package java.lang;
import java.lang.annotation.Native;

public final class Integer extends Number implements Comparable<Integer> {
    /**
     * 最小值 
     * -2的31次方  -2147483648  
     */
    @Native public static final int   MIN_VALUE = 0x80000000;

    /**
     * 最大值
     * have, 2的31次方-1   2147483647
     */
    @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");

    /**
     * 所有可能的将数字表示为字符串的字符集合做缓存。
     */
    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'
    };

    /**
     * 
     * @param   i     
     * @param   radix   基数
     * @see     MIN_RADIX： 最小基数  2 
     * @see     MAX_RADIX: 最大基数  36
     */
    public static String toString(int i, int radix) {
        if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
            radix = 10; //默认为10进制
        
        if (radix == 10) {
            return toString(i);
        }

        char buf[] = new char[33];
        boolean negative = (i < 0);
        int charPos = 32;

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

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

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

        return new String(buf, charPos, (33 - charPos));
    }



  

    /**
     *  int 抓换成String
     * @param i
     * @return
     */
    public static String toString(int i) {
        if (i == Integer.MIN_VALUE)
            return "-2147483648";
        int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
        char[] buf = new char[size];
        getChars(i, size, buf);
        return new String(buf, true);
    }

    /**
     * toString方法调用
     * 参考：https://blog.csdn.net/Jack__Frost/article/details/53792063
     * 
     */
    static void getChars(int i, int index, char[] buf) {
        int q, r;
        int charPos = index;
        char sign = 0;

        if (i < 0) { //如果i为负数，则设置i的符号字符为'-'。
            sign = '-';  //确定正负数
            i = -i;  //将负数转化为正数处理，提高效率 
        }

        // Generate two digits per iteration
        while (i >= 65536) { //如果i大于65536，则每一次都获取十位和个位上的数字对应的字符。将值判断大小后取每个数字，较大的数字一次取两位（大数字运算消耗大）
            q = i / 100;
        // really: r = i - (q * 100);
            r = i - ((q << 6) + (q << 5) + (q << 2)); //利用位运算，每次获得i的最后两位数，不断循环提取处理
            i = q;//重新赋值，准备下一次循环 
            buf [--charPos] = DigitOnes[r]; //存储r中在个位数集合中对应的字符
            buf [--charPos] = DigitTens[r]; //存储r中在十位数集合中对应的字符
        }

        // Fall thru to fast mode for smaller numbers
        // assert(i <= 65536, i);
        for (;;) { //i<65536的情况，小数字运算消耗较小，故一次只取一位
            q = (i * 52429) >>> (16+3);//52429/(2*19)约等于1，此处这样设计是为了提高精度
            r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ... //每次获得i的最后两位数
            buf [--charPos] = digits [r];//取最后一位的数字  
            i = q;//重新赋值，准备下一次循环  
            if (i == 0) break;
        }
        if (sign != 0) {
            buf [--charPos] = sign; //设置符号
        }
    }

    
    
    final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
                                      99999999, 999999999, Integer.MAX_VALUE };
    
    //获取字符串长度
    static int stringSize(int x) {
        for (int i=0; ; i++)
            if (x <= sizeTable[i])
                return i+1;
    }

   /**
    * parseInt(String s,int radix)使用第二个参数指定的基数，将字符串参数解析为有符号的整数。 
    * 参考：https://blog.csdn.net/Jack__Frost/article/details/53792063
    */
    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) {//参数检验，调用方法前检查参数的正确性。
           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();//i表示当前遍历的s的位数
       int limit = -Integer.MAX_VALUE;//设置最小值为负的Integer的最大值
       int multmin;
       int digit;

       if (len > 0) {//如果字符串长度大于0，则进行转换
           char firstChar = s.charAt(0);//获取第一位字符
           if (firstChar < '0') { // Possible leading "+" or "-"
               if (firstChar == '-') {//判断是否为负数 
                   negative = true; 
                   limit = Integer.MIN_VALUE;//将限制转换为Integer的最小值，不能小于Integer的最小值  
               } else if (firstChar != '+')
                   throw NumberFormatException.forInputString(s);//第一个char不为+也不为-，则抛出异常  

               if (len == 1) // Cannot have lone "+" or "-"
                   throw NumberFormatException.forInputString(s);//若只有一个符号，则抛出异常
               i++;
           }
           multmin = limit / radix;//设定不同进制下的极限值  
           while (i < len) {//进行进制的转换
               // Accumulating negatively avoids surprises near MAX_VALUE
               digit = Character.digit(s.charAt(i++),radix);//将数字字符串转换成要求的进制数，使用工具类，每次遍历对一个字符进行操作转换  
               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;//根据符号返回正数还是负数
   }
    
    

    /**
     *  默认基数为10的静态方法:只能将数字字符串转化十进制数
     */
    public static int parseInt(String s) throws NumberFormatException {
        return parseInt(s,10);
    }

    /**
     * 内部缓存类
     *  缓存范围[-128，127] 在该范围内可以直接取出 超出该范围会创建一个新对象 ，测试
     *       Integer a1 = 120;
             Integer a2 = 120;
             Integer b1 = 200;
             Integer b2 = 200;
             System.out.println("a1 == a2:"+(a1 == a2)); //true
             System.out.println("a3 == a4:"+(a3 == a4)); //false
             System.out.println("---------------------"); 
             System.out.println("a1.equals(a2):"+a1.equals(a2)); //true
             System.out.println("a3.equals(a4):"+a3.equals(a4)); //true
        因此   Integer类型的比较使用 equals 《阿里巴巴java开发规范》
        缓存上届，可以通过JVM属性来配置java.lang.Integer.IntegerCache.high
     */

    private static class IntegerCache {
         //缓存的下界，-128，不可变  
        static final int low = -128;
        //缓存的上届
        static final int high;
        static final Integer cache[];

        static {
            // 默认上限127， 判断有没有配置上限 
            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
     *     ，官方推荐的创建对象的
     */
    public static Integer valueOf(int i) {
        //如果i在Integer缓存中，则直接取出
        if (i >= IntegerCache.low && i <= IntegerCache.high)
            return IntegerCache.cache[i + (-IntegerCache.low)];
        //重新创建 
        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
     */
    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
        return i & -i;
    }

    /**
     * Returns the number of zero bits preceding the highest-order
     * ("leftmost") one-bit in the two's complement binary representation
     * of the specified {@code int} value.  Returns 32 if the
     * specified value has no one-bits in its two's complement representation,
     * in other words if it is equal to zero.
     *
     * <p>Note that this method is closely related to the logarithm base 2.
     * For all positive {@code int} values x:
     * <ul>
     * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
     * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
     * </ul>
     *
     * @param i the value whose number of leading zeros is to be computed
     * @return the number of zero bits preceding the highest-order
     *     ("leftmost") one-bit in the two's complement binary representation
     *     of the specified {@code int} value, or 32 if the value
     *     is equal to zero.
     * @since 1.5
     */
    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;
    }

    /**
     * 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;
}