guava/src/com/google/common/primitives/UnsignedLongs.java - platform/external/guava - Git at Google

 /*
  * Copyright (C) 2011 The Guava Authors
  *
  * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
  * in compliance with the License. You may obtain a copy of the License at
  *
  * http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software distributed under the License
  * is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
  * or implied. See the License for the specific language governing permissions and limitations under
  * the License.
  */

 package com.google.common.primitives;

 import static com.google.common.base.Preconditions.checkArgument;
 import static com.google.common.base.Preconditions.checkNotNull;
 import static com.google.common.base.Preconditions.checkPositionIndexes;

 import com.google.common.annotations.Beta;
 import com.google.common.annotations.GwtCompatible;
 import com.google.errorprone.annotations.CanIgnoreReturnValue;
 import java.math.BigInteger;
 import java.util.Arrays;
 import java.util.Comparator;

 /**
  * Static utility methods pertaining to {@code long} primitives that interpret values as
  * <i>unsigned</i> (that is, any negative value {@code x} is treated as the positive value {@code
  * 2^64 + x}). The methods for which signedness is not an issue are in {@link Longs}, as well as
  * signed versions of methods for which signedness is an issue.
  *
  * <p>In addition, this class provides several static methods for converting a {@code long} to a
  * {@code String} and a {@code String} to a {@code long} that treat the {@code long} as an unsigned
  * number.
  *
  * <p>Users of these utilities must be <i>extremely careful</i> not to mix up signed and unsigned
  * {@code long} values. When possible, it is recommended that the {@link UnsignedLong} wrapper class
  * be used, at a small efficiency penalty, to enforce the distinction in the type system.
  *
  * <p>See the Guava User Guide article on <a
  * href="https://github.com/google/guava/wiki/PrimitivesExplained#unsigned-support">unsigned
  * primitive utilities</a>.
  *
  * @author Louis Wasserman
  * @author Brian Milch
  * @author Colin Evans
  * @since 10.0
  */
 @Beta
 @GwtCompatible
 public final class UnsignedLongs {
   private UnsignedLongs() {}

   public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1

   /**
    * A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on
    * longs, that is, {@code a <= b} as unsigned longs if and only if {@code flip(a) <= flip(b)} as
    * signed longs.
    */
   private static long flip(long a) {
     return a ^ Long.MIN_VALUE;
   }

   /**
    * Compares the two specified {@code long} values, treating them as unsigned values between {@code
    * 0} and {@code 2^64 - 1} inclusive.
    *
    * <p><b>Java 8 users:</b> use {@link Long#compareUnsigned(long, long)} instead.
    *
    * @param a the first unsigned {@code long} to compare
    * @param b the second unsigned {@code long} to compare
    * @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
    *     greater than {@code b}; or zero if they are equal
    */
   public static int compare(long a, long b) {
     return Longs.compare(flip(a), flip(b));
   }

   /**
    * Returns the least value present in {@code array}, treating values as unsigned.
    *
    * @param array a <i>nonempty</i> array of unsigned {@code long} values
    * @return the value present in {@code array} that is less than or equal to every other value in
    *     the array according to {@link #compare}
    * @throws IllegalArgumentException if {@code array} is empty
    */
   public static long min(long... array) {
     checkArgument(array.length > 0);
     long min = flip(array[0]);
     for (int i = 1; i < array.length; i++) {
       long next = flip(array[i]);
       if (next < min) {
         min = next;
       }
     }
     return flip(min);
   }

   /**
    * Returns the greatest value present in {@code array}, treating values as unsigned.
    *
    * @param array a <i>nonempty</i> array of unsigned {@code long} values
    * @return the value present in {@code array} that is greater than or equal to every other value
    *     in the array according to {@link #compare}
    * @throws IllegalArgumentException if {@code array} is empty
    */
   public static long max(long... array) {
     checkArgument(array.length > 0);
     long max = flip(array[0]);
     for (int i = 1; i < array.length; i++) {
       long next = flip(array[i]);
       if (next > max) {
         max = next;
       }
     }
     return flip(max);
   }

   /**
    * Returns a string containing the supplied unsigned {@code long} values separated by {@code
    * separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
    *
    * @param separator the text that should appear between consecutive values in the resulting string
    *     (but not at the start or end)
    * @param array an array of unsigned {@code long} values, possibly empty
    */
   public static String join(String separator, long... array) {
     checkNotNull(separator);
     if (array.length == 0) {
       return "";
     }

     // For pre-sizing a builder, just get the right order of magnitude
     StringBuilder builder = new StringBuilder(array.length * 5);
     builder.append(toString(array[0]));
     for (int i = 1; i < array.length; i++) {
       builder.append(separator).append(toString(array[i]));
     }
     return builder.toString();
   }

   /**
    * Returns a comparator that compares two arrays of unsigned {@code long} values <a
    * href="http://en.wikipedia.org/wiki/Lexicographical_order">lexicographically</a>. That is, it
    * compares, using {@link #compare(long, long)}), the first pair of values that follow any common
    * prefix, or when one array is a prefix of the other, treats the shorter array as the lesser. For
    * example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
    *
    * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
    * support only identity equality), but it is consistent with {@link Arrays#equals(long[],
    * long[])}.
    */
   public static Comparator<long[]> lexicographicalComparator() {
     return LexicographicalComparator.INSTANCE;
   }

   enum LexicographicalComparator implements Comparator<long[]> {
     INSTANCE;

     @Override
     public int compare(long[] left, long[] right) {
       int minLength = Math.min(left.length, right.length);
       for (int i = 0; i < minLength; i++) {
         if (left[i] != right[i]) {
           return UnsignedLongs.compare(left[i], right[i]);
         }
       }
       return left.length - right.length;
     }

     @Override
     public String toString() {
       return "UnsignedLongs.lexicographicalComparator()";
     }
   }

   /**
    * Sorts the array, treating its elements as unsigned 64-bit integers.
    *
    * @since 23.1
    */
   public static void sort(long[] array) {
     checkNotNull(array);
     sort(array, 0, array.length);
   }

   /**
    * Sorts the array between {@code fromIndex} inclusive and {@code toIndex} exclusive, treating its
    * elements as unsigned 64-bit integers.
    *
    * @since 23.1
    */
   public static void sort(long[] array, int fromIndex, int toIndex) {
     checkNotNull(array);
     checkPositionIndexes(fromIndex, toIndex, array.length);
     for (int i = fromIndex; i < toIndex; i++) {
       array[i] = flip(array[i]);
     }
     Arrays.sort(array, fromIndex, toIndex);
     for (int i = fromIndex; i < toIndex; i++) {
       array[i] = flip(array[i]);
     }
   }

   /**
    * Sorts the elements of {@code array} in descending order, interpreting them as unsigned 64-bit
    * integers.
    *
    * @since 23.1
    */
   public static void sortDescending(long[] array) {
     checkNotNull(array);
     sortDescending(array, 0, array.length);
   }

   /**
    * Sorts the elements of {@code array} between {@code fromIndex} inclusive and {@code toIndex}
    * exclusive in descending order, interpreting them as unsigned 64-bit integers.
    *
    * @since 23.1
    */
   public static void sortDescending(long[] array, int fromIndex, int toIndex) {
     checkNotNull(array);
     checkPositionIndexes(fromIndex, toIndex, array.length);
     for (int i = fromIndex; i < toIndex; i++) {
       array[i] ^= Long.MAX_VALUE;
     }
     Arrays.sort(array, fromIndex, toIndex);
     for (int i = fromIndex; i < toIndex; i++) {
       array[i] ^= Long.MAX_VALUE;
     }
   }

   /**
    * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
    * quantities.
    *
    * <p><b>Java 8 users:</b> use {@link Long#divideUnsigned(long, long)} instead.
    *
    * @param dividend the dividend (numerator)
    * @param divisor the divisor (denominator)
    * @throws ArithmeticException if divisor is 0
    */
   public static long divide(long dividend, long divisor) {
     if (divisor < 0) { // i.e., divisor >= 2^63:
       if (compare(dividend, divisor) < 0) {
         return 0; // dividend < divisor
       } else {
         return 1; // dividend >= divisor
       }
     }

     // Optimization - use signed division if dividend < 2^63
     if (dividend >= 0) {
       return dividend / divisor;
     }

     /*
      * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
      * guaranteed to be either exact or one less than the correct value. This follows from fact that
      * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
      * trivial.
      */
     long quotient = ((dividend >>> 1) / divisor) << 1;
     long rem = dividend - quotient * divisor;
     return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
   }

   /**
    * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
    * quantities.
    *
    * <p><b>Java 8 users:</b> use {@link Long#remainderUnsigned(long, long)} instead.
    *
    * @param dividend the dividend (numerator)
    * @param divisor the divisor (denominator)
    * @throws ArithmeticException if divisor is 0
    * @since 11.0
    */
   public static long remainder(long dividend, long divisor) {
     if (divisor < 0) { // i.e., divisor >= 2^63:
       if (compare(dividend, divisor) < 0) {
         return dividend; // dividend < divisor
       } else {
         return dividend - divisor; // dividend >= divisor
       }
     }

     // Optimization - use signed modulus if dividend < 2^63
     if (dividend >= 0) {
       return dividend % divisor;
     }

     /*
      * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
      * guaranteed to be either exact or one less than the correct value. This follows from the fact
      * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
      * quite trivial.
      */
     long quotient = ((dividend >>> 1) / divisor) << 1;
     long rem = dividend - quotient * divisor;
     return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
   }

   /**
    * Returns the unsigned {@code long} value represented by the given decimal string.
    *
    * <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String)} instead.
    *
    * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
    *     value
    * @throws NullPointerException if {@code string} is null (in contrast to {@link
    *     Long#parseLong(String)})
    */
   @CanIgnoreReturnValue
   public static long parseUnsignedLong(String string) {
     return parseUnsignedLong(string, 10);
   }

   /**
    * Returns the unsigned {@code long} value represented by a string with the given radix.
    *
    * <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String, int)} instead.
    *
    * @param string the string containing the unsigned {@code long} representation to be parsed.
    * @param radix the radix to use while parsing {@code string}
    * @throws NumberFormatException if the string does not contain a valid unsigned {@code long} with
    *     the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX} and {@link
    *     Character#MAX_RADIX}.
    * @throws NullPointerException if {@code string} is null (in contrast to {@link
    *     Long#parseLong(String)})
    */
   @CanIgnoreReturnValue
   public static long parseUnsignedLong(String string, int radix) {
     checkNotNull(string);
     if (string.length() == 0) {
       throw new NumberFormatException("empty string");
     }
     if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
       throw new NumberFormatException("illegal radix: " + radix);
     }

     int maxSafePos = ParseOverflowDetection.maxSafeDigits[radix] - 1;
     long value = 0;
     for (int pos = 0; pos < string.length(); pos++) {
       int digit = Character.digit(string.charAt(pos), radix);
       if (digit == -1) {
         throw new NumberFormatException(string);
       }
       if (pos > maxSafePos && ParseOverflowDetection.overflowInParse(value, digit, radix)) {
         throw new NumberFormatException("Too large for unsigned long: " + string);
       }
       value = (value * radix) + digit;
     }

     return value;
   }

   /**
    * Returns the unsigned {@code long} value represented by the given string.
    *
    * <p>Accepts a decimal, hexadecimal, or octal number given by specifying the following prefix:
    *
    * <ul>
    *   <li>{@code 0x}<i>HexDigits</i>
    *   <li>{@code 0X}<i>HexDigits</i>
    *   <li>{@code #}<i>HexDigits</i>
    *   <li>{@code 0}<i>OctalDigits</i>
    * </ul>
    *
    * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
    *     value
    * @since 13.0
    */
   @CanIgnoreReturnValue
   public static long decode(String stringValue) {
     ParseRequest request = ParseRequest.fromString(stringValue);

     try {
       return parseUnsignedLong(request.rawValue, request.radix);
     } catch (NumberFormatException e) {
       NumberFormatException decodeException =
           new NumberFormatException("Error parsing value: " + stringValue);
       decodeException.initCause(e);
       throw decodeException;
     }
   }

   /*
    * We move the static constants into this class so ProGuard can inline UnsignedLongs entirely
    * unless the user is actually calling a parse method.
    */
   private static final class ParseOverflowDetection {
     private ParseOverflowDetection() {}

     // calculated as 0xffffffffffffffff / radix
     static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
     static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
     static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];

     static {
       BigInteger overflow = new BigInteger("10000000000000000", 16);
       for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
         maxValueDivs[i] = divide(MAX_VALUE, i);
         maxValueMods[i] = (int) remainder(MAX_VALUE, i);
         maxSafeDigits[i] = overflow.toString(i).length() - 1;
       }
     }

     /**
      * Returns true if (current * radix) + digit is a number too large to be represented by an
      * unsigned long. This is useful for detecting overflow while parsing a string representation of
      * a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
      * undefined results or an ArrayIndexOutOfBoundsException.
      */
     static boolean overflowInParse(long current, int digit, int radix) {
       if (current >= 0) {
         if (current < maxValueDivs[radix]) {
           return false;
         }
         if (current > maxValueDivs[radix]) {
           return true;
         }
         // current == maxValueDivs[radix]
         return (digit > maxValueMods[radix]);
       }

       // current < 0: high bit is set
       return true;
     }
   }

   /**
    * Returns a string representation of x, where x is treated as unsigned.
    *
    * <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long)} instead.
    */
   public static String toString(long x) {
     return toString(x, 10);
   }

   /**
    * Returns a string representation of {@code x} for the given radix, where {@code x} is treated as
    * unsigned.
    *
    * <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long, int)} instead.
    *
    * @param x the value to convert to a string.
    * @param radix the radix to use while working with {@code x}
    * @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
    *     and {@link Character#MAX_RADIX}.
    */
   public static String toString(long x, int radix) {
     checkArgument(
         radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
         "radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX",
         radix);
     if (x == 0) {
       // Simply return "0"
       return "0";
     } else if (x > 0) {
       return Long.toString(x, radix);
     } else {
       char[] buf = new char[64];
       int i = buf.length;
       if ((radix & (radix - 1)) == 0) {
         // Radix is a power of two so we can avoid division.
         int shift = Integer.numberOfTrailingZeros(radix);
         int mask = radix - 1;
         do {
           buf[--i] = Character.forDigit(((int) x) & mask, radix);
           x >>>= shift;
         } while (x != 0);
       } else {
         // Separate off the last digit using unsigned division. That will leave
         // a number that is nonnegative as a signed integer.
         long quotient;
         if ((radix & 1) == 0) {
           // Fast path for the usual case where the radix is even.
           quotient = (x >>> 1) / (radix >>> 1);
         } else {
           quotient = divide(x, radix);
         }
         long rem = x - quotient * radix;
         buf[--i] = Character.forDigit((int) rem, radix);
         x = quotient;
         // Simple modulo/division approach
         while (x > 0) {
           buf[--i] = Character.forDigit((int) (x % radix), radix);
           x /= radix;
         }
       }
       // Generate string
       return new String(buf, i, buf.length - i);
     }
   }
 }
	/*
	* Copyright (C) 2011 The Guava Authors
	*
	* Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
	* in compliance with the License. You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software distributed under the License
	* is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
	* or implied. See the License for the specific language governing permissions and limitations under
	* the License.
	*/

	package com.google.common.primitives;

	import static com.google.common.base.Preconditions.checkArgument;
	import static com.google.common.base.Preconditions.checkNotNull;
	import static com.google.common.base.Preconditions.checkPositionIndexes;

	import com.google.common.annotations.Beta;
	import com.google.common.annotations.GwtCompatible;
	import com.google.errorprone.annotations.CanIgnoreReturnValue;
	import java.math.BigInteger;
	import java.util.Arrays;
	import java.util.Comparator;

	/**
	* Static utility methods pertaining to {@code long} primitives that interpret values as
	* <i>unsigned</i> (that is, any negative value {@code x} is treated as the positive value {@code
	* 2^64 + x}). The methods for which signedness is not an issue are in {@link Longs}, as well as
	* signed versions of methods for which signedness is an issue.
	*
	* <p>In addition, this class provides several static methods for converting a {@code long} to a
	* {@code String} and a {@code String} to a {@code long} that treat the {@code long} as an unsigned
	* number.
	*
	* <p>Users of these utilities must be <i>extremely careful</i> not to mix up signed and unsigned
	* {@code long} values. When possible, it is recommended that the {@link UnsignedLong} wrapper class
	* be used, at a small efficiency penalty, to enforce the distinction in the type system.
	*
	* <p>See the Guava User Guide article on <a
	* href="https://github.com/google/guava/wiki/PrimitivesExplained#unsigned-support">unsigned
	* primitive utilities</a>.
	*
	* @author Louis Wasserman
	* @author Brian Milch
	* @author Colin Evans
	* @since 10.0
	*/
	@Beta
	@GwtCompatible
	public final class UnsignedLongs {
	private UnsignedLongs() {}

	public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1

	/**
	* A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on
	* longs, that is, {@code a <= b} as unsigned longs if and only if {@code flip(a) <= flip(b)} as
	* signed longs.
	*/
	private static long flip(long a) {
	return a ^ Long.MIN_VALUE;
	}

	/**
	* Compares the two specified {@code long} values, treating them as unsigned values between {@code
	* 0} and {@code 2^64 - 1} inclusive.
	*
	* <p><b>Java 8 users:</b> use {@link Long#compareUnsigned(long, long)} instead.
	*
	* @param a the first unsigned {@code long} to compare
	* @param b the second unsigned {@code long} to compare
	* @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
	* greater than {@code b}; or zero if they are equal
	*/
	public static int compare(long a, long b) {
	return Longs.compare(flip(a), flip(b));
	}

	/**
	* Returns the least value present in {@code array}, treating values as unsigned.
	*
	* @param array a <i>nonempty</i> array of unsigned {@code long} values
	* @return the value present in {@code array} that is less than or equal to every other value in
	* the array according to {@link #compare}
	* @throws IllegalArgumentException if {@code array} is empty
	*/
	public static long min(long... array) {
	checkArgument(array.length > 0);
	long min = flip(array[0]);
	for (int i = 1; i < array.length; i++) {
	long next = flip(array[i]);
	if (next < min) {
	min = next;
	}
	}
	return flip(min);
	}

	/**
	* Returns the greatest value present in {@code array}, treating values as unsigned.
	*
	* @param array a <i>nonempty</i> array of unsigned {@code long} values
	* @return the value present in {@code array} that is greater than or equal to every other value
	* in the array according to {@link #compare}
	* @throws IllegalArgumentException if {@code array} is empty
	*/
	public static long max(long... array) {
	checkArgument(array.length > 0);
	long max = flip(array[0]);
	for (int i = 1; i < array.length; i++) {
	long next = flip(array[i]);
	if (next > max) {
	max = next;
	}
	}
	return flip(max);
	}

	/**
	* Returns a string containing the supplied unsigned {@code long} values separated by {@code
	* separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
	*
	* @param separator the text that should appear between consecutive values in the resulting string
	* (but not at the start or end)
	* @param array an array of unsigned {@code long} values, possibly empty
	*/
	public static String join(String separator, long... array) {
	checkNotNull(separator);
	if (array.length == 0) {
	return "";
	}

	// For pre-sizing a builder, just get the right order of magnitude
	StringBuilder builder = new StringBuilder(array.length * 5);
	builder.append(toString(array[0]));
	for (int i = 1; i < array.length; i++) {
	builder.append(separator).append(toString(array[i]));
	}
	return builder.toString();
	}

	/**
	* Returns a comparator that compares two arrays of unsigned {@code long} values <a
	* href="http://en.wikipedia.org/wiki/Lexicographical_order">lexicographically</a>. That is, it
	* compares, using {@link #compare(long, long)}), the first pair of values that follow any common
	* prefix, or when one array is a prefix of the other, treats the shorter array as the lesser. For
	* example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
	*
	* <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
	* support only identity equality), but it is consistent with {@link Arrays#equals(long[],
	* long[])}.
	*/
	public static Comparator<long[]> lexicographicalComparator() {
	return LexicographicalComparator.INSTANCE;
	}

	enum LexicographicalComparator implements Comparator<long[]> {
	INSTANCE;

	@Override
	public int compare(long[] left, long[] right) {
	int minLength = Math.min(left.length, right.length);
	for (int i = 0; i < minLength; i++) {
	if (left[i] != right[i]) {
	return UnsignedLongs.compare(left[i], right[i]);
	}
	}
	return left.length - right.length;
	}

	@Override
	public String toString() {
	return "UnsignedLongs.lexicographicalComparator()";
	}
	}

	/**
	* Sorts the array, treating its elements as unsigned 64-bit integers.
	*
	* @since 23.1
	*/
	public static void sort(long[] array) {
	checkNotNull(array);
	sort(array, 0, array.length);
	}

	/**
	* Sorts the array between {@code fromIndex} inclusive and {@code toIndex} exclusive, treating its
	* elements as unsigned 64-bit integers.
	*
	* @since 23.1
	*/
	public static void sort(long[] array, int fromIndex, int toIndex) {
	checkNotNull(array);
	checkPositionIndexes(fromIndex, toIndex, array.length);
	for (int i = fromIndex; i < toIndex; i++) {
	array[i] = flip(array[i]);
	}
	Arrays.sort(array, fromIndex, toIndex);
	for (int i = fromIndex; i < toIndex; i++) {
	array[i] = flip(array[i]);
	}
	}

	/**
	* Sorts the elements of {@code array} in descending order, interpreting them as unsigned 64-bit
	* integers.
	*
	* @since 23.1
	*/
	public static void sortDescending(long[] array) {
	checkNotNull(array);
	sortDescending(array, 0, array.length);
	}

	/**
	* Sorts the elements of {@code array} between {@code fromIndex} inclusive and {@code toIndex}
	* exclusive in descending order, interpreting them as unsigned 64-bit integers.
	*
	* @since 23.1
	*/
	public static void sortDescending(long[] array, int fromIndex, int toIndex) {
	checkNotNull(array);
	checkPositionIndexes(fromIndex, toIndex, array.length);
	for (int i = fromIndex; i < toIndex; i++) {
	array[i] ^= Long.MAX_VALUE;
	}
	Arrays.sort(array, fromIndex, toIndex);
	for (int i = fromIndex; i < toIndex; i++) {
	array[i] ^= Long.MAX_VALUE;
	}
	}

	/**
	* Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
	* quantities.
	*
	* <p><b>Java 8 users:</b> use {@link Long#divideUnsigned(long, long)} instead.
	*
	* @param dividend the dividend (numerator)
	* @param divisor the divisor (denominator)
	* @throws ArithmeticException if divisor is 0
	*/
	public static long divide(long dividend, long divisor) {
	if (divisor < 0) { // i.e., divisor >= 2^63:
	if (compare(dividend, divisor) < 0) {
	return 0; // dividend < divisor
	} else {
	return 1; // dividend >= divisor
	}
	}

	// Optimization - use signed division if dividend < 2^63
	if (dividend >= 0) {
	return dividend / divisor;
	}

	/*
	* Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
	* guaranteed to be either exact or one less than the correct value. This follows from fact that
	* floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
	* trivial.
	*/
	long quotient = ((dividend >>> 1) / divisor) << 1;
	long rem = dividend - quotient * divisor;
	return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
	}

	/**
	* Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
	* quantities.
	*
	* <p><b>Java 8 users:</b> use {@link Long#remainderUnsigned(long, long)} instead.
	*
	* @param dividend the dividend (numerator)
	* @param divisor the divisor (denominator)
	* @throws ArithmeticException if divisor is 0
	* @since 11.0
	*/
	public static long remainder(long dividend, long divisor) {
	if (divisor < 0) { // i.e., divisor >= 2^63:
	if (compare(dividend, divisor) < 0) {
	return dividend; // dividend < divisor
	} else {
	return dividend - divisor; // dividend >= divisor
	}
	}

	// Optimization - use signed modulus if dividend < 2^63
	if (dividend >= 0) {
	return dividend % divisor;
	}

	/*
	* Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
	* guaranteed to be either exact or one less than the correct value. This follows from the fact
	* that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
	* quite trivial.
	*/
	long quotient = ((dividend >>> 1) / divisor) << 1;
	long rem = dividend - quotient * divisor;
	return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
	}

	/**
	* Returns the unsigned {@code long} value represented by the given decimal string.
	*
	* <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String)} instead.
	*
	* @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
	* value
	* @throws NullPointerException if {@code string} is null (in contrast to {@link
	* Long#parseLong(String)})
	*/
	@CanIgnoreReturnValue
	public static long parseUnsignedLong(String string) {
	return parseUnsignedLong(string, 10);
	}

	/**
	* Returns the unsigned {@code long} value represented by a string with the given radix.
	*
	* <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String, int)} instead.
	*
	* @param string the string containing the unsigned {@code long} representation to be parsed.
	* @param radix the radix to use while parsing {@code string}
	* @throws NumberFormatException if the string does not contain a valid unsigned {@code long} with
	* the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX} and {@link
	* Character#MAX_RADIX}.
	* @throws NullPointerException if {@code string} is null (in contrast to {@link
	* Long#parseLong(String)})
	*/
	@CanIgnoreReturnValue
	public static long parseUnsignedLong(String string, int radix) {
	checkNotNull(string);
	if (string.length() == 0) {
	throw new NumberFormatException("empty string");
	}
	if (radix < Character.MIN_RADIX \|\| radix > Character.MAX_RADIX) {
	throw new NumberFormatException("illegal radix: " + radix);
	}

	int maxSafePos = ParseOverflowDetection.maxSafeDigits[radix] - 1;
	long value = 0;
	for (int pos = 0; pos < string.length(); pos++) {
	int digit = Character.digit(string.charAt(pos), radix);
	if (digit == -1) {
	throw new NumberFormatException(string);
	}
	if (pos > maxSafePos && ParseOverflowDetection.overflowInParse(value, digit, radix)) {
	throw new NumberFormatException("Too large for unsigned long: " + string);
	}
	value = (value * radix) + digit;
	}

	return value;
	}

	/**
	* Returns the unsigned {@code long} value represented by the given string.
	*
	* <p>Accepts a decimal, hexadecimal, or octal number given by specifying the following prefix:
	*
	* <ul>
	* <li>{@code 0x}<i>HexDigits</i>
	* <li>{@code 0X}<i>HexDigits</i>
	* <li>{@code #}<i>HexDigits</i>
	* <li>{@code 0}<i>OctalDigits</i>
	* </ul>
	*
	* @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
	* value
	* @since 13.0
	*/
	@CanIgnoreReturnValue
	public static long decode(String stringValue) {
	ParseRequest request = ParseRequest.fromString(stringValue);

	try {
	return parseUnsignedLong(request.rawValue, request.radix);
	} catch (NumberFormatException e) {
	NumberFormatException decodeException =
	new NumberFormatException("Error parsing value: " + stringValue);
	decodeException.initCause(e);
	throw decodeException;
	}
	}

	/*
	* We move the static constants into this class so ProGuard can inline UnsignedLongs entirely
	* unless the user is actually calling a parse method.
	*/
	private static final class ParseOverflowDetection {
	private ParseOverflowDetection() {}

	// calculated as 0xffffffffffffffff / radix
	static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
	static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
	static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];

	static {
	BigInteger overflow = new BigInteger("10000000000000000", 16);
	for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
	maxValueDivs[i] = divide(MAX_VALUE, i);
	maxValueMods[i] = (int) remainder(MAX_VALUE, i);
	maxSafeDigits[i] = overflow.toString(i).length() - 1;
	}
	}

	/**
	* Returns true if (current * radix) + digit is a number too large to be represented by an
	* unsigned long. This is useful for detecting overflow while parsing a string representation of
	* a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
	* undefined results or an ArrayIndexOutOfBoundsException.
	*/
	static boolean overflowInParse(long current, int digit, int radix) {
	if (current >= 0) {
	if (current < maxValueDivs[radix]) {
	return false;
	}
	if (current > maxValueDivs[radix]) {
	return true;
	}
	// current == maxValueDivs[radix]
	return (digit > maxValueMods[radix]);
	}

	// current < 0: high bit is set
	return true;
	}
	}

	/**
	* Returns a string representation of x, where x is treated as unsigned.
	*
	* <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long)} instead.
	*/
	public static String toString(long x) {
	return toString(x, 10);
	}

	/**
	* Returns a string representation of {@code x} for the given radix, where {@code x} is treated as
	* unsigned.
	*
	* <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long, int)} instead.
	*
	* @param x the value to convert to a string.
	* @param radix the radix to use while working with {@code x}
	* @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
	* and {@link Character#MAX_RADIX}.
	*/
	public static String toString(long x, int radix) {
	checkArgument(
	radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
	"radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX",
	radix);
	if (x == 0) {
	// Simply return "0"
	return "0";
	} else if (x > 0) {
	return Long.toString(x, radix);
	} else {
	char[] buf = new char[64];
	int i = buf.length;
	if ((radix & (radix - 1)) == 0) {
	// Radix is a power of two so we can avoid division.
	int shift = Integer.numberOfTrailingZeros(radix);
	int mask = radix - 1;
	do {
	buf[--i] = Character.forDigit(((int) x) & mask, radix);
	x >>>= shift;
	} while (x != 0);
	} else {
	// Separate off the last digit using unsigned division. That will leave
	// a number that is nonnegative as a signed integer.
	long quotient;
	if ((radix & 1) == 0) {
	// Fast path for the usual case where the radix is even.
	quotient = (x >>> 1) / (radix >>> 1);
	} else {
	quotient = divide(x, radix);
	}
	long rem = x - quotient * radix;
	buf[--i] = Character.forDigit((int) rem, radix);
	x = quotient;
	// Simple modulo/division approach
	while (x > 0) {
	buf[--i] = Character.forDigit((int) (x % radix), radix);
	x /= radix;
	}
	}
	// Generate string
	return new String(buf, i, buf.length - i);
	}
	}
	}