { temp = a[i];
if (a[i]==0 && Float.floatToIntBits(a[i])==NEG_ZERO_BITS) { a[i] = a[n];
a[n] = temp;
}
else {
if (a[i] == 0 && Float.floatToIntBits(a[i]) == NEG_ZERO_BITS) {
a[i] = 0.0f; a[i] = 0.0f;
numNegZeros++; numNegZeros++;
} }
i++; i++;
} }
} }
// Main sort phase: quicksort everything but the NaN's // Main sort phase: quicksort everything but the NaN's
sort1(a, fromIndex, n-fromIndex); DualPivotQuicksort.sort(a, fromIndex, n - 1);
// Postprocessing phase: change 0.0's to -0.0's as required // Postprocessing phase: change 0.0f's to -0.0f's as required
if (numNegZeros != 0) { if (numNegZeros != 0) {
int j = binarySearch0(a, fromIndex, n, 0.0f); // posn of ANY zero int j = binarySearch0(a, fromIndex, n, 0.0f); // position of ANY zero
do { do {
j--; j--;
} while (j>=fromIndex && a[j]==0.0f); }
while (j >= fromIndex && a[j] == 0.0f);
// j is now one less than the index of the FIRST zero // j is now one less than the index of the FIRST zero
for (int k=0; k<numNegZeros; k++) for (int k = 0; k < numNegZeros; k++) {
a[++j] = -0.0f; a[++j] = -0.0f;
}
}
/*
* The code for each of the seven primitive types is largely identical.
* C'est la vie.
*/
/**
* Sorts the specified sub-array of longs into ascending order.
*/
private static void sort1(long x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
long v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(long x[], int a, int b) {
long t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(long x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed longs.
*/
private static int med3(long x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
}
/**
* Sorts the specified sub-array of integers into ascending order.
*/
private static void sort1(int x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
int v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(int x[], int a, int b) {
int t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(int x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed integers.
*/
private static int med3(int x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
}
/**
* Sorts the specified sub-array of shorts into ascending order.
*/
private static void sort1(short x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
short v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(short x[], int a, int b) {
short t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(short x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed shorts.
*/
private static int med3(short x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
}
/**
* Sorts the specified sub-array of chars into ascending order.
*/
private static void sort1(char x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
char v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
} }
if (b > c)
break;
swap(x, b++, c--);
} }
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(char x[], int a, int b) {
char t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(char x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed chars.
*/
private static int med3(char x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
}
/**
* Sorts the specified sub-array of bytes into ascending order.
*/
private static void sort1(byte x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
byte v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(byte x[], int a, int b) {
byte t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(byte x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed bytes.
*/
private static int med3(byte x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
}
/**
* Sorts the specified sub-array of doubles into ascending order.
*/
private static void sort1(double x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
double v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(double x[], int a, int b) {
double t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(double x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed doubles.
*/
private static int med3(double x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
}
/**
* Sorts the specified sub-array of floats into ascending order.
*/
private static void sort1(float x[], int off, int len) {
// Insertion sort on smallest arrays
if (len < 7) {
for (int i=off; i<len+off; i++)
for (int j=i; j>off && x[j-1]>x[j]; j--)
swap(x, j, j-1);
return;
}
// Choose a partition element, v
int m = off + (len >> 1); // Small arrays, middle element
if (len > 7) {
int l = off;
int n = off + len - 1;
if (len > 40) { // Big arrays, pseudomedian of 9
int s = len/8;
l = med3(x, l, l+s, l+2*s);
m = med3(x, m-s, m, m+s);
n = med3(x, n-2*s, n-s, n);
}
m = med3(x, l, m, n); // Mid-size, med of 3
}
float v = x[m];
// Establish Invariant: v* (<v)* (>v)* v*
int a = off, b = a, c = off + len - 1, d = c;
while(true) {
while (b <= c && x[b] <= v) {
if (x[b] == v)
swap(x, a++, b);
b++;
}
while (c >= b && x[c] >= v) {
if (x[c] == v)
swap(x, c, d--);
c--;
}
if (b > c)
break;
swap(x, b++, c--);
}
// Swap partition elements back to middle
int s, n = off + len;
s = Math.min(a-off, b-a ); vecswap(x, off, b-s, s);
s = Math.min(d-c, n-d-1); vecswap(x, b, n-s, s);
// Recursively sort non-partition-elements
if ((s = b-a) > 1)
sort1(x, off, s);
if ((s = d-c) > 1)
sort1(x, n-s, s);
}
/**
* Swaps x[a] with x[b].
*/
private static void swap(float x[], int a, int b) {
float t = x[a];
x[a] = x[b];
x[b] = t;
}
/**
* Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
*/
private static void vecswap(float x[], int a, int b, int n) {
for (int i=0; i<n; i++, a++, b++)
swap(x, a, b);
}
/**
* Returns the index of the median of the three indexed floats.
*/
private static int med3(float x[], int a, int b, int c) {
return (x[a] < x[b] ?
(x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
(x[b] > x[c] ? b : x[a] > x[c] ? c : a));
} }
/** /**
* Old merge sort implementation can be selected (for * Old merge sort implementation can be selected (for
* compatibility with broken comparators) using a system property. * compatibility with broken comparators) using a system property.
* Cannot be a static boolean in the enclosing class due to * Cannot be a static boolean in the enclosing class due to
* circular dependencies. To be removed in a future release. * circular dependencies. To be removed in a future release.
*/ */
static final class LegacyMergeSort { static final class LegacyMergeSort {
private static final boolean userRequested = private static final boolean userRequested =
...@@ -1235,7 +646,7 @@ public class Arrays { ...@@ -1235,7 +646,7 @@ public class Arrays {
/** /**
* Tuning parameter: list size at or below which insertion sort will be * Tuning parameter: list size at or below which insertion sort will be
* used in preference to mergesort or quicksort. * used in preference to mergesort.
* To be removed in a future release. * To be removed in a future release.
*/ */
private static final int INSERTIONSORT_THRESHOLD = 7; private static final int INSERTIONSORT_THRESHOLD = 7;
...@@ -1474,17 +885,20 @@ public class Arrays { ...@@ -1474,17 +885,20 @@ public class Arrays {
} }
/** /**
* Check that fromIndex and toIndex are in range, and throw an * Checks that {@code fromIndex} and {@code toIndex} are in
* appropriate exception if they aren't. * the range and throws an appropriate exception, if they aren't.
*/ */
private static void rangeCheck(int arrayLen, int fromIndex, int toIndex) { private static void rangeCheck(int length, int fromIndex, int toIndex) {
if (fromIndex > toIndex) if (fromIndex > toIndex) {
throw new IllegalArgumentException("fromIndex(" + fromIndex + throw new IllegalArgumentException(
") > toIndex(" + toIndex+")"); "fromIndex(" + fromIndex + ") > toIndex(" + toIndex + ")");
if (fromIndex < 0) }
if (fromIndex < 0) {
throw new ArrayIndexOutOfBoundsException(fromIndex); throw new ArrayIndexOutOfBoundsException(fromIndex);
if (toIndex > arrayLen) }
if (toIndex > length) {
throw new ArrayIndexOutOfBoundsException(toIndex); throw new ArrayIndexOutOfBoundsException(toIndex);
}
} }
// Searching // Searching
...@@ -1987,21 +1401,21 @@ public class Arrays { ...@@ -1987,21 +1401,21 @@ public class Arrays {
/** /**
* Searches the specified array of floats for the specified value using * Searches the specified array of floats for the specified value using
* the binary search algorithm. The array must be sorted * the binary search algorithm. The array must be sorted
* (as by the {@link #sort(float[])} method) prior to making this call. If * (as by the {@link #sort(float[])} method) prior to making this call. If
* it is not sorted, the results are undefined. If the array contains * it is not sorted, the results are undefined. If the array contains
* multiple elements with the specified value, there is no guarantee which * multiple elements with the specified value, there is no guarantee which
* one will be found. This method considers all NaN values to be * one will be found. This method considers all NaN values to be
* equivalent and equal. * equivalent and equal.
* *
* @param a the array to be searched * @param a the array to be searched
* @param key the value to be searched for * @param key the value to be searched for
* @return index of the search key, if it is contained in the array; * @return index of the search key, if it is contained in the array;
* otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>. The * otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>. The
* <i>insertion point</i> is defined as the point at which the * <i>insertion point</i> is defined as the point at which the
* key would be inserted into the array: the index of the first * key would be inserted into the array: the index of the first
* element greater than the key, or <tt>a.length</tt> if all * element greater than the key, or <tt>a.length</tt> if all
* elements in the array are less than the specified key. Note * elements in the array are less than the specified key. Note
* that this guarantees that the return value will be &gt;= 0 if * that this guarantees that the return value will be &gt;= 0 if
* and only if the key is found. * and only if the key is found.
*/ */
...@@ -2015,10 +1429,10 @@ public class Arrays { ...@@ -2015,10 +1429,10 @@ public class Arrays {
* the binary search algorithm. * the binary search algorithm.
* The range must be sorted * The range must be sorted
* (as by the {@link #sort(float[], int, int)} method) * (as by the {@link #sort(float[], int, int)} method)
* prior to making this call. If * prior to making this call. If
* it is not sorted, the results are undefined. If the range contains * it is not sorted, the results are undefined. If the range contains
* multiple elements with the specified value, there is no guarantee which * multiple elements with the specified value, there is no guarantee which
* one will be found. This method considers all NaN values to be * one will be found. This method considers all NaN values to be
* equivalent and equal. * equivalent and equal.
* *
* @param a the array to be searched * @param a the array to be searched
...@@ -2028,12 +1442,12 @@ public class Arrays { ...@@ -2028,12 +1442,12 @@ public class Arrays {
* @param key the value to be searched for * @param key the value to be searched for
* @return index of the search key, if it is contained in the array * @return index of the search key, if it is contained in the array
* within the specified range; * within the specified range;
* otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>. The * otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>. The
* <i>insertion point</i> is defined as the point at which the * <i>insertion point</i> is defined as the point at which the
* key would be inserted into the array: the index of the first * key would be inserted into the array: the index of the first
* element in the range greater than the key, * element in the range greater than the key,
* or <tt>toIndex</tt> if all * or <tt>toIndex</tt> if all
* elements in the range are less than the specified key. Note * elements in the range are less than the specified key. Note
* that this guarantees that the return value will be &gt;= 0 if * that this guarantees that the return value will be &gt;= 0 if
* and only if the key is found. * and only if the key is found.
* @throws IllegalArgumentException * @throws IllegalArgumentException
...@@ -2076,10 +1490,9 @@ public class Arrays { ...@@ -2076,10 +1490,9 @@ public class Arrays {
return -(low + 1); // key not found. return -(low + 1); // key not found.
} }
/** /**
* Searches the specified array for the specified object using the binary * Searches the specified array for the specified object using the binary
* search algorithm. The array must be sorted into ascending order * search algorithm. The array must be sorted into ascending order
* according to the * according to the
* {@linkplain Comparable natural ordering} * {@linkplain Comparable natural ordering}
* of its elements (as by the * of its elements (as by the
...@@ -2269,7 +1682,6 @@ public class Arrays { ...@@ -2269,7 +1682,6 @@ public class Arrays {
int mid = (low + high) >>> 1; int mid = (low + high) >>> 1;
T midVal = a[mid]; T midVal = a[mid];
int cmp = c.compare(midVal, key); int cmp = c.compare(midVal, key);
if (cmp < 0) if (cmp < 0)
low = mid + 1; low = mid + 1;
else if (cmp > 0) else if (cmp > 0)
...@@ -2280,7 +1692,6 @@ public class Arrays { ...@@ -2280,7 +1692,6 @@ public class Arrays {
return -(low + 1); // key not found. return -(low + 1); // key not found.
} }
// Equality Testing // Equality Testing
/** /**
...@@ -2527,7 +1938,6 @@ public class Arrays { ...@@ -2527,7 +1938,6 @@ public class Arrays {
return true; return true;
} }
/** /**
* Returns <tt>true</tt> if the two specified arrays of Objects are * Returns <tt>true</tt> if the two specified arrays of Objects are
* <i>equal</i> to one another. The two arrays are considered equal if * <i>equal</i> to one another. The two arrays are considered equal if
...@@ -2562,7 +1972,6 @@ public class Arrays { ...@@ -2562,7 +1972,6 @@ public class Arrays {
return true; return true;
} }
// Filling // Filling
/** /**
...@@ -2885,8 +2294,8 @@ public class Arrays { ...@@ -2885,8 +2294,8 @@ public class Arrays {
a[i] = val; a[i] = val;
} }
// Cloning // Cloning
/** /**
* Copies the specified array, truncating or padding with nulls (if necessary) * Copies the specified array, truncating or padding with nulls (if necessary)
* so the copy has the specified length. For all indices that are * so the copy has the specified length. For all indices that are
...@@ -3495,7 +2904,6 @@ public class Arrays { ...@@ -3495,7 +2904,6 @@ public class Arrays {
return copy; return copy;
} }
// Misc // Misc
/** /**
...@@ -4180,6 +3588,7 @@ public class Arrays { ...@@ -4180,6 +3588,7 @@ public class Arrays {
public static String toString(float[] a) { public static String toString(float[] a) {
if (a == null) if (a == null)
return "null"; return "null";
int iMax = a.length - 1; int iMax = a.length - 1;
if (iMax == -1) if (iMax == -1)
return "[]"; return "[]";
...@@ -4243,6 +3652,7 @@ public class Arrays { ...@@ -4243,6 +3652,7 @@ public class Arrays {
public static String toString(Object[] a) { public static String toString(Object[] a) {
if (a == null) if (a == null)
return "null"; return "null";
int iMax = a.length - 1; int iMax = a.length - 1;
if (iMax == -1) if (iMax == -1)
return "[]"; return "[]";
......
src/share/classes/java/util/DualPivotQuicksort.java 0 → 100644
浏览文件 @ dac3d340
/*
* 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 2009.10.22 m765.827.v4
*/
final class DualPivotQuicksort {
// Suppresses default constructor, ensuring non-instantiability.
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 range of the array into ascending order.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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
sort(a, less, great);
}
/**
* Sorts the specified range of the array into ascending order.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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;
}
}
} else { // Use Dual-Pivot Quicksort on large arrays
dualPivotQuicksort(a, left, right);
}
}
/** 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.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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
sort(a, less, great);
}
/** 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.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 large 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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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
sort(a, less, great);
}
/** 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.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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
sort(a, less, great);
}
/**
* Sorts the specified range of the array into ascending order.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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
sort(a, less, great);
}
/**
* Sorts the specified range of the array into ascending order.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, to be sorted
*/
static void sort(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 Dual-Pivot Quicksort.
*
* @param a the array to be sorted
* @param left the index of the first element, inclusively, to be sorted
* @param right the index of the last element, inclusively, 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
sort(a, left, less - 2);
sort(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
sort(a, less, great);
}
}
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