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	/*
	* Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
	* or visit www.oracle.com if you need additional information or have any
	* questions.
	*/

	package java.lang;

	import java.lang.annotation.Native;

	/**
	* The {@code Integer} class wraps a value of the primitive type
	* {@code int} in an object. An object of type {@code Integer}
	* contains a single field whose type is {@code int}.
	*
	* <p>In addition, this class provides several methods for converting
	* an {@code int} to a {@code String} and a {@code String} to an
	* {@code int}, as well as other constants and methods useful when
	* dealing with an {@code int}.
	*
	* <p>Implementation note: The implementations of the "bit twiddling"
	* methods (such as {@link #highestOneBit(int) highestOneBit} and
	* {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
	* based on material from Henry S. Warren, Jr.'s <i>Hacker's
	* Delight</i>, (Addison Wesley, 2002).
	*
	* @author Lee Boynton
	* @author Arthur van Hoff
	* @author Josh Bloch
	* @author Joseph D. Darcy
	* @since JDK1.0
	*/
	public final class Integer extends Number implements Comparable<Integer> {
	/**
	* A constant holding the minimum value an {@code int} can
	* have, -2<sup>31</sup>.
	*/
	@Native public static final int MIN_VALUE = 0x80000000;

	/**
	* A constant holding the maximum value an {@code int} can
	* have, 2<sup>31</sup>-1.
	*/
	@Native public static final int MAX_VALUE = 0x7fffffff;

	/**
	* The {@code Class} instance representing the primitive type
	* {@code int}.
	*
	* @since JDK1.1
	*/
	@SuppressWarnings("unchecked")
	public static final Class<Integer> TYPE = (Class<Integer>) Class.getPrimitiveClass("int");

	/**
	* All possible chars for representing a number as a String
	*/
	final static char[] digits = {
	'0' , '1' , '2' , '3' , '4' , '5' ,
	'6' , '7' , '8' , '9' , 'a' , 'b' ,
	'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
	'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
	'o' , 'p' , 'q' , 'r' , 's' , 't' ,
	'u' , 'v' , 'w' , 'x' , 'y' , 'z'
	};

	/**
	* Returns a string representation of the first argument in the
	* radix specified by the second argument.
	*
	* <p>If the radix is smaller than {@code Character.MIN_RADIX}
	* or larger than {@code Character.MAX_RADIX}, then the radix
	* {@code 10} is used instead.
	*
	* <p>If the first argument is negative, the first element of the
	* result is the ASCII minus character {@code '-'}
	* ({@code '\u005Cu002D'}). If the first argument is not
	* negative, no sign character appears in the result.
	*
	* <p>The remaining characters of the result represent the magnitude
	* of the first argument. If the magnitude is zero, it is
	* represented by a single zero character {@code '0'}
	* ({@code '\u005Cu0030'}); otherwise, the first character of
	* the representation of the magnitude will not be the zero
	* character. The following ASCII characters are used as digits:
	*
	* <blockquote>
	* {@code 0123456789abcdefghijklmnopqrstuvwxyz}
	* </blockquote>
	*
	* These are {@code '\u005Cu0030'} through
	* {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
	* {@code '\u005Cu007A'}. If {@code radix} is
	* <var>N</var>, then the first <var>N</var> of these characters
	* are used as radix-<var>N</var> digits in the order shown. Thus,
	* the digits for hexadecimal (radix 16) are
	* {@code 0123456789abcdef}. If uppercase letters are
	* desired, the {@link java.lang.String#toUpperCase()} method may
	* be called on the result:
	*
	* <blockquote>
	* {@code Integer.toString(n, 16).toUpperCase()}
	* </blockquote>
	*
	* @param i an integer to be converted to a string.
	* @param radix the radix to use in the string representation.
	* @return a string representation of the argument in the specified radix.
	* @see java.lang.Character#MAX_RADIX
	* @see java.lang.Character#MIN_RADIX
	*/
	public static String toString(int i, int radix) {
	if (radix < Character.MIN_RADIX \|\| radix > Character.MAX_RADIX)
	radix = 10;

	/* Use the faster version */
	if (radix == 10) {
	return toString(i);
	}

	char buf[] = new char[33];
	boolean negative = (i < 0);
	int charPos = 32;

	if (!negative) {
	i = -i;
	}

	while (i <= -radix) {
	buf[charPos--] = digits[-(i % radix)];
	i = i / radix;
	}
	buf[charPos] = digits[-i];

	if (negative) {
	buf[--charPos] = '-';
	}

	return new String(buf, charPos, (33 - charPos));
	}

	/**
	* Returns a string representation of the first argument as an
	* unsigned integer value in the radix specified by the second
	* argument.
	*
	* <p>If the radix is smaller than {@code Character.MIN_RADIX}
	* or larger than {@code Character.MAX_RADIX}, then the radix
	* {@code 10} is used instead.
	*
	* <p>Note that since the first argument is treated as an unsigned
	* value, no leading sign character is printed.
	*
	* <p>If the magnitude is zero, it is represented by a single zero
	* character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
	* the first character of the representation of the magnitude will
	* not be the zero character.
	*
	* <p>The behavior of radixes and the characters used as digits
	* are the same as {@link #toString(int, int) toString}.
	*
	* @param i an integer to be converted to an unsigned string.
	* @param radix the radix to use in the string representation.
	* @return an unsigned string representation of the argument in the specified radix.
	* @see #toString(int, int)
	* @since 1.8
	*/
	public static String toUnsignedString(int i, int radix) {
	return Long.toUnsignedString(toUnsignedLong(i), radix);
	}

	/**
	* Returns a string representation of the integer argument as an
	* unsigned integer in base 16.
	*
	* <p>The unsigned integer value is the argument plus 2<sup>32</sup>
	* if the argument is negative; otherwise, it is equal to the
	* argument. This value is converted to a string of ASCII digits
	* in hexadecimal (base 16) with no extra leading
	* {@code 0}s.
	*
	* <p>The value of the argument can be recovered from the returned
	* string {@code s} by calling {@link
	* Integer#parseUnsignedInt(String, int)
	* Integer.parseUnsignedInt(s, 16)}.
	*
	* <p>If the unsigned magnitude is zero, it is represented by a
	* single zero character {@code '0'} ({@code '\u005Cu0030'});
	* otherwise, the first character of the representation of the
	* unsigned magnitude will not be the zero character. The
	* following characters are used as hexadecimal digits:
	*
	* <blockquote>
	* {@code 0123456789abcdef}
	* </blockquote>
	*
	* These are the characters {@code '\u005Cu0030'} through
	* {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
	* {@code '\u005Cu0066'}. If uppercase letters are
	* desired, the {@link java.lang.String#toUpperCase()} method may
	* be called on the result:
	*
	* <blockquote>
	* {@code Integer.toHexString(n).toUpperCase()}
	* </blockquote>
	*
	* @param i an integer to be converted to a string.
	* @return the string representation of the unsigned integer value
	* represented by the argument in hexadecimal (base 16).
	* @see #parseUnsignedInt(String, int)
	* @see #toUnsignedString(int, int)
	* @since JDK1.0.2
	*/
	public static String toHexString(int i) {
	return toUnsignedString0(i, 4);
	}

	/**
	* Returns a string representation of the integer argument as an
	* unsigned integer in base 8.
	*
	* <p>The unsigned integer value is the argument plus 2<sup>32</sup>
	* if the argument is negative; otherwise, it is equal to the
	* argument. This value is converted to a string of ASCII digits
	* in octal (base 8) with no extra leading {@code 0}s.
	*
	* <p>The value of the argument can be recovered from the returned
	* string {@code s} by calling {@link
	* Integer#parseUnsignedInt(String, int)
	* Integer.parseUnsignedInt(s, 8)}.
	*
	* <p>If the unsigned magnitude is zero, it is represented by a
	* single zero character {@code '0'} ({@code '\u005Cu0030'});
	* otherwise, the first character of the representation of the
	* unsigned magnitude will not be the zero character. The
	* following characters are used as octal digits:
	*
	* <blockquote>
	* {@code 01234567}
	* </blockquote>
	*
	* These are the characters {@code '\u005Cu0030'} through
	* {@code '\u005Cu0037'}.
	*
	* @param i an integer to be converted to a string.
	* @return the string representation of the unsigned integer value
	* represented by the argument in octal (base 8).
	* @see #parseUnsignedInt(String, int)
	* @see #toUnsignedString(int, int)
	* @since JDK1.0.2
	*/
	public static String toOctalString(int i) {
	return toUnsignedString0(i, 3);
	}

	/**
	* Returns a string representation of the integer argument as an
	* unsigned integer in base 2.
	*
	* <p>The unsigned integer value is the argument plus 2<sup>32</sup>
	* if the argument is negative; otherwise it is equal to the
	* argument. This value is converted to a string of ASCII digits
	* in binary (base 2) with no extra leading {@code 0}s.
	*
	* <p>The value of the argument can be recovered from the returned
	* string {@code s} by calling {@link
	* Integer#parseUnsignedInt(String, int)
	* Integer.parseUnsignedInt(s, 2)}.
	*
	* <p>If the unsigned magnitude is zero, it is represented by a
	* single zero character {@code '0'} ({@code '\u005Cu0030'});
	* otherwise, the first character of the representation of the
	* unsigned magnitude will not be the zero character. The
	* characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
	* '1'} ({@code '\u005Cu0031'}) are used as binary digits.
	*
	* @param i an integer to be converted to a string.
	* @return the string representation of the unsigned integer value
	* represented by the argument in binary (base 2).
	* @see #parseUnsignedInt(String, int)
	* @see #toUnsignedString(int, int)
	* @since JDK1.0.2
	*/
	public static String toBinaryString(int i) {
	return toUnsignedString0(i, 1);
	}

	/**
	* Convert the integer to an unsigned number.
	*/
	private static String toUnsignedString0(int val, int shift) {
	// assert shift > 0 && shift <=5 : "Illegal shift value";
	int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
	int chars = Math.max(((mag + (shift - 1)) / shift), 1);
	char[] buf = new char[chars];

	formatUnsignedInt(val, shift, buf, 0, chars);

	// Use special constructor which takes over "buf".
	return new String(buf, true);
	}

	/**
	* Format a long (treated as unsigned) into a character buffer.
	* @param val the unsigned int to format
	* @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
	* @param buf the character buffer to write to
	* @param offset the offset in the destination buffer to start at
	* @param len the number of characters to write
	* @return the lowest character location used
	*/
	static int formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
	int charPos = len;
	int radix = 1 << shift;
	int mask = radix - 1;
	do {
	buf[offset + --charPos] = Integer.digits[val & mask];
	val >>>= shift;
	} while (val != 0 && charPos > 0);

	return charPos;
	}

	final static char [] DigitTens = {
	'0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
	'1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
	'2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
	'3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
	'4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
	'5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
	'6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
	'7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
	'8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
	'9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
	} ;

	final static char [] DigitOnes = {
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	'0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
	} ;

	// I use the "invariant division by multiplication" trick to
	// accelerate Integer.toString. In particular we want to
	// avoid division by 10.
	//
	// The "trick" has roughly the same performance characteristics
	// as the "classic" Integer.toString code on a non-JIT VM.
	// The trick avoids .rem and .div calls but has a longer code
	// path and is thus dominated by dispatch overhead. In the
	// JIT case the dispatch overhead doesn't exist and the
	// "trick" is considerably faster than the classic code.
	//
	// TODO-FIXME: convert (x * 52429) into the equiv shift-add
	// sequence.
	//
	// RE: Division by Invariant Integers using Multiplication
	// T Gralund, P Montgomery
	// ACM PLDI 1994
	//

	/**
	* Returns a {@code String} object representing the
	* specified integer. The argument is converted to signed decimal
	* representation and returned as a string, exactly as if the
	* argument and radix 10 were given as arguments to the {@link
	* #toString(int, int)} method.
	*
	* @param i an integer to be converted.
	* @return a string representation of the argument in base 10.
	*/
	public static String toString(int i) {
	if (i == Integer.MIN_VALUE)
	return "-2147483648";
	int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
	char[] buf = new char[size];
	getChars(i, size, buf);
	return new String(buf, true);
	}

	/**
	* Returns a string representation of the argument as an unsigned
	* decimal value.
	*
	* The argument is converted to unsigned decimal representation
	* and returned as a string exactly as if the argument and radix
	* 10 were given as arguments to the {@link #toUnsignedString(int,
	* int)} method.
	*
	* @param i an integer to be converted to an unsigned string.
	* @return an unsigned string representation of the argument.
	* @see #toUnsignedString(int, int)
	* @since 1.8
	*/
	public static String toUnsignedString(int i) {
	return Long.toString(toUnsignedLong(i));
	}

	/**
	* Places characters representing the integer i into the
	* character array buf. The characters are placed into
	* the buffer backwards starting with the least significant
	* digit at the specified index (exclusive), and working
	* backwards from there.
	*
	* Will fail if i == Integer.MIN_VALUE
	*/
	static void getChars(int i, int index, char[] buf) {
	int q, r;
	int charPos = index;
	char sign = 0;

	if (i < 0) {
	sign = '-';
	i = -i;
	}

	// Generate two digits per iteration
	while (i >= 65536) {
	q = i / 100;
	// really: r = i - (q * 100);
	r = i - ((q << 6) + (q << 5) + (q << 2));
	i = q;
	buf [--charPos] = DigitOnes[r];
	buf [--charPos] = DigitTens[r];
	}

	// Fall thru to fast mode for smaller numbers
	// assert(i <= 65536, i);
	for (;;) {
	q = (i * 52429) >>> (16+3);
	r = i - ((q << 3) + (q << 1)); // r = i-(q*10) ...
	buf [--charPos] = digits [r];
	i = q;
	if (i == 0) break;
	}
	if (sign != 0) {
	buf [--charPos] = sign;
	}
	}

	final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
	99999999, 999999999, Integer.MAX_VALUE };

	// Requires positive x
	static int stringSize(int x) {
	for (int i=0; ; i++)
	if (x <= sizeTable[i])
	return i+1;
	}

	/**
	* Parses the string argument as a signed integer in the radix
	* specified by the second argument. The characters in the string
	* must all be digits of the specified radix (as determined by
	* whether {@link java.lang.Character#digit(char, int)} returns a
	* nonnegative value), except that the first character may be an
	* ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
	* indicate a negative value or an ASCII plus sign {@code '+'}
	* ({@code '\u005Cu002B'}) to indicate a positive value. The
	* resulting integer value is returned.
	*
	* <p>An exception of type {@code NumberFormatException} is
	* thrown if any of the following situations occurs:
	* <ul>
	* <li>The first argument is {@code null} or is a string of
	* length zero.
	*
	* <li>The radix is either smaller than
	* {@link java.lang.Character#MIN_RADIX} or
	* larger than {@link java.lang.Character#MAX_RADIX}.
	*
	* <li>Any character of the string is not a digit of the specified
	* radix, except that the first character may be a minus sign
	* {@code '-'} ({@code '\u005Cu002D'}) or plus sign
	* {@code '+'} ({@code '\u005Cu002B'}) provided that the
	* string is longer than length 1.
	*
	* <li>The value represented by the string is not a value of type
	* {@code int}.
	* </ul>
	*
	* <p>Examples:
	* <blockquote><pre>
	* parseInt("0", 10) returns 0
	* parseInt("473", 10) returns 473
	* parseInt("+42", 10) returns 42
	* parseInt("-0", 10) returns 0
	* parseInt("-FF", 16) returns -255
	* parseInt("1100110", 2) returns 102
	* parseInt("2147483647", 10) returns 2147483647
	* parseInt("-2147483648", 10) returns -2147483648
	* parseInt("2147483648", 10) throws a NumberFormatException
	* parseInt("99", 8) throws a NumberFormatException
	* parseInt("Kona", 10) throws a NumberFormatException
	* parseInt("Kona", 27) returns 411787
	* </pre></blockquote>
	*
	* @param s the {@code String} containing the integer
	* representation to be parsed
	* @param radix the radix to be used while parsing {@code s}.
	* @return the integer represented by the string argument in the
	* specified radix.
	* @exception NumberFormatException if the {@code String}
	* does not contain a parsable {@code int}.
	*/
	public static int parseInt(String s, int radix)
	throws NumberFormatException
	{
	/*
	* WARNING: This method may be invoked early during VM initialization
	* before IntegerCache is initialized. Care must be taken to not use
	* the valueOf method.
	*/

	if (s == null) {
	throw new NumberFormatException("null");
	}

	if (radix < Character.MIN_RADIX) {
	throw new NumberFormatException("radix " + radix +
	" less than Character.MIN_RADIX");
	}

	if (radix > Character.MAX_RADIX) {
	throw new NumberFormatException("radix " + radix +
	" greater than Character.MAX_RADIX");
	}

	int result = 0;
	boolean negative = false;
	int i = 0, len = s.length();
	int limit = -Integer.MAX_VALUE;
	int multmin;
	int digit;

	if (len > 0) {
	char firstChar = s.charAt(0);
	if (firstChar < '0') { // Possible leading "+" or "-"
	if (firstChar == '-') {
	negative = true;
	limit = Integer.MIN_VALUE;
	} else if (firstChar != '+')
	throw NumberFormatException.forInputString(s);

	if (len == 1) // Cannot have lone "+" or "-"
	throw NumberFormatException.forInputString(s);
	i++;
	}
	multmin = limit / radix;
	while (i < len) {
	// Accumulating negatively avoids surprises near MAX_VALUE
	digit = Character.digit(s.charAt(i++),radix);
	if (digit < 0) {
	throw NumberFormatException.forInputString(s);
	}
	if (result < multmin) {
	throw NumberFormatException.forInputString(s);
	}
	result *= radix;
	if (result < limit + digit) {
	throw NumberFormatException.forInputString(s);
	}
	result -= digit;
	}
	} else {
	throw NumberFormatException.forInputString(s);
	}
	return negative ? result : -result;
	}

	/**
	* Parses the string argument as a signed decimal integer. The
	* characters in the string must all be decimal digits, except
	* that the first character may be an ASCII minus sign {@code '-'}
	* ({@code '\u005Cu002D'}) to indicate a negative value or an
	* ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
	* indicate a positive value. The resulting integer value is
	* returned, exactly as if the argument and the radix 10 were
	* given as arguments to the {@link #parseInt(java.lang.String,
	* int)} method.
	*
	* @param s a {@code String} containing the {@code int}
	* representation to be parsed
	* @return the integer value represented by the argument in decimal.
	* @exception NumberFormatException if the string does not contain a
	* parsable integer.
	*/
	public static int parseInt(String s) throws NumberFormatException {
	return parseInt(s,10);
	}

	/**
	* Parses the string argument as an unsigned integer in the radix
	* specified by the second argument. An unsigned integer maps the
	* values usually associated with negative numbers to positive
	* numbers larger than {@code MAX_VALUE}.
	*
	* The characters in the string must all be digits of the
	* specified radix (as determined by whether {@link
	* java.lang.Character#digit(char, int)} returns a nonnegative
	* value), except that the first character may be an ASCII plus
	* sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
	* integer value is returned.
	*
	* <p>An exception of type {@code NumberFormatException} is
	* thrown if any of the following situations occurs:
	* <ul>
	* <li>The first argument is {@code null} or is a string of
	* length zero.
	*
	* <li>The radix is either smaller than
	* {@link java.lang.Character#MIN_RADIX} or
	* larger than {@link java.lang.Character#MAX_RADIX}.
	*
	* <li>Any character of the string is not a digit of the specified
	* radix, except that the first character may be a plus sign
	* {@code '+'} ({@code '\u005Cu002B'}) provided that the
	* string is longer than length 1.
	*
	* <li>The value represented by the string is larger than the
	* largest unsigned {@code int}, 2<sup>32</sup>-1.
	*
	* </ul>
	*
	*
	* @param s the {@code String} containing the unsigned integer
	* representation to be parsed
	* @param radix the radix to be used while parsing {@code s}.
	* @return the integer represented by the string argument in the
	* specified radix.
	* @throws NumberFormatException if the {@code String}
	* does not contain a parsable {@code int}.
	* @since 1.8
	*/
	public static int parseUnsignedInt(String s, int radix)
	throws NumberFormatException {
	if (s == null) {
	throw new NumberFormatException("null");
	}

	int len = s.length();
	if (len > 0) {
	char firstChar = s.charAt(0);
	if (firstChar == '-') {
	throw new
	NumberFormatException(String.format("Illegal leading minus sign " +
	"on unsigned string %s.", s));
	} else {
	if (len <= 5 \|\| // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
	(radix == 10 && len <= 9) ) { // Integer.MAX_VALUE in base 10 is 10 digits
	return parseInt(s, radix);
	} else {
	long ell = Long.parseLong(s, radix);
	if ((ell & 0xffff_ffff_0000_0000L) == 0) {
	return (int) ell;
	} else {
	throw new
	NumberFormatException(String.format("String value %s exceeds " +
	"range of unsigned int.", s));
	}
	}
	}
	} else {
	throw NumberFormatException.forInputString(s);
	}
	}

	/**
	* Parses the string argument as an unsigned decimal integer. The
	* characters in the string must all be decimal digits, except
	* that the first character may be an an ASCII plus sign {@code
	* '+'} ({@code '\u005Cu002B'}). The resulting integer value
	* is returned, exactly as if the argument and the radix 10 were
	* given as arguments to the {@link
	* #parseUnsignedInt(java.lang.String, int)} method.
	*
	* @param s a {@code String} containing the unsigned {@code int}
	* representation to be parsed
	* @return the unsigned integer value represented by the argument in decimal.
	* @throws NumberFormatException if the string does not contain a
	* parsable unsigned integer.
	* @since 1.8
	*/
	public static int parseUnsignedInt(String s) throws NumberFormatException {
	return parseUnsignedInt(s, 10);
	}

	/**
	* Returns an {@code Integer} object holding the value
	* extracted from the specified {@code String} when parsed
	* with the radix given by the second argument. The first argument
	* is interpreted as representing a signed integer in the radix
	* specified by the second argument, exactly as if the arguments
	* were given to the {@link #parseInt(java.lang.String, int)}
	* method. The result is an {@code Integer} object that
	* represents the integer value specified by the string.
	*
	* <p>In other words, this method returns an {@code Integer}
	* object equal to the value of:
	*
	* <blockquote>
	* {@code new Integer(Integer.parseInt(s, radix))}
	* </blockquote>
	*
	* @param s the string to be parsed.
	* @param radix the radix to be used in interpreting {@code s}
	* @return an {@code Integer} object holding the value
	* represented by the string argument in the specified
	* radix.
	* @exception NumberFormatException if the {@code String}
	* does not contain a parsable {@code int}.
	*/
	public static Integer valueOf(String s, int radix) throws NumberFormatException {
	return Integer.valueOf(parseInt(s,radix));
	}

	/**
	* Returns an {@code Integer} object holding the
	* value of the specified {@code String}. The argument is
	* interpreted as representing a signed decimal integer, exactly
	* as if the argument were given to the {@link
	* #parseInt(java.lang.String)} method. The result is an
	* {@code Integer} object that represents the integer value
	* specified by the string.
	*
	* <p>In other words, this method returns an {@code Integer}
	* object equal to the value of:
	*
	* <blockquote>
	* {@code new Integer(Integer.parseInt(s))}
	* </blockquote>
	*
	* @param s the string to be parsed.
	* @return an {@code Integer} object holding the value
	* represented by the string argument.
	* @exception NumberFormatException if the string cannot be parsed
	* as an integer.
	*/
	public static Integer valueOf(String s) throws NumberFormatException {
	return Integer.valueOf(parseInt(s, 10));
	}

	/**
	* Cache to support the object identity semantics of autoboxing for values between
	* -128 and 127 (inclusive) as required by JLS.
	*
	* The cache is initialized on first usage. The size of the cache
	* may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
	* During VM initialization, java.lang.Integer.IntegerCache.high property
	* may be set and saved in the private system properties in the
	* sun.misc.VM class.
	*/

	private static class IntegerCache {
	static final int low = -128;
	static final int high;
	static final Integer cache[];

	static {
	// high value may be configured by property
	int h = 127;
	String integerCacheHighPropValue =
	sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
	if (integerCacheHighPropValue != null) {
	try {
	int i = parseInt(integerCacheHighPropValue);
	i = Math.max(i, 127);
	// Maximum array size is Integer.MAX_VALUE
	h = Math.min(i, Integer.MAX_VALUE - (-low) -1);
	} catch( NumberFormatException nfe) {
	// If the property cannot be parsed into an int, ignore it.
	}
	}
	high = h;

	cache = new Integer[(high - low) + 1];
	int j = low;
	for(int k = 0; k < cache.length; k++)
	cache[k] = new Integer(j++);

	// range [-128, 127] must be interned (JLS7 5.1.7)
	assert IntegerCache.high >= 127;
	}

	private IntegerCache() {}
	}

	/**
	* Returns an {@code Integer} instance representing the specified
	* {@code int} value. If a new {@code Integer} instance is not
	* required, this method should generally be used in preference to
	* the constructor {@link #Integer(int)}, as this method is likely
	* to yield significantly better space and time performance by
	* caching frequently requested values.
	*
	* This method will always cache values in the range -128 to 127,
	* inclusive, and may cache other values outside of this range.
	*
	* @param i an {@code int} value.
	* @return an {@code Integer} instance representing {@code i}.
	* @since 1.5
	*/
	public static Integer valueOf(int i) {
	if (i >= IntegerCache.low && i <= IntegerCache.high)
	return IntegerCache.cache[i + (-IntegerCache.low)];
	return new Integer(i);
	}

	/**
	* The value of the {@code Integer}.
	*
	* @serial
	*/
	private final int value;

	/**
	* Constructs a newly allocated {@code Integer} object that
	* represents the specified {@code int} value.
	*
	* @param value the value to be represented by the
	* {@code Integer} object.
	*/
	public Integer(int value) {
	this.value = value;
	}

	/**
	* Constructs a newly allocated {@code Integer} object that
	* represents the {@code int} value indicated by the
	* {@code String} parameter. The string is converted to an
	* {@code int} value in exactly the manner used by the
	* {@code parseInt} method for radix 10.
	*
	* @param s the {@code String} to be converted to an
	* {@code Integer}.
	* @exception NumberFormatException if the {@code String} does not
	* contain a parsable integer.
	* @see java.lang.Integer#parseInt(java.lang.String, int)
	*/
	public Integer(String s) throws NumberFormatException {
	this.value = parseInt(s, 10);
	}

	/**
	* Returns the value of this {@code Integer} as a {@code byte}
	* after a narrowing primitive conversion.
	* @jls 5.1.3 Narrowing Primitive Conversions
	*/
	public byte byteValue() {
	return (byte)value;
	}

	/**
	* Returns the value of this {@code Integer} as a {@code short}
	* after a narrowing primitive conversion.
	* @jls 5.1.3 Narrowing Primitive Conversions
	*/
	public short shortValue() {
	return (short)value;
	}

	/**
	* Returns the value of this {@code Integer} as an
	* {@code int}.
	*/
	public int intValue() {
	return value;
	}

	/**
	* Returns the value of this {@code Integer} as a {@code long}
	* after a widening primitive conversion.
	* @jls 5.1.2 Widening Primitive Conversions
	* @see Integer#toUnsignedLong(int)
	*/
	public long longValue() {
	return (long)value;
	}

	/**
	* Returns the value of this {@code Integer} as a {@code float}
	* after a widening primitive conversion.
	* @jls 5.1.2 Widening Primitive Conversions
	*/
	public float floatValue() {
	return (float)value;
	}

	/**
	* Returns the value of this {@code Integer} as a {@code double}
	* after a widening primitive conversion.
	* @jls 5.1.2 Widening Primitive Conversions
	*/
	public double doubleValue() {
	return (double)value;
	}

	/**
	* Returns a {@code String} object representing this
	* {@code Integer}'s value. The value is converted to signed
	* decimal representation and returned as a string, exactly as if
	* the integer value were given as an argument to the {@link
	* java.lang.Integer#toString(int)} method.
	*
	* @return a string representation of the value of this object in
	* base 10.
	*/
	public String toString() {
	return toString(value);
	}

	/**
	* Returns a hash code for this {@code Integer}.
	*
	* @return a hash code value for this object, equal to the
	* primitive {@code int} value represented by this
	* {@code Integer} object.
	*/
	@Override
	public int hashCode() {
	return Integer.hashCode(value);
	}

	/**
	* Returns a hash code for a {@code int} value; compatible with
	* {@code Integer.hashCode()}.
	*
	* @param value the value to hash
	* @since 1.8
	*
	* @return a hash code value for a {@code int} value.
	*/
	public static int hashCode(int value) {
	return value;
	}

	/**
	* Compares this object to the specified object. The result is
	* {@code true} if and only if the argument is not
	* {@code null} and is an {@code Integer} object that
	* contains the same {@code int} value as this object.
	*
	* @param obj the object to compare with.
	* @return {@code true} if the objects are the same;
	* {@code false} otherwise.
	*/
	public boolean equals(Object obj) {
	if (obj instanceof Integer) {
	return value == ((Integer)obj).intValue();
	}
	return false;
	}

	/**
	* Determines the integer value of the system property with the
	* specified name.
	*
	* <p>The first argument is treated as the name of a system
	* property. System properties are accessible through the {@link
	* java.lang.System#getProperty(java.lang.String)} method. The
	* string value of this property is then interpreted as an integer
	* value using the grammar supported by {@link Integer#decode decode} and
	* an {@code Integer} object representing this value is returned.
	*
	* <p>If there is no property with the specified name, if the
	* specified name is empty or {@code null}, or if the property
	* does not have the correct numeric format, then {@code null} is
	* returned.
	*
	* <p>In other words, this method returns an {@code Integer}
	* object equal to the value of:
	*
	* <blockquote>
	* {@code getInteger(nm, null)}
	* </blockquote>
	*
	* @param nm property name.
	* @return the {@code Integer} value of the property.
	* @throws SecurityException for the same reasons as
	* {@link System#getProperty(String) System.getProperty}
	* @see java.lang.System#getProperty(java.lang.String)
	* @see java.lang.System#getProperty(java.lang.String, java.lang.String)
	*/
	public static Integer getInteger(String nm) {
	return getInteger(nm, null);
	}

	/**
	* Determines the integer value of the system property with the
	* specified name.
	*
	* <p>The first argument is treated as the name of a system
	* property. System properties are accessible through the {@link
	* java.lang.System#getProperty(java.lang.String)} method. The
	* string value of this property is then interpreted as an integer
	* value using the grammar supported by {@link Integer#decode decode} and
	* an {@code Integer} object representing this value is returned.
	*
	* <p>The second argument is the default value. An {@code Integer} object
	* that represents the value of the second argument is returned if there
	* is no property of the specified name, if the property does not have
	* the correct numeric format, or if the specified name is empty or
	* {@code null}.
	*
	* <p>In other words, this method returns an {@code Integer} object
	* equal to the value of:
	*
	* <blockquote>
	* {@code getInteger(nm, new Integer(val))}
	* </blockquote>
	*
	* but in practice it may be implemented in a manner such as:
	*
	* <blockquote><pre>
	* Integer result = getInteger(nm, null);
	* return (result == null) ? new Integer(val) : result;
	* </pre></blockquote>
	*
	* to avoid the unnecessary allocation of an {@code Integer}
	* object when the default value is not needed.
	*
	* @param nm property name.
	* @param val default value.
	* @return the {@code Integer} value of the property.
	* @throws SecurityException for the same reasons as
	* {@link System#getProperty(String) System.getProperty}
	* @see java.lang.System#getProperty(java.lang.String)
	* @see java.lang.System#getProperty(java.lang.String, java.lang.String)
	*/
	public static Integer getInteger(String nm, int val) {
	Integer result = getInteger(nm, null);
	return (result == null) ? Integer.valueOf(val) : result;
	}

	/**
	* Returns the integer value of the system property with the
	* specified name. The first argument is treated as the name of a
	* system property. System properties are accessible through the
	* {@link java.lang.System#getProperty(java.lang.String)} method.
	* The string value of this property is then interpreted as an
	* integer value, as per the {@link Integer#decode decode} method,
	* and an {@code Integer} object representing this value is
	* returned; in summary:
	*
	* <ul><li>If the property value begins with the two ASCII characters
	* {@code 0x} or the ASCII character {@code #}, not
	* followed by a minus sign, then the rest of it is parsed as a
	* hexadecimal integer exactly as by the method
	* {@link #valueOf(java.lang.String, int)} with radix 16.
	* <li>If the property value begins with the ASCII character
	* {@code 0} followed by another character, it is parsed as an
	* octal integer exactly as by the method
	* {@link #valueOf(java.lang.String, int)} with radix 8.
	* <li>Otherwise, the property value is parsed as a decimal integer
	* exactly as by the method {@link #valueOf(java.lang.String, int)}
	* with radix 10.
	* </ul>
	*
	* <p>The second argument is the default value. The default value is
	* returned if there is no property of the specified name, if the
	* property does not have the correct numeric format, or if the
	* specified name is empty or {@code null}.
	*
	* @param nm property name.
	* @param val default value.
	* @return the {@code Integer} value of the property.
	* @throws SecurityException for the same reasons as
	* {@link System#getProperty(String) System.getProperty}
	* @see System#getProperty(java.lang.String)
	* @see System#getProperty(java.lang.String, java.lang.String)
	*/
	public static Integer getInteger(String nm, Integer val) {
	String v = null;
	try {
	v = System.getProperty(nm);
	} catch (IllegalArgumentException \| NullPointerException e) {
	}
	if (v != null) {
	try {
	return Integer.decode(v);
	} catch (NumberFormatException e) {
	}
	}
	return val;
	}

	/**
	* Decodes a {@code String} into an {@code Integer}.
	* Accepts decimal, hexadecimal, and octal numbers given
	* by the following grammar:
	*
	* <blockquote>
	* <dl>
	* <dt><i>DecodableString:</i>
	* <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
	* <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
	* <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
	* <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
	* <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
	*
	* <dt><i>Sign:</i>
	* <dd>{@code -}
	* <dd>{@code +}
	* </dl>
	* </blockquote>
	*
	* <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
	* are as defined in section 3.10.1 of
	* <cite>The Java™ Language Specification</cite>,
	* except that underscores are not accepted between digits.
	*
	* <p>The sequence of characters following an optional
	* sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
	* "{@code #}", or leading zero) is parsed as by the {@code
	* Integer.parseInt} method with the indicated radix (10, 16, or
	* 8). This sequence of characters must represent a positive
	* value or a {@link NumberFormatException} will be thrown. The
	* result is negated if first character of the specified {@code
	* String} is the minus sign. No whitespace characters are
	* permitted in the {@code String}.
	*
	* @param nm the {@code String} to decode.
	* @return an {@code Integer} object holding the {@code int}
	* value represented by {@code nm}
	* @exception NumberFormatException if the {@code String} does not
	* contain a parsable integer.
	* @see java.lang.Integer#parseInt(java.lang.String, int)
	*/
	public static Integer decode(String nm) throws NumberFormatException {
	int radix = 10;
	int index = 0;
	boolean negative = false;
	Integer result;

	if (nm.length() == 0)
	throw new NumberFormatException("Zero length string");
	char firstChar = nm.charAt(0);
	// Handle sign, if present
	if (firstChar == '-') {
	negative = true;
	index++;
	} else if (firstChar == '+')
	index++;

	// Handle radix specifier, if present
	if (nm.startsWith("0x", index) \|\| nm.startsWith("0X", index)) {
	index += 2;
	radix = 16;
	}
	else if (nm.startsWith("#", index)) {
	index ++;
	radix = 16;
	}
	else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
	index ++;
	radix = 8;
	}

	if (nm.startsWith("-", index) \|\| nm.startsWith("+", index))
	throw new NumberFormatException("Sign character in wrong position");

	try {
	result = Integer.valueOf(nm.substring(index), radix);
	result = negative ? Integer.valueOf(-result.intValue()) : result;
	} catch (NumberFormatException e) {
	// If number is Integer.MIN_VALUE, we'll end up here. The next line
	// handles this case, and causes any genuine format error to be
	// rethrown.
	String constant = negative ? ("-" + nm.substring(index))
	: nm.substring(index);
	result = Integer.valueOf(constant, radix);
	}
	return result;
	}

	/**
	* Compares two {@code Integer} objects numerically.
	*
	* @param anotherInteger the {@code Integer} to be compared.
	* @return the value {@code 0} if this {@code Integer} is
	* equal to the argument {@code Integer}; a value less than
	* {@code 0} if this {@code Integer} is numerically less
	* than the argument {@code Integer}; and a value greater
	* than {@code 0} if this {@code Integer} is numerically
	* greater than the argument {@code Integer} (signed
	* comparison).
	* @since 1.2
	*/
	public int compareTo(Integer anotherInteger) {
	return compare(this.value, anotherInteger.value);
	}

	/**
	* Compares two {@code int} values numerically.
	* The value returned is identical to what would be returned by:
	* <pre>
	* Integer.valueOf(x).compareTo(Integer.valueOf(y))
	* </pre>
	*
	* @param x the first {@code int} to compare
	* @param y the second {@code int} to compare
	* @return the value {@code 0} if {@code x == y};
	* a value less than {@code 0} if {@code x < y}; and
	* a value greater than {@code 0} if {@code x > y}
	* @since 1.7
	*/
	public static int compare(int x, int y) {
	return (x < y) ? -1 : ((x == y) ? 0 : 1);
	}

	/**
	* Compares two {@code int} values numerically treating the values
	* as unsigned.
	*
	* @param x the first {@code int} to compare
	* @param y the second {@code int} to compare
	* @return the value {@code 0} if {@code x == y}; a value less
	* than {@code 0} if {@code x < y} as unsigned values; and
	* a value greater than {@code 0} if {@code x > y} as
	* unsigned values
	* @since 1.8
	*/
	public static int compareUnsigned(int x, int y) {
	return compare(x + MIN_VALUE, y + MIN_VALUE);
	}

	/**
	* Converts the argument to a {@code long} by an unsigned
	* conversion. In an unsigned conversion to a {@code long}, the
	* high-order 32 bits of the {@code long} are zero and the
	* low-order 32 bits are equal to the bits of the integer
	* argument.
	*
	* Consequently, zero and positive {@code int} values are mapped
	* to a numerically equal {@code long} value and negative {@code
	* int} values are mapped to a {@code long} value equal to the
	* input plus 2<sup>32</sup>.
	*
	* @param x the value to convert to an unsigned {@code long}
	* @return the argument converted to {@code long} by an unsigned
	* conversion
	* @since 1.8
	*/
	public static long toUnsignedLong(int x) {
	return ((long) x) & 0xffffffffL;
	}

	/**
	* Returns the unsigned quotient of dividing the first argument by
	* the second where each argument and the result is interpreted as
	* an unsigned value.
	*
	* <p>Note that in two's complement arithmetic, the three other
	* basic arithmetic operations of add, subtract, and multiply are
	* bit-wise identical if the two operands are regarded as both
	* being signed or both being unsigned. Therefore separate {@code
	* addUnsigned}, etc. methods are not provided.
	*
	* @param dividend the value to be divided
	* @param divisor the value doing the dividing
	* @return the unsigned quotient of the first argument divided by
	* the second argument
	* @see #remainderUnsigned
	* @since 1.8
	*/
	public static int divideUnsigned(int dividend, int divisor) {
	// In lieu of tricky code, for now just use long arithmetic.
	return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
	}

	/**
	* Returns the unsigned remainder from dividing the first argument
	* by the second where each argument and the result is interpreted
	* as an unsigned value.
	*
	* @param dividend the value to be divided
	* @param divisor the value doing the dividing
	* @return the unsigned remainder of the first argument divided by
	* the second argument
	* @see #divideUnsigned
	* @since 1.8
	*/
	public static int remainderUnsigned(int dividend, int divisor) {
	// In lieu of tricky code, for now just use long arithmetic.
	return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
	}


	// Bit twiddling

	/**
	* The number of bits used to represent an {@code int} value in two's
	* complement binary form.
	*
	* @since 1.5
	*/
	@Native public static final int SIZE = 32;

	/**
	* The number of bytes used to represent a {@code int} value in two's
	* complement binary form.
	*
	* @since 1.8
	*/
	public static final int BYTES = SIZE / Byte.SIZE;

	/**
	* Returns an {@code int} value with at most a single one-bit, in the
	* position of the highest-order ("leftmost") one-bit in the specified
	* {@code int} value. Returns zero if the specified value has no
	* one-bits in its two's complement binary representation, that is, if it
	* is equal to zero.
	*
	* @param i the value whose highest one bit is to be computed
	* @return an {@code int} value with a single one-bit, in the position
	* of the highest-order one-bit in the specified value, or zero if
	* the specified value is itself equal to zero.
	* @since 1.5
	*/
	public static int highestOneBit(int i) {
	// HD, Figure 3-1
	i \|= (i >> 1);
	i \|= (i >> 2);
	i \|= (i >> 4);
	i \|= (i >> 8);
	i \|= (i >> 16);
	return i - (i >>> 1);
	}

	/**
	* Returns an {@code int} value with at most a single one-bit, in the
	* position of the lowest-order ("rightmost") one-bit in the specified
	* {@code int} value. Returns zero if the specified value has no
	* one-bits in its two's complement binary representation, that is, if it
	* is equal to zero.
	*
	* @param i the value whose lowest one bit is to be computed
	* @return an {@code int} value with a single one-bit, in the position
	* of the lowest-order one-bit in the specified value, or zero if
	* the specified value is itself equal to zero.
	* @since 1.5
	*/
	public static int lowestOneBit(int i) {
	// HD, Section 2-1
	return i & -i;
	}

	/**
	* Returns the number of zero bits preceding the highest-order
	* ("leftmost") one-bit in the two's complement binary representation
	* of the specified {@code int} value. Returns 32 if the
	* specified value has no one-bits in its two's complement representation,
	* in other words if it is equal to zero.
	*
	* <p>Note that this method is closely related to the logarithm base 2.
	* For all positive {@code int} values x:
	* <ul>
	* <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
	* <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
	* </ul>
	*
	* @param i the value whose number of leading zeros is to be computed
	* @return the number of zero bits preceding the highest-order
	* ("leftmost") one-bit in the two's complement binary representation
	* of the specified {@code int} value, or 32 if the value
	* is equal to zero.
	* @since 1.5
	*/
	public static int numberOfLeadingZeros(int i) {
	// HD, Figure 5-6
	if (i == 0)
	return 32;
	int n = 1;
	if (i >>> 16 == 0) { n += 16; i <<= 16; }
	if (i >>> 24 == 0) { n += 8; i <<= 8; }
	if (i >>> 28 == 0) { n += 4; i <<= 4; }
	if (i >>> 30 == 0) { n += 2; i <<= 2; }
	n -= i >>> 31;
	return n;
	}

	/**
	* Returns the number of zero bits following the lowest-order ("rightmost")
	* one-bit in the two's complement binary representation of the specified
	* {@code int} value. Returns 32 if the specified value has no
	* one-bits in its two's complement representation, in other words if it is
	* equal to zero.
	*
	* @param i the value whose number of trailing zeros is to be computed
	* @return the number of zero bits following the lowest-order ("rightmost")
	* one-bit in the two's complement binary representation of the
	* specified {@code int} value, or 32 if the value is equal
	* to zero.
	* @since 1.5
	*/
	public static int numberOfTrailingZeros(int i) {
	// HD, Figure 5-14
	int y;
	if (i == 0) return 32;
	int n = 31;
	y = i <<16; if (y != 0) { n = n -16; i = y; }
	y = i << 8; if (y != 0) { n = n - 8; i = y; }
	y = i << 4; if (y != 0) { n = n - 4; i = y; }
	y = i << 2; if (y != 0) { n = n - 2; i = y; }
	return n - ((i << 1) >>> 31);
	}

	/**
	* Returns the number of one-bits in the two's complement binary
	* representation of the specified {@code int} value. This function is
	* sometimes referred to as the <i>population count</i>.
	*
	* @param i the value whose bits are to be counted
	* @return the number of one-bits in the two's complement binary
	* representation of the specified {@code int} value.
	* @since 1.5
	*/
	public static int bitCount(int i) {
	// HD, Figure 5-2
	i = i - ((i >>> 1) & 0x55555555);
	i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
	i = (i + (i >>> 4)) & 0x0f0f0f0f;
	i = i + (i >>> 8);
	i = i + (i >>> 16);
	return i & 0x3f;
	}

	/**
	* Returns the value obtained by rotating the two's complement binary
	* representation of the specified {@code int} value left by the
	* specified number of bits. (Bits shifted out of the left hand, or
	* high-order, side reenter on the right, or low-order.)
	*
	* <p>Note that left rotation with a negative distance is equivalent to
	* right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
	* distance)}. Note also that rotation by any multiple of 32 is a
	* no-op, so all but the last five bits of the rotation distance can be
	* ignored, even if the distance is negative: {@code rotateLeft(val,
	* distance) == rotateLeft(val, distance & 0x1F)}.
	*
	* @param i the value whose bits are to be rotated left
	* @param distance the number of bit positions to rotate left
	* @return the value obtained by rotating the two's complement binary
	* representation of the specified {@code int} value left by the
	* specified number of bits.
	* @since 1.5
	*/
	public static int rotateLeft(int i, int distance) {
	return (i << distance) \| (i >>> -distance);
	}

	/**
	* Returns the value obtained by rotating the two's complement binary
	* representation of the specified {@code int} value right by the
	* specified number of bits. (Bits shifted out of the right hand, or
	* low-order, side reenter on the left, or high-order.)
	*
	* <p>Note that right rotation with a negative distance is equivalent to
	* left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
	* distance)}. Note also that rotation by any multiple of 32 is a
	* no-op, so all but the last five bits of the rotation distance can be
	* ignored, even if the distance is negative: {@code rotateRight(val,
	* distance) == rotateRight(val, distance & 0x1F)}.
	*
	* @param i the value whose bits are to be rotated right
	* @param distance the number of bit positions to rotate right
	* @return the value obtained by rotating the two's complement binary
	* representation of the specified {@code int} value right by the
	* specified number of bits.
	* @since 1.5
	*/
	public static int rotateRight(int i, int distance) {
	return (i >>> distance) \| (i << -distance);
	}

	/**
	* Returns the value obtained by reversing the order of the bits in the
	* two's complement binary representation of the specified {@code int}
	* value.
	*
	* @param i the value to be reversed
	* @return the value obtained by reversing order of the bits in the
	* specified {@code int} value.
	* @since 1.5
	*/
	public static int reverse(int i) {
	// HD, Figure 7-1
	i = (i & 0x55555555) << 1 \| (i >>> 1) & 0x55555555;
	i = (i & 0x33333333) << 2 \| (i >>> 2) & 0x33333333;
	i = (i & 0x0f0f0f0f) << 4 \| (i >>> 4) & 0x0f0f0f0f;
	i = (i << 24) \| ((i & 0xff00) << 8) \|
	((i >>> 8) & 0xff00) \| (i >>> 24);
	return i;
	}

	/**
	* Returns the signum function of the specified {@code int} value. (The
	* return value is -1 if the specified value is negative; 0 if the
	* specified value is zero; and 1 if the specified value is positive.)
	*
	* @param i the value whose signum is to be computed
	* @return the signum function of the specified {@code int} value.
	* @since 1.5
	*/
	public static int signum(int i) {
	// HD, Section 2-7
	return (i >> 31) \| (-i >>> 31);
	}

	/**
	* Returns the value obtained by reversing the order of the bytes in the
	* two's complement representation of the specified {@code int} value.
	*
	* @param i the value whose bytes are to be reversed
	* @return the value obtained by reversing the bytes in the specified
	* {@code int} value.
	* @since 1.5
	*/
	public static int reverseBytes(int i) {
	return ((i >>> 24) ) \|
	((i >> 8) & 0xFF00) \|
	((i << 8) & 0xFF0000) \|
	((i << 24));
	}

	/**
	* Adds two integers together as per the + operator.
	*
	* @param a the first operand
	* @param b the second operand
	* @return the sum of {@code a} and {@code b}
	* @see java.util.function.BinaryOperator
	* @since 1.8
	*/
	public static int sum(int a, int b) {
	return a + b;
	}

	/**
	* Returns the greater of two {@code int} values
	* as if by calling {@link Math#max(int, int) Math.max}.
	*
	* @param a the first operand
	* @param b the second operand
	* @return the greater of {@code a} and {@code b}
	* @see java.util.function.BinaryOperator
	* @since 1.8
	*/
	public static int max(int a, int b) {
	return Math.max(a, b);
	}

	/**
	* Returns the smaller of two {@code int} values
	* as if by calling {@link Math#min(int, int) Math.min}.
	*
	* @param a the first operand
	* @param b the second operand
	* @return the smaller of {@code a} and {@code b}
	* @see java.util.function.BinaryOperator
	* @since 1.8
	*/
	public static int min(int a, int b) {
	return Math.min(a, b);
	}

	/** use serialVersionUID from JDK 1.0.2 for interoperability */
	@Native private static final long serialVersionUID = 1360826667806852920L;
	}

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