/*
 * Copyright (c) 1994, 2025, 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 jdk.internal.misc.CDS;
import jdk.internal.misc.VM;
import jdk.internal.util.DecimalDigits;
import jdk.internal.vm.annotation.ForceInline;
import jdk.internal.vm.annotation.IntrinsicCandidate;
import jdk.internal.vm.annotation.Stable;

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

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 Integer} class is the {@linkplain
 * java.lang##wrapperClass wrapper class} for values of the primitive
 * type {@code int}. An object of type {@code Integer} contains a
 * single field whose type is {@code int}.
 *
 * <p>In addition, this class provides several methods for converting
 * an {@code int} to a {@code String} and a {@code String} to an
 * {@code int}, as well as other constants and methods useful when
 * dealing with an {@code int}.
 *
 * <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(int) highestOneBit} and
 * {@link #numberOfTrailingZeros(int) 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 Integer extends Number
        implements Comparable<Integer>, Constable, ConstantDesc {
    /**
     * A constant holding the minimum value an {@code int} can
     * have, -2<sup>31</sup>.
     */
    @Native public static final int   MIN_VALUE = 0x80000000;

    /**
     * A constant holding the maximum value an {@code int} can
     * have, 2<sup>31</sup>-1.
     */
    @Native public static final int   MAX_VALUE = 0x7fffffff;

    /**
     * The {@code Class} instance representing the primitive type
     * {@code int}.
     *
     * @since   1.1
     */
    public static final Class<Integer> TYPE = Class.getPrimitiveClass("int");

    /**
     * All possible chars for representing a number as a String
     */
    @Stable
    static final byte[] digits = {
        '0' , '1' , '2' , '3' , '4' , '5' ,
        '6' , '7' , '8' , '9' , 'a' , 'b' ,
        'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
        'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
        'o' , 'p' , 'q' , 'r' , 's' , 't' ,
        'u' , 'v' , 'w' , 'x' , 'y' , 'z'
    };

    /**
     * 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 character {@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 Integer.toString(n, 16).toUpperCase()}
     * </blockquote>
     *
     * @param   i       an integer 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(int i, int radix) {
        if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
            radix = 10;

        /* Use the faster version */
        if (radix == 10) {
            return toString(i);
        }

        if (COMPACT_STRINGS) {
            byte[] buf = new byte[33];
            boolean negative = (i < 0);
            int charPos = 32;

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

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

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

            return StringLatin1.newString(buf, charPos, (33 - charPos));
        }
        return toStringUTF16(i, radix);
    }

    private static String toStringUTF16(int i, int radix) {
        byte[] buf = new byte[33 * 2];
        boolean negative = (i < 0);
        int charPos = 32;
        if (!negative) {
            i = -i;
        }
        while (i <= -radix) {
            StringUTF16.putChar(buf, charPos--, digits[-(i % radix)]);
            i = i / radix;
        }
        StringUTF16.putChar(buf, charPos, digits[-i]);

        if (negative) {
            StringUTF16.putChar(buf, --charPos, '-');
        }
        return StringUTF16.newString(buf, charPos, (33 - 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(int, 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(int, int)
     * @since 1.8
     */
    public static String toUnsignedString(int i, int radix) {
        return Long.toUnsignedString(toUnsignedLong(i), radix);
    }

    /**
     * Returns a string representation of the integer argument as an
     * unsigned integer in base&nbsp;16.
     *
     * <p>The unsigned integer value is the argument plus 2<sup>32</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
     * Integer#parseUnsignedInt(String, int)
     * Integer.parseUnsignedInt(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 Integer.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   an integer to be converted to a string.
     * @return  the string representation of the unsigned integer value
     *          represented by the argument in hexadecimal (base&nbsp;16).
     * @see java.util.HexFormat
     * @see #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since   1.0.2
     */
    public static String toHexString(int i) {
        return toUnsignedString0(i, 4);
    }

    /**
     * Returns a string representation of the integer argument as an
     * unsigned integer in base&nbsp;8.
     *
     * <p>The unsigned integer value is the argument plus 2<sup>32</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
     * Integer#parseUnsignedInt(String, int)
     * Integer.parseUnsignedInt(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   an integer to be converted to a string.
     * @return  the string representation of the unsigned integer value
     *          represented by the argument in octal (base&nbsp;8).
     * @see #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since   1.0.2
     */
    public static String toOctalString(int i) {
        return toUnsignedString0(i, 3);
    }

    /**
     * Returns a string representation of the integer argument as an
     * unsigned integer in base&nbsp;2.
     *
     * <p>The unsigned integer value is the argument plus 2<sup>32</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
     * Integer#parseUnsignedInt(String, int)
     * Integer.parseUnsignedInt(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   an integer to be converted to a string.
     * @return  the string representation of the unsigned integer value
     *          represented by the argument in binary (base&nbsp;2).
     * @see #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since   1.0.2
     */
    public static String toBinaryString(int i) {
        return toUnsignedString0(i, 1);
    }

    /**
     * Convert the integer to an unsigned number.
     */
    private static String toUnsignedString0(int val, int shift) {
        // assert shift > 0 && shift <=5 : "Illegal shift value";
        int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
        int chars = Math.max(((mag + (shift - 1)) / shift), 1);
        if (COMPACT_STRINGS) {
            byte[] buf = new byte[chars];
            formatUnsignedInt(val, shift, buf, chars);
            return new String(buf, LATIN1);
        } else {
            byte[] buf = new byte[chars * 2];
            formatUnsignedIntUTF16(val, shift, buf, chars);
            return new String(buf, UTF16);
        }
    }

    /**
     * Format an {@code int} (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 int 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 len the number of characters to write
     */
    private static void formatUnsignedInt(int val, int shift, byte[] buf, int len) {
        int charPos = len;
        int radix = 1 << shift;
        int mask = radix - 1;
        do {
            buf[--charPos] = Integer.digits[val & mask];
            val >>>= shift;
        } while (charPos > 0);
    }

    /**
     * Format an {@code int} (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 int 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 len the number of characters to write
     */
    private static void formatUnsignedIntUTF16(int val, int shift, byte[] buf, int len) {
        int charPos = len;
        int radix = 1 << shift;
        int mask = radix - 1;
        do {
            StringUTF16.putChar(buf, --charPos, Integer.digits[val & mask]);
            val >>>= shift;
        } while (charPos > 0);
    }

    /**
     * Returns a {@code String} object representing the
     * specified integer. The argument is converted to signed decimal
     * representation and returned as a string, exactly as if the
     * argument and radix 10 were given as arguments to the {@link
     * #toString(int, int)} method.
     *
     * @param   i   an integer to be converted.
     * @return  a string representation of the argument in base&nbsp;10.
     */
    @IntrinsicCandidate
    public static String toString(int i) {
        int size = DecimalDigits.stringSize(i);
        if (COMPACT_STRINGS) {
            byte[] buf = new byte[size];
            DecimalDigits.uncheckedGetCharsLatin1(i, size, buf);
            return new String(buf, LATIN1);
        } else {
            byte[] buf = new byte[size * 2];
            DecimalDigits.uncheckedGetCharsUTF16(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(int,
     * int)} method.
     *
     * @param   i  an integer to be converted to an unsigned string.
     * @return  an unsigned string representation of the argument.
     * @see     #toUnsignedString(int, int)
     * @since 1.8
     */
    public static String toUnsignedString(int i) {
        return Long.toString(toUnsignedLong(i));
    }

    /**
     * Parses the string argument as a signed integer 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 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 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 int}.
     * </ul>
     *
     * <p>Examples:
     * <blockquote><pre>
     * parseInt("0", 10) returns 0
     * parseInt("473", 10) returns 473
     * parseInt("+42", 10) returns 42
     * parseInt("-0", 10) returns 0
     * parseInt("-FF", 16) returns -255
     * parseInt("1100110", 2) returns 102
     * parseInt("2147483647", 10) returns 2147483647
     * parseInt("-2147483648", 10) returns -2147483648
     * parseInt("2147483648", 10) throws a NumberFormatException
     * parseInt("99", 8) throws a NumberFormatException
     * parseInt("Kona", 10) throws a NumberFormatException
     * parseInt("Kona", 27) returns 411787
     * </pre></blockquote>
     *
     * @param      s   the {@code String} containing the integer
     *                  representation to be parsed
     * @param      radix   the radix to be used while parsing {@code s}.
     * @return     the integer represented by the string argument in the
     *             specified radix.
     * @throws     NumberFormatException if the {@code String}
     *             does not contain a parsable {@code int}.
     */
    public static int parseInt(String s, int radix)
                throws NumberFormatException {
        /*
         * WARNING: This method may be invoked early during VM initialization
         * before IntegerCache is initialized. Care must be taken to not use
         * the valueOf method.
         */

        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) {
            int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
            int multmin = limit / radix;
            int 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 <= 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 int} 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 int}
     *                  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 int} 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 int} 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 int parseInt(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;
        int i = beginIndex;
        char firstChar = s.charAt(i++);
        if (firstChar != '-' && firstChar != '+') {
            digit = digit(firstChar, radix);
        }
        if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
            int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
            int multmin = limit / radix;
            int 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 <= 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 integer. 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 integer value is
     * returned, exactly as if the argument and the radix 10 were
     * given as arguments to the {@link #parseInt(java.lang.String,
     * int)} method.
     *
     * @param s    a {@code String} containing the {@code int}
     *             representation to be parsed
     * @return     the integer value represented by the argument in decimal.
     * @throws     NumberFormatException  if the string does not contain a
     *               parsable integer.
     */
    public static int parseInt(String s) throws NumberFormatException {
        return parseInt(s, 10);
    }

    /**
     * Parses the string argument as an unsigned integer 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 int}, 2<sup>32</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 integer represented by the string argument in the
     *             specified radix.
     * @throws     NumberFormatException if the {@code String}
     *             does not contain a parsable {@code int}.
     * @since 1.8
     */
    public static int parseUnsignedInt(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) {
            int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
            int result = digit & 0xFF;
            boolean inRange = true;
            while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
                    && (inRange = compareUnsigned(result, multmax) < 0
                        || result == multmax && digit < -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 int.", s));
    }

    /**
     * Parses the {@link CharSequence} argument as an unsigned {@code int} 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 int} 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 int} 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 int} 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 int parseUnsignedInt(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) {
            int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
            int result = digit & 0xFF;
            boolean inRange = true;
            while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
                    && (inRange = compareUnsigned(result, multmax) < 0
                        || result == multmax && digit < -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 int.", s));
    }

    /**
     * Parses the string argument as an unsigned decimal integer. 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
     * #parseUnsignedInt(java.lang.String, int)} method.
     *
     * @param s   a {@code String} containing the unsigned {@code int}
     *            representation to be parsed
     * @return    the unsigned integer value represented by the argument in decimal.
     * @throws    NumberFormatException  if the string does not contain a
     *            parsable unsigned integer.
     * @since 1.8
     */
    public static int parseUnsignedInt(String s) throws NumberFormatException {
        return parseUnsignedInt(s, 10);
    }

    /**
     * Returns an {@code Integer} 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 integer in the radix
     * specified by the second argument, exactly as if the arguments
     * were given to the {@link #parseInt(java.lang.String, int)}
     * method. The result is an {@code Integer} object that
     * represents the integer value specified by the string.
     *
     * <p>In other words, this method returns an {@code Integer}
     * object equal to the value of:
     *
     * <blockquote>
     *  {@code Integer.valueOf(Integer.parseInt(s, radix))}
     * </blockquote>
     *
     * @param      s   the string to be parsed.
     * @param      radix the radix to be used in interpreting {@code s}
     * @return     an {@code Integer} 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 int}.
     */
    public static Integer valueOf(String s, int radix) throws NumberFormatException {
        return Integer.valueOf(parseInt(s,radix));
    }

    /**
     * Returns an {@code Integer} object holding the
     * value of the specified {@code String}. The argument is
     * interpreted as representing a signed decimal integer, exactly
     * as if the argument were given to the {@link
     * #parseInt(java.lang.String)} method. The result is an
     * {@code Integer} object that represents the integer value
     * specified by the string.
     *
     * <p>In other words, this method returns an {@code Integer}
     * object equal to the value of:
     *
     * <blockquote>
     *  {@code Integer.valueOf(Integer.parseInt(s))}
     * </blockquote>
     *
     * @param      s   the string to be parsed.
     * @return     an {@code Integer} object holding the value
     *             represented by the string argument.
     * @throws     NumberFormatException  if the string cannot be parsed
     *             as an integer.
     */
    public static Integer valueOf(String s) throws NumberFormatException {
        return Integer.valueOf(parseInt(s, 10));
    }

    /**
     * Cache to support the object identity semantics of autoboxing for values between
     * -128 and 127 (inclusive) as required by JLS.
     *
     * The cache is initialized on first usage.  The size of the cache
     * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
     * During VM initialization, java.lang.Integer.IntegerCache.high property
     * may be set and saved in the private system properties in the
     * jdk.internal.misc.VM class.
     *
     * WARNING: The cache is archived with CDS and reloaded from the shared
     * archive at runtime. The archived cache (Integer[]) and Integer objects
     * reside in the closed archive heap regions. Care should be taken when
     * changing the implementation and the cache array should not be assigned
     * with new Integer object(s) after initialization.
     */

    private static final class IntegerCache {
        static final int low = -128;
        static final int high;

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

        static {
            // high value may be configured by property
            int h = 127;
            String integerCacheHighPropValue =
                VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
            if (integerCacheHighPropValue != null) {
                try {
                    h = Math.max(parseInt(integerCacheHighPropValue), 127);
                    // Maximum array size is Integer.MAX_VALUE
                    h = Math.min(h, Integer.MAX_VALUE - (-low) -1);
                } catch( NumberFormatException nfe) {
                    // If the property cannot be parsed into an int, ignore it.
                }
            }
            high = h;

            // Load IntegerCache.archivedCache from archive, if possible
            CDS.initializeFromArchive(IntegerCache.class);
            int size = (high - low) + 1;

            // Use the archived cache if it exists and is large enough
            if (archivedCache == null || size > archivedCache.length) {
                Integer[] c = new Integer[size];
                int j = low;
                // If archive has Integer cache, we must use all instances from it.
                // Otherwise, the identity checks between archived Integers and
                // runtime-cached Integers would fail.
                int archivedSize = (archivedCache == null) ? 0 : archivedCache.length;
                for (int i = 0; i < archivedSize; i++) {
                    c[i] = archivedCache[i];
                    assert j == archivedCache[i];
                    j++;
                }
                // Fill the rest of the cache.
                for (int i = archivedSize; i < size; i++) {
                    c[i] = new Integer(j++);
                }
                archivedCache = c;
            }
            cache = archivedCache;
            // range [-128, 127] must be interned (JLS7 5.1.7)
            assert IntegerCache.high >= 127;
        }

        private IntegerCache() {}
    }

    /**
     * Returns an {@code Integer} instance representing the specified
     * {@code int} value.  If a new {@code Integer} instance is not
     * required, this method should generally be used in preference to
     * the constructor {@link #Integer(int)}, 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  i an {@code int} value.
     * @return an {@code Integer} instance representing {@code i}.
     * @since  1.5
     */
    @IntrinsicCandidate
    public static Integer valueOf(int i) {
        if (i >= IntegerCache.low && i <= IntegerCache.high)
            return IntegerCache.cache[i + (-IntegerCache.low)];
        return new Integer(i);
    }

    /**
     * The value of the {@code Integer}.
     *
     * @serial
     */
    private final int value;

    /**
     * Constructs a newly allocated {@code Integer} object that
     * represents the specified {@code int} value.
     *
     * @param   value   the value to be represented by the
     *                  {@code Integer} object.
     *
     * @deprecated
     * It is rarely appropriate to use this constructor. The static factory
     * {@link #valueOf(int)} is generally a better choice, as it is
     * likely to yield significantly better space and time performance.
     */
    @Deprecated(since="9")
    public Integer(int value) {
        this.value = value;
    }

    /**
     * Constructs a newly allocated {@code Integer} object that
     * represents the {@code int} value indicated by the
     * {@code String} parameter. The string is converted to an
     * {@code int} value in exactly the manner used by the
     * {@code parseInt} method for radix 10.
     *
     * @param   s   the {@code String} to be converted to an {@code Integer}.
     * @throws      NumberFormatException if the {@code String} does not
     *              contain a parsable integer.
     *
     * @deprecated
     * It is rarely appropriate to use this constructor.
     * Use {@link #parseInt(String)} to convert a string to a
     * {@code int} primitive, or use {@link #valueOf(String)}
     * to convert a string to an {@code Integer} object.
     */
    @Deprecated(since="9")
    public Integer(String s) throws NumberFormatException {
        this.value = parseInt(s, 10);
    }

    /**
     * Returns the value of this {@code Integer} 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 Integer} 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 Integer} as an
     * {@code int}.
     */
    @IntrinsicCandidate
    public int intValue() {
        return value;
    }

    /**
     * Returns the value of this {@code Integer} as a {@code long}
     * after a widening primitive conversion.
     * @jls 5.1.2 Widening Primitive Conversion
     * @see Integer#toUnsignedLong(int)
     */
    public long longValue() {
        return (long)value;
    }

    /**
     * Returns the value of this {@code Integer} 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 Integer} 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 Integer}'s value. The value is converted to signed
     * decimal representation and returned as a string, exactly as if
     * the integer value were given as an argument to the {@link
     * java.lang.Integer#toString(int)} 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 Integer}.
     *
     * @return  a hash code value for this object, equal to the
     *          primitive {@code int} value represented by this
     *          {@code Integer} object.
     */
    @Override
    public int hashCode() {
        return Integer.hashCode(value);
    }

    /**
     * Returns a hash code for an {@code int} value; compatible with
     * {@code Integer.hashCode()}.
     *
     * @param value the value to hash
     * @since 1.8
     *
     * @return a hash code value for an {@code int} value.
     */
    public static int hashCode(int value) {
        return value;
    }

    /**
     * Compares this object to the specified object.  The result is
     * {@code true} if and only if the argument is not
     * {@code null} and is an {@code Integer} object that
     * contains the same {@code int} 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 Integer i) {
            return value == i.intValue();
        }
        return false;
    }

    /**
     * Determines the integer 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 an integer
     * value using the grammar supported by {@link Integer#decode decode} and
     * an {@code Integer} 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 an {@code Integer}
     * object equal to the value of:
     *
     * <blockquote>
     *  {@code getInteger(nm, null)}
     * </blockquote>
     *
     * @param   nm   property name.
     * @return  the {@code Integer} 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 Integer getInteger(String nm) {
        return getInteger(nm, null);
    }

    /**
     * Determines the integer 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 an integer
     * value using the grammar supported by {@link Integer#decode decode} and
     * an {@code Integer} object representing this value is returned.
     *
     * <p>The second argument is the default value. An {@code Integer} 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
     * {@code null}.
     *
     * <p>In other words, this method returns an {@code Integer} object
     * equal to the value of:
     *
     * <blockquote>
     *  {@code getInteger(nm, Integer.valueOf(val))}
     * </blockquote>
     *
     * but in practice it may be implemented in a manner such as:
     *
     * <blockquote><pre>
     * Integer result = getInteger(nm, null);
     * return (result == null) ? Integer.valueOf(val) : result;
     * </pre></blockquote>
     *
     * to avoid the unnecessary allocation of an {@code Integer}
     * object when the default value is not needed.
     *
     * @param   nm   property name.
     * @param   val   default value.
     * @return  the {@code Integer} 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 Integer getInteger(String nm, int val) {
        Integer result = getInteger(nm, null);
        return (result == null) ? Integer.valueOf(val) : result;
    }

    /**
     * Returns the integer 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 an
     * integer value, as per the {@link Integer#decode decode} method,
     * and an {@code Integer} 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 by 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>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 Integer} value of the property.
     * @see     System#getProperty(java.lang.String)
     * @see     System#getProperty(java.lang.String, java.lang.String)
     */
    public static Integer getInteger(String nm, Integer val) {
        String v = nm != null && !nm.isEmpty() ? System.getProperty(nm) : null;
        if (v != null) {
            try {
                return Integer.decode(v);
            } catch (NumberFormatException e) {
            }
        }
        return val;
    }

    /**
     * Decodes a {@code String} into an {@code Integer}.
     * 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
     * Integer.parseInt} 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    an {@code Integer} object holding the {@code int}
     *             value represented by {@code nm}
     * @throws    NumberFormatException  if the {@code String} does not
     *            contain a parsable integer.
     * @see java.lang.Integer#parseInt(java.lang.String, int)
     */
    public static Integer decode(String nm) throws NumberFormatException {
        int radix = 10;
        int index = 0;
        boolean negative = false;
        int 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 = parseInt(nm, index, nm.length(), radix);
            result = negative ? -result : result;
        } catch (NumberFormatException e) {
            // If number is Integer.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 = parseInt(constant, radix);
        }
        return result;
    }

    /**
     * Compares two {@code Integer} objects numerically.
     *
     * @param   anotherInteger   the {@code Integer} to be compared.
     * @return  the value {@code 0} if this {@code Integer} is
     *          equal to the argument {@code Integer}; a value less than
     *          {@code 0} if this {@code Integer} is numerically less
     *          than the argument {@code Integer}; and a value greater
     *          than {@code 0} if this {@code Integer} is numerically
     *           greater than the argument {@code Integer} (signed
     *           comparison).
     * @since   1.2
     */
    public int compareTo(Integer anotherInteger) {
        return compare(this.value, anotherInteger.value);
    }

    /**
     * Compares two {@code int} values numerically.
     * The value returned is identical to what would be returned by:
     * <pre>
     *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
     * </pre>
     *
     * @param  x the first {@code int} to compare
     * @param  y the second {@code int} 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(int x, int y) {
        return (x < y) ? -1 : ((x == y) ? 0 : 1);
    }

    /**
     * Compares two {@code int} values numerically treating the values
     * as unsigned.
     *
     * @param  x the first {@code int} to compare
     * @param  y the second {@code int} 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(int x, int y) {
        return compare(x + MIN_VALUE, y + MIN_VALUE);
    }

    /**
     * Converts the argument to a {@code long} by an unsigned
     * conversion.  In an unsigned conversion to a {@code long}, the
     * high-order 32 bits of the {@code long} are zero and the
     * low-order 32 bits are equal to the bits of the integer
     * argument.
     *
     * Consequently, zero and positive {@code int} values are mapped
     * to a numerically equal {@code long} value and negative {@code
     * int} values are mapped to a {@code long} value equal to the
     * input plus 2<sup>32</sup>.
     *
     * @param  x the value to convert to an unsigned {@code long}
     * @return the argument converted to {@code long} by an unsigned
     *         conversion
     * @since 1.8
     */
    public static long toUnsignedLong(int x) {
        return ((long) x) & 0xffffffffL;
    }

    /**
     * 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 int divideUnsigned(int dividend, int divisor) {
        // In lieu of tricky code, for now just use long arithmetic.
        return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
    }

    /**
     * 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 int remainderUnsigned(int dividend, int divisor) {
        // In lieu of tricky code, for now just use long arithmetic.
        return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
    }


    // Bit twiddling

    /**
     * The number of bits used to represent an {@code int} value in two's
     * complement binary form.
     *
     * @since 1.5
     */
    @Native public static final int SIZE = 32;

    /**
     * The number of bytes used to represent an {@code int} value in two's
     * complement binary form.
     *
     * @since 1.8
     */
    public static final int BYTES = SIZE / Byte.SIZE;

    /**
     * Returns an {@code int} value with at most a single one-bit, in the
     * position of the highest-order ("leftmost") one-bit in the specified
     * {@code int} 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 an {@code int} 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 int highestOneBit(int i) {
        return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
    }

    /**
     * Returns an {@code int} value with at most a single one-bit, in the
     * position of the lowest-order ("rightmost") one-bit in the specified
     * {@code int} 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 an {@code int} 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 int lowestOneBit(int 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 int} value.  Returns 32 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 int} values x:
     * <ul>
     * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
     * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - 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 int} value, or 32 if the value
     *     is equal to zero.
     * @since 1.5
     */
    @IntrinsicCandidate
    public static int numberOfLeadingZeros(int i) {
        // HD, Count leading 0's
        if (i <= 0)
            return i == 0 ? 32 : 0;
        int n = 31;
        if (i >= 1 << 16) { n -= 16; i >>>= 16; }
        if (i >= 1 <<  8) { n -=  8; i >>>=  8; }
        if (i >= 1 <<  4) { n -=  4; i >>>=  4; }
        if (i >= 1 <<  2) { n -=  2; i >>>=  2; }
        return n - (i >>> 1);
    }

    /**
     * Returns the number of zero bits following the lowest-order ("rightmost")
     * one-bit in the two's complement binary representation of the specified
     * {@code int} value.  Returns 32 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 int} value, or 32 if the value is equal
     *     to zero.
     * @since 1.5
     */
    @IntrinsicCandidate
    public static int numberOfTrailingZeros(int i) {
        // HD, Count trailing 0's
        i = ~i & (i - 1);
        if (i <= 0) return i & 32;
        int n = 1;
        if (i > 1 << 16) { n += 16; i >>>= 16; }
        if (i > 1 <<  8) { n +=  8; i >>>=  8; }
        if (i > 1 <<  4) { n +=  4; i >>>=  4; }
        if (i > 1 <<  2) { n +=  2; i >>>=  2; }
        return n + (i >>> 1);
    }

    /**
     * Returns the number of one-bits in the two's complement binary
     * representation of the specified {@code int} 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 int} value.
     * @since 1.5
     */
    @IntrinsicCandidate
    public static int bitCount(int i) {
        // HD, Figure 5-2
        i = i - ((i >>> 1) & 0x55555555);
        i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
        i = (i + (i >>> 4)) & 0x0f0f0f0f;
        i = i + (i >>> 8);
        i = i + (i >>> 16);
        return i & 0x3f;
    }

    /**
     * Returns the value obtained by rotating the two's complement binary
     * representation of the specified {@code int} 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 32 is a
     * no-op, so all but the last five bits of the rotation distance can be
     * ignored, even if the distance is negative: {@code rotateLeft(val,
     * distance) == rotateLeft(val, distance & 0x1F)}.
     *
     * @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 int} value left by the
     *     specified number of bits.
     * @since 1.5
     */
    public static int rotateLeft(int i, int distance) {
        return (i << distance) | (i >>> -distance);
    }

    /**
     * Returns the value obtained by rotating the two's complement binary
     * representation of the specified {@code int} 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 32 is a
     * no-op, so all but the last five bits of the rotation distance can be
     * ignored, even if the distance is negative: {@code rotateRight(val,
     * distance) == rotateRight(val, distance & 0x1F)}.
     *
     * @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 int} value right by the
     *     specified number of bits.
     * @since 1.5
     */
    public static int rotateRight(int 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 int}
     * value.
     *
     * @param i the value to be reversed
     * @return the value obtained by reversing order of the bits in the
     *     specified {@code int} value.
     * @since 1.5
     */
    @IntrinsicCandidate
    public static int reverse(int i) {
        // HD, Figure 7-1
        i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
        i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
        i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;

        return reverseBytes(i);
    }

    /**
     * Returns the value obtained by compressing the bits of the
     * specified {@code int} 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(0xCAFEBABE, 0xFF00FFF0) == 0xCABAB
     * }
     * 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, 1 << n) == (x >> n & 1)
     *
     * // Logical shift right
     * compress(x, -1 << 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 : (1 << 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" :
     * int compressLeft(int i, int mask) {
     *     // This implementation follows the description in Hacker's Delight which
     *     // is informative. A more optimal implementation is:
     *     //   Integer.compress(i, mask) << -Integer.bitCount(mask)
     *     return Integer.reverse(
     *         Integer.compress(Integer.reverse(i), Integer.reverse(mask)));
     * }
     *
     * int sag(int i, int mask) {
     *     return compressLeft(i, mask) | Integer.compress(i, ~mask);
     * }
     *
     * // Separate the sheep from the goats
     * sag(0xCAFEBABE, 0xFF00FFF0) == 0xCABABFEE
     * }
     *
     * @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 int compress(int i, int mask) {
        // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract

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

        for (int j = 0; j < 5; j++) {
            // Parallel prefix
            // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
            int maskPrefix = parallelSuffix(maskCount);
            // Bits to move
            int maskMove = maskPrefix & mask;
            // Compress mask
            mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
            // Bits of i to be moved
            int 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 int} 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(0x0000CABAB, 0xFF00FFF0) == 0xCA00BAB0
     * }
     * 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, 1 << n) == (x & 1) << n
     *
     * // Logically shift right
     * expand(x, -1 << n) == x << n
     *
     * // Expanding all bits returns the mask
     * expand(-1, 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 int} value can be implemented as follows:
     * {@snippet lang="java" :
     * int select(int i, int n) {
     *     // the one-bit in i (the mask) with index n
     *     int nthBit = Integer.expand(1 << n, i);
     *     // the bit position of the one-bit with index n
     *     return Integer.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 int expand(int i, int mask) {
        // Save original mask
        int originalMask = mask;
        // Count 0's to right
        int maskCount = ~mask << 1;
        int maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        int maskMove1 = maskPrefix & mask;
        // Compress mask
        mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
        maskCount = maskCount & ~maskPrefix;

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

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

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

        maskPrefix = parallelSuffix(maskCount);
        // Bits to move
        int maskMove5 = maskPrefix & mask;

        int 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 int parallelSuffix(int maskCount) {
        int maskPrefix = maskCount ^ (maskCount << 1);
        maskPrefix = maskPrefix ^ (maskPrefix << 2);
        maskPrefix = maskPrefix ^ (maskPrefix << 4);
        maskPrefix = maskPrefix ^ (maskPrefix << 8);
        maskPrefix = maskPrefix ^ (maskPrefix << 16);
        return maskPrefix;
    }

    /**
     * Returns the signum function of the specified {@code int} 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 int} value.
     * @since 1.5
     */
    public static int signum(int i) {
        // HD, Section 2-7
        return (i >> 31) | (-i >>> 31);
    }

    /**
     * Returns the value obtained by reversing the order of the bytes in the
     * two's complement representation of the specified {@code int} value.
     *
     * @param i the value whose bytes are to be reversed
     * @return the value obtained by reversing the bytes in the specified
     *     {@code int} value.
     * @since 1.5
     */
    @IntrinsicCandidate
    public static int reverseBytes(int i) {
        return (i << 24)            |
               ((i & 0xff00) << 8)  |
               ((i >>> 8) & 0xff00) |
               (i >>> 24);
    }

    /**
     * Adds two integers 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 int sum(int a, int b) {
        return a + b;
    }

    /**
     * Returns the greater of two {@code int} values
     * as if by calling {@link Math#max(int, int) 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 int max(int a, int b) {
        return Math.max(a, b);
    }

    /**
     * Returns the smaller of two {@code int} values
     * as if by calling {@link Math#min(int, int) 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 int min(int a, int 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 Integer} instance
     * @since 12
     */
    @Override
    public Optional<Integer> 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 Integer} instance
     * @since 12
     */
    @Override
    public Integer resolveConstantDesc(MethodHandles.Lookup lookup) {
        return this;
    }

    /** use serialVersionUID from JDK 1.0.2 for interoperability */
    @java.io.Serial
    @Native private static final long serialVersionUID = 1360826667806852920L;
}