/*
 * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 */

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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&nbsp;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&trade; 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;
}