/*
 
* 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;
import java.math.*;


/**
 
* The {@code Long} class wraps a value of the primitive type {@code
 
* long} in an object. An object of type {@code Long} contains a
 
* single field whose type is {@code long}.
 
*
 
* <p> In addition, this class provides several methods for converting
 
* a {@code long} to a {@code String} and a {@code String} to a {@code
 
* long}, as well as other constants and methods useful when dealing
 
* with a {@code long}.
 
*
 
* <p>Implementation note: The implementations of the "bit twiddling"
 
* methods (such as {@link #highestOneBit(long) highestOneBit} and
 
* {@link #numberOfTrailingZeros(long) 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 Long extends Number implements Comparable<Long> {
    
/**
     
* A constant holding the minimum value a {@code long} can
     
* have, -2<sup>63</sup>.
     
*/

    
@Native public static final long MIN_VALUE = 0x8000000000000000L;

    
/**
     
* A constant holding the maximum value a {@code long} can
     
* have, 2<sup>63</sup>-1.
     
*/

    
@Native public static final long MAX_VALUE = 0x7fffffffffffffffL;

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

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

    
/**
     
* 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 sign {@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 Long.toString(n, 16).toUpperCase()}
     
* </blockquote>
     
*
     
* @param
   
i
       
a {@code long} 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(long i, int radix) {
        
if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
            
radix = 10;
        
if (radix == 10)
            
return toString(i);
        
char[] buf = new char[65];
        
int charPos = 64;
        
boolean negative = (i < 0);

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

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

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

        
return new String(buf, charPos, (65 - 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(long, 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(long, int)
     
* @since 1.8
     
*/

    
public static String toUnsignedString(long i, int radix) {
        
if (i >= 0)
            
return toString(i, radix);
        
else {
            
switch (radix) {
            
case 2:
                
return toBinaryString(i);

            
case 4:
                
return toUnsignedString0(i, 2);

            
case 8:
                
return toOctalString(i);

            
case 10:
                
/*
                 
* We can get the effect of an unsigned division by 10
                 
* on a long value by first shifting right, yielding a
                 
* positive value, and then dividing by 5.
  
This
                 
* allows the last digit and preceding digits to be
                 
* isolated more quickly than by an initial conversion
                 
* to BigInteger.
                 
*/

                
long quot = (i >>> 1) / 5;
                
long rem = i - quot * 10;
                
return toString(quot) + rem;

            
case 16:
                
return toHexString(i);

            
case 32:
                
return toUnsignedString0(i, 5);

            
default:
                
return toUnsignedBigInteger(i).toString(radix);
            
}
        
}
    
}

    
/**
     
* Return a BigInteger equal to the unsigned value of the
     
* argument.
     
*/

    
private static BigInteger toUnsignedBigInteger(long i) {
        
if (i >= 0L)
            
return BigInteger.valueOf(i);
        
else {
            
int upper = (int) (i >>> 32);
            
int lower = (int) i;

            
// return (upper << 32) + lower
            
return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
                
add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
        
}
    
}

    
/**
     
* Returns a string representation of the {@code long}
     
* argument as an unsigned integer in base&nbsp;16.
     
*
     
* <p>The unsigned {@code long} value is the argument plus
     
* 2<sup>64</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
     
* Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(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 Long.toHexString(n).toUpperCase()}
     
* </blockquote>
     
*
     
* @param
   
ia {@code long} to be converted to a string.
     
* @return
  
the string representation of the unsigned {@code long}
     
*
          
value represented by the argument in hexadecimal
     
*
          
(base&nbsp;16).
     
* @see #parseUnsignedLong(String, int)
     
* @see #toUnsignedString(long, int)
     
* @since
   
JDK 1.0.2
     
*/

    
public static String toHexString(long i) {
        
return toUnsignedString0(i, 4);
    
}

    
/**
     
* Returns a string representation of the {@code long}
     
* argument as an unsigned integer in base&nbsp;8.
     
*
     
* <p>The unsigned {@code long} value is the argument plus
     
* 2<sup>64</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
     
* Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(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
   
ia {@code long} to be converted to a string.
     
* @return
  
the string representation of the unsigned {@code long}
     
*
          
value represented by the argument in octal (base&nbsp;8).
     
* @see #parseUnsignedLong(String, int)
     
* @see #toUnsignedString(long, int)
     
* @since
   
JDK 1.0.2
     
*/

    
public static String toOctalString(long i) {
        
return toUnsignedString0(i, 3);
    
}

    
/**
     
* Returns a string representation of the {@code long}
     
* argument as an unsigned integer in base&nbsp;2.
     
*
     
* <p>The unsigned {@code long} value is the argument plus
     
* 2<sup>64</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
     
* Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(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
   
ia {@code long} to be converted to a string.
     
* @return
  
the string representation of the unsigned {@code long}
     
*
          
value represented by the argument in binary (base&nbsp;2).
     
* @see #parseUnsignedLong(String, int)
     
* @see #toUnsignedString(long, int)
     
* @since
   
JDK 1.0.2
     
*/

    
public static String toBinaryString(long i) {
        
return toUnsignedString0(i, 1);
    
}

    
/**
     
* Format a long (treated as unsigned) into a String.
     
* @param val the value to format
     
* @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
     
*/

    
static String toUnsignedString0(long val, int shift) {
        
// assert shift > 0 && shift <=5 : "Illegal shift value";
        
int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
        
int chars = Math.max(((mag + (shift - 1)) / shift), 1);
        
char[] buf = new char[chars];

        
formatUnsignedLong(val, shift, buf, 0, chars);
        
return new String(buf, true);
    
}

    
/**
     
* Format a long (treated as unsigned) into a character buffer.
     
* @param val the unsigned long 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 formatUnsignedLong(long 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[((int) val) & mask];
            
val >>>= shift;
        
} while (val != 0 && charPos > 0);

        
return charPos;
    
}

    
/**
     
* Returns a {@code String} object representing the specified
     
* {@code long}.
  
The argument is converted to signed decimal
     
* representation and returned as a string, exactly as if the
     
* argument and the radix 10 were given as arguments to the {@link
     
* #toString(long, int)} method.
     
*
     
* @param
   
ia {@code long} to be converted.
     
* @return
  
a string representation of the argument in base&nbsp;10.
     
*/

    
public static String toString(long i) {
        
if (i == Long.MIN_VALUE)
            
return "-9223372036854775808";
        
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(long,
     
* int)} method.
     
*
     
* @param
   
i
  
an integer to be converted to an unsigned string.
     
* @return
  
an unsigned string representation of the argument.
     
* @see#toUnsignedString(long, int)
     
* @since 1.8
     
*/

    
public static String toUnsignedString(long i) {
        
return toUnsignedString(i, 10);
    
}

    
/**
     
* 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 == Long.MIN_VALUE
     
*/

    
static void getChars(long i, int index, char[] buf) {
        
long q;
        
int r;
        
int charPos = index;
        
char sign = 0;

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

        
// Get 2 digits/iteration using longs until quotient fits into an int
        
while (i > Integer.MAX_VALUE) {
            
q = i / 100;
            
// really: r = i - (q * 100);
            
r = (int)(i - ((q << 6) + (q << 5) + (q << 2)));
            
i = q;
            
buf[--charPos] = Integer.DigitOnes[r];
            
buf[--charPos] = Integer.DigitTens[r];
        
}

        
// Get 2 digits/iteration using ints
        
int q2;
        
int i2 = (int)i;
        
while (i2 >= 65536) {
            
q2 = i2 / 100;
            
// really: r = i2 - (q * 100);
            
r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
            
i2 = q2;
            
buf[--charPos] = Integer.DigitOnes[r];
            
buf[--charPos] = Integer.DigitTens[r];
        
}

        
// Fall thru to fast mode for smaller numbers
        
// assert(i2 <= 65536, i2);
        
for (;;) {
            
q2 = (i2 * 52429) >>> (16+3);
            
r = i2 - ((q2 << 3) + (q2 << 1));
  
// r = i2-(q2*10) ...
            
buf[--charPos] = Integer.digits[r];
            
i2 = q2;
            
if (i2 == 0) break;
        
}
        
if (sign != 0) {
            
buf[--charPos] = sign;
        
}
    
}

    
// Requires positive x
    
static int stringSize(long x) {
        
long p = 10;
        
for (int i=1; i<19; i++) {
            
if (x < p)
                
return i;
            
p = 10*p;
        
}
        
return 19;
    
}

    
/**
     
* Parses the string argument as a signed {@code long} 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 {@code long} value is returned.
     
*
     
* <p>Note that neither the character {@code L}
     
* ({@code '\u005Cu004C'}) nor {@code l}
     
* ({@code '\u005Cu006C'}) is permitted to appear at the end
     
* of the string as a type indicator, as would be permitted in
     
* Java programming language source code - except that either
     
* {@code L} or {@code l} may appear as a digit for a
     
* radix greater than or equal to 22.
     
*
     
* <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 {@code radix} is either smaller than {@link
     
* java.lang.Character#MIN_RADIX} or larger than {@link
     
* java.lang.Character#MAX_RADIX}.
     
*
     
* <li>Any character of the string is not a digit of the specified
     
* radix, except that the first character may be a minus sign
     
* {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
     
* '+'} ({@code '\u005Cu002B'}) provided that the string is
     
* longer than length 1.
     
*
     
* <li>The value represented by the string is not a value of type
     
*
      
{@code long}.
     
* </ul>
     
*
     
* <p>Examples:
     
* <blockquote><pre>
     
* parseLong("0", 10) returns 0L
     
* parseLong("473", 10) returns 473L
     
* parseLong("+42", 10) returns 42L
     
* parseLong("-0", 10) returns 0L
     
* parseLong("-FF", 16) returns -255L
     
* parseLong("1100110", 2) returns 102L
     
* parseLong("99", 8) throws a NumberFormatException
     
* parseLong("Hazelnut", 10) throws a NumberFormatException
     
* parseLong("Hazelnut", 36) returns 1356099454469L
     
* </pre></blockquote>
     
*
     
* @param
      
s
       
the {@code String} containing the
     
*
                     
{@code long} representation to be parsed.
     
* @param
      
radix
   
the radix to be used while parsing {@code s}.
     
* @returnthe {@code long} represented by the string argument in
     
*
             
the specified radix.
     
* @throwsNumberFormatException
  
if the string does not contain a
     
*
             
parsable {@code long}.
     
*/

    
public static long parseLong(String s, int radix)
              
throws NumberFormatException
    
{
        
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");
        
}

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

        
if (len > 0) {
            
char firstChar = s.charAt(0);
            
if (firstChar < '0') { // Possible leading "+" or "-"
                
if (firstChar == '-') {
                    
negative = true;
                    
limit = Long.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 {@code long}.
     
* 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 {@code long} value is
     
* returned, exactly as if the argument and the radix {@code 10}
     
* were given as arguments to the {@link
     
* #parseLong(java.lang.String, int)} method.
     
*
     
* <p>Note that neither the character {@code L}
     
* ({@code '\u005Cu004C'}) nor {@code l}
     
* ({@code '\u005Cu006C'}) is permitted to appear at the end
     
* of the string as a type indicator, as would be permitted in
     
* Java programming language source code.
     
*
     
* @param
      
s
   
a {@code String} containing the {@code long}
     
*
             
representation to be parsed
     
* @returnthe {@code long} represented by the argument in
     
*
             
decimal.
     
* @throwsNumberFormatException
  
if the string does not contain a
     
*
             
parsable {@code long}.
     
*/

    
public static long parseLong(String s) throws NumberFormatException {
        
return parseLong(s, 10);
    
}

    
/**
     
* Parses the string argument as an unsigned {@code long} 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 long}, 2<sup>64</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 unsigned {@code long} represented by the string
     
*
             
argument in the specified radix.
     
* @throwsNumberFormatException if the {@code String}
     
*
             
does not contain a parsable {@code long}.
     
* @since 1.8
     
*/

    
public static long parseUnsignedLong(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 <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
                    
(radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
                    
return parseLong(s, radix);
                
}

                
// No need for range checks on len due to testing above.
                
long first = parseLong(s.substring(0, len - 1), radix);
                
int second = Character.digit(s.charAt(len - 1), radix);
                
if (second < 0) {
                    
throw new NumberFormatException("Bad digit at end of " + s);
                
}
                
long result = first * radix + second;
                
if (compareUnsigned(result, first) < 0) {
                    
/*
                     
* The maximum unsigned value, (2^64)-1, takes at
                     
* most one more digit to represent than the
                     
* maximum signed value, (2^63)-1.
  
Therefore,
                     
* parsing (len - 1) digits will be appropriately
                     
* in-range of the signed parsing.
  
In other
                     
* words, if parsing (len -1) digits overflows
                     
* signed parsing, parsing len digits will
                     
* certainly overflow unsigned parsing.
                     
*
                     
* The compareUnsigned check above catches
                     
* situations where an unsigned overflow occurs
                     
* incorporating the contribution of the final
                     
* digit.
                     
*/

                    
throw new NumberFormatException(String.format("String value %s exceeds " +
                                                                  
"range of unsigned long.", s));
                
}
                
return result;
            
}
        
} else {
            
throw NumberFormatException.forInputString(s);
        
}
    
}

    
/**
     
* Parses the string argument as an unsigned decimal {@code long}. 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
     
* #parseUnsignedLong(java.lang.String, int)} method.
     
*
     
* @param s
   
a {@code String} containing the unsigned {@code long}
     
*
            
representation to be parsed
     
* @return
    
the unsigned {@code long} value represented by the decimal string argument
     
* @throws
    
NumberFormatException
  
if the string does not contain a
     
*
            
parsable unsigned integer.
     
* @since 1.8
     
*/

    
public static long parseUnsignedLong(String s) throws NumberFormatException {
        
return parseUnsignedLong(s, 10);
    
}

    
/**
     
* Returns a {@code Long} 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
     
* {@code long} in the radix specified by the second
     
* argument, exactly as if the arguments were given to the {@link
     
* #parseLong(java.lang.String, int)} method. The result is a
     
* {@code Long} object that represents the {@code long}
     
* value specified by the string.
     
*
     
* <p>In other words, this method returns a {@code Long} object equal
     
* to the value of:
     
*
     
* <blockquote>
     
*
  
{@code new Long(Long.parseLong(s, radix))}
     
* </blockquote>
     
*
     
* @param
      
s
       
the string to be parsed
     
* @param
      
radix
   
the radix to be used in interpreting {@code s}
     
* @returna {@code Long} object holding the value
     
*
             
represented by the string argument in the specified
     
*
             
radix.
     
* @throwsNumberFormatException
  
If the {@code String} does not
     
*
             
contain a parsable {@code long}.
     
*/

    
public static Long valueOf(String s, int radix) throws NumberFormatException {
        
return Long.valueOf(parseLong(s, radix));
    
}

    
/**
     
* Returns a {@code Long} object holding the value
     
* of the specified {@code String}. The argument is
     
* interpreted as representing a signed decimal {@code long},
     
* exactly as if the argument were given to the {@link
     
* #parseLong(java.lang.String)} method. The result is a
     
* {@code Long} object that represents the integer value
     
* specified by the string.
     
*
     
* <p>In other words, this method returns a {@code Long} object
     
* equal to the value of:
     
*
     
* <blockquote>
     
*
  
{@code new Long(Long.parseLong(s))}
     
* </blockquote>
     
*
     
* @param
      
s
   
the string to be parsed.
     
* @returna {@code Long} object holding the value
     
*
             
represented by the string argument.
     
* @throwsNumberFormatException
  
If the string cannot be parsed
     
*
             
as a {@code long}.
     
*/

    
public static Long valueOf(String s) throws NumberFormatException
    
{
        
return Long.valueOf(parseLong(s, 10));
    
}

    
private static class LongCache {
        
private LongCache(){}

        
static final Long cache[] = new Long[-(-128) + 127 + 1];

        
static {
            
for(int i = 0; i < cache.length; i++)
                
cache[i] = new Long(i - 128);
        
}
    
}

    
/**
     
* Returns a {@code Long} instance representing the specified
     
* {@code long} value.
     
* If a new {@code Long} instance is not required, this method
     
* should generally be used in preference to the constructor
     
* {@link #Long(long)}, as this method is likely to yield
     
* significantly better space and time performance by caching
     
* frequently requested values.
     
*
     
* Note that unlike the {@linkplain Integer#valueOf(int)
     
* corresponding method} in the {@code Integer} class, this method
     
* is <em>not</em> required to cache values within a particular
     
* range.
     
*
     
* @param
  
l a long value.
     
* @return a {@code Long} instance representing {@code l}.
     
* @since
  
1.5
     
*/

    
public static Long valueOf(long l) {
        
final int offset = 128;
        
if (l >= -128 && l <= 127) { // will cache
            
return LongCache.cache[(int)l + offset];
        
}
        
return new Long(l);
    
}

    
/**
     
* Decodes a {@code String} into a {@code Long}.
     
* 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
     
* Long.parseLong} 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
    
a {@code Long} object holding the {@code long}
     
*
            
value represented by {@code nm}
     
* @throws
    
NumberFormatException
  
if the {@code String} does not
     
*
            
contain a parsable {@code long}.
     
* @see java.lang.Long#parseLong(String, int)
     
* @since 1.2
     
*/

    
public static Long decode(String nm) throws NumberFormatException {
        
int radix = 10;
        
int index = 0;
        
boolean negative = false;
        
Long 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 = Long.valueOf(nm.substring(index), radix);
            
result = negative ? Long.valueOf(-result.longValue()) : result;
        
} catch (NumberFormatException e) {
            
// If number is Long.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 = Long.valueOf(constant, radix);
        
}
        
return result;
    
}

    
/**
     
* The value of the {@code Long}.
     
*
     
* @serial
     
*/
    
private final long value;

    
/**
     
* Constructs a newly allocated {@code Long} object that
     
* represents the specified {@code long} argument.
     
*
     
* @param
   
valuethe value to be represented by the
     
*
          
{@code Long} object.
     
*/

    
public Long(long value) {
        
this.value = value;
    
}

    
/**
     
* Constructs a newly allocated {@code Long} object that
     
* represents the {@code long} value indicated by the
     
* {@code String} parameter. The string is converted to a
     
* {@code long} value in exactly the manner used by the
     
* {@code parseLong} method for radix 10.
     
*
     
* @param
      
s
   
the {@code String} to be converted to a
     
*
             
{@code Long}.
     
* @throwsNumberFormatException
  
if the {@code String} does not
     
*
             
contain a parsable {@code long}.
     
* @see
        
java.lang.Long#parseLong(java.lang.String, int)
     
*/

    
public Long(String s) throws NumberFormatException {
        
this.value = parseLong(s, 10);
    
}

    
/**
     
* Returns the value of this {@code Long} 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 Long} 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 Long} as an {@code int} after
     
* a narrowing primitive conversion.
     
* @jls 5.1.3 Narrowing Primitive Conversions
     
*/

    
public int intValue() {
        
return (int)value;
    
}

    
/**
     
* Returns the value of this {@code Long} as a
     
* {@code long} value.
     
*/

    
public long longValue() {
        
return value;
    
}

    
/**
     
* Returns the value of this {@code Long} 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 Long} 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 Long}'s value.
  
The value is converted to signed
     
* decimal representation and returned as a string, exactly as if
     
* the {@code long} value were given as an argument to the
     
* {@link java.lang.Long#toString(long)} 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 Long}. The result is
     
* the exclusive OR of the two halves of the primitive
     
* {@code long} value held by this {@code Long}
     
* object. That is, the hashcode is the value of the expression:
     
*
     
* <blockquote>
     
*
  
{@code (int)(this.longValue()^(this.longValue()>>>32))}
     
* </blockquote>
     
*
     
* @return
  
a hash code value for this object.
     
*/

    
@Override
    
public int hashCode() {
        
return Long.hashCode(value);
    
}

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

    
public static int hashCode(long value) {
        
return (int)(value ^ (value >>> 32));
    
}

    
/**
     
* Compares this object to the specified object.
  
The result is
     
* {@code true} if and only if the argument is not
     
* {@code null} and is a {@code Long} object that
     
* contains the same {@code long} 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 Long) {
            
return value == ((Long)obj).longValue();
        
}
        
return false;
    
}

    
/**
     
* Determines the {@code long} 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 a {@code
     
* long} value using the grammar supported by {@link Long#decode decode}
     
* and a {@code Long} 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 a {@code Long} object
     
* equal to the value of:
     
*
     
* <blockquote>
     
*
  
{@code getLong(nm, null)}
     
* </blockquote>
     
*
     
* @param
   
nmproperty name.
     
* @return
  
the {@code Long} 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 Long getLong(String nm) {
        
return getLong(nm, null);
    
}

    
/**
     
* Determines the {@code long} 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 a {@code
     
* long} value using the grammar supported by {@link Long#decode decode}
     
* and a {@code Long} object representing this value is returned.
     
*
     
* <p>The second argument is the default value. A {@code Long} 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 null.
     
*
     
* <p>In other words, this method returns a {@code Long} object equal
     
* to the value of:
     
*
     
* <blockquote>
     
*
  
{@code getLong(nm, new Long(val))}
     
* </blockquote>
     
*
     
* but in practice it may be implemented in a manner such as:
     
*
     
* <blockquote><pre>
     
* Long result = getLong(nm, null);
     
* return (result == null) ? new Long(val) : result;
     
* </pre></blockquote>
     
*
     
* to avoid the unnecessary allocation of a {@code Long} object when
     
* the default value is not needed.
     
*
     
* @param
   
nm
    
property name.
     
* @param
   
valdefault value.
     
* @return
  
the {@code Long} 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 Long getLong(String nm, long val) {
        
Long result = Long.getLong(nm, null);
        
return (result == null) ? Long.valueOf(val) : result;
    
}

    
/**
     
* Returns the {@code long} 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 a {@code long} value, as per the
     
* {@link Long#decode decode} method, and a {@code Long} 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 for 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>Note that, in every case, neither {@code L}
     
* ({@code '\u005Cu004C'}) nor {@code l}
     
* ({@code '\u005Cu006C'}) is permitted to appear at the end
     
* of the property value as a type indicator, as would be
     
* permitted in Java programming language source code.
     
*
     
* <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 Long} 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 Long getLong(String nm, Long val) {
        
String v = null;
        
try {
            
v = System.getProperty(nm);
        
} catch (IllegalArgumentException | NullPointerException e) {
        
}
        
if (v != null) {
            
try {
                
return Long.decode(v);
            
} catch (NumberFormatException e) {
            
}
        
}
        
return val;
    
}

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

    
public int compareTo(Long anotherLong) {
        
return compare(this.value, anotherLong.value);
    
}

    
/**
     
* Compares two {@code long} values numerically.
     
* The value returned is identical to what would be returned by:
     
* <pre>
     
*
    
Long.valueOf(x).compareTo(Long.valueOf(y))
     
* </pre>
     
*
     
* @param
  
x the first {@code long} to compare
     
* @param
  
y the second {@code long} 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(long x, long y) {
        
return (x < y) ? -1 : ((x == y) ? 0 : 1);
    
}

    
/**
     
* Compares two {@code long} values numerically treating the values
     
* as unsigned.
     
*
     
* @param
  
x the first {@code long} to compare
     
* @param
  
y the second {@code long} 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(long x, long y) {
        
return compare(x + MIN_VALUE, y + MIN_VALUE);
    
}


    
/**
     
* 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 long divideUnsigned(long dividend, long divisor) {
        
if (divisor < 0L) { // signed comparison
            
// Answer must be 0 or 1 depending on relative magnitude
            
// of dividend and divisor.
            
return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
        
}

        
if (dividend > 0) //
  
Both inputs non-negative
            
return dividend/divisor;
        
else {
            
/*
             
* For simple code, leveraging BigInteger.
  
Longer and faster
             
* code written directly in terms of operations on longs is
             
* possible; see "Hacker's Delight" for divide and remainder
             
* algorithms.
             
*/

            
return toUnsignedBigInteger(dividend).
                
divide(toUnsignedBigInteger(divisor)).longValue();
        
}
    
}

    
/**
     
* 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 long remainderUnsigned(long dividend, long divisor) {
        
if (dividend > 0 && divisor > 0) { // signed comparisons
            
return dividend % divisor;
        
} else {
            
if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
                
return dividend;
            
else
                
return
toUnsignedBigInteger(dividend).
                    
remainder(toUnsignedBigInteger(divisor)).longValue();
        
}
    
}

    
// Bit Twiddling

    
/**
     
* The number of bits used to represent a {@code long} value in two's
     
* complement binary form.
     
*
     
* @since 1.5
     
*/

    
@Native public static final int SIZE = 64;

    
/**
     
* The number of bytes used to represent a {@code long} value in two's
     
* complement binary form.
     
*
     
* @since 1.8
     
*/

    
public static final int BYTES = SIZE / Byte.SIZE;

    
/**
     
* Returns a {@code long} value with at most a single one-bit, in the
     
* position of the highest-order ("leftmost") one-bit in the specified
     
* {@code long} 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 a {@code long} 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 long highestOneBit(long i) {
        
// HD, Figure 3-1
        
i |= (i >>
  
1);
        
i |= (i >>
  
2);
        
i |= (i >>
  
4);
        
i |= (i >>
  
8);
        
i |= (i >> 16);
        
i |= (i >> 32);
        
return i - (i >>> 1);
    
}

    
/**
     
* Returns a {@code long} value with at most a single one-bit, in the
     
* position of the lowest-order ("rightmost") one-bit in the specified
     
* {@code long} 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 a {@code long} 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 long lowestOneBit(long 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 long} value.
  
Returns 64 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 long} values x:
     
* <ul>
     
* <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
     
* <li>ceil(log<sub>2</sub>(x)) = {@code 64 - 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 long} value, or 64 if the value
     
*is equal to zero.
     
* @since 1.5
     
*/

    
public static int numberOfLeadingZeros(long i) {
        
// HD, Figure 5-6
         
if (i == 0)
            
return 64;
        
int n = 1;
        
int x = (int)(i >>> 32);
        
if (x == 0) { n += 32; x = (int)i; }
        
if (x >>> 16 == 0) { n += 16; x <<= 16; }
        
if (x >>> 24 == 0) { n +=
  
8; x <<=
  
8; }
        
if (x >>> 28 == 0) { n +=
  
4; x <<=
  
4; }
        
if (x >>> 30 == 0) { n +=
  
2; x <<=
  
2; }
        
n -= x >>> 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 long} value.
  
Returns 64 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 long} value, or 64 if the value is equal
     
*to zero.
     
* @since 1.5
     
*/

    
public static int numberOfTrailingZeros(long i) {
        
// HD, Figure 5-14
        
int x, y;
        
if (i == 0) return 64;
        
int n = 63;
        
y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
        
y = x <<16; if (y != 0) { n = n -16; x = y; }
        
y = x << 8; if (y != 0) { n = n - 8; x = y; }
        
y = x << 4; if (y != 0) { n = n - 4; x = y; }
        
y = x << 2; if (y != 0) { n = n - 2; x = y; }
        
return n - ((x << 1) >>> 31);
    
}

    
/**
     
* Returns the number of one-bits in the two's complement binary
     
* representation of the specified {@code long} 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 long} value.
     
* @since 1.5
     
*/

     
public static int bitCount(long i) {
        
// HD, Figure 5-14
        
i = i - ((i >>> 1) & 0x5555555555555555L);
        
i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
        
i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
        
i = i + (i >>> 8);
        
i = i + (i >>> 16);
        
i = i + (i >>> 32);
        
return (int)i & 0x7f;
     
}

    
/**
     
* Returns the value obtained by rotating the two's complement binary
     
* representation of the specified {@code long} 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 64 is a
     
* no-op, so all but the last six bits of the rotation distance can be
     
* ignored, even if the distance is negative: {@code rotateLeft(val,
     
* distance) == rotateLeft(val, distance & 0x3F)}.
     
*
     
* @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 long} value left by the
     
*specified number of bits.
     
* @since 1.5
     
*/

    
public static long rotateLeft(long i, int distance) {
        
return (i << distance) | (i >>> -distance);
    
}

    
/**
     
* Returns the value obtained by rotating the two's complement binary
     
* representation of the specified {@code long} 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 64 is a
     
* no-op, so all but the last six bits of the rotation distance can be
     
* ignored, even if the distance is negative: {@code rotateRight(val,
     
* distance) == rotateRight(val, distance & 0x3F)}.
     
*
     
* @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 long} value right by the
     
*specified number of bits.
     
* @since 1.5
     
*/

    
public static long rotateRight(long 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 long}
     
* value.
     
*
     
* @param i the value to be reversed
     
* @return the value obtained by reversing order of the bits in the
     
*specified {@code long} value.
     
* @since 1.5
     
*/

    
public static long reverse(long i) {
        
// HD, Figure 7-1
        
i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
        
i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
        
i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
        
i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
        
i = (i << 48) | ((i & 0xffff0000L) << 16) |
            
((i >>> 16) & 0xffff0000L) | (i >>> 48);
        
return i;
    
}

    
/**
     
* Returns the signum function of the specified {@code long} 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 long} value.
     
* @since 1.5
     
*/

    
public static int signum(long i) {
        
// HD, Section 2-7
        
return (int) ((i >> 63) | (-i >>> 63));
    
}

    
/**
     
* Returns the value obtained by reversing the order of the bytes in the
     
* two's complement representation of the specified {@code long} value.
     
*
     
* @param i the value whose bytes are to be reversed
     
* @return the value obtained by reversing the bytes in the specified
     
*{@code long} value.
     
* @since 1.5
     
*/

    
public static long reverseBytes(long i) {
        
i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
        
return (i << 48) | ((i & 0xffff0000L) << 16) |
            
((i >>> 16) & 0xffff0000L) | (i >>> 48);
    
}

    
/**
     
* Adds two {@code long} values 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 long sum(long a, long b) {
        
return a + b;
    
}

    
/**
     
* Returns the greater of two {@code long} values
     
* as if by calling {@link Math#max(long, long) 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 long max(long a, long b) {
        
return Math.max(a, b);
    
}

    
/**
     
* Returns the smaller of two {@code long} values
     
* as if by calling {@link Math#min(long, long) 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 long min(long a, long b) {
        
return Math.min(a, b);
    
}

    
/** use serialVersionUID from JDK 1.0.2 for interoperability */
    
@Native private static final long serialVersionUID = 4290774380558885855L;
}