Integer.java

/*
 * Copyright (c) 1994, 2018, 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.HotSpotIntrinsicCandidate;
import jdk.internal.misc.VM;

import java.lang.annotation.Native;
import java.util.Objects;

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

/**
 * The {@code Integer} class wraps a value of the primitive type
 * {@code int} in an object. 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>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 <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
 */
// int的包装类
public final class Integer extends Number implements Comparable<Integer> {
    
    /** use serialVersionUID from JDK 1.0.2 for interoperability */
    @Native
    private static final long serialVersionUID = 1360826667806852920L;
    
    /**
     * The {@code Class} instance representing the primitive type
     * {@code int}.
     *
     * @since 1.1
     */
    // 相当于int.class
    @SuppressWarnings("unchecked")
    public static final Class<Integer> TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
    
    /**
     * A constant holding the minimum value an {@code int} can
     * have, -2<sup>31</sup>.
     */
    @Native
    public static final int MIN_VALUE = 0x80000000; // int最小值
    
    /**
     * A constant holding the maximum value an {@code int} can
     * have, 2<sup>31</sup>-1.
     */
    @Native
    public static final int MAX_VALUE = 0x7fffffff; // int最大值
    
    /**
     * 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;  // 当前类型所占bit[位]数
    
    /**
     * 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;   // 当前类型所占字节数
    
    /**
     * The value of the {@code Integer}.
     *
     * @serial
     */
    private final int value; // 当前类包装的值
    
    /**
     * All possible chars for representing a number as a String
     */
    // 进制
    static final char[] 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'
    };
    
    // 个位数
    static final byte[] DigitOnes = {
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
    };
    
    // 十位数
    static final byte[] DigitTens = {
        '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
        '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
        '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
        '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
        '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
        '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
        '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
        '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
        '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
        '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
    };
    
    // Left here for compatibility reasons, see JDK-8143900.
    static final int[] sizeTable = {9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, Integer.MAX_VALUE};
    
    
    
    /*▼ 构造方法 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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);
    }
    
    /*▲ 构造方法 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ [装箱] ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // int-->Integer 默认的装箱行为
    @HotSpotIntrinsicCandidate
    public static Integer valueOf(int i) {
        if(i >= IntegerCache.low && i<=IntegerCache.high)
            return IntegerCache.cache[i + (-IntegerCache.low)];
        return new Integer(i);
    }
    
    /**
     * 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 new Integer(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.
     */
    // 按10进制形式将字符串s解析为int值，随后再装箱
    public static Integer valueOf(String s) throws NumberFormatException {
        return Integer.valueOf(parseInt(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 new Integer(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}.
     */
    // 按radix进制形式将字符串s解析为int值，随后再装箱
    public static Integer valueOf(String s, int radix) throws NumberFormatException {
        return Integer.valueOf(parseInt(s, radix));
    }
    
    /**
     * 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 3.10.1 of
     * <cite>The Java&trade; Language Specification</cite>,
     * except that underscores are not accepted between digits.
     *
     * <p>The sequence of characters following an optional
     * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
     * "{@code #}", or leading zero) is parsed as by the {@code
     * 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)
     */
    /*
     * 将字符串nm解析为int，随后再装箱
     *
     * 采用哪种进制解析nm取决于nm的格式：
     * > 0x、0X、#开头，代表按16进制解析
     * > 0开头，代表按8进制解析
     * > 其他情形默认按10进制解析
     */
    public static Integer decode(String nm) throws NumberFormatException {
        int radix = 10;
        int index = 0;
        boolean negative = false;
        Integer result;
        
        if(nm.length() == 0)
            throw new NumberFormatException("Zero length string");
        char firstChar = nm.charAt(0);
        // Handle sign, if present
        if(firstChar == '-') {
            negative = true;
            index++;
        } else if(firstChar == '+')
            index++;
        
        // Handle radix specifier, if present
        if(nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
            index += 2;
            radix = 16;
        } else if(nm.startsWith("#", index)) {
            index++;
            radix = 16;
        } else if(nm.startsWith("0", index) && nm.length()>1 + index) {
            index++;
            radix = 8;
        }
        
        if(nm.startsWith("-", index) || nm.startsWith("+", index))
            throw new NumberFormatException("Sign character in wrong position");
        
        try {
            result = Integer.valueOf(nm.substring(index), radix);
            result = negative ? Integer.valueOf(-result.intValue()) : 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 = Integer.valueOf(constant, radix);
        }
        
        return result;
    }
    
    /*▲ [装箱] ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ [拆箱] ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * Returns the value of this {@code Integer} as a {@code byte}
     * after a narrowing primitive conversion.
     *
     * @jls 5.1.3 Narrowing Primitive Conversions
     */
    // 以byte形式返回当前对象的值
    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 Conversions
     */
    // 以short形式返回当前对象的值
    public short shortValue() {
        return (short) value;
    }
    
    /**
     * Returns the value of this {@code Integer} as an
     * {@code int}.
     */
    // Integer-->int 默认的拆箱行为
    @HotSpotIntrinsicCandidate
    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 Conversions
     * @see Integer#toUnsignedLong(int)
     */
    // 以long形式返回当前对象的值
    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 Conversions
     */
    // 以float形式返回当前对象的值
    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 Conversions
     */
    // 以double形式返回当前对象的值
    public double doubleValue() {
        return (double) value;
    }
    
    /*▲ [拆箱] ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 从属性中解析值 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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.
     *
     * @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)
     */
    /*
     * 从系统属性中获取值，然后再装箱
     * 其中，nm为某个系统属性，val为备用值
     *
     * 比如：
     * System.setProperty("age", "20");
     * Integer x = getInteger("age", 25);
     * 如果属性age存在（被提前设置），x的值为20。
     * 如果属性age不存在，则x的值为备用值25。
     */
    public static Integer getInteger(String nm, Integer val) {
        String v = null;
        try {
            v = System.getProperty(nm);
        } catch(IllegalArgumentException | NullPointerException e) {
        }
        if(v != null) {
            try {
                return Integer.decode(v);
            } catch(NumberFormatException e) {
            }
        }
        return val;
    }
    
    /**
     * 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, new Integer(val))}
     * </blockquote>
     *
     * but in practice it may be implemented in a manner such as:
     *
     * <blockquote><pre>
     * Integer result = getInteger(nm, null);
     * return (result == null) ? new Integer(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.
     *
     * @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)
     */
    // 从系统属性中获取值，然后再装箱。如果取不到值，选用val
    public static Integer getInteger(String nm, int val) {
        Integer result = getInteger(nm, null);
        return (result == null) ? Integer.valueOf(val) : result;
    }
    
    /**
     * 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.
     *
     * @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)
     */
    // 从系统属性中获取值，然后再装箱。如果取不到值，返回null。
    public static Integer getInteger(String nm) {
        return getInteger(nm, null);
    }
    
    /*▲ 从属性中解析值 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 逆字符串化 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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}.
     */
    // 按radix进制形式将字符串s解析为int值
    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("null");
        }
        
        if(radix<Character.MIN_RADIX) {
            throw new NumberFormatException("radix " + radix + " less than Character.MIN_RADIX");
        }
        
        if(radix>Character.MAX_RADIX) {
            throw new NumberFormatException("radix " + radix + " greater than Character.MAX_RADIX");
        }
        
        boolean negative = false;
        int i = 0, len = s.length();
        int limit = -Integer.MAX_VALUE;
        
        if(len>0) {
            char firstChar = s.charAt(0);
            if(firstChar<'0') { // Possible leading "+" or "-"
                if(firstChar == '-') {
                    negative = true;
                    limit = Integer.MIN_VALUE;
                } else if(firstChar != '+') {
                    throw NumberFormatException.forInputString(s);
                }
                
                if(len == 1) { // Cannot have lone "+" or "-"
                    throw NumberFormatException.forInputString(s);
                }
                i++;
            }
            int multmin = limit / radix;
            int 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);
                }
                result *= radix;
                if(result<limit + digit) {
                    throw NumberFormatException.forInputString(s);
                }
                result -= digit;
            }
            return negative ? result : -result;
        } else {
            throw NumberFormatException.forInputString(s);
        }
    }
    
    /**
     * 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.
     */
    // 按10进制形式将字符串s解析为int值
    public static int parseInt(String s) throws NumberFormatException {
        return parseInt(s, 10);
    }
    
    /**
     * 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
     */
    // 按radix进制形式将字符序列s的[beginIndex, endIndex)部分解析为int值
    public static int parseInt(CharSequence s, int beginIndex, int endIndex, int radix) throws NumberFormatException {
        s = 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;
        int limit = -Integer.MAX_VALUE;
        
        if(i<endIndex) {
            char firstChar = s.charAt(i);
            if(firstChar<'0') { // Possible leading "+" or "-"
                if(firstChar == '-') {
                    negative = true;
                    limit = Integer.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);
                }
            }
            int multmin = limit / radix;
            int 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 NumberFormatException.forInputString("");
        }
    }
    
    /**
     * 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
     */
    // 按radix进制形式将无符号整型字符串s解析为有符号整型值
    public static int parseUnsignedInt(String s, int radix) throws NumberFormatException {
        if(s == null) {
            throw new NumberFormatException("null");
        }
        
        int len = s.length();
        if(len>0) {
            char firstChar = s.charAt(0);
            if(firstChar == '-') {
                throw new NumberFormatException(String.format("Illegal leading minus sign " + "on unsigned string %s.", s));
            } else {
                if(len<=5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
                    (radix == 10 && len<=9)) { // Integer.MAX_VALUE in base 10 is 10 digits
                    return parseInt(s, radix);
                } else {
                    long ell = Long.parseLong(s, radix);
                    if((ell & 0xffff_ffff_0000_0000L) == 0) {
                        return (int) ell;
                    } else {
                        throw new NumberFormatException(String.format("String value %s exceeds " + "range of unsigned int.", s));
                    }
                }
            }
        } else {
            throw NumberFormatException.forInputString(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
     */
    // 按10进制形式将无符号整型字符串s解析为有符号整型值
    public static int parseUnsignedInt(String s) throws NumberFormatException {
        return parseUnsignedInt(s, 10);
    }
    
    /**
     * 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
     */
    // 按radix进制形式将无符号整型字符序列s的[beginIndex, endIndex)部分解析为有符号整型值
    public static int parseUnsignedInt(CharSequence s, int beginIndex, int endIndex, int radix) throws NumberFormatException {
        s = 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));
            } else {
                if(len<=5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
                    (radix == 10 && len<=9)) { // Integer.MAX_VALUE in base 10 is 10 digits
                    return parseInt(s, start, start + len, radix);
                } else {
                    long ell = Long.parseLong(s, start, start + len, radix);
                    if((ell & 0xffff_ffff_0000_0000L) == 0) {
                        return (int) ell;
                    } else {
                        throw new NumberFormatException(String.format("String value %s exceeds " + "range of unsigned int.", s));
                    }
                }
            }
        } else {
            throw new NumberFormatException("");
        }
    }
    
    /*▲ 逆字符串化 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 字符串化 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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.
     */
    // 按10进制返回当前int的值
    public String toString() {
        return toString(value);
    }
    
    /**
     * 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.
     */
    // 按10进制返回i的值
    @HotSpotIntrinsicCandidate
    public static String toString(int i) {
        // 统计整数i中包含的符号数量（包括负号），即计算整数i转为字符串后的长度
        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 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
     */
    // 按radix进制返回i的值
    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--] = (byte) digits[-(i % radix)];
                i = i / radix;
            }
            buf[charPos] = (byte) digits[-i];
            
            if(negative) {
                buf[--charPos] = '-';
            }
            
            return StringLatin1.newString(buf, charPos, (33 - charPos));
        }
        
        return toStringUTF16(i, radix);
    }
    
    /**
     * 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
     */
    // 按2进制返回i的无符号值
    public static String toBinaryString(int i) {
        return toUnsignedString0(i, 1);
    }
    
    /**
     * 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
     */
    // 按8进制返回i的无符号值
    public static String toOctalString(int i) {
        return toUnsignedString0(i, 3);
    }
    
    /**
     * 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
     */
    // 按10进制返回i的无符号值
    public static String toUnsignedString(int i) {
        return Long.toString(toUnsignedLong(i));
    }
    
    /**
     * 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>
     *
     * @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 #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since 1.0.2
     */
    // 按16进制返回i的无符号值
    public static String toHexString(int i) {
        return toUnsignedString0(i, 4);
    }
    
    /**
     * 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
     */
    // 按radix进制返回i的无符号值
    public static String toUnsignedString(int i, int radix) {
        return Long.toUnsignedString(toUnsignedLong(i), radix);
    }
    
    
    
    /**
     * Convert the integer to an unsigned number.
     */
    // 按2^shift进制返回val的无符号值
    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, 0, chars);
            return new String(buf, LATIN1);
        } else {
            byte[] buf = new byte[chars * 2];
            formatUnsignedIntUTF16(val, shift, buf, 0, chars);
            return new String(buf, UTF16);
        }
    }
    
    // 按radix进制返回i的无符号值，UTF16版本
    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));
    }
    
    /**
     * Format an {@code int} (treated as unsigned) into a character buffer.
     * 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 character buffer to write to
     * @param offset the offset in the destination buffer to start at
     * @param len    the number of characters to write
     */
    /*
     * 从buf的offset索引处开始，存入变量val在2^shift进制下的后len位
     * shift取1、3、4时分别代表二进制、八进制、16进制
     * 如果len的长度超过该进制下的有效数位长度，则前面空白部分补0
     *
     * 举例：
     * 十进制数12345的八进制形式为30071
     *
     * char[] buf = new char[10];
     *
     * formatUnsignedInt(12345, 3, buf, 0, 5) // buf={'3','0','0','7','1','\0','\0','\0','\0','\0'}
     * formatUnsignedInt(12345, 3, buf, 0, 7) // buf={'0','0','3','0','0','7','1','\0','\0','\0'}
     * formatUnsignedInt(12345, 3, buf, 2, 7) // buf={'\0','\0','0','0','3','0','0','7','1','\0'}
     */
    static void formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
        // assert shift > 0 && shift <=5 : "Illegal shift value";
        // assert offset >= 0 && offset < buf.length : "illegal offset";
        // assert len > 0 && (offset + len) <= buf.length : "illegal length";
        int charPos = offset + len;
        int radix = 1 << shift;
        int mask = radix - 1;
        
        // 循环len次
        do {
            buf[--charPos] = Integer.digits[val & mask];
            val >>>= shift;
        } while(charPos>offset);
    }
    
    /** byte[]/LATIN1 version */
    // formatUnsignedInt方法的byte[]/LATIN1版本，将数字0到9分别存储为对应的ANSI码，'\0'存储为数字0
    static void formatUnsignedInt(int 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[val & mask];
            val >>>= shift;
        } while(charPos>offset);
    }
    
    /** byte[]/UTF16 version */
    // formatUnsignedInt方法的byte[]/UTF16版本，每个char存为两个byte
    private static void formatUnsignedIntUTF16(int 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[val & mask]);
            val >>>= shift;
        } while(charPos>offset);
    }
    
    /**
     * Returns the string representation size for a given int value.
     *
     * @param x int 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.
     */
    /*
     * 统计整数i中包含的符号数量（包括负号），为转为字符串做准备
     * 比如stringSize(12345)返回5，stringSize(-12345)返回6
     */
    static int stringSize(int x) {
        int d = 1;
        if(x >= 0) {
            d = 0;
            x = -x;
        }
        int p = -10;
        for(int i = 1; i<10; i++) {
            if(x>p)
                return i + d;
            p = 10 * p;
        }
        return 10 + d;
    }
    
    /**
     * Places characters representing the integer i into the
     * character array buf. The characters are placed into
     * the buffer backwards starting with the least significant
     * digit at the specified index (exclusive), and working
     * backwards from there.
     *
     * @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
     *
     * @implNote This method converts positive inputs into negative
     * values, to cover the Integer.MIN_VALUE case. Converting otherwise
     * (negative to positive) will expose -Integer.MIN_VALUE that overflows
     * integer.
     */
    // 将整数i中包含的符号转为byte存入buf
    static int getChars(int i, int index, byte[] buf) {
        int q, r;
        int charPos = index;
        
        boolean negative = i<0;
        if(!negative) {
            i = -i;
        }
        
        // Generate two digits per iteration
        while(i<=-100) {
            q = i / 100;
            r = (q * 100) - i;
            i = q;
            buf[--charPos] = DigitOnes[r];
            buf[--charPos] = DigitTens[r];
        }
        
        // We know there are at most two digits left at this point.
        q = i / 10;
        r = (q * 10) - i;
        buf[--charPos] = (byte) ('0' + r);
        
        // Whatever left is the remaining digit.
        if(q<0) {
            buf[--charPos] = (byte) ('0' - q);
        }
        
        if(negative) {
            buf[--charPos] = (byte) '-';
        }
        
        return charPos;
    }
    
    /*▲ 字符串化 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 无符号化 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // 将当前int转换为无符号形式，用long存储
    public static long toUnsignedLong(int x) {
        return ((long) x) & 0xffffffffL;
    }
    
    /*▲ 无符号化 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 比较 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // 比较两个int（按自然顺序比较）
    public static int compare(int x, int y) {
        return (x<y) ? -1 : ((x == y) ? 0 : 1);
    }
    
    /**
     * 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
     */
    // 比较两个Integer（按自然顺序比较）
    public int compareTo(Integer anotherInteger) {
        return compare(this.value, anotherInteger.value);
    }
    
    /**
     * 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
     */
    // 以无符号形式比较两个int（按自然顺序比较）
    public static int compareUnsigned(int x, int y) {
        return compare(x + MIN_VALUE, y + MIN_VALUE);
    }
    
    /*▲ 比较 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 位操作 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // 返回二进制位中值为1的bit位的数量（把int值i表示为二进制形式）
    @HotSpotIntrinsicCandidate
    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
     */
    // 将i中的bit循环左移distance位
    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
     */
    // 将i中的bit循环右移distance位
    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
     */
    // 以bit为单位逆置bit顺序
    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 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
     */
    // 以字节为单位逆置字节顺序
    @HotSpotIntrinsicCandidate
    public static int reverseBytes(int i) {
        return (i << 24) | ((i & 0xff00) << 8) | ((i >>> 8) & 0xff00) | (i >>> 24);
    }
    
    /**
     * 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
     */
    // 判断i的正负。遇到负数返回-1，正数返回1，0返回0。
    public static int signum(int i) {
        // HD, Section 2-7
        return (i >> 31) | (-i >>> 31);
    }
    
    /**
     * 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
     */
    // 返回二进制位中开头连续的0的个数（把int值i表示为二进制形式）
    @HotSpotIntrinsicCandidate
    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
     */
    // 返回二进制位中末尾连续的0的个数（把int值i表示为二进制形式）
    @HotSpotIntrinsicCandidate
    public static int numberOfTrailingZeros(int i) {
        // HD, Figure 5-14
        int y;
        if(i == 0)
            return 32;
        int n = 31;
        y = i << 16;
        if(y != 0) {
            n = n - 16;
            i = y;
        }
        y = i << 8;
        if(y != 0) {
            n = n - 8;
            i = y;
        }
        y = i << 4;
        if(y != 0) {
            n = n - 4;
            i = y;
        }
        y = i << 2;
        if(y != 0) {
            n = n - 2;
            i = y;
        }
        return n - ((i << 1) >>> 31);
    }
    
    /**
     * 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
     */
    // 返回二进制位中开头首次出现的1所占的数位，比如00110100，返回32
    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
     */
    // 返回二进制位中末尾最后出现的1所占的数位，比如00110100，返回4
    public static int lowestOneBit(int i) {
        // HD, Section 2-1
        return i & -i;
    }
    
    /*▲ 位操作 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 简单运算 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // 求和
    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
     */
    // 最大值
    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
     */
    // 最小值
    public static int min(int a, int b) {
        return Math.min(a, b);
    }
    
    /**
     * 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
     */
    // 除法运算，计算结果转为int后返回。计算前需要先将两个int值转换为无符号形式，并用long存储。
    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
     */
    // 取余运算，计算结果转为int后返回。计算前需要先将两个int值转换为无符号形式，并用long存储。
    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));
    }
    
    /*▲ 简单运算 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /**
     * 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
     *
     * @return a hash code value for an {@code int} value.
     *
     * @since 1.8
     */
    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) {
            return value == ((Integer) obj).intValue();
        }
        return false;
    }
    
    
    
    /**
     * 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.
     */
    /*
     * Integer缓存，默认缓存了-128~127之间的Integer对象
     * 如果想增加缓存数字的上限，比如将缓存范围改为[-128, 200]，
     * 则可以设置运行参数：
     * -XX:AutoBoxCacheMax=200
     * 或
     * -Djava.lang.Integer.IntegerCache.high=200
     */
    private static class IntegerCache {
        static final int low = -128;
        static final int high;
        static final Integer cache[];
        
        static {
            // high value may be configured by property
            int h = 127;
            String integerCacheHighPropValue = VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
            if(integerCacheHighPropValue != null) {
                try {
                    int i = parseInt(integerCacheHighPropValue);
                    i = Math.max(i, 127);
                    // Maximum array size is Integer.MAX_VALUE
                    h = Math.min(i, Integer.MAX_VALUE - (-low) - 1); // [low, high]的个数不能超过Integer.MAX_VALUE
                } catch(NumberFormatException nfe) {
                    // If the property cannot be parsed into an int, ignore it.
                }
            }
            high = h;
            
            cache = new Integer[(high - low) + 1];
            int j = low;
            for(int k = 0; k<cache.length; k++) {
                cache[k] = new Integer(j++);
            }
            
            // range [-128, 127] must be interned (JLS7 5.1.7)
            assert IntegerCache.high >= 127;
        }
        
        private IntegerCache() {
        }
    }
}