content: /*
   * Copyright (C) 2014 The Android Open Source Project
   * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
   * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   *
   * This code is free software; you can redistribute it and/or modify it
   * under the terms of the GNU General Public License version 2 only, as
   * published by the Free Software Foundation.  Oracle designates this
   * particular file as subject to the "Classpath" exception as provided
   * by Oracle in the LICENSE file that accompanied this code.
   *
   * This code is distributed in the hope that it will be useful, but WITHOUT
   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
   * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   * version 2 for more details (a copy is included in the LICENSE file that
   * accompanied this code).
   *
   * You should have received a copy of the GNU General Public License version
   * 2 along with this work; if not, write to the Free Software Foundation,
   * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
   *
   * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
   * or visit www.oracle.com if you need additional information or have any
   * questions.
   */
  
  package java.lang;
  
  import java.lang.annotation.Native;
  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 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   radix   the radix to use in the string representation.
       * @return  a string representation of the argument in the specified radix.
       * @see     Character#MAX_RADIX
       * @see     Character#MIN_RADIX
       */
      public static String toString(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   radix   the 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 String#toUpperCase()} method may be called
       * on the result:
       *
       * <blockquote>
       *  {@code Long.toHexString(n).toUpperCase()}
       * </blockquote>
       *
       * @param   i   a {@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   i   a {@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   i   a {@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);
          // Android-changed: Use regular constructor instead of one which takes over "buf".
          // return new String(buf, true);
          return new String(buf);
      }
  
      /**
       * Format a long (treated as unsigned) into a character buffer.
       * @param val the unsigned 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   i   a {@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);
          // Android-changed: Use regular constructor instead of one which takes over "buf".
          // return new String(buf, true);
          return new String(buf);
      }
  
      /**
       * Returns a string representation of the argument as an unsigned
       * decimal value.
       *
       * The argument is converted to unsigned decimal representation
       * and returned as a string exactly as if the argument and radix
       * 10 were given as arguments to the {@link #toUnsignedString(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 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
       * Character#MIN_RADIX} or larger than {@link
       * Character#MAX_RADIX}.
       *
       * <li>Any character of the string is not a digit of the specified
       * radix, except that the first character may be a minus sign
       * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
       * '+'} ({@code '\u005Cu002B'}) provided that the string is
       * longer than length 1.
       *
       * <li>The value represented by the string is not a value of type
       *      {@code 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}.
       * @return     the {@code long} represented by the string argument in
       *             the specified radix.
       * @throws     NumberFormatException  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(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
       * @return     the {@code long} represented by the argument in
       *             decimal.
       * @throws     NumberFormatException  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
       * Character#digit(char, int)} returns a nonnegative
       * value), except that the first character may be an ASCII plus
       * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
       * integer value is returned.
       *
       * <p>An exception of type {@code NumberFormatException} is
       * thrown if any of the following situations occurs:
       * <ul>
       * <li>The first argument is {@code null} or is a string of
       * length zero.
       *
       * <li>The radix is either smaller than
       * {@link Character#MIN_RADIX} or
       * larger than {@link Character#MAX_RADIX}.
       *
       * <li>Any character of the string is not a digit of the specified
       * radix, except that the first character may be a plus sign
       * {@code '+'} ({@code '\u005Cu002B'}) provided that the
       * string is longer than length 1.
       *
       * <li>The value represented by the string is larger than the
       * largest unsigned {@code 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}.
       * @return     the unsigned {@code long} represented by the string
       *             argument in the specified radix.
       * @throws     NumberFormatException 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(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(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}
       * @return     a {@code Long} object holding the value
       *             represented by the string argument in the specified
       *             radix.
       * @throws     NumberFormatException  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(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.
       * @return     a {@code Long} object holding the value
       *             represented by the string argument.
       * @throws     NumberFormatException  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}.
       *
       * @param     nm 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 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   value   the 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}.
       * @throws     NumberFormatException  if the {@code String} does not
       *             contain a parsable {@code long}.
       * @see        Long#parseLong(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 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   obj   the object to compare with.
       * @return  {@code true} if the objects are the same;
       *          {@code false} otherwise.
       */
      public boolean equals(Object obj) {
          if (obj instanceof 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
       * System#getProperty(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   nm   property name.
       * @return  the {@code Long} value of the property.
       * @throws  SecurityException for the same reasons as
       *          {@link System#getProperty(String) System.getProperty}
       * @see     System#getProperty(String)
       * @see     System#getProperty(String, String)
       */
      public static 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
       * System#getProperty(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   val   default value.
       * @return  the {@code Long} value of the property.
       * @throws  SecurityException for the same reasons as
       *          {@link System#getProperty(String) System.getProperty}
       * @see     System#getProperty(String)
       * @see     System#getProperty(String, String)
       */
      public static 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 System#getProperty(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(String, int)}
       * with radix 16.
       * <li>If the property value begins with the ASCII character
       * {@code 0} followed by another character, it is parsed as
       * an octal integer exactly as by the method {@link
       * #valueOf(String, int)} with radix 8.
       * <li>Otherwise the property value is parsed as a decimal
       * integer exactly as by the method
       * {@link #valueOf(String, int)} with radix 10.
       * </ul>
       *
       * <p>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   nm   property name.
       * @param   val   default value.
       * @return  the {@code Long} value of the property.
       * @throws  SecurityException for the same reasons as
       *          {@link System#getProperty(String) System.getProperty}
       * @see     System#getProperty(String)
       * @see     System#getProperty(String, String)
       */
      public static 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   anotherLong   the {@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}
       * @see java.util.function.BinaryOperator
       * @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}
       * @see java.util.function.BinaryOperator
       * @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}
       * @see java.util.function.BinaryOperator
       * @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;
  }
  