Long

作者: LaMole | 来源:发表于2021-01-25 10:19 被阅读0次
    /*
     * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
     * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
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    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
     *
     * My Note
     * 和Integer的主要区别是这个方法,里面涉及了一个类,需要看下实现
     * BigInteger
     * @see #toUnsignedString
     * 主要是这个方法
     * @see #toUnsignedString0
     * 计算位数的方法
     * int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
     * int chars = Math.max(((mag + (shift - 1)) / shift), 1);
     * 再然后是
     * @see #formatUnsignedLong
     * 通过数组配合掩码相与实现,可以强转为int是因为每次计算低位,不影响整体
     * buf[offset + --charPos] = Integer.digits[((int) val) & mask];
     */
    public final class Long extends Number implements Comparable<Long> {
        /**
         * A constant holding the minimum value a {@code long} can
         * have, -2<sup>63</sup>.
         */
        @Native public static final long MIN_VALUE = 0x8000000000000000L;
    
        /**
         * A constant holding the maximum value a {@code long} can
         * have, 2<sup>63</sup>-1.
         */
        @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
    
        /**
         * The {@code Class} instance representing the primitive type
         * {@code long}.
         *
         * @since   JDK1.1
         */
        @SuppressWarnings("unchecked")
        public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
    
        /**
         * Returns a string representation of the first argument in the
         * radix specified by the second argument.
         *
         * <p>If the radix is smaller than {@code Character.MIN_RADIX}
         * or larger than {@code Character.MAX_RADIX}, then the radix
         * {@code 10} is used instead.
         *
         * <p>If the first argument is negative, the first element of the
         * result is the ASCII minus sign {@code '-'}
         * ({@code '\u005Cu002d'}). If the first argument is not
         * negative, no sign character appears in the result.
         *
         * <p>The remaining characters of the result represent the magnitude
         * of the first argument. If the magnitude is zero, it is
         * represented by a single zero character {@code '0'}
         * ({@code '\u005Cu0030'}); otherwise, the first character of
         * the representation of the magnitude will not be the zero
         * character.  The following ASCII characters are used as digits:
         *
         * <blockquote>
         *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
         * </blockquote>
         *
         * These are {@code '\u005Cu0030'} through
         * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
         * {@code '\u005Cu007a'}. If {@code radix} is
         * <var>N</var>, then the first <var>N</var> of these characters
         * are used as radix-<var>N</var> digits in the order shown. Thus,
         * the digits for hexadecimal (radix 16) are
         * {@code 0123456789abcdef}. If uppercase letters are
         * desired, the {@link java.lang.String#toUpperCase()} method may
         * be called on the result:
         *
         * <blockquote>
         *  {@code Long.toString(n, 16).toUpperCase()}
         * </blockquote>
         *
         * @param   i       a {@code long} to be converted to a string.
         * @param   radix   the radix to use in the string representation.
         * @return  a string representation of the argument in the specified radix.
         * @see     java.lang.Character#MAX_RADIX
         * @see     java.lang.Character#MIN_RADIX
         */
        public static String toString(long i, int radix) {
            if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
                radix = 10;
            if (radix == 10)
                return toString(i);
            char[] buf = new char[65];
            int charPos = 64;
            boolean negative = (i < 0);
    
            if (!negative) {
                i = -i;
            }
    
            while (i <= -radix) {
                buf[charPos--] = Integer.digits[(int)(-(i % radix))];
                i = i / radix;
            }
            buf[charPos] = Integer.digits[(int)(-i)];
    
            if (negative) {
                buf[--charPos] = '-';
            }
    
            return new String(buf, charPos, (65 - charPos));
        }
    
        /**
         * Returns a string representation of the first argument as an
         * unsigned integer value in the radix specified by the second
         * argument.
         *
         * <p>If the radix is smaller than {@code Character.MIN_RADIX}
         * or larger than {@code Character.MAX_RADIX}, then the radix
         * {@code 10} is used instead.
         *
         * <p>Note that since the first argument is treated as an unsigned
         * value, no leading sign character is printed.
         *
         * <p>If the magnitude is zero, it is represented by a single zero
         * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
         * the first character of the representation of the magnitude will
         * not be the zero character.
         *
         * <p>The behavior of radixes and the characters used as digits
         * are the same as {@link #toString(long, int) toString}.
         *
         * @param   i       an integer to be converted to an unsigned string.
         * @param   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 java.lang.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);
            return new String(buf, true);
        }
    
        /**
         * Format a long (treated as unsigned) into a character buffer.
         * @param val the unsigned long to format
         * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
         * @param buf the character buffer to write to
         * @param offset the offset in the destination buffer to start at
         * @param len the number of characters to write
         * @return the lowest character location used
         */
         static int formatUnsignedLong(long val, int shift, char[] buf, int offset, int len) {
            int charPos = len;
            int radix = 1 << shift;
            int mask = radix - 1;
            do {
                buf[offset + --charPos] = Integer.digits[((int) val) & mask];
                val >>>= shift;
            } while (val != 0 && charPos > 0);
    
            return charPos;
        }
    
        /**
         * Returns a {@code String} object representing the specified
         * {@code long}.  The argument is converted to signed decimal
         * representation and returned as a string, exactly as if the
         * argument and the radix 10 were given as arguments to the {@link
         * #toString(long, int)} method.
         *
         * @param   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);
            return new String(buf, true);
        }
    
        /**
         * Returns a string representation of the argument as an unsigned
         * decimal value.
         *
         * The argument is converted to unsigned decimal representation
         * and returned as a string exactly as if the argument and radix
         * 10 were given as arguments to the {@link #toUnsignedString(long,
         * int)} method.
         *
         * @param   i  an integer to be converted to an unsigned string.
         * @return  an unsigned string representation of the argument.
         * @see     #toUnsignedString(long, int)
         * @since 1.8
         */
        public static String toUnsignedString(long i) {
            return toUnsignedString(i, 10);
        }
    
        /**
         * Places characters representing the integer i into the
         * character array buf. The characters are placed into
         * the buffer backwards starting with the least significant
         * digit at the specified index (exclusive), and working
         * backwards from there.
         *
         * Will fail if i == Long.MIN_VALUE
         *
         * 大于Integer单独拆出来,为了后续使用int不用long
         *
         */
        static void getChars(long i, int index, char[] buf) {
            long q;
            int r;
            int charPos = index;
            char sign = 0;
    
            if (i < 0) {
                sign = '-';
                i = -i;
            }
    
            // Get 2 digits/iteration using longs until quotient fits into an int
            while (i > Integer.MAX_VALUE) {
                q = i / 100;
                // really: r = i - (q * 100);
                r = (int)(i - ((q << 6) + (q << 5) + (q << 2)));
                i = q;
                buf[--charPos] = Integer.DigitOnes[r];
                buf[--charPos] = Integer.DigitTens[r];
            }
    
            // Get 2 digits/iteration using ints
            int q2;
            int i2 = (int)i;
            while (i2 >= 65536) {
                q2 = i2 / 100;
                // really: r = i2 - (q * 100);
                r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
                i2 = q2;
                buf[--charPos] = Integer.DigitOnes[r];
                buf[--charPos] = Integer.DigitTens[r];
            }
    
            // Fall thru to fast mode for smaller numbers
            // assert(i2 <= 65536, i2);
            for (;;) {
                q2 = (i2 * 52429) >>> (16+3);
                r = i2 - ((q2 << 3) + (q2 << 1));  // r = i2-(q2*10) ...
                buf[--charPos] = Integer.digits[r];
                i2 = q2;
                if (i2 == 0) break;
            }
            if (sign != 0) {
                buf[--charPos] = sign;
            }
        }
    
        // Requires positive x
        static int stringSize(long x) {
            long p = 10;
            for (int i=1; i<19; i++) {
                if (x < p)
                    return i;
                p = 10*p;
            }
            return 19;
        }
    
        /**
         * Parses the string argument as a signed {@code long} in the
         * radix specified by the second argument. The characters in the
         * string must all be digits of the specified radix (as determined
         * by whether {@link java.lang.Character#digit(char, int)} returns
         * a nonnegative value), except that the first character may be an
         * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
         * indicate a negative value or an ASCII plus sign {@code '+'}
         * ({@code '\u005Cu002B'}) to indicate a positive value. The
         * resulting {@code long} value is returned.
         *
         * <p>Note that neither the character {@code L}
         * ({@code '\u005Cu004C'}) nor {@code l}
         * ({@code '\u005Cu006C'}) is permitted to appear at the end
         * of the string as a type indicator, as would be permitted in
         * Java programming language source code - except that either
         * {@code L} or {@code l} may appear as a digit for a
         * radix greater than or equal to 22.
         *
         * <p>An exception of type {@code NumberFormatException} is
         * thrown if any of the following situations occurs:
         * <ul>
         *
         * <li>The first argument is {@code null} or is a string of
         * length zero.
         *
         * <li>The {@code radix} is either smaller than {@link
         * java.lang.Character#MIN_RADIX} or larger than {@link
         * java.lang.Character#MAX_RADIX}.
         *
         * <li>Any character of the string is not a digit of the specified
         * radix, except that the first character may be a minus sign
         * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
         * '+'} ({@code '\u005Cu002B'}) provided that the string is
         * longer than length 1.
         *
         * <li>The value represented by the string is not a value of type
         *      {@code long}.
         * </ul>
         *
         * <p>Examples:
         * <blockquote><pre>
         * parseLong("0", 10) returns 0L
         * parseLong("473", 10) returns 473L
         * parseLong("+42", 10) returns 42L
         * parseLong("-0", 10) returns 0L
         * parseLong("-FF", 16) returns -255L
         * parseLong("1100110", 2) returns 102L
         * parseLong("99", 8) throws a NumberFormatException
         * parseLong("Hazelnut", 10) throws a NumberFormatException
         * parseLong("Hazelnut", 36) returns 1356099454469L
         * </pre></blockquote>
         *
         * @param      s       the {@code String} containing the
         *                     {@code long} representation to be parsed.
         * @param      radix   the radix to be used while parsing {@code s}.
         * @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(java.lang.String, int)} method.
         *
         * <p>Note that neither the character {@code L}
         * ({@code '\u005Cu004C'}) nor {@code l}
         * ({@code '\u005Cu006C'}) is permitted to appear at the end
         * of the string as a type indicator, as would be permitted in
         * Java programming language source code.
         *
         * @param      s   a {@code String} containing the {@code long}
         *             representation to be parsed
         * @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
         * java.lang.Character#digit(char, int)} returns a nonnegative
         * value), except that the first character may be an ASCII plus
         * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
         * integer value is returned.
         *
         * <p>An exception of type {@code NumberFormatException} is
         * thrown if any of the following situations occurs:
         * <ul>
         * <li>The first argument is {@code null} or is a string of
         * length zero.
         *
         * <li>The radix is either smaller than
         * {@link java.lang.Character#MIN_RADIX} or
         * larger than {@link java.lang.Character#MAX_RADIX}.
         *
         * <li>Any character of the string is not a digit of the specified
         * radix, except that the first character may be a 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(java.lang.String, int)} method.
         *
         * @param s   a {@code String} containing the unsigned {@code long}
         *            representation to be parsed
         * @return    the unsigned {@code long} value represented by the decimal string argument
         * @throws    NumberFormatException  if the string does not contain a
         *            parsable unsigned integer.
         * @since 1.8
         */
        public static long parseUnsignedLong(String s) throws NumberFormatException {
            return parseUnsignedLong(s, 10);
        }
    
        /**
         * Returns a {@code Long} object holding the value
         * extracted from the specified {@code String} when parsed
         * with the radix given by the second argument.  The first
         * argument is interpreted as representing a signed
         * {@code long} in the radix specified by the second
         * argument, exactly as if the arguments were given to the {@link
         * #parseLong(java.lang.String, int)} method. The result is a
         * {@code Long} object that represents the {@code long}
         * value specified by the string.
         *
         * <p>In other words, this method returns a {@code Long} object equal
         * to the value of:
         *
         * <blockquote>
         *  {@code new Long(Long.parseLong(s, radix))}
         * </blockquote>
         *
         * @param      s       the string to be parsed
         * @param      radix   the radix to be used in interpreting {@code s}
         * @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(java.lang.String)} method. The result is a
         * {@code Long} object that represents the integer value
         * specified by the string.
         *
         * <p>In other words, this method returns a {@code Long} object
         * equal to the value of:
         *
         * <blockquote>
         *  {@code new Long(Long.parseLong(s))}
         * </blockquote>
         *
         * @param      s   the string to be parsed.
         * @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 java.lang.Long#parseLong(String, int)
         * @since 1.2
         */
        public static Long decode(String nm) throws NumberFormatException {
            int radix = 10;
            int index = 0;
            boolean negative = false;
            Long result;
    
            if (nm.length() == 0)
                throw new NumberFormatException("Zero length string");
            char firstChar = nm.charAt(0);
            // Handle sign, if present
            if (firstChar == '-') {
                negative = true;
                index++;
            } else if (firstChar == '+')
                index++;
    
            // Handle radix specifier, if present
            if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
                index += 2;
                radix = 16;
            }
            else if (nm.startsWith("#", index)) {
                index ++;
                radix = 16;
            }
            else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
                index ++;
                radix = 8;
            }
    
            if (nm.startsWith("-", index) || nm.startsWith("+", index))
                throw new NumberFormatException("Sign character in wrong position");
    
            try {
                result = Long.valueOf(nm.substring(index), radix);
                result = negative ? Long.valueOf(-result.longValue()) : result;
            } catch (NumberFormatException e) {
                // If number is Long.MIN_VALUE, we'll end up here. The next line
                // handles this case, and causes any genuine format error to be
                // rethrown.
                String constant = negative ? ("-" + nm.substring(index))
                                           : nm.substring(index);
                result = Long.valueOf(constant, radix);
            }
            return result;
        }
    
        /**
         * The value of the {@code Long}.
         *
         * @serial
         */
        private final long value;
    
        /**
         * Constructs a newly allocated {@code Long} object that
         * represents the specified {@code long} argument.
         *
         * @param   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        java.lang.Long#parseLong(java.lang.String, int)
         */
        public Long(String s) throws NumberFormatException {
            this.value = parseLong(s, 10);
        }
    
        /**
         * Returns the value of this {@code Long} as a {@code byte} after
         * a narrowing primitive conversion.
         * @jls 5.1.3 Narrowing Primitive Conversions
         */
        public byte byteValue() {
            return (byte)value;
        }
    
        /**
         * Returns the value of this {@code Long} as a {@code short} after
         * a narrowing primitive conversion.
         * @jls 5.1.3 Narrowing Primitive Conversions
         */
        public short shortValue() {
            return (short)value;
        }
    
        /**
         * Returns the value of this {@code Long} as an {@code int} after
         * a narrowing primitive conversion.
         * @jls 5.1.3 Narrowing Primitive Conversions
         */
        public int intValue() {
            return (int)value;
        }
    
        /**
         * Returns the value of this {@code Long} as a
         * {@code long} value.
         */
        public long longValue() {
            return value;
        }
    
        /**
         * Returns the value of this {@code Long} as a {@code float} after
         * a widening primitive conversion.
         * @jls 5.1.2 Widening Primitive Conversions
         */
        public float floatValue() {
            return (float)value;
        }
    
        /**
         * Returns the value of this {@code Long} as a {@code double}
         * after a widening primitive conversion.
         * @jls 5.1.2 Widening Primitive Conversions
         */
        public double doubleValue() {
            return (double)value;
        }
    
        /**
         * Returns a {@code String} object representing this
         * {@code Long}'s value.  The value is converted to signed
         * decimal representation and returned as a string, exactly as if
         * the {@code long} value were given as an argument to the
         * {@link java.lang.Long#toString(long)} method.
         *
         * @return  a string representation of the value of this object in
         *          base&nbsp;10.
         */
        public String toString() {
            return toString(value);
        }
    
        /**
         * Returns a hash code for this {@code Long}. The result is
         * the exclusive OR of the two halves of the primitive
         * {@code long} value held by this {@code Long}
         * object. That is, the hashcode is the value of the expression:
         *
         * <blockquote>
         *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
         * </blockquote>
         *
         * @return  a hash code value for this object.
         */
        @Override
        public int hashCode() {
            return Long.hashCode(value);
        }
    
        /**
         * Returns a hash code for a {@code long} value; compatible with
         * {@code Long.hashCode()}.
         *
         * @param value the value to hash
         * @return a hash code value for a {@code long} value.
         * @since 1.8
         */
        public static int hashCode(long value) {
            return (int)(value ^ (value >>> 32));
        }
    
        /**
         * Compares this object to the specified object.  The result is
         * {@code true} if and only if the argument is not
         * {@code null} and is a {@code Long} object that
         * contains the same {@code long} value as this object.
         *
         * @param   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
         * java.lang.System#getProperty(java.lang.String)} method. The
         * string value of this property is then interpreted as a {@code
         * long} value using the grammar supported by {@link Long#decode decode}
         * and a {@code Long} object representing this value is returned.
         *
         * <p>If there is no property with the specified name, if the
         * specified name is empty or {@code null}, or if the property
         * does not have the correct numeric format, then {@code null} is
         * returned.
         *
         * <p>In other words, this method returns a {@code Long} object
         * equal to the value of:
         *
         * <blockquote>
         *  {@code getLong(nm, null)}
         * </blockquote>
         *
         * @param   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     java.lang.System#getProperty(java.lang.String)
         * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
         */
        public static Long getLong(String nm) {
            return getLong(nm, null);
        }
    
        /**
         * Determines the {@code long} value of the system property
         * with the specified name.
         *
         * <p>The first argument is treated as the name of a system
         * property.  System properties are accessible through the {@link
         * java.lang.System#getProperty(java.lang.String)} method. The
         * string value of this property is then interpreted as a {@code
         * long} value using the grammar supported by {@link Long#decode decode}
         * and a {@code Long} object representing this value is returned.
         *
         * <p>The second argument is the default value. A {@code Long} object
         * that represents the value of the second argument is returned if there
         * is no property of the specified name, if the property does not have
         * the correct numeric format, or if the specified name is empty or null.
         *
         * <p>In other words, this method returns a {@code Long} object equal
         * to the value of:
         *
         * <blockquote>
         *  {@code getLong(nm, new Long(val))}
         * </blockquote>
         *
         * but in practice it may be implemented in a manner such as:
         *
         * <blockquote><pre>
         * Long result = getLong(nm, null);
         * return (result == null) ? new Long(val) : result;
         * </pre></blockquote>
         *
         * to avoid the unnecessary allocation of a {@code Long} object when
         * the default value is not needed.
         *
         * @param   nm    property name.
         * @param   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     java.lang.System#getProperty(java.lang.String)
         * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
         */
        public static Long getLong(String nm, long val) {
            Long result = Long.getLong(nm, null);
            return (result == null) ? Long.valueOf(val) : result;
        }
    
        /**
         * Returns the {@code long} value of the system property with
         * the specified name.  The first argument is treated as the name
         * of a system property.  System properties are accessible through
         * the {@link java.lang.System#getProperty(java.lang.String)}
         * method. The string value of this property is then interpreted
         * as a {@code long} value, as per the
         * {@link Long#decode decode} method, and a {@code Long} object
         * representing this value is returned; in summary:
         *
         * <ul>
         * <li>If the property value begins with the two ASCII characters
         * {@code 0x} or the ASCII character {@code #}, not followed by
         * a minus sign, then the rest of it is parsed as a hexadecimal integer
         * exactly as for the method {@link #valueOf(java.lang.String, int)}
         * with radix 16.
         * <li>If the property value begins with the ASCII character
         * {@code 0} followed by another character, it is parsed as
         * an octal integer exactly as by the method {@link
         * #valueOf(java.lang.String, int)} with radix 8.
         * <li>Otherwise the property value is parsed as a decimal
         * integer exactly as by the method
         * {@link #valueOf(java.lang.String, int)} with radix 10.
         * </ul>
         *
         * <p>Note that, in every case, neither {@code L}
         * ({@code '\u005Cu004C'}) nor {@code l}
         * ({@code '\u005Cu006C'}) is permitted to appear at the end
         * of the property value as a type indicator, as would be
         * permitted in Java programming language source code.
         *
         * <p>The second argument is the default value. The default value is
         * returned if there is no property of the specified name, if the
         * property does not have the correct numeric format, or if the
         * specified name is empty or {@code null}.
         *
         * @param   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(java.lang.String)
         * @see     System#getProperty(java.lang.String, java.lang.String)
         */
        public static Long getLong(String nm, Long val) {
            String v = null;
            try {
                v = System.getProperty(nm);
            } catch (IllegalArgumentException | NullPointerException e) {
            }
            if (v != null) {
                try {
                    return Long.decode(v);
                } catch (NumberFormatException e) {
                }
            }
            return val;
        }
    
        /**
         * Compares two {@code Long} objects numerically.
         *
         * @param   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;
    }
    
    

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