Integer

作者: LaMole | 来源:发表于2021-01-24 15:32 被阅读0次

    Integer

    /*
     * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
     * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     *
     */
    
    package java.lang;
    
    import java.lang.annotation.Native;
    
    /**
     * 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).
     * 和Short一样提供了和String的互转,和一些其他处理Integer的方法
     * 关于bit twiddling(摆弄(操作)bit) 的方法是参考别人的资料的
     *
     * @author  Lee Boynton
     * @author  Arthur van Hoff
     * @author  Josh Bloch
     * @author  Joseph D. Darcy
     * @since JDK1.0
     *
     * My Note
     * 迷之@Native, 看注释大概是说这个东西会用c++的header定义,就引用c++的东西,不懂,太高深
     *
     * 最大最小值,用16进制表示的明明白白
     * 定义了digits数组存储了所有可能的数字,为啥是最大36进制这里得到了验证
     * 带进制的toString:
     * 1. 进制别瞎JB写,会默认用10进制
     * 2. 不是负数不会有正号
     * 3. 高位不会补零
     * 4. 默认只返回小写字母
     * 5. 转为负数算,防止溢出
     *
     * 涉及到valueOf的方法基本都走了常量池
     *
     * 转化成无符号数的算法
     * 如果是Integer范围内的,直接走parseInt
     * 不是的话走Long.parseLong & 0xffff_ffff_0000_0000
     *
     * 常量池,可以手动指定(java.lang.Integer.IntegerCache.high)大小,最小-128 ~ 127,最大 -128 ~ Integer.MAX_VALUE - 129
     *
     * parseInt
     * 用负数进行计算,正数会溢出
     *
     *  public static Integer getInteger(String nm, int val) {
     *         Integer result = getInteger(nm, null);
     *         return (result == null) ? Integer.valueOf(val) : result;
     *     }
     *     获取系统参数,没有指定默认值
     *
     *     最高位1
     *     public static int highestOneBit(int i) {
     *         // HD, Figure 3-1
     *         i |= (i >>  1);
     *         i |= (i >>  2);
     *         i |= (i >>  4);
     *         i |= (i >>  8);
     *         i |= (i >> 16);
     *         return i - (i >>> 1);
     *     }
     *
     *    最低位1
     *    public static int lowestOneBit(int i) {
     *         // HD, Section 2-1
     *         // 1000 0000 0000 0001 0000
     *         // 0111 1111 1111 1111 0000
     *         return i & -i;
     *     }
     *
     *     循环左移
     *      * 两个事实
     *      * 1. 循环位移distance,相当于直接将高distance位搬过去
     *      * 2. 位移多少位之前会,位移的位数 & 0x0000_001f
     *     public static int rotateLeft(int i, int distance) {
     *         return (i << distance) | (i >>> -distance);
     *     }
     *
     *     public static int rotateRight(int i, int distance) {
     *         return (i >>> distance) | (i << -distance);
     *     }
     */
    public final class Integer extends Number implements Comparable<Integer> {
        /**
         * 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   JDK1.1
         */
        @SuppressWarnings("unchecked")
        public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
    
        /**
         * All possible chars for representing a number as a String
         * 为啥最大36进制体现的明明白白的
         */
        final static 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'
        };
    
        /**
         * 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.
         * 进制别瞎JB写,会默认用10进制
         *
         * <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.
         * 不是负数不会有正号
         * <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:
         * 高位不会补零, 除非是0
         *
         * <blockquote>
         *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
         * </blockquote>
         *
         * 只返回小写字母
         * 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);
            }
    
            // 最小的二进制,int是32位算上符号为1位,33位,
            char buf[] = new char[33];
            boolean negative = (i < 0);
            int charPos = 32;
            // 取负数算,应该是怕负最小值转正时的溢出
            if (!negative) {
                i = -i;
            }
    
            while (i <= -radix) {
                buf[charPos--] = digits[-(i % radix)];
                i = i / radix;
            }
            buf[charPos] = digits[-i];
    
            if (negative) {
                buf[--charPos] = '-';
            }
    
            return new String(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.
         *
         * 这段说,如果是个负数,就返回+2^32,要么就返回参数本身
         * <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   JDK1.0.2
         */
        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   JDK1.0.2
         */
        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   JDK1.0.2
         */
        public static String toBinaryString(int i) {
            return toUnsignedString0(i, 1);
        }
    
        /**
         * Convert the integer to an unsigned number.
         * shift是进制的位移
         */
        private static String toUnsignedString0(int val, int shift) {
            // assert shift > 0 && shift <=5 : "Illegal shift value";
            int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
            // 最大值16进制8,8进制11,2进制32,
            int chars = Math.max(((mag + (shift - 1)) / shift), 1);
            char[] buf = new char[chars];
    
            formatUnsignedInt(val, shift, buf, 0, chars);
    
            // Use special constructor which takes over "buf".
            return new String(buf, true);
        }
    
        /**
         * Format a long (treated as unsigned) into a character buffer.
         * @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
         * @return the lowest character  location used
         */
         static int formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
            int charPos = len;
            int radix = 1 << shift;
            int mask = radix - 1;
            do {
                buf[offset + --charPos] = Integer.digits[val & mask];
                val >>>= shift;
            } while (val != 0 && charPos > 0);
    
            return charPos;
        }
    
        final static char [] 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',
            } ;
    
        final static char [] 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',
            } ;
    
            // I use the "invariant division by multiplication" trick to
            // accelerate Integer.toString.  In particular we want to
            // avoid division by 10.
            //
            // The "trick" has roughly the same performance characteristics
            // as the "classic" Integer.toString code on a non-JIT VM.
            // The trick avoids .rem and .div calls but has a longer code
            // path and is thus dominated by dispatch overhead.  In the
            // JIT case the dispatch overhead doesn't exist and the
            // "trick" is considerably faster than the classic code.
            //
            // TODO-FIXME: convert (x * 52429) into the equiv shift-add
            // sequence.
            //
            // RE:  Division by Invariant Integers using Multiplication
            //      T Gralund, P Montgomery
            //      ACM PLDI 1994
            //
    
        /**
         * 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.
         * 十进制的转换
         *
         *
         *
         * @param   i   an integer to be converted.
         * @return  a string representation of the argument in base&nbsp;10.
         */
        public static String toString(int i) {
            // 处理边界,否则下面的取反会越界
            if (i == Integer.MIN_VALUE)
                return "-2147483648";
            // 获得最后String有几位,用来申请char数组,负数多一个-位置
            int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
            char[] buf = new char[size];
            getChars(i, size, buf);
            return new String(buf, true);
        }
    
        /**
         * Returns a string representation of the argument as an unsigned
         * decimal value.
         * 需要借用long的方法,防止溢出
         * 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));
        }
    
        /**
         * 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.
         * 牛逼的方法
         *
         *
         * Will fail if i == Integer.MIN_VALUE
         */
        static void getChars(int i, int index, char[] buf) {
            int q, r;
            int charPos = index;
            char sign = 0;
    
            if (i < 0) {
                sign = '-';
                i = -i;
            }
    
            // Generate two digits per iteration
            // 65536 / 100 = 655(10 1000 1111) 下面的高效算法会乘以 52429(1100 1100 1100 1101)9 + 15 < 32
            while (i >= 65536) {
                q = i / 100;
            // really: r = i - (q * 100);
                // 。。。 r=i-(q * 2^6 + q * 2^5 + q*2^2)=i-(q * 64 + q * 32 + q * 4) = i - (q * 100)
                // 就是i的后两位
                r = i - ((q << 6) + (q << 5) + (q << 2));
                i = q;
                // DigitOnes 保证个位和数字一样,DigitTens 保证十位和数字一样
                buf [--charPos] = DigitOnes[r];
                buf [--charPos] = DigitTens[r];
            }
    
            // Fall thru to fast mode for smaller numbers
            // 用乘法和位移替换除法
            // assert(i <= 65536, i);
            for (;;) {
                q = (i * 52429) >>> (16+3);
                r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
                buf [--charPos] = digits [r];
                i = q;
                if (i == 0) break;
            }
            if (sign != 0) {
                buf [--charPos] = sign;
            }
        }
    
        final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
                                          99999999, 999999999, Integer.MAX_VALUE };
    
        // Requires positive x
        static int stringSize(int x) {
            for (int i=0; ; i++)
                if (x <= sizeTable[i])
                    return i+1;
        }
    
        /**
         * 用负数进行计算,正数会溢出
         * 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.
         * @exception  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("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");
            }
    
            int result = 0;
            boolean negative = false;
            int i = 0, len = s.length();
            int limit = -Integer.MAX_VALUE;
            int multmin;
            int digit;
    
            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++;
                }
                multmin = limit / radix;
                while (i < len) {
                    // Accumulating negatively avoids surprises near MAX_VALUE
                    // digit < 0表示获取数字失败
                    digit = Character.digit(s.charAt(i++),radix);
                    if (digit < 0) {
                        throw NumberFormatException.forInputString(s);
                    }
                    if (result < multmin) {
                        throw NumberFormatException.forInputString(s);
                    }
                    result *= radix;
                    if (result < limit + digit) {
                        throw NumberFormatException.forInputString(s);
                    }
                    result -= digit;
                }
            } else {
                throw NumberFormatException.forInputString(s);
            }
            return negative ? result : -result;
        }
    
        /**
         *
         * 转为10进制
         * 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.
         * @exception  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
         *
         * 如果大于MAX_VALUE返回,返回负数,从MIN_VALUE开始,实际返回的是2进制的数
         * MAX_VALUE + 1 返回的 1000 0000 0000 0000 0000 0000 0000 0000
         *
         *
         *
         *
         */
        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 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 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.
         * @exception 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 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.
         * @exception  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.
         *
         * 常量池,可以手动指定大小,最小-128 ~ 127,最大 -128 ~ Integer.MAX_VALUE - 129
         * 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
         * sun.misc.VM class.
         */
    
        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 =
                    sun.misc.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);
                    } 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() {}
        }
    
        /**
         * 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
         * 常量池内返回池中的数
         */
        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.
         */
        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}.
         * @exception  NumberFormatException  if the {@code String} does not
         *               contain a parsable integer.
         * @see        java.lang.Integer#parseInt(java.lang.String, int)
         */
        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 Conversions
         */
        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
         */
        public short shortValue() {
            return (short)value;
        }
    
        /**
         * Returns the value of this {@code Integer} as an
         * {@code int}.
         */
        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)
         */
        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
         */
        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
         */
        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 a {@code int} value; compatible with
         * {@code Integer.hashCode()}.
         *
         * @param value the value to hash
         * @since 1.8
         *
         * @return a hash code value for a {@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) {
                return value == ((Integer)obj).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.
         * @throws  SecurityException for the same reasons as
         *          {@link System#getProperty(String) System.getProperty}
         * @see     java.lang.System#getProperty(java.lang.String)
         * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
         */
        public static 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, 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)
         */
        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.
         * @throws  SecurityException for the same reasons as
         *          {@link System#getProperty(String) System.getProperty}
         * @see     System#getProperty(java.lang.String)
         * @see     System#getProperty(java.lang.String, java.lang.String)
         */
        public static 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;
        }
    
        /**
         * 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}
         * @exception 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;
            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;
        }
    
        /**
         * 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
         */
        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
         *
         * 卧槽,牛逼
         * 强转是高位根据符号为补,正数不变,负数补1,然后在取低32位,符号位为0
         * 还避免了 int的溢出
         *
         */
        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
         */
        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
         */
        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 a {@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) {
            // HD, Figure 3-1
            i |= (i >>  1);
            i |= (i >>  2);
            i |= (i >>  4);
            i |= (i >>  8);
            i |= (i >> 16);
            return i - (i >>> 1);
        }
    
        /**
         * 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
            // 1000 0000 0000 0001 0000
            // 0111 1111 1111 1111 0000
            return i & -i;
        }
    
        /**
         * 返回高位0的个数
         * 先看高16位是不是0,是的话,把低16位位移到高16位
         * 后面以此类推
         *
         * 高16位不是0的话,就看高8位,依此类推
         *
         * 负数返回0
         *
         * 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
         */
        public static int numberOfLeadingZeros(int i) {
            // HD, Figure 5-6
            if (i == 0)
                return 32;
            int n = 1;
            if (i >>> 16 == 0) { n += 16; i <<= 16; }
            if (i >>> 24 == 0) { n +=  8; i <<=  8; }
            if (i >>> 28 == 0) { n +=  4; i <<=  4; }
            if (i >>> 30 == 0) { n +=  2; i <<=  2; }
            n -= i >>> 31;
            return n;
        }
    
        /**
         * Returns the number of zero bits following the lowest-order ("rightmost")
         * one-bit in the two's complement binary representation of the specified
         * {@code 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
         */
        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 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
         */
        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;
        }
    
        /**
         * 循环左移
         * 两个事实
         * 1. 循环位移distance,相当于直接将高distance位搬过去
         * 2. 位移多少位之前会,位移的位数 & 0x0000_001f
         * 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
         */
        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;
            i = (i << 24) | ((i & 0xff00) << 8) |
                ((i >>> 8) & 0xff00) | (i >>> 24);
            return i;
        }
    
        /**
         * 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
         */
        public static int reverseBytes(int i) {
            return ((i >>> 24)           ) |
                   ((i >>   8) &   0xFF00) |
                   ((i <<   8) & 0xFF0000) |
                   ((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);
        }
    
        /** use serialVersionUID from JDK 1.0.2 for interoperability */
        @Native private static final long serialVersionUID = 1360826667806852920L;
    }
    
    

    相关文章

      网友评论

          本文标题:Integer

          本文链接:https://www.haomeiwen.com/subject/jbumzktx.html