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Arrays.javaAPI DocJava SE 5 API116729Fri Aug 26 14:57:22 BST 2005java.util

Arrays

public class Arrays extends Object
This class contains various methods for manipulating arrays (such as sorting and searching). This class also contains a static factory that allows arrays to be viewed as lists.

The methods in this class all throw a NullPointerException if the specified array reference is null, except where noted.

The documentation for the methods contained in this class includes briefs description of the implementations. Such descriptions should be regarded as implementation notes, rather than parts of the specification. Implementors should feel free to substitute other algorithms, so long as the specification itself is adhered to. (For example, the algorithm used by sort(Object[]) does not have to be a mergesort, but it does have to be stable.)

This class is a member of the Java Collections Framework.

author
Josh Bloch
author
Neal Gafter
version
1.59, 04/01/04
see
Comparable
see
Comparator
since
1.2

Fields Summary
private static final int
INSERTIONSORT_THRESHOLD
Tuning parameter: list size at or below which insertion sort will be used in preference to mergesort or quicksort.
Constructors Summary
private Arrays()

    
Methods Summary
public static java.util.ListasList(T a)
Returns a fixed-size list backed by the specified array. (Changes to the returned list "write through" to the array.) This method acts as bridge between array-based and collection-based APIs, in combination with Collection.toArray. The returned list is serializable and implements {@link RandomAccess}.

This method also provides a convenient way to create a fixed-size list initialized to contain several elements:

List stooges = Arrays.asList("Larry", "Moe", "Curly");

param
a the array by which the list will be backed.
return
a list view of the specified array.
see
Collection#toArray()

	return new ArrayList<T>(a);
    
public static intbinarySearch(long[] a, long key)
Searches the specified array of longs for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(long[])

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    long midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(int[] a, int key)
Searches the specified array of ints for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(int[])

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    int midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(short[] a, short key)
Searches the specified array of shorts for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(short[])

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    short midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(char[] a, char key)
Searches the specified array of chars for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(char[])

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    char midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(byte[] a, byte key)
Searches the specified array of bytes for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(byte[])

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    byte midVal = a[mid];

	    if (midVal < key)
		low = mid + 1;
	    else if (midVal > key)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(double[] a, double key)
Searches the specified array of doubles for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. This method considers all NaN values to be equivalent and equal.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(double[])

        return binarySearch(a, key, 0, a.length-1);
    
private static intbinarySearch(double[] a, double key, int low, int high)

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    double midVal = a[mid];

            int cmp;
            if (midVal < key) {
                cmp = -1;   // Neither val is NaN, thisVal is smaller
            } else if (midVal > key) {
                cmp = 1;    // Neither val is NaN, thisVal is larger
            } else {
                long midBits = Double.doubleToLongBits(midVal);
                long keyBits = Double.doubleToLongBits(key);
                cmp = (midBits == keyBits ?  0 : // Values are equal
                       (midBits < keyBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                        1));                     // (0.0, -0.0) or (NaN, !NaN)
            }

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(float[] a, float key)
Searches the specified array of floats for the specified value using the binary search algorithm. The array must be sorted (as by the sort method, above) prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements with the specified value, there is no guarantee which one will be found. This method considers all NaN values to be equivalent and equal.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
see
#sort(float[])

        return binarySearch(a, key, 0, a.length-1);
    
private static intbinarySearch(float[] a, float key, int low, int high)

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    float midVal = a[mid];

            int cmp;
            if (midVal < key) {
                cmp = -1;   // Neither val is NaN, thisVal is smaller
            } else if (midVal > key) {
                cmp = 1;    // Neither val is NaN, thisVal is larger
            } else {
                int midBits = Float.floatToIntBits(midVal);
                int keyBits = Float.floatToIntBits(key);
                cmp = (midBits == keyBits ?  0 : // Values are equal
                       (midBits < keyBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                        1));                     // (0.0, -0.0) or (NaN, !NaN)
            }

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(java.lang.Object[] a, java.lang.Object key)
Searches the specified array for the specified object using the binary search algorithm. The array must be sorted into ascending order according to the natural ordering of its elements (as by Sort(Object[]), above) prior to making this call. If it is not sorted, the results are undefined. (If the array contains elements that are not mutually comparable (for example,strings and integers), it cannot be sorted according to the natural order of its elements, hence results are undefined.) If the array contains multiple elements equal to the specified object, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
throws
ClassCastException if the search key in not comparable to the elements of the array.
see
Comparable
see
#sort(Object[])

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    Comparable midVal = (Comparable)a[mid];
	    int cmp = midVal.compareTo(key);

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
public static intbinarySearch(T[] a, T key, java.util.Comparator c)
Searches the specified array for the specified object using the binary search algorithm. The array must be sorted into ascending order according to the specified comparator (as by the Sort(Object[], Comparator) method, above), prior to making this call. If it is not sorted, the results are undefined. If the array contains multiple elements equal to the specified object, there is no guarantee which one will be found.

param
a the array to be searched.
param
key the value to be searched for.
param
c the comparator by which the array is ordered. A null value indicates that the elements' natural ordering should be used.
return
index of the search key, if it is contained in the list; otherwise, (-(insertion point) - 1). The insertion point is defined as the point at which the key would be inserted into the list: the index of the first element greater than the key, or list.size(), if all elements in the list are less than the specified key. Note that this guarantees that the return value will be >= 0 if and only if the key is found.
throws
ClassCastException if the array contains elements that are not mutually comparable using the specified comparator, or the search key in not mutually comparable with the elements of the array using this comparator.
see
Comparable
see
#sort(Object[], Comparator)

        if (c==null) {
            return binarySearch(a, key);
	}

	int low = 0;
	int high = a.length-1;

	while (low <= high) {
	    int mid = (low + high) >> 1;
	    T midVal = a[mid];
	    int cmp = c.compare(midVal, key);

	    if (cmp < 0)
		low = mid + 1;
	    else if (cmp > 0)
		high = mid - 1;
	    else
		return mid; // key found
	}
	return -(low + 1);  // key not found.
    
private static T[]cloneSubarray(T[] a, int from, int to)
Clones an array within the specified bounds. This method assumes that a is an array.


                        
              
        int n = to - from;
	T[] result = (T[])Array.newInstance(a.getClass().getComponentType(), n);
        System.arraycopy(a, from, result, 0, n);
        return result;
    
public static booleandeepEquals(java.lang.Object[] a1, java.lang.Object[] a2)
Returns true if the two specified arrays are deeply equal to one another. Unlike the @link{#equals{Object[],Object[]) method, this method is appropriate for use with nested arrays of arbitrary depth.

Two array references are considered deeply equal if both are null, or if they refer to arrays that contain the same number of elements and all corresponding pairs of elements in the two arrays are deeply equal.

Two possibly null elements e1 and e2 are deeply equal if any of the following conditions hold:

  • e1 and e2 are both arrays of object reference types, and Arrays.deepEquals(e1, e2) would return true
  • e1 and e2 are arrays of the same primitive type, and the appropriate overloading of Arrays.equals(e1, e2) would return true.
  • e1 == e2
  • e1.equals(e2) would return true.
Note that this definition permits null elements at any depth.

If either of the specified arrays contain themselves as elements either directly or indirectly through one or more levels of arrays, the behavior of this method is undefined.

param
a1 one array to be tested for equality
param
a2 the other array to be tested for equality
return
true if the two arrays are equal
see
#equals(Object[],Object[])
since
1.5

        if (a1 == a2)
            return true;
        if (a1 == null || a2==null)
            return false;
        int length = a1.length;
        if (a2.length != length)
            return false;
 
        for (int i = 0; i < length; i++) {
            Object e1 = a1[i];
            Object e2 = a2[i];
 
            if (e1 == e2)
                continue;
            if (e1 == null)
                return false;
 
            // Figure out whether the two elements are equal
            boolean eq;
            if (e1 instanceof Object[] && e2 instanceof Object[])
                eq = deepEquals ((Object[]) e1, (Object[]) e2);
            else if (e1 instanceof byte[] && e2 instanceof byte[])
                eq = equals((byte[]) e1, (byte[]) e2);
            else if (e1 instanceof short[] && e2 instanceof short[])
                eq = equals((short[]) e1, (short[]) e2);
            else if (e1 instanceof int[] && e2 instanceof int[])
                eq = equals((int[]) e1, (int[]) e2);
            else if (e1 instanceof long[] && e2 instanceof long[])
                eq = equals((long[]) e1, (long[]) e2);
            else if (e1 instanceof char[] && e2 instanceof char[])
                eq = equals((char[]) e1, (char[]) e2);
            else if (e1 instanceof float[] && e2 instanceof float[])
                eq = equals((float[]) e1, (float[]) e2);
            else if (e1 instanceof double[] && e2 instanceof double[])
                eq = equals((double[]) e1, (double[]) e2);
            else if (e1 instanceof boolean[] && e2 instanceof boolean[])
                eq = equals((boolean[]) e1, (boolean[]) e2);
            else
                eq = e1.equals(e2);
 
            if (!eq)
                return false;
        }
        return true;
    
public static intdeepHashCode(java.lang.Object[] a)
Returns a hash code based on the "deep contents" of the specified array. If the array contains other arrays as elements, the hash code is based on their contents and so on, ad infinitum. It is therefore unacceptable to invoke this method on an array that contains itself as an element, either directly or indirectly through one or more levels of arrays. The behavior of such an invocation is undefined.

For any two arrays a and b such that Arrays.deepEquals(a, b), it is also the case that Arrays.deepHashCode(a) == Arrays.deepHashCode(b).

The computation of the value returned by this method is similar to that of the value returned by {@link List#hashCode()} on a list containing the same elements as a in the same order, with one difference: If an element e of a is itself an array, its hash code is computed not by calling e.hashCode(), but as by calling the appropriate overloading of Arrays.hashCode(e) if e is an array of a primitive type, or as by calling Arrays.deepHashCode(e) recursively if e is an array of a reference type. If a is null, this method returns 0.

param
a the array whose deep-content-based hash code to compute
return
a deep-content-based hash code for a
see
#hashCode(Object[])
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
 
        for (Object element : a) {
            int elementHash = 0;
            if (element instanceof Object[])
                elementHash = deepHashCode((Object[]) element);
            else if (element instanceof byte[])
                elementHash = hashCode((byte[]) element);
            else if (element instanceof short[])
                elementHash = hashCode((short[]) element);
            else if (element instanceof int[])
                elementHash = hashCode((int[]) element);
            else if (element instanceof long[])
                elementHash = hashCode((long[]) element);
            else if (element instanceof char[])
                elementHash = hashCode((char[]) element);
            else if (element instanceof float[])
                elementHash = hashCode((float[]) element);
            else if (element instanceof double[])
                elementHash = hashCode((double[]) element);
            else if (element instanceof boolean[])
                elementHash = hashCode((boolean[]) element);
            else if (element != null)
                elementHash = element.hashCode();
 
            result = 31 * result + elementHash;
        }
 
        return result;
    
public static java.lang.StringdeepToString(java.lang.Object[] a)
Returns a string representation of the "deep contents" of the specified array. If the array contains other arrays as elements, the string representation contains their contents and so on. This method is designed for converting multidimensional arrays to strings.

The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(Object), unless they are themselves arrays.

If an element e is an array of a primitive type, it is converted to a string as by invoking the appropriate overloading of Arrays.toString(e). If an element e is an array of a reference type, it is converted to a string as by invoking this method recursively.

To avoid infinite recursion, if the specified array contains itself as an element, or contains an indirect reference to itself through one or more levels of arrays, the self-reference is converted to the string "[...]". For example, an array containing only a reference to itself would be rendered as "[[...]]".

This method returns "null" if the specified array is null.

param
a the array whose string representation to return
return
a string representation of a
see
#toString(Object[])
since
1.5

        if (a == null)
            return "null";

        int bufLen = 20 * a.length;
        if (a.length != 0 && bufLen <= 0)
            bufLen = Integer.MAX_VALUE;
        StringBuilder buf = new StringBuilder(bufLen);
        deepToString(a, buf, new HashSet());
        return buf.toString();
    
private static voiddeepToString(java.lang.Object[] a, java.lang.StringBuilder buf, java.util.Set dejaVu)

        if (a == null) {
            buf.append("null");
            return;
        }
        dejaVu.add(a);
        buf.append('[");
        for (int i = 0; i < a.length; i++) {
            if (i != 0)
                buf.append(", ");

            Object element = a[i];
            if (element == null) {
                buf.append("null");
            } else {
                Class eClass = element.getClass();

                if (eClass.isArray()) {
                    if (eClass == byte[].class)
                        buf.append(toString((byte[]) element));
                    else if (eClass == short[].class)
                        buf.append(toString((short[]) element));
                    else if (eClass == int[].class)
                        buf.append(toString((int[]) element));
                    else if (eClass == long[].class)
                        buf.append(toString((long[]) element));
                    else if (eClass == char[].class)
                        buf.append(toString((char[]) element));
                    else if (eClass == float[].class)
                        buf.append(toString((float[]) element));
                    else if (eClass == double[].class)
                        buf.append(toString((double[]) element));
                    else if (eClass == boolean[].class)
                        buf.append(toString((boolean[]) element));
                    else { // element is an array of object references
                        if (dejaVu.contains(element))
                            buf.append("[...]");
                        else
                            deepToString((Object[])element, buf, dejaVu);
                    }
                } else {  // element is non-null and not an array
                    buf.append(element.toString());
                }
            }
        }
        buf.append("]");
        dejaVu.remove(a);
    
public static booleanequals(long[] a, long[] a2)
Returns true if the two specified arrays of longs are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    
public static booleanequals(int[] a, int[] a2)
Returns true if the two specified arrays of ints are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    
public static booleanequals(short[] a, short[] a2)
Returns true if the two specified arrays of shorts are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    
public static booleanequals(char[] a, char[] a2)
Returns true if the two specified arrays of chars are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    
public static booleanequals(byte[] a, byte[] a2)
Returns true if the two specified arrays of bytes are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    
public static booleanequals(boolean[] a, boolean[] a2)
Returns true if the two specified arrays of booleans are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    
public static booleanequals(double[] a, double[] a2)
Returns true if the two specified arrays of doubles are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

Two doubles d1 and d2 are considered equal if:

 new Double(d1).equals(new Double(d2))
(Unlike the == operator, this method considers NaN equals to itself, and 0.0d unequal to -0.0d.)

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.
see
Double#equals(Object)

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
	    if (Double.doubleToLongBits(a[i])!=Double.doubleToLongBits(a2[i]))
                return false;

        return true;
    
public static booleanequals(float[] a, float[] a2)
Returns true if the two specified arrays of floats are equal to one another. Two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. In other words, two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

Two floats f1 and f2 are considered equal if:

 new Float(f1).equals(new Float(f2))
(Unlike the == operator, this method considers NaN equals to itself, and 0.0f unequal to -0.0f.)

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.
see
Float#equals(Object)

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
	    if (Float.floatToIntBits(a[i])!=Float.floatToIntBits(a2[i]))
                return false;

        return true;
    
public static booleanequals(java.lang.Object[] a, java.lang.Object[] a2)
Returns true if the two specified arrays of Objects are equal to one another. The two arrays are considered equal if both arrays contain the same number of elements, and all corresponding pairs of elements in the two arrays are equal. Two objects e1 and e2 are considered equal if (e1==null ? e2==null : e1.equals(e2)). In other words, the two arrays are equal if they contain the same elements in the same order. Also, two array references are considered equal if both are null.

param
a one array to be tested for equality.
param
a2 the other array to be tested for equality.
return
true if the two arrays are equal.

        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++) {
            Object o1 = a[i];
            Object o2 = a2[i];
            if (!(o1==null ? o2==null : o1.equals(o2)))
                return false;
        }

        return true;
    
public static voidfill(long[] a, long val)
Assigns the specified long value to each element of the specified array of longs.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(long[] a, int fromIndex, int toIndex, long val)
Assigns the specified long value to each element of the specified range of the specified array of longs. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(int[] a, int val)
Assigns the specified int value to each element of the specified array of ints.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(int[] a, int fromIndex, int toIndex, int val)
Assigns the specified int value to each element of the specified range of the specified array of ints. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(short[] a, short val)
Assigns the specified short value to each element of the specified array of shorts.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(short[] a, int fromIndex, int toIndex, short val)
Assigns the specified short value to each element of the specified range of the specified array of shorts. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(char[] a, char val)
Assigns the specified char value to each element of the specified array of chars.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(char[] a, int fromIndex, int toIndex, char val)
Assigns the specified char value to each element of the specified range of the specified array of chars. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(byte[] a, byte val)
Assigns the specified byte value to each element of the specified array of bytes.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(byte[] a, int fromIndex, int toIndex, byte val)
Assigns the specified byte value to each element of the specified range of the specified array of bytes. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(boolean[] a, boolean val)
Assigns the specified boolean value to each element of the specified array of booleans.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(boolean[] a, int fromIndex, int toIndex, boolean val)
Assigns the specified boolean value to each element of the specified range of the specified array of booleans. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(double[] a, double val)
Assigns the specified double value to each element of the specified array of doubles.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(double[] a, int fromIndex, int toIndex, double val)
Assigns the specified double value to each element of the specified range of the specified array of doubles. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(float[] a, float val)
Assigns the specified float value to each element of the specified array of floats.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        fill(a, 0, a.length, val);
    
public static voidfill(float[] a, int fromIndex, int toIndex, float val)
Assigns the specified float value to each element of the specified range of the specified array of floats. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static voidfill(java.lang.Object[] a, java.lang.Object val)
Assigns the specified Object reference to each element of the specified array of Objects.

param
a the array to be filled.
param
val the value to be stored in all elements of the array.

        Arrays.fill(a, 0, a.length, val);
    
public static voidfill(java.lang.Object[] a, int fromIndex, int toIndex, java.lang.Object val)
Assigns the specified Object reference to each element of the specified range of the specified array of Objects. The range to be filled extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be filled is empty.)

param
a the array to be filled.
param
fromIndex the index of the first element (inclusive) to be filled with the specified value.
param
toIndex the index of the last element (exclusive) to be filled with the specified value.
param
val the value to be stored in all elements of the array.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    
public static inthashCode(float[] a)
Returns a hash code based on the contents of the specified array. For any two float arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Float} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (float element : a)
            result = 31 * result + Float.floatToIntBits(element);
 
        return result;
    
public static inthashCode(double[] a)
Returns a hash code based on the contents of the specified array. For any two double arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Double} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (double element : a) {
            long bits = Double.doubleToLongBits(element);
            result = 31 * result + (int)(bits ^ (bits >>> 32));
        }
        return result;
    
public static inthashCode(java.lang.Object[] a)
Returns a hash code based on the contents of the specified array. If the array contains other arrays as elements, the hash code is based on their identities rather than their contents. It is therefore acceptable to invoke this method on an array that contains itself as an element, either directly or indirectly through one or more levels of arrays.

For any two arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is equal to the value that would be returned by Arrays.asList(a).hashCode(), unless a is null, in which case 0 is returned.

param
a the array whose content-based hash code to compute
return
a content-based hash code for a
see
#deepHashCode(Object[])
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
 
        for (Object element : a)
            result = 31 * result + (element == null ? 0 : element.hashCode());
 
        return result;
    
public static inthashCode(long[] a)
Returns a hash code based on the contents of the specified array. For any two long arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Long} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (long element : a) {
            int elementHash = (int)(element ^ (element >>> 32));
            result = 31 * result + elementHash;
        }
 
        return result;
    
public static inthashCode(int[] a)
Returns a hash code based on the contents of the specified array. For any two non-null int arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Integer} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (int element : a)
            result = 31 * result + element;
 
        return result;
    
public static inthashCode(short[] a)
Returns a hash code based on the contents of the specified array. For any two short arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Short} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (short element : a)
            result = 31 * result + element;
 
        return result;
    
public static inthashCode(char[] a)
Returns a hash code based on the contents of the specified array. For any two char arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Character} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (char element : a)
            result = 31 * result + element;
 
        return result;
    
public static inthashCode(byte[] a)
Returns a hash code based on the contents of the specified array. For any two byte arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Byte} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (byte element : a)
            result = 31 * result + element;
 
        return result;
    
public static inthashCode(boolean[] a)
Returns a hash code based on the contents of the specified array. For any two boolean arrays a and b such that Arrays.equals(a, b), it is also the case that Arrays.hashCode(a) == Arrays.hashCode(b).

The value returned by this method is the same value that would be obtained by invoking the {@link List#hashCode() hashCode} method on a {@link List} containing a sequence of {@link Boolean} instances representing the elements of a in the same order. If a is null, this method returns 0.

param
a the array whose hash value to compute
return
a content-based hash code for a
since
1.5

        if (a == null)
            return 0;
 
        int result = 1;
        for (boolean element : a)
            result = 31 * result + (element ? 1231 : 1237);
 
        return result;
    
private static intmed3(long[] x, int a, int b, int c)
Returns the index of the median of the three indexed longs.

	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));
    
private static intmed3(int[] x, int a, int b, int c)
Returns the index of the median of the three indexed integers.

	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));
    
private static intmed3(short[] x, int a, int b, int c)
Returns the index of the median of the three indexed shorts.

	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));
    
private static intmed3(char[] x, int a, int b, int c)
Returns the index of the median of the three indexed chars.

	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));
    
private static intmed3(byte[] x, int a, int b, int c)
Returns the index of the median of the three indexed bytes.

	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));
    
private static intmed3(double[] x, int a, int b, int c)
Returns the index of the median of the three indexed doubles.

	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));
    
private static intmed3(float[] x, int a, int b, int c)
Returns the index of the median of the three indexed floats.

	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));
    
private static voidmergeSort(java.lang.Object[] src, java.lang.Object[] dest, int low, int high, int off)
Src is the source array that starts at index 0 Dest is the (possibly larger) array destination with a possible offset low is the index in dest to start sorting high is the end index in dest to end sorting off is the offset to generate corresponding low, high in src

	int length = high - low;

	// Insertion sort on smallest arrays
        if (length < INSERTIONSORT_THRESHOLD) {
            for (int i=low; i<high; i++)
                for (int j=i; j>low &&
			 ((Comparable) dest[j-1]).compareTo(dest[j])>0; j--)
                    swap(dest, j, j-1);
            return;
        }

        // Recursively sort halves of dest into src
        int destLow  = low;
        int destHigh = high;
        low  += off;
        high += off;
        int mid = (low + high) >> 1;
        mergeSort(dest, src, low, mid, -off);
        mergeSort(dest, src, mid, high, -off);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (((Comparable)src[mid-1]).compareTo(src[mid]) <= 0) {
            System.arraycopy(src, low, dest, destLow, length);
            return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
            if (q >= high || p < mid && ((Comparable)src[p]).compareTo(src[q])<=0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    
private static voidmergeSort(java.lang.Object[] src, java.lang.Object[] dest, int low, int high, int off, java.util.Comparator c)
Src is the source array that starts at index 0 Dest is the (possibly larger) array destination with a possible offset low is the index in dest to start sorting high is the end index in dest to end sorting off is the offset into src corresponding to low in dest

	int length = high - low;

	// Insertion sort on smallest arrays
	if (length < INSERTIONSORT_THRESHOLD) {
	    for (int i=low; i<high; i++)
		for (int j=i; j>low && c.compare(dest[j-1], dest[j])>0; j--)
		    swap(dest, j, j-1);
	    return;
	}

        // Recursively sort halves of dest into src
        int destLow  = low;
        int destHigh = high;
        low  += off;
        high += off;
        int mid = (low + high) >> 1;
        mergeSort(dest, src, low, mid, -off, c);
        mergeSort(dest, src, mid, high, -off, c);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (c.compare(src[mid-1], src[mid]) <= 0) {
           System.arraycopy(src, low, dest, destLow, length);
           return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = destLow, p = low, q = mid; i < destHigh; i++) {
            if (q >= high || p < mid && c.compare(src[p], src[q]) <= 0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    
private static voidrangeCheck(int arrayLen, int fromIndex, int toIndex)
Check that fromIndex and toIndex are in range, and throw an appropriate exception if they aren't.

        if (fromIndex > toIndex)
            throw new IllegalArgumentException("fromIndex(" + fromIndex +
                       ") > toIndex(" + toIndex+")");
        if (fromIndex < 0)
            throw new ArrayIndexOutOfBoundsException(fromIndex);
        if (toIndex > arrayLen)
            throw new ArrayIndexOutOfBoundsException(toIndex);
    
public static voidsort(byte[] a)
Sorts the specified array of bytes 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", 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.

	sort1(a, 0, a.length);
    
public static voidsort(byte[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of bytes into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    
public static voidsort(double[] a)
Sorts the specified array of doubles into ascending numerical order.

The < relation does not provide a total order on all floating-point values; although they are distinct numbers -0.0 == 0.0 is 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 < relation to determine ascending numerical order, this method uses the total order imposed by {@link Double#compareTo}. This ordering differs from the < relation in that -0.0 is treated as less than 0.0 and NaN is considered greater than any other floating-point value. For the purposes of sorting, all NaN values are considered equivalent and equal.

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.

	sort2(a, 0, a.length);
    
public static voidsort(double[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of doubles into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

The < relation does not provide a total order on all floating-point values; although they are distinct numbers -0.0 == 0.0 is 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 < relation to determine ascending numerical order, this method uses the total order imposed by {@link Double#compareTo}. This ordering differs from the < relation in that -0.0 is treated as less than 0.0 and NaN is considered greater than any other floating-point value. For the purposes of sorting, all NaN values are considered equivalent and equal.

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort2(a, fromIndex, toIndex);
    
public static voidsort(float[] a)
Sorts the specified array of floats into ascending numerical order.

The < relation does not provide a total order on all floating-point values; although they are distinct numbers -0.0f == 0.0f is 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 < relation to determine ascending numerical order, this method uses the total order imposed by {@link Float#compareTo}. This ordering differs from the < relation in that -0.0f is treated as less than 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.

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.

	sort2(a, 0, a.length);
    
public static voidsort(float[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of floats into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

The < relation does not provide a total order on all floating-point values; although they are distinct numbers -0.0f == 0.0f is 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 < relation to determine ascending numerical order, this method uses the total order imposed by {@link Float#compareTo}. This ordering differs from the < relation in that -0.0f is treated as less than 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.

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort2(a, fromIndex, toIndex);
    
public static voidsort(long[] a)
Sorts the specified array of longs 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", 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.

	sort1(a, 0, a.length);
    
public static voidsort(long[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of longs into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    
public static voidsort(int[] a)
Sorts the specified array of ints 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", 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.

	sort1(a, 0, a.length);
    
public static voidsort(java.lang.Object[] a)
Sorts the specified array of objects into ascending order, according to the natural ordering of its elements. All elements in the array must implement the Comparable interface. Furthermore, all elements in the array must be mutually comparable (that is, e1.compareTo(e2) must not throw a ClassCastException for any elements e1 and e2 in the array).

This sort is guaranteed to be stable: equal elements will not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is omitted if the highest element in the low sublist is less than the lowest element in the high sublist). This algorithm offers guaranteed n*log(n) performance.

param
a the array to be sorted.
throws
ClassCastException if the array contains elements that are not mutually comparable (for example, strings and integers).
see
Comparable

        Object[] aux = (Object[])a.clone();
        mergeSort(aux, a, 0, a.length, 0);
    
public static voidsort(java.lang.Object[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of objects into ascending order, according to the natural ordering of its elements. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.) All elements in this range must implement the Comparable interface. Furthermore, all elements in this range must be mutually comparable (that is, e1.compareTo(e2) must not throw a ClassCastException for any elements e1 and e2 in the array).

This sort is guaranteed to be stable: equal elements will not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is omitted if the highest element in the low sublist is less than the lowest element in the high sublist). This algorithm offers guaranteed n*log(n) performance.

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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length
throws
ClassCastException if the array contains elements that are not mutually comparable (for example, strings and integers).
see
Comparable

        rangeCheck(a.length, fromIndex, toIndex);
	Object[] aux = cloneSubarray(a, fromIndex, toIndex);
        mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
    
public static voidsort(int[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of ints into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    
public static voidsort(T[] a, java.util.Comparator c)
Sorts the specified array of objects according to the order induced by the specified comparator. All elements in the array must be mutually comparable by the specified comparator (that is, c.compare(e1, e2) must not throw a ClassCastException for any elements e1 and e2 in the array).

This sort is guaranteed to be stable: equal elements will not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is omitted if the highest element in the low sublist is less than the lowest element in the high sublist). This algorithm offers guaranteed n*log(n) performance.

param
a the array to be sorted.
param
c the comparator to determine the order of the array. A null value indicates that the elements' natural ordering should be used.
throws
ClassCastException if the array contains elements that are not mutually comparable using the specified comparator.
see
Comparator

	T[] aux = (T[])a.clone();
        if (c==null)
            mergeSort(aux, a, 0, a.length, 0);
        else
            mergeSort(aux, a, 0, a.length, 0, c);
    
public static voidsort(T[] a, int fromIndex, int toIndex, java.util.Comparator c)
Sorts the specified range of the specified array of objects according to the order induced by the specified comparator. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.) All elements in the range must be mutually comparable by the specified comparator (that is, c.compare(e1, e2) must not throw a ClassCastException for any elements e1 and e2 in the range).

This sort is guaranteed to be stable: equal elements will not be reordered as a result of the sort.

The sorting algorithm is a modified mergesort (in which the merge is omitted if the highest element in the low sublist is less than the lowest element in the high sublist). This algorithm offers guaranteed n*log(n) performance.

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.
param
c the comparator to determine the order of the array. A null value indicates that the elements' natural ordering should be used.
throws
ClassCastException if the array contains elements that are not mutually comparable using the specified comparator.
throws
IllegalArgumentException if fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length
see
Comparator

        rangeCheck(a.length, fromIndex, toIndex);
	T[] aux = (T[])cloneSubarray(a, fromIndex, toIndex);
        if (c==null)
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex);
        else
            mergeSort(aux, a, fromIndex, toIndex, -fromIndex, c);
    
public static voidsort(short[] a)
Sorts the specified array of shorts 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", 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.

	sort1(a, 0, a.length);
    
public static voidsort(short[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of shorts into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    
public static voidsort(char[] a)
Sorts the specified array of chars 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", 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.

	sort1(a, 0, a.length);
    
public static voidsort(char[] a, int fromIndex, int toIndex)
Sorts the specified range of the specified array of chars into ascending numerical order. The range to be sorted extends from index fromIndex, inclusive, to index toIndex, exclusive. (If fromIndex==toIndex, the range to be sorted is empty.)

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.
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 fromIndex > toIndex
throws
ArrayIndexOutOfBoundsException if fromIndex < 0 or toIndex > a.length

        rangeCheck(a.length, fromIndex, toIndex);
	sort1(a, fromIndex, toIndex-fromIndex);
    
private static voidsort1(long[] x, int off, int len)
Sorts the specified sub-array of longs into ascending order.

	// 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);
    
private static voidsort1(int[] x, int off, int len)
Sorts the specified sub-array of integers into ascending order.

	// 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);
    
private static voidsort1(short[] x, int off, int len)
Sorts the specified sub-array of shorts into ascending order.

	// 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);
    
private static voidsort1(char[] x, int off, int len)
Sorts the specified sub-array of chars into ascending order.

	// 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);
    
private static voidsort1(byte[] x, int off, int len)
Sorts the specified sub-array of bytes into ascending order.

	// 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);
    
private static voidsort1(double[] x, int off, int len)
Sorts the specified sub-array of doubles into ascending order.

	// 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);
    
private static voidsort1(float[] x, int off, int len)
Sorts the specified sub-array of floats into ascending order.

	// 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);
    
private static voidsort2(double[] a, int fromIndex, int toIndex)

        final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * 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 i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
		double swap = a[i];
                a[i] = a[--n];
                a[n] = swap;
            } else {
                if (a[i]==0 && Double.doubleToLongBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0d;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
	sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch(a, 0.0d, fromIndex, n-1); // posn of ANY zero
            do {
                j--;
            } while (j>=0 && a[j]==0.0d);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0d;
        }
    
private static voidsort2(float[] a, int fromIndex, int toIndex)

        final int NEG_ZERO_BITS = Float.floatToIntBits(-0.0f);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * 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 i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
		float swap = a[i];
                a[i] = a[--n];
                a[n] = swap;
            } else {
                if (a[i]==0 && Float.floatToIntBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0f;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
	sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch(a, 0.0f, fromIndex, n-1); // posn of ANY zero
            do {
                j--;
            } while (j>=0 && a[j]==0.0f);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0f;
        }
    
private static voidswap(long[] x, int a, int b)
Swaps x[a] with x[b].

	long t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(int[] x, int a, int b)
Swaps x[a] with x[b].

	int t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(short[] x, int a, int b)
Swaps x[a] with x[b].

	short t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(char[] x, int a, int b)
Swaps x[a] with x[b].

	char t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(byte[] x, int a, int b)
Swaps x[a] with x[b].

	byte t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(double[] x, int a, int b)
Swaps x[a] with x[b].

	double t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(float[] x, int a, int b)
Swaps x[a] with x[b].

	float t = x[a];
	x[a] = x[b];
	x[b] = t;
    
private static voidswap(java.lang.Object[] x, int a, int b)
Swaps x[a] with x[b].

	Object t = x[a];
	x[a] = x[b];
	x[b] = t;
    
public static java.lang.StringtoString(long[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(long). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(int[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(int). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(short[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(short). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(char[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(char). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(byte[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(byte). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(boolean[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(boolean). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(float[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(float). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(double[] a)
Returns a string representation of the contents of the specified array. The string representation consists of a list of the array's elements, enclosed in square brackets ("[]"). Adjacent elements are separated by the characters ", " (a comma followed by a space). Elements are converted to strings as by String.valueOf(double). Returns "null" if a is null.

param
a the array whose string representation to return
return
a string representation of a
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
        buf.append('[");
        buf.append(a[0]);
 
        for (int i = 1; i < a.length; i++) {
            buf.append(", ");
            buf.append(a[i]);
        }
 
        buf.append("]");
        return buf.toString();
    
public static java.lang.StringtoString(java.lang.Object[] a)
Returns a string representation of the contents of the specified array. If the array contains other arrays as elements, they are converted to strings by the {@link Object#toString} method inherited from Object, which describes their identities rather than their contents.

The value returned by this method is equal to the value that would be returned by Arrays.asList(a).toString(), unless a is null, in which case "null" is returned.

param
a the array whose string representation to return
return
a string representation of a
see
#deepToString(Object[])
since
1.5

        if (a == null)
            return "null";
        if (a.length == 0)
            return "[]";
 
        StringBuilder buf = new StringBuilder();
 
        for (int i = 0; i < a.length; i++) {
            if (i == 0)
                buf.append('[");
            else
                buf.append(", ");
 
            buf.append(String.valueOf(a[i]));
        }
 
        buf.append("]");
        return buf.toString();
    
private static voidvecswap(long[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    
private static voidvecswap(int[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    
private static voidvecswap(short[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    
private static voidvecswap(char[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    
private static voidvecswap(byte[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    
private static voidvecswap(double[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);
    
private static voidvecswap(float[] x, int a, int b, int n)
Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].

	for (int i=0; i<n; i++, a++, b++)
	    swap(x, a, b);