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

package java.lang;

import java.lang.annotation.Native;

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

public final class Integer extends Number implements Comparable<Integer> {
    
/**
     
* A constant holding the minimum value an {@code int} can
     
* have, -2<sup>31</sup>.
     
*/

    
@Native public static final int
   
MIN_VALUE = 0x80000000;

    
/**
     
* A constant holding the maximum value an {@code int} can
     
* have, 2<sup>31</sup>-1.
     
*/

    
@Native public static final int
   
MAX_VALUE = 0x7fffffff;

    
/**
     
* The {@code Class} instance representing the primitive type
     
* {@code int}.
     
*
     
* @since
   
JDK1.1
     
*/

    
@SuppressWarnings("unchecked")
    
public static final Class<Integer>
  
TYPE = (Class<Integer>) Class.getPrimitiveClass("int");

    
/**
     
* All possible chars for representing a number as a String
     
*/

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

    
/**
     
* Returns a string representation of the first argument in the
     
* radix specified by the second argument.
     
*
     
* <p>If the radix is smaller than {@code Character.MIN_RADIX}
     
* or larger than {@code Character.MAX_RADIX}, then the radix
     
* {@code 10} is used instead.
     
*
     
* <p>If the first argument is negative, the first element of the
     
* result is the ASCII minus character {@code '-'}
     
* ({@code '\u005Cu002D'}). If the first argument is not
     
* negative, no sign character appears in the result.
     
*
     
* <p>The remaining characters of the result represent the magnitude
     
* of the first argument. If the magnitude is zero, it is
     
* represented by a single zero character {@code '0'}
     
* ({@code '\u005Cu0030'}); otherwise, the first character of
     
* the representation of the magnitude will not be the zero
     
* character.
  
The following ASCII characters are used as digits:
     
*
     
* <blockquote>
     
*
   
{@code 0123456789abcdefghijklmnopqrstuvwxyz}
     
* </blockquote>
     
*
     
* These are {@code '\u005Cu0030'} through
     
* {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
     
* {@code '\u005Cu007A'}. If {@code radix} is
     
* <var>N</var>, then the first <var>N</var> of these characters
     
* are used as radix-<var>N</var> digits in the order shown. Thus,
     
* the digits for hexadecimal (radix 16) are
     
* {@code 0123456789abcdef}. If uppercase letters are
     
* desired, the {@link java.lang.String#toUpperCase()} method may
     
* be called on the result:
     
*
     
* <blockquote>
     
*
  
{@code Integer.toString(n, 16).toUpperCase()}
     
* </blockquote>
     
*
     
* @param
   
i
       
an integer to be converted to a string.
     
* @param
   
radixthe radix to use in the string representation.
     
* @return
  
a string representation of the argument in the specified radix.
     
* @seejava.lang.Character#MAX_RADIX
     
* @seejava.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
   
radixthe 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
   
ian 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
   
ian 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
   
ian 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
   
ian 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
     
*
 
 
or
     
* larger than
 
.
     
*
     
* <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}.
     
* @returnthe 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
     
* @returnthe integer value represented by the argument in decimal.
     
* @exception
  
NumberFormatExceptionif 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
     
*
 
 
or
     
* larger than
 
.
     
*
     
* <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}.
     
* @returnthe integer represented by the string argument in the
     
*
             
specified radix.
     
* @throwsNumberFormatException 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}
     
* @returnan {@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.
     
* @returnan {@code Integer} object holding the value
     
*
             
represented by the string argument.
     
* @exception
  
NumberFormatExceptionif 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
   
valuethe 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
  
NumberFormatExceptionif 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
   
objthe 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
   
nmproperty name.
     
* @return
  
the {@code Integer} value of the property.
     
* @throws
  
SecurityException for the same reasons as
     
*
          
{@link System#getProperty(String) System.getProperty}
     
* @seejava.lang.System#getProperty(java.lang.String)
     
* @seejava.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
   
nmproperty name.
     
* @param
   
valdefault value.
     
* @return
  
the {@code Integer} value of the property.
     
* @throws
  
SecurityException for the same reasons as
     
*
          
{@link System#getProperty(String) System.getProperty}
     
* @seejava.lang.System#getProperty(java.lang.String)
     
* @seejava.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
   
nmproperty name.
     
* @param
   
valdefault value.
     
* @return
  
the {@code Integer} value of the property.
     
* @throws
  
SecurityException for the same reasons as
     
*
          
{@link System#getProperty(String) System.getProperty}
     
* @seeSystem#getProperty(java.lang.String)
     
* @seeSystem#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}.
     
*
     
* @paramnm 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
   
anotherIntegerthe {@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}
     
*
 

     
* @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}
     
*
 

     
* @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}
     
*
 

     
* @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;
}