content: /*
   * Copyright (C) 2014 The Android Open Source Project
   * 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 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     Character#MAX_RADIX
       * @see     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 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);
  
          // Android-changed: Use regular constructor instead of one which takes over "buf".
          // return new String(buf, true);
          return new String(buf);
      }
  
      /**
       * 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;
      }
  
      // BEGIN Android-changed: Cache the toString() result for small values.
      private static final String[] SMALL_NEG_VALUES  = new String[100];
      private static final String[] SMALL_NONNEG_VALUES = new String[100];
      // END Android-changed: Cache the toString() result for small values.
  
      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";
  
          // BEGIN Android-changed: Cache the String for small values.
          // int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
          boolean negative = i < 0;
          boolean small = negative ? i > -100 : i < 100;
          if (small) {
              final String[] smallValues = negative ? SMALL_NEG_VALUES : SMALL_NONNEG_VALUES;
  
              if (negative) {
                  i = -i;
                  if (smallValues[i] == null) {
                      smallValues[i] =
                          i < 10 ? new String(new char[]{'-', DigitOnes[i]})
                                 : new String(new char[]{'-', DigitTens[i], DigitOnes[i]});
                  }
              } else {
                  if (smallValues[i] == null) {
                      smallValues[i] =
                          i < 10 ? new String(new char[]{DigitOnes[i]})
                                 : new String(new char[]{DigitTens[i], DigitOnes[i]});
                  }
              }
              return smallValues[i];
          }
          int size = negative ? stringSize(-i) + 1 : stringSize(i);
          // END Android-changed: Cache the String for small values.
          char[] buf = new char[size];
          getChars(i, size, buf);
          // Android-changed: Use regular constructor instead of one which takes over "buf".
          // return new String(buf, true);
          return new String(buf);
      }
  
      /**
       * 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 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 Character#MIN_RADIX} or
       * larger than {@link 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) {
              // Android-changed: Improve exception message for parseInt.
              throw new NumberFormatException("s == 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(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
       * 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 Character#MIN_RADIX} or
       * larger than {@link 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(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(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(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        Integer#parseInt(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
       * 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
       * System#getProperty(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     System#getProperty(String)
       * @see     System#getProperty(String, 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
       * System#getProperty(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     System#getProperty(String)
       * @see     System#getProperty(String, 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 System#getProperty(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(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(String, int)} with radix 8.
       * <li>Otherwise, the property value is parsed as a decimal integer
       * exactly as by the method {@link #valueOf(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(String)
       * @see     System#getProperty(String, 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 Integer#parseInt(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;
  }
  