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	/*
	* Copyright (c) 1994, 2021, Oracle and/or its affiliates. All rights reserved.
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
	* or visit www.oracle.com if you need additional information or have any
	* questions.
	*/

	package java.lang;

	import java.lang.annotation.Native;
	import java.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.vm.annotation.IntrinsicCandidate;

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

	/**
	* 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>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 <i>Hacker's
	* Delight</i>, (Addison Wesley, 2002).
	*
	* @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
	*/
	@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);

	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 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 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 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 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 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 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 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 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 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);
	}

	static String fastUUID(long lsb, long msb) {
	if (COMPACT_STRINGS) {
	byte[] buf = new byte[36];
	formatUnsignedLong0(lsb, 4, buf, 24, 12);
	formatUnsignedLong0(lsb >>> 48, 4, buf, 19, 4);
	formatUnsignedLong0(msb, 4, buf, 14, 4);
	formatUnsignedLong0(msb >>> 16, 4, buf, 9, 4);
	formatUnsignedLong0(msb >>> 32, 4, buf, 0, 8);

	buf[23] = '-';
	buf[18] = '-';
	buf[13] = '-';
	buf[8] = '-';

	return new String(buf, LATIN1);
	} else {
	byte[] buf = new byte[72];

	formatUnsignedLong0UTF16(lsb, 4, buf, 24, 12);
	formatUnsignedLong0UTF16(lsb >>> 48, 4, buf, 19, 4);
	formatUnsignedLong0UTF16(msb, 4, buf, 14, 4);
	formatUnsignedLong0UTF16(msb >>> 16, 4, buf, 9, 4);
	formatUnsignedLong0UTF16(msb >>> 32, 4, buf, 0, 8);

	StringUTF16.putChar(buf, 23, '-');
	StringUTF16.putChar(buf, 18, '-');
	StringUTF16.putChar(buf, 13, '-');
	StringUTF16.putChar(buf, 8, '-');

	return new String(buf, UTF16);
	}
	}

	/**
	* 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 10.
	*/
	public static String toString(long i) {
	int size = stringSize(i);
	if (COMPACT_STRINGS) {
	byte[] buf = new byte[size];
	getChars(i, size, buf);
	return new String(buf, LATIN1);
	} else {
	byte[] buf = new byte[size * 2];
	StringUTF16.getChars(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);
	}

	/**
	* Places characters representing the long 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.
	*
	* @implNote This method converts positive inputs into negative
	* values, to cover the Long.MIN_VALUE case. Converting otherwise
	* (negative to positive) will expose -Long.MIN_VALUE that overflows
	* long.
	*
	* @param i value to convert
	* @param index next index, after the least significant digit
	* @param buf target buffer, Latin1-encoded
	* @return index of the most significant digit or minus sign, if present
	*/
	static int getChars(long i, int index, byte[] buf) {
	long q;
	int r;
	int charPos = index;

	boolean negative = (i < 0);
	if (!negative) {
	i = -i;
	}

	// Get 2 digits/iteration using longs until quotient fits into an int
	while (i <= Integer.MIN_VALUE) {
	q = i / 100;
	r = (int)((q * 100) - i);
	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 <= -100) {
	q2 = i2 / 100;
	r = (q2 * 100) - i2;
	i2 = q2;
	buf[--charPos] = Integer.DigitOnes[r];
	buf[--charPos] = Integer.DigitTens[r];
	}

	// We know there are at most two digits left at this point.
	q2 = i2 / 10;
	r = (q2 * 10) - i2;
	buf[--charPos] = (byte)('0' + r);

	// Whatever left is the remaining digit.
	if (q2 < 0) {
	buf[--charPos] = (byte)('0' - q2);
	}

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

	/**
	* Returns the string representation size for a given long value.
	*
	* @param x long value
	* @return string size
	*
	* @implNote There are other ways to compute this: e.g. binary search,
	* but values are biased heavily towards zero, and therefore linear search
	* wins. The iteration results are also routinely inlined in the generated
	* code after loop unrolling.
	*/
	static int stringSize(long x) {
	int d = 1;
	if (x >= 0) {
	d = 0;
	x = -x;
	}
	long p = -10;
	for (int i = 1; i < 19; i++) {
	if (x > p)
	return i + d;
	p = 10 * p;
	}
	return 19 + d;
	}

	/**
	* 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("radix " + radix +
	" less than Character.MIN_RADIX");
	}
	if (radix > Character.MAX_RADIX) {
	throw new NumberFormatException("radix " + radix +
	" greater than Character.MAX_RADIX");
	}

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

	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, radix);
	}

	if (len == 1) { // Cannot have lone "+" or "-"
	throw NumberFormatException.forInputString(s, radix);
	}
	i++;
	}
	long multmin = limit / radix;
	long result = 0;
	while (i < len) {
	// Accumulating negatively avoids surprises near MAX_VALUE
	int digit = Character.digit(s.charAt(i++),radix);
	if (digit < 0 \|\| result < multmin) {
	throw NumberFormatException.forInputString(s, radix);
	}
	result *= radix;
	if (result < limit + digit) {
	throw NumberFormatException.forInputString(s, radix);
	}
	result -= digit;
	}
	return negative ? result : -result;
	} else {
	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);

	if (beginIndex < 0 \|\| beginIndex > endIndex \|\| endIndex > s.length()) {
	throw new IndexOutOfBoundsException();
	}
	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");
	}

	boolean negative = false;
	int i = beginIndex;
	long limit = -Long.MAX_VALUE;

	if (i < endIndex) {
	char firstChar = s.charAt(i);
	if (firstChar < '0') { // Possible leading "+" or "-"
	if (firstChar == '-') {
	negative = true;
	limit = Long.MIN_VALUE;
	} else if (firstChar != '+') {
	throw NumberFormatException.forCharSequence(s, beginIndex,
	endIndex, i);
	}
	i++;
	}
	if (i >= endIndex) { // Cannot have lone "+", "-" or ""
	throw NumberFormatException.forCharSequence(s, beginIndex,
	endIndex, i);
	}
	long multmin = limit / radix;
	long result = 0;
	while (i < endIndex) {
	// Accumulating negatively avoids surprises near MAX_VALUE
	int digit = Character.digit(s.charAt(i), radix);
	if (digit < 0 \|\| result < multmin) {
	throw NumberFormatException.forCharSequence(s, beginIndex,
	endIndex, i);
	}
	result *= radix;
	if (result < limit + digit) {
	throw NumberFormatException.forCharSequence(s, beginIndex,
	endIndex, i);
	}
	i++;
	result -= digit;
	}
	return negative ? result : -result;
	} else {
	throw new NumberFormatException("");
	}
	}

	/**
	* 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");
	}

	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, 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;

	/*
	* Test leftmost bits of multiprecision extension of first*radix
	* for overflow. The number of bits needed is defined by
	* GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
	* int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
	* overflow is tested by splitting guard in the ranges
	* guard < 92, 92 <= guard < 128, and 128 <= guard, where
	* 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
	* on a value which does not include a prime factor in the legal
	* radix range.
	*/
	int guard = radix * (int) (first >>> 57);
	if (guard >= 128 \|\|
	(result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
	/*
	* For purposes of exposition, the programmatic statements
	* below should be taken to be multi-precision, i.e., not
	* subject to overflow.
	*
	* A) Condition guard >= 128:
	* If guard >= 128 then firstradix >= 2^7 2^57 = 2^64
	* hence always overflow.
	*
	* B) Condition guard < 92:
	* Define left7 = first >>> 57.
	* Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
	* result <= (radixleft7)2^57 + radix*(2^57 - 1) + second.
	* Thus if radix*left7 < 92, radix <= 36, and second < 36,
	* then result < 922^57 + 36(2^57 - 1) + 36 = 2^64 hence
	* never overflow.
	*
	* C) Condition 92 <= guard < 128:
	* firstradix + second >= radixleft7*2^57 + second
	* so that firstradix + second >= 922^57 + 0 > 2^63
	*
	* D) Condition guard < 128:
	* radixfirst <= (radixleft7) * 2^57 + radix*(2^57 - 1)
	* so
	* radixfirst + second <= (radixleft7) * 2^57 + radix*(2^57 - 1) + 36
	* thus
	* radixfirst + second < 128 2^57 + 36*2^57 - radix + 36
	* whence
	* radixfirst + second < 2^64 + 2^62^57 = 2^64 + 2^63
	*
	* E) Conditions C, D, and result >= 0:
	* C and D combined imply the mathematical result
	* 2^63 < first*radix + second < 2^64 + 2^63. The lower
	* bound is therefore negative as a signed long, but the
	* upper bound is too small to overflow again after the
	* signed long overflows to positive above 2^64 - 1. Hence
	* result >= 0 implies overflow given C and D.
	*/
	throw new NumberFormatException(String.format("String value %s exceeds " +
	"range of unsigned long.", s));
	}
	return result;
	}
	} else {
	throw NumberFormatException.forInputString(s, radix);
	}
	}

	/**
	* 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);

	if (beginIndex < 0 \|\| beginIndex > endIndex \|\| endIndex > s.length()) {
	throw new IndexOutOfBoundsException();
	}
	int start = beginIndex, len = endIndex - beginIndex;

	if (len > 0) {
	char firstChar = s.charAt(start);
	if (firstChar == '-') {
	throw new NumberFormatException(String.format("Illegal leading minus sign " +
	"on unsigned string %s.", s.subSequence(start, start + len)));
	} 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, start, start + len, radix);
	}

	// No need for range checks on end due to testing above.
	long first = parseLong(s, start, start + len - 1, radix);
	int second = Character.digit(s.charAt(start + len - 1), radix);
	if (second < 0) {
	throw new NumberFormatException("Bad digit at end of " +
	s.subSequence(start, start + len));
	}
	long result = first * radix + second;

	/*
	* Test leftmost bits of multiprecision extension of first*radix
	* for overflow. The number of bits needed is defined by
	* GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
	* int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
	* overflow is tested by splitting guard in the ranges
	* guard < 92, 92 <= guard < 128, and 128 <= guard, where
	* 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
	* on a value which does not include a prime factor in the legal
	* radix range.
	*/
	int guard = radix * (int) (first >>> 57);
	if (guard >= 128 \|\|
	(result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
	/*
	* For purposes of exposition, the programmatic statements
	* below should be taken to be multi-precision, i.e., not
	* subject to overflow.
	*
	* A) Condition guard >= 128:
	* If guard >= 128 then firstradix >= 2^7 2^57 = 2^64
	* hence always overflow.
	*
	* B) Condition guard < 92:
	* Define left7 = first >>> 57.
	* Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
	* result <= (radixleft7)2^57 + radix*(2^57 - 1) + second.
	* Thus if radix*left7 < 92, radix <= 36, and second < 36,
	* then result < 922^57 + 36(2^57 - 1) + 36 = 2^64 hence
	* never overflow.
	*
	* C) Condition 92 <= guard < 128:
	* firstradix + second >= radixleft7*2^57 + second
	* so that firstradix + second >= 922^57 + 0 > 2^63
	*
	* D) Condition guard < 128:
	* radixfirst <= (radixleft7) * 2^57 + radix*(2^57 - 1)
	* so
	* radixfirst + second <= (radixleft7) * 2^57 + radix*(2^57 - 1) + 36
	* thus
	* radixfirst + second < 128 2^57 + 36*2^57 - radix + 36
	* whence
	* radixfirst + second < 2^64 + 2^62^57 = 2^64 + 2^63
	*
	* E) Conditions C, D, and result >= 0:
	* C and D combined imply the mathematical result
	* 2^63 < first*radix + second < 2^64 + 2^63. The lower
	* bound is therefore negative as a signed long, but the
	* upper bound is too small to overflow again after the
	* signed long overflows to positive above 2^64 - 1. Hence
	* result >= 0 implies overflow given C and D.
	*/
	throw new NumberFormatException(String.format("String value %s exceeds " +
	"range of unsigned long.", s.subSequence(start, start + len)));
	}
	return result;
	}
	} else {
	throw NumberFormatException.forInputString("", radix);
	}
	}

	/**
	* 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 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;
	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 \|\| archivedCache.length != size) {
	Long[] c = new Long[size];
	long value = -128;
	for(int i = 0; i < size; i++) {
	c[i] = new Long(value++);
	}
	archivedCache = c;
	}
	cache = archivedCache;
	}
	}

	/**
	* 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 = 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.
	*
	* @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 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) {
	/* 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
	*/
	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
	*/
	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 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;
	}

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