Long.java

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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
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 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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package java.lang;

import java.lang.annotation.Native;
import java.lang.invoke.MethodHandles;
import java.lang.constant.Constable;
import java.lang.constant.ConstantDesc;
import java.math.*;
import java.util.Objects;
import java.util.Optional;

import jdk.internal.misc.CDS;
import jdk.internal.util.DecimalDigits;
import jdk.internal.vm.annotation.ForceInline;
import jdk.internal.vm.annotation.IntrinsicCandidate;
import jdk.internal.vm.annotation.Stable;

import static java.lang.Character.digit;
import static java.lang.String.COMPACT_STRINGS;
import static java.lang.String.LATIN1;
import static java.lang.String.UTF16;

/**
 * The {@code Long} class is the {@linkplain
 * java.lang##wrapperClass wrapper class} for values of the primitive
 * type {@code long}. 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>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
 * class; programmers should treat instances that are
 * {@linkplain #equals(Object) equal} as interchangeable and should not
 * use instances for synchronization, or unpredictable behavior may
 * occur. For example, in a future release, synchronization may fail.
 *
 * <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 <cite>Hacker's
 * Delight</cite>, (Addison Wesley, 2002) and <cite>Hacker's
 * Delight, Second Edition</cite>, (Pearson Education, 2013).
 *
 * @author  Lee Boynton
 * @author  Arthur van Hoff
 * @author  Josh Bloch
 * @author  Joseph D. Darcy
 * @since   1.0
 */
@jdk.internal.ValueBased
public final class Long extends Number
        implements Comparable<Long>, Constable, ConstantDesc {
    /**
     * 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   1.1
     */
    public static final Class<Long> TYPE = 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);

        if (COMPACT_STRINGS) {
            byte[] buf = new byte[65];
            int charPos = 64;
            boolean negative = (i < 0);

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

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

            if (negative) {
                buf[--charPos] = '-';
            }
            return StringLatin1.newString(buf, charPos, (65 - charPos));
        }
        return toStringUTF16(i, radix);
    }

    private static String toStringUTF16(long i, int radix) {
        byte[] buf = new byte[65 * 2];
        int charPos = 64;
        boolean negative = (i < 0);
        if (!negative) {
            i = -i;
        }
        while (i <= -radix) {
            StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
            i = i / radix;
        }
        StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
        if (negative) {
            StringUTF16.putChar(buf, --charPos, '-');
        }
        return StringUTF16.newString(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 {
            return switch (radix) {
                case 2  -> toBinaryString(i);
                case 4  -> toUnsignedString0(i, 2);
                case 8  -> 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;
                    yield toString(quot) + rem;
                }
                case 16 -> toHexString(i);
                case 32 -> toUnsignedString0(i, 5);
                default -> 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>
     *
     * @apiNote
     * The {@link java.util.HexFormat} class provides formatting and parsing
     * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
     * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
     * with leading zeros and for byte arrays includes for each byte
     * a delimiter, prefix, and suffix.
     *
     * @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 java.util.HexFormat
     * @see #parseUnsignedLong(String, int)
     * @see #toUnsignedString(long, int)
     * @since   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   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   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);
        if (COMPACT_STRINGS) {
            byte[] buf = new byte[chars];
            formatUnsignedLong0(val, shift, buf, 0, chars);
            return new String(buf, LATIN1);
        } else {
            byte[] buf = new byte[chars * 2];
            formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
            return new String(buf, UTF16);
        }
    }

    /**
     * Format a long (treated as unsigned) into a byte buffer (LATIN1 version). If
     * {@code len} exceeds the formatted ASCII representation of {@code val},
     * {@code buf} will be padded with leading zeroes.
     *
     * @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 byte buffer to write to
     * @param offset the offset in the destination buffer to start at
     * @param len the number of characters to write
     */
    private static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
        int charPos = offset + len;
        int radix = 1 << shift;
        int mask = radix - 1;
        do {
            buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
            val >>>= shift;
        } while (charPos > offset);
    }

    /**
     * Format a long (treated as unsigned) into a byte buffer (UTF16 version). If
     * {@code len} exceeds the formatted ASCII representation of {@code val},
     * {@code buf} will be padded with leading zeroes.
     *
     * @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 byte buffer to write to
     * @param offset the offset in the destination buffer to start at
     * @param len the number of characters to write
     */
    private static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
        int charPos = offset + len;
        int radix = 1 << shift;
        int mask = radix - 1;
        do {
            StringUTF16.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
            val >>>= shift;
        } while (charPos > offset);
    }

    /**
     * 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) {
        int size = DecimalDigits.stringSize(i);
        if (COMPACT_STRINGS) {
            byte[] buf = new byte[size];
            DecimalDigits.getCharsLatin1(i, size, buf);
            return new String(buf, LATIN1);
        } else {
            byte[] buf = new byte[size * 2];
            DecimalDigits.getCharsUTF16(i, size, buf);
            return new String(buf, UTF16);
        }
    }

    /**
     * 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);
    }

    /**
     * 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("Cannot parse null string");
        }

        if (radix < Character.MIN_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s less than Character.MIN_RADIX", radix));
        }

        if (radix > Character.MAX_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s greater than Character.MAX_RADIX", radix));
        }

        int len = s.length();
        if (len == 0) {
            throw NumberFormatException.forInputString("", radix);
        }
        int digit = ~0xFF;
        int i = 0;
        char firstChar = s.charAt(i++);
        if (firstChar != '-' && firstChar != '+') {
            digit = digit(firstChar, radix);
        }
        if (digit >= 0 || digit == ~0xFF && len > 1) {
            long limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
            long multmin = limit / radix;
            long result = -(digit & 0xFF);
            boolean inRange = true;
            /* Accumulating negatively avoids surprises near MAX_VALUE */
            while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
                    && (inRange = result > multmin
                        || result == multmin && digit <= (int) (radix * multmin - limit))) {
                result = radix * result - digit;
            }
            if (inRange && i == len && digit >= 0) {
                return firstChar != '-' ? -result : result;
            }
        }
        throw NumberFormatException.forInputString(s, radix);
    }

    /**
     * Parses the {@link CharSequence} argument as a signed {@code long} in
     * the specified {@code radix}, beginning at the specified
     * {@code beginIndex} and extending to {@code endIndex - 1}.
     *
     * <p>The method does not take steps to guard against the
     * {@code CharSequence} being mutated while parsing.
     *
     * @param      s   the {@code CharSequence} containing the {@code long}
     *                  representation to be parsed
     * @param      beginIndex   the beginning index, inclusive.
     * @param      endIndex     the ending index, exclusive.
     * @param      radix   the radix to be used while parsing {@code s}.
     * @return     the signed {@code long} represented by the subsequence in
     *             the specified radix.
     * @throws     NullPointerException  if {@code s} is null.
     * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
     *             negative, or if {@code beginIndex} is greater than
     *             {@code endIndex} or if {@code endIndex} is greater than
     *             {@code s.length()}.
     * @throws     NumberFormatException  if the {@code CharSequence} does not
     *             contain a parsable {@code long} in the specified
     *             {@code radix}, or if {@code radix} is either smaller than
     *             {@link java.lang.Character#MIN_RADIX} or larger than
     *             {@link java.lang.Character#MAX_RADIX}.
     * @since  9
     */
    public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
                throws NumberFormatException {
        Objects.requireNonNull(s);
        Objects.checkFromToIndex(beginIndex, endIndex, s.length());

        if (radix < Character.MIN_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s less than Character.MIN_RADIX", radix));
        }

        if (radix > Character.MAX_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s greater than Character.MAX_RADIX", radix));
        }

        /*
         * While s can be concurrently modified, it is ensured that each
         * of its characters is read at most once, from lower to higher indices.
         * This is obtained by reading them using the pattern s.charAt(i++),
         * and by not updating i anywhere else.
         */
        if (beginIndex == endIndex) {
            throw NumberFormatException.forInputString("", radix);
        }
        int digit = ~0xFF;  // ~0xFF means firstChar char is sign
        int i = beginIndex;
        char firstChar = s.charAt(i++);
        if (firstChar != '-' && firstChar != '+') {
            digit = digit(firstChar, radix);
        }
        if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
            long limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
            long multmin = limit / radix;
            long result = -(digit & 0xFF);
            boolean inRange = true;
            /* Accumulating negatively avoids surprises near MAX_VALUE */
            while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
                    && (inRange = result > multmin
                        || result == multmin && digit <= (int) (radix * multmin - limit))) {
                result = radix * result - digit;
            }
            if (inRange && i == endIndex && digit >= 0) {
                return firstChar != '-' ? -result : result;
            }
        }
        throw NumberFormatException.forCharSequence(s, beginIndex,
            endIndex, i - (digit < -1 ? 0 : 1));
    }

    /**
     * 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("Cannot parse null string");
        }

        if (radix < Character.MIN_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s less than Character.MIN_RADIX", radix));
        }

        if (radix > Character.MAX_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s greater than Character.MAX_RADIX", radix));
        }

        int len = s.length();
        if (len == 0) {
            throw NumberFormatException.forInputString(s, radix);
        }
        int i = 0;
        char firstChar = s.charAt(i++);
        if (firstChar == '-') {
            throw new NumberFormatException(String.format(
                "Illegal leading minus sign on unsigned string %s.", s));
        }
        int digit = ~0xFF;
        if (firstChar != '+') {
            digit = digit(firstChar, radix);
        }
        if (digit >= 0 || digit == ~0xFF && len > 1) {
            long multmax = divideUnsigned(-1L, radix);  // -1L is max unsigned long
            long result = digit & 0xFF;
            boolean inRange = true;
            while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
                    && (inRange = compareUnsigned(result, multmax) < 0
                        || result == multmax && digit < (int) (-radix * multmax))) {
                result = radix * result + digit;
            }
            if (inRange && i == len && digit >= 0) {
                return result;
            }
        }
        if (digit < 0) {
            throw NumberFormatException.forInputString(s, radix);
        }
        throw new NumberFormatException(String.format(
            "String value %s exceeds range of unsigned long.", s));
    }

    /**
     * Parses the {@link CharSequence} argument as an unsigned {@code long} in
     * the specified {@code radix}, beginning at the specified
     * {@code beginIndex} and extending to {@code endIndex - 1}.
     *
     * <p>The method does not take steps to guard against the
     * {@code CharSequence} being mutated while parsing.
     *
     * @param      s   the {@code CharSequence} containing the unsigned
     *                 {@code long} representation to be parsed
     * @param      beginIndex   the beginning index, inclusive.
     * @param      endIndex     the ending index, exclusive.
     * @param      radix   the radix to be used while parsing {@code s}.
     * @return     the unsigned {@code long} represented by the subsequence in
     *             the specified radix.
     * @throws     NullPointerException  if {@code s} is null.
     * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
     *             negative, or if {@code beginIndex} is greater than
     *             {@code endIndex} or if {@code endIndex} is greater than
     *             {@code s.length()}.
     * @throws     NumberFormatException  if the {@code CharSequence} does not
     *             contain a parsable unsigned {@code long} in the specified
     *             {@code radix}, or if {@code radix} is either smaller than
     *             {@link java.lang.Character#MIN_RADIX} or larger than
     *             {@link java.lang.Character#MAX_RADIX}.
     * @since  9
     */
    public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
                throws NumberFormatException {
        Objects.requireNonNull(s);
        Objects.checkFromToIndex(beginIndex, endIndex, s.length());

        if (radix < Character.MIN_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s less than Character.MIN_RADIX", radix));
        }

        if (radix > Character.MAX_RADIX) {
            throw new NumberFormatException(String.format(
                "radix %s greater than Character.MAX_RADIX", radix));
        }

        /*
         * While s can be concurrently modified, it is ensured that each
         * of its characters is read at most once, from lower to higher indices.
         * This is obtained by reading them using the pattern s.charAt(i++),
         * and by not updating i anywhere else.
         */
        if (beginIndex == endIndex) {
            throw NumberFormatException.forInputString("", radix);
        }
        int i = beginIndex;
        char firstChar = s.charAt(i++);
        if (firstChar == '-') {
            throw new NumberFormatException(
                "Illegal leading minus sign on unsigned string " + s + ".");
        }
        int digit = ~0xFF;
        if (firstChar != '+') {
            digit = digit(firstChar, radix);
        }
        if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
            long multmax = divideUnsigned(-1L, radix);  // -1L is max unsigned long
            long result = digit & 0xFF;
            boolean inRange = true;
            while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
                    && (inRange = compareUnsigned(result, multmax) < 0
                        || result == multmax && digit < (int) (-radix * multmax))) {
                result = radix * result + digit;
            }
            if (inRange && i == endIndex && digit >= 0) {
                return result;
            }
        }
        if (digit < 0) {
            throw NumberFormatException.forCharSequence(s, beginIndex,
                endIndex, i - (digit < -1 ? 0 : 1));
        }
        throw new NumberFormatException(String.format(
            "String value %s exceeds range of unsigned long.", 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 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 Long.valueOf(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 Long.valueOf(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 final class LongCache {
        private LongCache() {}

        @Stable
        static final Long[] cache;
        static Long[] archivedCache;

        static {
            int size = -(-128) + 127 + 1;

            // Load and use the archived cache if it exists
            CDS.initializeFromArchive(LongCache.class);
            if (archivedCache == null) {
                Long[] c = new Long[size];
                long value = -128;
                for(int i = 0; i < size; i++) {
                    c[i] = new Long(value++);
                }
                archivedCache = c;
            }
            cache = archivedCache;
            assert cache.length == size;
        }
    }

    /**
     * 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.
     *
     * This method will always cache values in the range -128 to 127,
     * inclusive, and may cache other values outside of this range.
     *
     * @param  l a long value.
     * @return a {@code Long} instance representing {@code l}.
     * @since  1.5
     */
    @IntrinsicCandidate
    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 {@jls 3.10.1} of
     * <cite>The Java 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.isEmpty())
            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 = parseLong(nm, index, nm.length(), radix);
            result = negative ? -result : 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 = parseLong(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.
     *
     * @deprecated
     * It is rarely appropriate to use this constructor. The static factory
     * {@link #valueOf(long)} is generally a better choice, as it is
     * likely to yield significantly better space and time performance.
     */
    @Deprecated(since="9", forRemoval = true)
    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}.
     *
     * @deprecated
     * It is rarely appropriate to use this constructor.
     * Use {@link #parseLong(String)} to convert a string to a
     * {@code long} primitive, or use {@link #valueOf(String)}
     * to convert a string to a {@code Long} object.
     */
    @Deprecated(since="9", forRemoval = true)
    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 Conversion
     */
    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 Conversion
     */
    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 Conversion
     */
    public int intValue() {
        return (int)value;
    }

    /**
     * Returns the value of this {@code Long} as a
     * {@code long} value.
     */
    @IntrinsicCandidate
    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 Conversion
     */
    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 Conversion
     */
    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 ell) {
            return value == ell.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.
     * @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, Long.valueOf(val))}
     * </blockquote>
     *
     * but in practice it may be implemented in a manner such as:
     *
     * <blockquote><pre>
     * Long result = getLong(nm, null);
     * return (result == null) ? Long.valueOf(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.
     * @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.
     * @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 = nm != null && !nm.isEmpty() ? System.getProperty(nm) : null;
        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
     */
    @IntrinsicCandidate
    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
     */
    @IntrinsicCandidate
    public static long divideUnsigned(long dividend, long divisor) {
        /* See Hacker's Delight (2nd ed), section 9.3 */
        if (divisor >= 0) {
            final long q = (dividend >>> 1) / divisor << 1;
            final long r = dividend - q * divisor;
            return q + ((r | ~(r - divisor)) >>> (Long.SIZE - 1));
        }
        return (dividend & ~(dividend - divisor)) >>> (Long.SIZE - 1);
    }

    /**
     * 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
     */
    @IntrinsicCandidate
    public static long remainderUnsigned(long dividend, long divisor) {
        /* See Hacker's Delight (2nd ed), section 9.3 */
        if (divisor >= 0) {
            final long q = (dividend >>> 1) / divisor << 1;
            final long r = dividend - q * divisor;
            /*
             * Here, 0 <= r < 2 * divisor
             * (1) When 0 <= r < divisor, the remainder is simply r.
             * (2) Otherwise the remainder is r - divisor.
             *
             * In case (1), r - divisor < 0. Applying ~ produces a long with
             * sign bit 0, so >> produces 0. The returned value is thus r.
             *
             * In case (2), a similar reasoning shows that >> produces -1,
             * so the returned value is r - divisor.
             */
            return r - ((~(r - divisor) >> (Long.SIZE - 1)) & divisor);
        }
        /*
         * (1) When dividend >= 0, the remainder is dividend.
         * (2) Otherwise
         *      (2.1) When dividend < divisor, the remainder is dividend.
         *      (2.2) Otherwise the remainder is dividend - divisor
         *
         * A reasoning similar to the above shows that the returned value
         * is as expected.
         */
        return dividend - (((dividend & ~(dividend - divisor)) >> (Long.SIZE - 1)) & divisor);
    }

    // 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) {
        return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
    }

    /**
     * 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
     */
    @IntrinsicCandidate
    public static int numberOfLeadingZeros(long i) {
        int x = (int)(i >>> 32);
        return x == 0 ? 32 + Integer.numberOfLeadingZeros((int)i)
                : Integer.numberOfLeadingZeros(x);
    }

    /**
     * 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
     */
    @IntrinsicCandidate
    public static int numberOfTrailingZeros(long i) {
        int x = (int)i;
        return x == 0 ? 32 + Integer.numberOfTrailingZeros((int)(i >>> 32))
                : Integer.numberOfTrailingZeros(x);
    }

    /**
     * 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
     */
     @IntrinsicCandidate
     public static int bitCount(long i) {
        // HD, Figure 5-2
        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
     */
    @IntrinsicCandidate
    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;

        return reverseBytes(i);
    }

    /**
     * Returns the value obtained by compressing the bits of the
     * specified {@code long} value, {@code i}, in accordance with
     * the specified bit mask.
     * <p>
     * For each one-bit value {@code mb} of the mask, from least
     * significant to most significant, the bit value of {@code i} at
     * the same bit location as {@code mb} is assigned to the compressed
     * value contiguously starting from the least significant bit location.
     * All the upper remaining bits of the compressed value are set
     * to zero.
     *
     * @apiNote
     * Consider the simple case of compressing the digits of a hexadecimal
     * value:
     * {@snippet lang="java" :
     * // Compressing drink to food
     * compress(0xCAFEBABEL, 0xFF00FFF0L) == 0xCABABL
     * }
     * Starting from the least significant hexadecimal digit at position 0
     * from the right, the mask {@code 0xFF00FFF0} selects hexadecimal digits
     * at positions 1, 2, 3, 6 and 7 of {@code 0xCAFEBABE}. The selected digits
     * occur in the resulting compressed value contiguously from digit position
     * 0 in the same order.
     * <p>
     * The following identities all return {@code true} and are helpful to
     * understand the behaviour of {@code compress}:
     * {@snippet lang="java" :
     * // Returns 1 if the bit at position n is one
     * compress(x, 1L << n) == (x >> n & 1)
     *
     * // Logical shift right
     * compress(x, -1L << n) == x >>> n
     *
     * // Any bits not covered by the mask are ignored
     * compress(x, m) == compress(x & m, m)
     *
     * // Compressing a value by itself
     * compress(m, m) == (m == -1 || m == 0) ? m : (1L << bitCount(m)) - 1
     *
     * // Expanding then compressing with the same mask
     * compress(expand(x, m), m) == x & compress(m, m)
     * }
     * <p>
     * The Sheep And Goats (SAG) operation (see Hacker's Delight, Second Edition, section 7.7)
     * can be implemented as follows:
     * {@snippet lang="java" :
     * long compressLeft(long i, long mask) {
     *     // This implementation follows the description in Hacker's Delight which
     *     // is informative. A more optimal implementation is:
     *     //   Long.compress(i, mask) << -Long.bitCount(mask)
     *     return Long.reverse(
     *         Long.compress(Long.reverse(i), Long.reverse(mask)));
     * }
     *
     * long sag(long i, long mask) {
     *     return compressLeft(i, mask) | Long.compress(i, ~mask);
     * }
     *
     * // Separate the sheep from the goats
     * sag(0x00000000_CAFEBABEL, 0xFFFFFFFF_FF00FFF0L) == 0x00000000_CABABFEEL
     * }
     *
     * @param i the value whose bits are to be compressed
     * @param mask the bit mask
     * @return the compressed value
     * @see #expand
     * @since 19
     */
    @IntrinsicCandidate
    public static long compress(long i, long mask) {
        // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract

        i = i & mask; // Clear irrelevant bits
        long maskCount = ~mask << 1; // Count 0's to right

        for (int j = 0; j < 6; j++) {
            // Parallel prefix
            // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
            long maskPrefix = parallelSuffix(maskCount);
            // Bits to move
            long maskMove = maskPrefix & mask;
            // Compress mask
            mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
            // Bits of i to be moved
            long t = i & maskMove;
            // Compress i
            i = (i ^ t) | (t >>> (1 << j));
            // Adjust the mask count by identifying bits that have 0 to the right
            maskCount = maskCount & ~maskPrefix;
        }
        return i;
    }

    /**
     * Returns the value obtained by expanding the bits of the
     * specified {@code long} value, {@code i}, in accordance with
     * the specified bit mask.
     * <p>
     * For each one-bit value {@code mb} of the mask, from least
     * significant to most significant, the next contiguous bit value
     * of {@code i} starting at the least significant bit is assigned
     * to the expanded value at the same bit location as {@code mb}.
     * All other remaining bits of the expanded value are set to zero.
     *
     * @apiNote
     * Consider the simple case of expanding the digits of a hexadecimal
     * value:
     * {@snippet lang="java" :
     * expand(0x0000CABABL, 0xFF00FFF0L) == 0xCA00BAB0L
     * }
     * Starting from the least significant hexadecimal digit at position 0
     * from the right, the mask {@code 0xFF00FFF0} selects the first five
     * hexadecimal digits of {@code 0x0000CABAB}. The selected digits occur
     * in the resulting expanded value in order at positions 1, 2, 3, 6, and 7.
     * <p>
     * The following identities all return {@code true} and are helpful to
     * understand the behaviour of {@code expand}:
     * {@snippet lang="java" :
     * // Logically shift right the bit at position 0
     * expand(x, 1L << n) == (x & 1) << n
     *
     * // Logically shift right
     * expand(x, -1L << n) == x << n
     *
     * // Expanding all bits returns the mask
     * expand(-1L, m) == m
     *
     * // Any bits not covered by the mask are ignored
     * expand(x, m) == expand(x, m) & m
     *
     * // Compressing then expanding with the same mask
     * expand(compress(x, m), m) == x & m
     * }
     * <p>
     * The select operation for determining the position of the one-bit with
     * index {@code n} in a {@code long} value can be implemented as follows:
     * {@snippet lang="java" :
     * long select(long i, long n) {
     *     // the one-bit in i (the mask) with index n
     *     long nthBit = Long.expand(1L << n, i);
     *     // the bit position of the one-bit with index n
     *     return Long.numberOfTrailingZeros(nthBit);
     * }
     *
     * // The one-bit with index 0 is at bit position 1
     * select(0b10101010_10101010, 0) == 1
     * // The one-bit with index 3 is at bit position 7
     * select(0b10101010_10101010, 3) == 7
     * }
     *
     * @param i the value whose bits are to be expanded
     * @param mask the bit mask
     * @return the expanded value
     * @see #compress
     * @since 19
     */
    @IntrinsicCandidate
    public static long expand(long i, long mask) {
        // Save original mask
        long originalMask = mask;
        // Count 0's to right
        long maskCount = ~mask << 1;
        long maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        long maskMove1 = maskPrefix & mask;
        // Compress mask
        mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
        maskCount = maskCount & ~maskPrefix;

        maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        long maskMove2 = maskPrefix & mask;
        // Compress mask
        mask = (mask ^ maskMove2) | (maskMove2 >>> (1 << 1));
        maskCount = maskCount & ~maskPrefix;

        maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        long maskMove3 = maskPrefix & mask;
        // Compress mask
        mask = (mask ^ maskMove3) | (maskMove3 >>> (1 << 2));
        maskCount = maskCount & ~maskPrefix;

        maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        long maskMove4 = maskPrefix & mask;
        // Compress mask
        mask = (mask ^ maskMove4) | (maskMove4 >>> (1 << 3));
        maskCount = maskCount & ~maskPrefix;

        maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        long maskMove5 = maskPrefix & mask;
        // Compress mask
        mask = (mask ^ maskMove5) | (maskMove5 >>> (1 << 4));
        maskCount = maskCount & ~maskPrefix;

        maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        long maskMove6 = maskPrefix & mask;

        long t = i << (1 << 5);
        i = (i & ~maskMove6) | (t & maskMove6);
        t = i << (1 << 4);
        i = (i & ~maskMove5) | (t & maskMove5);
        t = i << (1 << 3);
        i = (i & ~maskMove4) | (t & maskMove4);
        t = i << (1 << 2);
        i = (i & ~maskMove3) | (t & maskMove3);
        t = i << (1 << 1);
        i = (i & ~maskMove2) | (t & maskMove2);
        t = i << (1 << 0);
        i = (i & ~maskMove1) | (t & maskMove1);

        // Clear irrelevant bits
        return i & originalMask;
    }

    @ForceInline
    private static long parallelSuffix(long maskCount) {
        long maskPrefix = maskCount ^ (maskCount << 1);
        maskPrefix = maskPrefix ^ (maskPrefix << 2);
        maskPrefix = maskPrefix ^ (maskPrefix << 4);
        maskPrefix = maskPrefix ^ (maskPrefix << 8);
        maskPrefix = maskPrefix ^ (maskPrefix << 16);
        maskPrefix = maskPrefix ^ (maskPrefix << 32);
        return maskPrefix;
    }

    /**
     * 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
     */
    @IntrinsicCandidate
    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);
    }

    /**
     * Returns an {@link Optional} containing the nominal descriptor for this
     * instance, which is the instance itself.
     *
     * @return an {@link Optional} describing the {@linkplain Long} instance
     * @since 12
     */
    @Override
    public Optional<Long> describeConstable() {
        return Optional.of(this);
    }

    /**
     * Resolves this instance as a {@link ConstantDesc}, the result of which is
     * the instance itself.
     *
     * @param lookup ignored
     * @return the {@linkplain Long} instance
     * @since 12
     */
    @Override
    public Long resolveConstantDesc(MethodHandles.Lookup lookup) {
        return this;
    }

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