1 /*
   2  * Copyright (c) 1994, 2012, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.lang;
  27 
  28 import java.util.Properties;
  29 
  30 /**
  31  * The {@code Integer} class wraps a value of the primitive type
  32  * {@code int} in an object. An object of type {@code Integer}
  33  * contains a single field whose type is {@code int}.
  34  *
  35  * <p>In addition, this class provides several methods for converting
  36  * an {@code int} to a {@code String} and a {@code String} to an
  37  * {@code int}, as well as other constants and methods useful when
  38  * dealing with an {@code int}.
  39  *
  40  * <p>Implementation note: The implementations of the "bit twiddling"
  41  * methods (such as {@link #highestOneBit(int) highestOneBit} and
  42  * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
  43  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  44  * Delight</i>, (Addison Wesley, 2002).
  45  *
  46  * @author  Lee Boynton
  47  * @author  Arthur van Hoff
  48  * @author  Josh Bloch
  49  * @author  Joseph D. Darcy
  50  * @since JDK1.0
  51  */
  52 public final class Integer extends Number implements Comparable<Integer> {
  53     /**
  54      * A constant holding the minimum value an {@code int} can
  55      * have, -2<sup>31</sup>.
  56      */
  57     public static final int   MIN_VALUE = 0x80000000;
  58 
  59     /**
  60      * A constant holding the maximum value an {@code int} can
  61      * have, 2<sup>31</sup>-1.
  62      */
  63     public static final int   MAX_VALUE = 0x7fffffff;
  64 
  65     /**
  66      * The {@code Class} instance representing the primitive type
  67      * {@code int}.
  68      *
  69      * @since   JDK1.1
  70      */
  71     @SuppressWarnings("unchecked")
  72     public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
  73 
  74     /**
  75      * All possible chars for representing a number as a String
  76      */
  77     final static char[] digits = {
  78         '0' , '1' , '2' , '3' , '4' , '5' ,
  79         '6' , '7' , '8' , '9' , 'a' , 'b' ,
  80         'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
  81         'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
  82         'o' , 'p' , 'q' , 'r' , 's' , 't' ,
  83         'u' , 'v' , 'w' , 'x' , 'y' , 'z'
  84     };
  85 
  86     /**
  87      * Returns a string representation of the first argument in the
  88      * radix specified by the second argument.
  89      *
  90      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  91      * or larger than {@code Character.MAX_RADIX}, then the radix
  92      * {@code 10} is used instead.
  93      *
  94      * <p>If the first argument is negative, the first element of the
  95      * result is the ASCII minus character {@code '-'}
  96      * ({@code '\u005Cu002D'}). If the first argument is not
  97      * negative, no sign character appears in the result.
  98      *
  99      * <p>The remaining characters of the result represent the magnitude
 100      * of the first argument. If the magnitude is zero, it is
 101      * represented by a single zero character {@code '0'}
 102      * ({@code '\u005Cu0030'}); otherwise, the first character of
 103      * the representation of the magnitude will not be the zero
 104      * character.  The following ASCII characters are used as digits:
 105      *
 106      * <blockquote>
 107      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 108      * </blockquote>
 109      *
 110      * These are {@code '\u005Cu0030'} through
 111      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 112      * {@code '\u005Cu007A'}. If {@code radix} is
 113      * <var>N</var>, then the first <var>N</var> of these characters
 114      * are used as radix-<var>N</var> digits in the order shown. Thus,
 115      * the digits for hexadecimal (radix 16) are
 116      * {@code 0123456789abcdef}. If uppercase letters are
 117      * desired, the {@link java.lang.String#toUpperCase()} method may
 118      * be called on the result:
 119      *
 120      * <blockquote>
 121      *  {@code Integer.toString(n, 16).toUpperCase()}
 122      * </blockquote>
 123      *
 124      * @param   i       an integer to be converted to a string.
 125      * @param   radix   the radix to use in the string representation.
 126      * @return  a string representation of the argument in the specified radix.
 127      * @see     java.lang.Character#MAX_RADIX
 128      * @see     java.lang.Character#MIN_RADIX
 129      */
 130     public static String toString(int i, int radix) {
 131         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 132             radix = 10;
 133 
 134         /* Use the faster version */
 135         if (radix == 10) {
 136             return toString(i);
 137         }
 138 
 139         char buf[] = new char[33];
 140         boolean negative = (i < 0);
 141         int charPos = 32;
 142 
 143         if (!negative) {
 144             i = -i;
 145         }
 146 
 147         while (i <= -radix) {
 148             buf[charPos--] = digits[-(i % radix)];
 149             i = i / radix;
 150         }
 151         buf[charPos] = digits[-i];
 152 
 153         if (negative) {
 154             buf[--charPos] = '-';
 155         }
 156 
 157         return new String(buf, charPos, (33 - charPos));
 158     }
 159 
 160     /**
 161      * Returns a string representation of the first argument as an
 162      * unsigned integer value in the radix specified by the second
 163      * argument.
 164      *
 165      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 166      * or larger than {@code Character.MAX_RADIX}, then the radix
 167      * {@code 10} is used instead.
 168      *
 169      * <p>Note that since the first argument is treated as an unsigned
 170      * value, no leading sign character is printed.
 171      *
 172      * <p>If the magnitude is zero, it is represented by a single zero
 173      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 174      * the first character of the representation of the magnitude will
 175      * not be the zero character.
 176      *
 177      * <p>The behavior of radixes and the characters used as digits
 178      * are the same as {@link #toString(int, int) toString}.
 179      *
 180      * @param   i       an integer to be converted to an unsigned string.
 181      * @param   radix   the radix to use in the string representation.
 182      * @return  an unsigned string representation of the argument in the specified radix.
 183      * @see     #toString(int, int)
 184      * @since 1.8
 185      */
 186     public static String toUnsignedString(int i, int radix) {
 187         return Long.toString(toUnsignedLong(i), radix);
 188     }
 189 
 190     /**
 191      * Returns a string representation of the integer argument as an
 192      * unsigned integer in base&nbsp;16.
 193      *
 194      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 195      * if the argument is negative; otherwise, it is equal to the
 196      * argument.  This value is converted to a string of ASCII digits
 197      * in hexadecimal (base&nbsp;16) with no extra leading
 198      * {@code 0}s.
 199      *
 200      * <p>The value of the argument can be recovered from the returned
 201      * string {@code s} by calling {@link
 202      * Integer#parseUnsignedInt(String, int)
 203      * Integer.parseUnsignedInt(s, 16)}.
 204      *
 205      * <p>If the unsigned magnitude is zero, it is represented by a
 206      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 207      * otherwise, the first character of the representation of the
 208      * unsigned magnitude will not be the zero character. The
 209      * following characters are used as hexadecimal digits:
 210      *
 211      * <blockquote>
 212      *  {@code 0123456789abcdef}
 213      * </blockquote>
 214      *
 215      * These are the characters {@code '\u005Cu0030'} through
 216      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 217      * {@code '\u005Cu0066'}. If uppercase letters are
 218      * desired, the {@link java.lang.String#toUpperCase()} method may
 219      * be called on the result:
 220      *
 221      * <blockquote>
 222      *  {@code Integer.toHexString(n).toUpperCase()}
 223      * </blockquote>
 224      *
 225      * @param   i   an integer to be converted to a string.
 226      * @return  the string representation of the unsigned integer value
 227      *          represented by the argument in hexadecimal (base&nbsp;16).
 228      * @see #parseUnsignedInt(String, int)
 229      * @see #toUnsignedString(int, int)
 230      * @since   JDK1.0.2
 231      */
 232     public static String toHexString(int i) {
 233         return toUnsignedString0(i, 4);
 234     }
 235 
 236     /**
 237      * Returns a string representation of the integer argument as an
 238      * unsigned integer in base&nbsp;8.
 239      *
 240      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 241      * if the argument is negative; otherwise, it is equal to the
 242      * argument.  This value is converted to a string of ASCII digits
 243      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
 244      *
 245      * <p>The value of the argument can be recovered from the returned
 246      * string {@code s} by calling {@link
 247      * Integer#parseUnsignedInt(String, int)
 248      * Integer.parseUnsignedInt(s, 8)}.
 249      *
 250      * <p>If the unsigned magnitude is zero, it is represented by a
 251      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 252      * otherwise, the first character of the representation of the
 253      * unsigned magnitude will not be the zero character. The
 254      * following characters are used as octal digits:
 255      *
 256      * <blockquote>
 257      * {@code 01234567}
 258      * </blockquote>
 259      *
 260      * These are the characters {@code '\u005Cu0030'} through
 261      * {@code '\u005Cu0037'}.
 262      *
 263      * @param   i   an integer to be converted to a string.
 264      * @return  the string representation of the unsigned integer value
 265      *          represented by the argument in octal (base&nbsp;8).
 266      * @see #parseUnsignedInt(String, int)
 267      * @see #toUnsignedString(int, int)
 268      * @since   JDK1.0.2
 269      */
 270     public static String toOctalString(int i) {
 271         return toUnsignedString0(i, 3);
 272     }
 273 
 274     /**
 275      * Returns a string representation of the integer argument as an
 276      * unsigned integer in base&nbsp;2.
 277      *
 278      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 279      * if the argument is negative; otherwise it is equal to the
 280      * argument.  This value is converted to a string of ASCII digits
 281      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
 282      *
 283      * <p>The value of the argument can be recovered from the returned
 284      * string {@code s} by calling {@link
 285      * Integer#parseUnsignedInt(String, int)
 286      * Integer.parseUnsignedInt(s, 2)}.
 287      *
 288      * <p>If the unsigned magnitude is zero, it is represented by a
 289      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 290      * otherwise, the first character of the representation of the
 291      * unsigned magnitude will not be the zero character. The
 292      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 293      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 294      *
 295      * @param   i   an integer to be converted to a string.
 296      * @return  the string representation of the unsigned integer value
 297      *          represented by the argument in binary (base&nbsp;2).
 298      * @see #parseUnsignedInt(String, int)
 299      * @see #toUnsignedString(int, int)
 300      * @since   JDK1.0.2
 301      */
 302     public static String toBinaryString(int i) {
 303         return toUnsignedString0(i, 1);
 304     }
 305 
 306     /**
 307      * Convert the integer to an unsigned number.
 308      */
 309     private static String toUnsignedString0(int i, int shift) {
 310         char[] buf = new char[32];
 311         int charPos = 32;
 312         int radix = 1 << shift;
 313         int mask = radix - 1;
 314         do {
 315             buf[--charPos] = digits[i & mask];
 316             i >>>= shift;
 317         } while (i != 0);
 318 
 319         return new String(buf, charPos, (32 - charPos));
 320     }
 321 
 322 
 323     final static char [] DigitTens = {
 324         '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
 325         '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
 326         '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
 327         '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
 328         '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
 329         '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
 330         '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
 331         '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
 332         '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
 333         '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
 334         } ;
 335 
 336     final static char [] DigitOnes = {
 337         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 338         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 339         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 340         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 341         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 342         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 343         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 344         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 345         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 346         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 347         } ;
 348 
 349         // I use the "invariant division by multiplication" trick to
 350         // accelerate Integer.toString.  In particular we want to
 351         // avoid division by 10.
 352         //
 353         // The "trick" has roughly the same performance characteristics
 354         // as the "classic" Integer.toString code on a non-JIT VM.
 355         // The trick avoids .rem and .div calls but has a longer code
 356         // path and is thus dominated by dispatch overhead.  In the
 357         // JIT case the dispatch overhead doesn't exist and the
 358         // "trick" is considerably faster than the classic code.
 359         //
 360         // TODO-FIXME: convert (x * 52429) into the equiv shift-add
 361         // sequence.
 362         //
 363         // RE:  Division by Invariant Integers using Multiplication
 364         //      T Gralund, P Montgomery
 365         //      ACM PLDI 1994
 366         //
 367 
 368     /**
 369      * Returns a {@code String} object representing the
 370      * specified integer. The argument is converted to signed decimal
 371      * representation and returned as a string, exactly as if the
 372      * argument and radix 10 were given as arguments to the {@link
 373      * #toString(int, int)} method.
 374      *
 375      * @param   i   an integer to be converted.
 376      * @return  a string representation of the argument in base&nbsp;10.
 377      */
 378     public static String toString(int i) {
 379         if (i == Integer.MIN_VALUE)
 380             return "-2147483648";
 381         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
 382         char[] buf = new char[size];
 383         getChars(i, size, buf);
 384         return new String(buf, true);
 385     }
 386 
 387     /**
 388      * Returns a string representation of the argument as an unsigned
 389      * decimal value.
 390      *
 391      * The argument is converted to unsigned decimal representation
 392      * and returned as a string exactly as if the argument and radix
 393      * 10 were given as arguments to the {@link #toUnsignedString(int,
 394      * int)} method.
 395      *
 396      * @param   i  an integer to be converted to an unsigned string.
 397      * @return  an unsigned string representation of the argument.
 398      * @see     #toUnsignedString(int, int)
 399      * @since 1.8
 400      */
 401     public static String toUnsignedString(int i) {
 402         return Long.toString(toUnsignedLong(i));
 403     }
 404 
 405     /**
 406      * Places characters representing the integer i into the
 407      * character array buf. The characters are placed into
 408      * the buffer backwards starting with the least significant
 409      * digit at the specified index (exclusive), and working
 410      * backwards from there.
 411      *
 412      * Will fail if i == Integer.MIN_VALUE
 413      */
 414     static void getChars(int i, int index, char[] buf) {
 415         int q, r;
 416         int charPos = index;
 417         char sign = 0;
 418 
 419         if (i < 0) {
 420             sign = '-';
 421             i = -i;
 422         }
 423 
 424         // Generate two digits per iteration
 425         while (i >= 65536) {
 426             q = i / 100;
 427         // really: r = i - (q * 100);
 428             r = i - ((q << 6) + (q << 5) + (q << 2));
 429             i = q;
 430             buf [--charPos] = DigitOnes[r];
 431             buf [--charPos] = DigitTens[r];
 432         }
 433 
 434         // Fall thru to fast mode for smaller numbers
 435         // assert(i <= 65536, i);
 436         for (;;) {
 437             q = (i * 52429) >>> (16+3);
 438             r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
 439             buf [--charPos] = digits [r];
 440             i = q;
 441             if (i == 0) break;
 442         }
 443         if (sign != 0) {
 444             buf [--charPos] = sign;
 445         }
 446     }
 447 
 448     final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
 449                                       99999999, 999999999, Integer.MAX_VALUE };
 450 
 451     // Requires positive x
 452     static int stringSize(int x) {
 453         for (int i=0; ; i++)
 454             if (x <= sizeTable[i])
 455                 return i+1;
 456     }
 457 
 458     /**
 459      * Parses the string argument as a signed integer in the radix
 460      * specified by the second argument. The characters in the string
 461      * must all be digits of the specified radix (as determined by
 462      * whether {@link java.lang.Character#digit(char, int)} returns a
 463      * nonnegative value), except that the first character may be an
 464      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 465      * indicate a negative value or an ASCII plus sign {@code '+'}
 466      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 467      * resulting integer value is returned.
 468      *
 469      * <p>An exception of type {@code NumberFormatException} is
 470      * thrown if any of the following situations occurs:
 471      * <ul>
 472      * <li>The first argument is {@code null} or is a string of
 473      * length zero.
 474      *
 475      * <li>The radix is either smaller than
 476      * {@link java.lang.Character#MIN_RADIX} or
 477      * larger than {@link java.lang.Character#MAX_RADIX}.
 478      *
 479      * <li>Any character of the string is not a digit of the specified
 480      * radix, except that the first character may be a minus sign
 481      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
 482      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 483      * string is longer than length 1.
 484      *
 485      * <li>The value represented by the string is not a value of type
 486      * {@code int}.
 487      * </ul>
 488      *
 489      * <p>Examples:
 490      * <blockquote><pre>
 491      * parseInt("0", 10) returns 0
 492      * parseInt("473", 10) returns 473
 493      * parseInt("+42", 10) returns 42
 494      * parseInt("-0", 10) returns 0
 495      * parseInt("-FF", 16) returns -255
 496      * parseInt("1100110", 2) returns 102
 497      * parseInt("2147483647", 10) returns 2147483647
 498      * parseInt("-2147483648", 10) returns -2147483648
 499      * parseInt("2147483648", 10) throws a NumberFormatException
 500      * parseInt("99", 8) throws a NumberFormatException
 501      * parseInt("Kona", 10) throws a NumberFormatException
 502      * parseInt("Kona", 27) returns 411787
 503      * </pre></blockquote>
 504      *
 505      * @param      s   the {@code String} containing the integer
 506      *                  representation to be parsed
 507      * @param      radix   the radix to be used while parsing {@code s}.
 508      * @return     the integer represented by the string argument in the
 509      *             specified radix.
 510      * @exception  NumberFormatException if the {@code String}
 511      *             does not contain a parsable {@code int}.
 512      */
 513     public static int parseInt(String s, int radix)
 514                 throws NumberFormatException
 515     {
 516         /*
 517          * WARNING: This method may be invoked early during VM initialization
 518          * before IntegerCache is initialized. Care must be taken to not use
 519          * the valueOf method.
 520          */
 521 
 522         if (s == null) {
 523             throw new NumberFormatException("null");
 524         }
 525 
 526         if (radix < Character.MIN_RADIX) {
 527             throw new NumberFormatException("radix " + radix +
 528                                             " less than Character.MIN_RADIX");
 529         }
 530 
 531         if (radix > Character.MAX_RADIX) {
 532             throw new NumberFormatException("radix " + radix +
 533                                             " greater than Character.MAX_RADIX");
 534         }
 535 
 536         int result = 0;
 537         boolean negative = false;
 538         int i = 0, len = s.length();
 539         int limit = -Integer.MAX_VALUE;
 540         int multmin;
 541         int digit;
 542 
 543         if (len > 0) {
 544             char firstChar = s.charAt(0);
 545             if (firstChar < '0') { // Possible leading "+" or "-"
 546                 if (firstChar == '-') {
 547                     negative = true;
 548                     limit = Integer.MIN_VALUE;
 549                 } else if (firstChar != '+')
 550                     throw NumberFormatException.forInputString(s);
 551 
 552                 if (len == 1) // Cannot have lone "+" or "-"
 553                     throw NumberFormatException.forInputString(s);
 554                 i++;
 555             }
 556             multmin = limit / radix;
 557             while (i < len) {
 558                 // Accumulating negatively avoids surprises near MAX_VALUE
 559                 digit = Character.digit(s.charAt(i++),radix);
 560                 if (digit < 0) {
 561                     throw NumberFormatException.forInputString(s);
 562                 }
 563                 if (result < multmin) {
 564                     throw NumberFormatException.forInputString(s);
 565                 }
 566                 result *= radix;
 567                 if (result < limit + digit) {
 568                     throw NumberFormatException.forInputString(s);
 569                 }
 570                 result -= digit;
 571             }
 572         } else {
 573             throw NumberFormatException.forInputString(s);
 574         }
 575         return negative ? result : -result;
 576     }
 577 
 578     /**
 579      * Parses the string argument as a signed decimal integer. The
 580      * characters in the string must all be decimal digits, except
 581      * that the first character may be an ASCII minus sign {@code '-'}
 582      * ({@code '\u005Cu002D'}) to indicate a negative value or an
 583      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 584      * indicate a positive value. The resulting integer value is
 585      * returned, exactly as if the argument and the radix 10 were
 586      * given as arguments to the {@link #parseInt(java.lang.String,
 587      * int)} method.
 588      *
 589      * @param s    a {@code String} containing the {@code int}
 590      *             representation to be parsed
 591      * @return     the integer value represented by the argument in decimal.
 592      * @exception  NumberFormatException  if the string does not contain a
 593      *               parsable integer.
 594      */
 595     public static int parseInt(String s) throws NumberFormatException {
 596         return parseInt(s,10);
 597     }
 598 
 599     /**
 600      * Parses the string argument as an unsigned integer in the radix
 601      * specified by the second argument.  An unsigned integer maps the
 602      * values usually associated with negative numbers to positive
 603      * numbers larger than {@code MAX_VALUE}.
 604      *
 605      * The characters in the string must all be digits of the
 606      * specified radix (as determined by whether {@link
 607      * java.lang.Character#digit(char, int)} returns a nonnegative
 608      * value), except that the first character may be an ASCII plus
 609      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 610      * integer value is returned.
 611      *
 612      * <p>An exception of type {@code NumberFormatException} is
 613      * thrown if any of the following situations occurs:
 614      * <ul>
 615      * <li>The first argument is {@code null} or is a string of
 616      * length zero.
 617      *
 618      * <li>The radix is either smaller than
 619      * {@link java.lang.Character#MIN_RADIX} or
 620      * larger than {@link java.lang.Character#MAX_RADIX}.
 621      *
 622      * <li>Any character of the string is not a digit of the specified
 623      * radix, except that the first character may be a plus sign
 624      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 625      * string is longer than length 1.
 626      *
 627      * <li>The value represented by the string is larger than the
 628      * largest unsigned {@code int}, 2<sup>32</sup>-1.
 629      *
 630      * </ul>
 631      *
 632      *
 633      * @param      s   the {@code String} containing the unsigned integer
 634      *                  representation to be parsed
 635      * @param      radix   the radix to be used while parsing {@code s}.
 636      * @return     the integer represented by the string argument in the
 637      *             specified radix.
 638      * @throws     NumberFormatException if the {@code String}
 639      *             does not contain a parsable {@code int}.
 640      * @since 1.8
 641      */
 642     public static int parseUnsignedInt(String s, int radix)
 643                 throws NumberFormatException {
 644         if (s == null)  {
 645             throw new NumberFormatException("null");
 646         }
 647 
 648         int len = s.length();
 649         if (len > 0) {
 650             char firstChar = s.charAt(0);
 651             if (firstChar == '-') {
 652                 throw new
 653                     NumberFormatException(String.format("Illegal leading minus sign " +
 654                                                        "on unsigned string %s.", s));
 655             } else {
 656                 if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
 657                     (radix == 10 && len <= 9) ) { // Integer.MAX_VALUE in base 10 is 10 digits
 658                     return parseInt(s, radix);
 659                 } else {
 660                     long ell = Long.parseLong(s, radix);
 661                     if ((ell & 0xffff_ffff_0000_0000L) == 0) {
 662                         return (int) ell;
 663                     } else {
 664                         throw new
 665                             NumberFormatException(String.format("String value %s exceeds " +
 666                                                                 "range of unsigned int.", s));
 667                     }
 668                 }
 669             }
 670         } else {
 671             throw NumberFormatException.forInputString(s);
 672         }
 673     }
 674 
 675     /**
 676      * Parses the string argument as an unsigned decimal integer. The
 677      * characters in the string must all be decimal digits, except
 678      * that the first character may be an an ASCII plus sign {@code
 679      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 680      * is returned, exactly as if the argument and the radix 10 were
 681      * given as arguments to the {@link
 682      * #parseUnsignedInt(java.lang.String, int)} method.
 683      *
 684      * @param s   a {@code String} containing the unsigned {@code int}
 685      *            representation to be parsed
 686      * @return    the unsigned integer value represented by the argument in decimal.
 687      * @throws    NumberFormatException  if the string does not contain a
 688      *            parsable unsigned integer.
 689      * @since 1.8
 690      */
 691     public static int parseUnsignedInt(String s) throws NumberFormatException {
 692         return parseUnsignedInt(s, 10);
 693     }
 694 
 695     /**
 696      * Returns an {@code Integer} object holding the value
 697      * extracted from the specified {@code String} when parsed
 698      * with the radix given by the second argument. The first argument
 699      * is interpreted as representing a signed integer in the radix
 700      * specified by the second argument, exactly as if the arguments
 701      * were given to the {@link #parseInt(java.lang.String, int)}
 702      * method. The result is an {@code Integer} object that
 703      * represents the integer value specified by the string.
 704      *
 705      * <p>In other words, this method returns an {@code Integer}
 706      * object equal to the value of:
 707      *
 708      * <blockquote>
 709      *  {@code new Integer(Integer.parseInt(s, radix))}
 710      * </blockquote>
 711      *
 712      * @param      s   the string to be parsed.
 713      * @param      radix the radix to be used in interpreting {@code s}
 714      * @return     an {@code Integer} object holding the value
 715      *             represented by the string argument in the specified
 716      *             radix.
 717      * @exception NumberFormatException if the {@code String}
 718      *            does not contain a parsable {@code int}.
 719      */
 720     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 721         return Integer.valueOf(parseInt(s,radix));
 722     }
 723 
 724     /**
 725      * Returns an {@code Integer} object holding the
 726      * value of the specified {@code String}. The argument is
 727      * interpreted as representing a signed decimal integer, exactly
 728      * as if the argument were given to the {@link
 729      * #parseInt(java.lang.String)} method. The result is an
 730      * {@code Integer} object that represents the integer value
 731      * specified by the string.
 732      *
 733      * <p>In other words, this method returns an {@code Integer}
 734      * object equal to the value of:
 735      *
 736      * <blockquote>
 737      *  {@code new Integer(Integer.parseInt(s))}
 738      * </blockquote>
 739      *
 740      * @param      s   the string to be parsed.
 741      * @return     an {@code Integer} object holding the value
 742      *             represented by the string argument.
 743      * @exception  NumberFormatException  if the string cannot be parsed
 744      *             as an integer.
 745      */
 746     public static Integer valueOf(String s) throws NumberFormatException {
 747         return Integer.valueOf(parseInt(s, 10));
 748     }
 749 
 750     /**
 751      * Cache to support the object identity semantics of autoboxing for values between
 752      * -128 and 127 (inclusive) as required by JLS.
 753      *
 754      * The cache is initialized on first usage.  The size of the cache
 755      * may be controlled by the -XX:AutoBoxCacheMax=<size> option.
 756      * During VM initialization, java.lang.Integer.IntegerCache.high property
 757      * may be set and saved in the private system properties in the
 758      * sun.misc.VM class.
 759      */
 760 
 761     private static class IntegerCache {
 762         static final int low = -128;
 763         static final int high;
 764         static final Integer cache[];
 765 
 766         static {
 767             // high value may be configured by property
 768             int h = 127;
 769             String integerCacheHighPropValue =
 770                 sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 771             if (integerCacheHighPropValue != null) {
 772                 int i = parseInt(integerCacheHighPropValue);
 773                 i = Math.max(i, 127);
 774                 // Maximum array size is Integer.MAX_VALUE
 775                 h = Math.min(i, Integer.MAX_VALUE - (-low));
 776             }
 777             high = h;
 778 
 779             cache = new Integer[(high - low) + 1];
 780             int j = low;
 781             for(int k = 0; k < cache.length; k++)
 782                 cache[k] = new Integer(j++);
 783 
 784             // range [-128, 127] must be interned (JLS7 5.1.7)
 785             assert IntegerCache.high >= 127;
 786         }
 787 
 788         private IntegerCache() {}
 789     }
 790 
 791     /**
 792      * Returns an {@code Integer} instance representing the specified
 793      * {@code int} value.  If a new {@code Integer} instance is not
 794      * required, this method should generally be used in preference to
 795      * the constructor {@link #Integer(int)}, as this method is likely
 796      * to yield significantly better space and time performance by
 797      * caching frequently requested values.
 798      *
 799      * This method will always cache values in the range -128 to 127,
 800      * inclusive, and may cache other values outside of this range.
 801      *
 802      * @param  i an {@code int} value.
 803      * @return an {@code Integer} instance representing {@code i}.
 804      * @since  1.5
 805      */
 806     public static Integer valueOf(int i) {
 807         if (i >= IntegerCache.low && i <= IntegerCache.high)
 808             return IntegerCache.cache[i + (-IntegerCache.low)];
 809         return new Integer(i);
 810     }
 811 
 812     /**
 813      * The value of the {@code Integer}.
 814      *
 815      * @serial
 816      */
 817     private final int value;
 818 
 819     /**
 820      * Constructs a newly allocated {@code Integer} object that
 821      * represents the specified {@code int} value.
 822      *
 823      * @param   value   the value to be represented by the
 824      *                  {@code Integer} object.
 825      */
 826     public Integer(int value) {
 827         this.value = value;
 828     }
 829 
 830     /**
 831      * Constructs a newly allocated {@code Integer} object that
 832      * represents the {@code int} value indicated by the
 833      * {@code String} parameter. The string is converted to an
 834      * {@code int} value in exactly the manner used by the
 835      * {@code parseInt} method for radix 10.
 836      *
 837      * @param      s   the {@code String} to be converted to an
 838      *                 {@code Integer}.
 839      * @exception  NumberFormatException  if the {@code String} does not
 840      *               contain a parsable integer.
 841      * @see        java.lang.Integer#parseInt(java.lang.String, int)
 842      */
 843     public Integer(String s) throws NumberFormatException {
 844         this.value = parseInt(s, 10);
 845     }
 846 
 847     /**
 848      * Returns the value of this {@code Integer} as a {@code byte}
 849      * after a narrowing primitive conversion.
 850      * @jls 5.1.3 Narrowing Primitive Conversions
 851      */
 852     public byte byteValue() {
 853         return (byte)value;
 854     }
 855 
 856     /**
 857      * Returns the value of this {@code Integer} as a {@code short}
 858      * after a narrowing primitive conversion.
 859      * @jls 5.1.3 Narrowing Primitive Conversions
 860      */
 861     public short shortValue() {
 862         return (short)value;
 863     }
 864 
 865     /**
 866      * Returns the value of this {@code Integer} as an
 867      * {@code int}.
 868      */
 869     public int intValue() {
 870         return value;
 871     }
 872 
 873     /**
 874      * Returns the value of this {@code Integer} as a {@code long}
 875      * after a widening primitive conversion.
 876      * @jls 5.1.2 Widening Primitive Conversions
 877      */
 878     public long longValue() {
 879         return (long)value;
 880     }
 881 
 882     /**
 883      * Returns the value of this {@code Integer} as a {@code float}
 884      * after a widening primitive conversion.
 885      * @jls 5.1.2 Widening Primitive Conversions
 886      */
 887     public float floatValue() {
 888         return (float)value;
 889     }
 890 
 891     /**
 892      * Returns the value of this {@code Integer} as a {@code double}
 893      * after a widening primitive conversion.
 894      * @jls 5.1.2 Widening Primitive Conversions
 895      */
 896     public double doubleValue() {
 897         return (double)value;
 898     }
 899 
 900     /**
 901      * Returns a {@code String} object representing this
 902      * {@code Integer}'s value. The value is converted to signed
 903      * decimal representation and returned as a string, exactly as if
 904      * the integer value were given as an argument to the {@link
 905      * java.lang.Integer#toString(int)} method.
 906      *
 907      * @return  a string representation of the value of this object in
 908      *          base&nbsp;10.
 909      */
 910     public String toString() {
 911         return toString(value);
 912     }
 913 
 914     /**
 915      * Returns a hash code for this {@code Integer}.
 916      *
 917      * @return  a hash code value for this object, equal to the
 918      *          primitive {@code int} value represented by this
 919      *          {@code Integer} object.
 920      */
 921     public int hashCode() {
 922         return value;
 923     }
 924 
 925     /**
 926      * Compares this object to the specified object.  The result is
 927      * {@code true} if and only if the argument is not
 928      * {@code null} and is an {@code Integer} object that
 929      * contains the same {@code int} value as this object.
 930      *
 931      * @param   obj   the object to compare with.
 932      * @return  {@code true} if the objects are the same;
 933      *          {@code false} otherwise.
 934      */
 935     public boolean equals(Object obj) {
 936         if (obj instanceof Integer) {
 937             return value == ((Integer)obj).intValue();
 938         }
 939         return false;
 940     }
 941 
 942     /**
 943      * Determines the integer value of the system property with the
 944      * specified name.
 945      *
 946      * <p>The first argument is treated as the name of a system
 947      * property.  System properties are accessible through the {@link
 948      * java.lang.System#getProperty(java.lang.String)} method. The
 949      * string value of this property is then interpreted as an integer
 950      * value using the grammar supported by {@link Integer#decode decode} and
 951      * an {@code Integer} object representing this value is returned.
 952      *
 953      * <p>If there is no property with the specified name, if the
 954      * specified name is empty or {@code null}, or if the property
 955      * does not have the correct numeric format, then {@code null} is
 956      * returned.
 957      *
 958      * <p>In other words, this method returns an {@code Integer}
 959      * object equal to the value of:
 960      *
 961      * <blockquote>
 962      *  {@code getInteger(nm, null)}
 963      * </blockquote>
 964      *
 965      * @param   nm   property name.
 966      * @return  the {@code Integer} value of the property.
 967      * @throws  SecurityException for the same reasons as
 968      *          {@link System#getProperty(String) System.getProperty}
 969      * @see     java.lang.System#getProperty(java.lang.String)
 970      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
 971      */
 972     public static Integer getInteger(String nm) {
 973         return getInteger(nm, null);
 974     }
 975 
 976     /**
 977      * Determines the integer value of the system property with the
 978      * specified name.
 979      *
 980      * <p>The first argument is treated as the name of a system
 981      * property.  System properties are accessible through the {@link
 982      * java.lang.System#getProperty(java.lang.String)} method. The
 983      * string value of this property is then interpreted as an integer
 984      * value using the grammar supported by {@link Integer#decode decode} and
 985      * an {@code Integer} object representing this value is returned.
 986      *
 987      * <p>The second argument is the default value. An {@code Integer} object
 988      * that represents the value of the second argument is returned if there
 989      * is no property of the specified name, if the property does not have
 990      * the correct numeric format, or if the specified name is empty or
 991      * {@code null}.
 992      *
 993      * <p>In other words, this method returns an {@code Integer} object
 994      * equal to the value of:
 995      *
 996      * <blockquote>
 997      *  {@code getInteger(nm, new Integer(val))}
 998      * </blockquote>
 999      *
1000      * but in practice it may be implemented in a manner such as:
1001      *
1002      * <blockquote><pre>
1003      * Integer result = getInteger(nm, null);
1004      * return (result == null) ? new Integer(val) : result;
1005      * </pre></blockquote>
1006      *
1007      * to avoid the unnecessary allocation of an {@code Integer}
1008      * object when the default value is not needed.
1009      *
1010      * @param   nm   property name.
1011      * @param   val   default value.
1012      * @return  the {@code Integer} value of the property.
1013      * @throws  SecurityException for the same reasons as
1014      *          {@link System#getProperty(String) System.getProperty}
1015      * @see     java.lang.System#getProperty(java.lang.String)
1016      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1017      */
1018     public static Integer getInteger(String nm, int val) {
1019         Integer result = getInteger(nm, null);
1020         return (result == null) ? Integer.valueOf(val) : result;
1021     }
1022 
1023     /**
1024      * Returns the integer value of the system property with the
1025      * specified name.  The first argument is treated as the name of a
1026      * system property.  System properties are accessible through the
1027      * {@link java.lang.System#getProperty(java.lang.String)} method.
1028      * The string value of this property is then interpreted as an
1029      * integer value, as per the {@link Integer#decode decode} method,
1030      * and an {@code Integer} object representing this value is
1031      * returned; in summary:
1032      *
1033      * <ul><li>If the property value begins with the two ASCII characters
1034      *         {@code 0x} or the ASCII character {@code #}, not
1035      *      followed by a minus sign, then the rest of it is parsed as a
1036      *      hexadecimal integer exactly as by the method
1037      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1038      * <li>If the property value begins with the ASCII character
1039      *     {@code 0} followed by another character, it is parsed as an
1040      *     octal integer exactly as by the method
1041      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1042      * <li>Otherwise, the property value is parsed as a decimal integer
1043      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1044      * with radix 10.
1045      * </ul>
1046      *
1047      * <p>The second argument is the default value. The default value is
1048      * returned if there is no property of the specified name, if the
1049      * property does not have the correct numeric format, or if the
1050      * specified name is empty or {@code null}.
1051      *
1052      * @param   nm   property name.
1053      * @param   val   default value.
1054      * @return  the {@code Integer} value of the property.
1055      * @throws  SecurityException for the same reasons as
1056      *          {@link System#getProperty(String) System.getProperty}
1057      * @see     System#getProperty(java.lang.String)
1058      * @see     System#getProperty(java.lang.String, java.lang.String)
1059      */
1060     public static Integer getInteger(String nm, Integer val) {
1061         String v = null;
1062         try {
1063             v = System.getProperty(nm);
1064         } catch (IllegalArgumentException | NullPointerException e) {
1065         }
1066         if (v != null) {
1067             try {
1068                 return Integer.decode(v);
1069             } catch (NumberFormatException e) {
1070             }
1071         }
1072         return val;
1073     }
1074 
1075     /**
1076      * Decodes a {@code String} into an {@code Integer}.
1077      * Accepts decimal, hexadecimal, and octal numbers given
1078      * by the following grammar:
1079      *
1080      * <blockquote>
1081      * <dl>
1082      * <dt><i>DecodableString:</i>
1083      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1084      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1085      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1086      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1087      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1088      * <p>
1089      * <dt><i>Sign:</i>
1090      * <dd>{@code -}
1091      * <dd>{@code +}
1092      * </dl>
1093      * </blockquote>
1094      *
1095      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1096      * are as defined in section 3.10.1 of
1097      * <cite>The Java&trade; Language Specification</cite>,
1098      * except that underscores are not accepted between digits.
1099      *
1100      * <p>The sequence of characters following an optional
1101      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1102      * "{@code #}", or leading zero) is parsed as by the {@code
1103      * Integer.parseInt} method with the indicated radix (10, 16, or
1104      * 8).  This sequence of characters must represent a positive
1105      * value or a {@link NumberFormatException} will be thrown.  The
1106      * result is negated if first character of the specified {@code
1107      * String} is the minus sign.  No whitespace characters are
1108      * permitted in the {@code String}.
1109      *
1110      * @param     nm the {@code String} to decode.
1111      * @return    an {@code Integer} object holding the {@code int}
1112      *             value represented by {@code nm}
1113      * @exception NumberFormatException  if the {@code String} does not
1114      *            contain a parsable integer.
1115      * @see java.lang.Integer#parseInt(java.lang.String, int)
1116      */
1117     public static Integer decode(String nm) throws NumberFormatException {
1118         int radix = 10;
1119         int index = 0;
1120         boolean negative = false;
1121         Integer result;
1122 
1123         if (nm.length() == 0)
1124             throw new NumberFormatException("Zero length string");
1125         char firstChar = nm.charAt(0);
1126         // Handle sign, if present
1127         if (firstChar == '-') {
1128             negative = true;
1129             index++;
1130         } else if (firstChar == '+')
1131             index++;
1132 
1133         // Handle radix specifier, if present
1134         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1135             index += 2;
1136             radix = 16;
1137         }
1138         else if (nm.startsWith("#", index)) {
1139             index ++;
1140             radix = 16;
1141         }
1142         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1143             index ++;
1144             radix = 8;
1145         }
1146 
1147         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1148             throw new NumberFormatException("Sign character in wrong position");
1149 
1150         try {
1151             result = Integer.valueOf(nm.substring(index), radix);
1152             result = negative ? Integer.valueOf(-result.intValue()) : result;
1153         } catch (NumberFormatException e) {
1154             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1155             // handles this case, and causes any genuine format error to be
1156             // rethrown.
1157             String constant = negative ? ("-" + nm.substring(index))
1158                                        : nm.substring(index);
1159             result = Integer.valueOf(constant, radix);
1160         }
1161         return result;
1162     }
1163 
1164     /**
1165      * Compares two {@code Integer} objects numerically.
1166      *
1167      * @param   anotherInteger   the {@code Integer} to be compared.
1168      * @return  the value {@code 0} if this {@code Integer} is
1169      *          equal to the argument {@code Integer}; a value less than
1170      *          {@code 0} if this {@code Integer} is numerically less
1171      *          than the argument {@code Integer}; and a value greater
1172      *          than {@code 0} if this {@code Integer} is numerically
1173      *           greater than the argument {@code Integer} (signed
1174      *           comparison).
1175      * @since   1.2
1176      */
1177     public int compareTo(Integer anotherInteger) {
1178         return compare(this.value, anotherInteger.value);
1179     }
1180 
1181     /**
1182      * Compares two {@code int} values numerically.
1183      * The value returned is identical to what would be returned by:
1184      * <pre>
1185      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1186      * </pre>
1187      *
1188      * @param  x the first {@code int} to compare
1189      * @param  y the second {@code int} to compare
1190      * @return the value {@code 0} if {@code x == y};
1191      *         a value less than {@code 0} if {@code x < y}; and
1192      *         a value greater than {@code 0} if {@code x > y}
1193      * @since 1.7
1194      */
1195     public static int compare(int x, int y) {
1196         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1197     }
1198 
1199     /**
1200      * Compares two {@code int} values numerically treating the values
1201      * as unsigned.
1202      *
1203      * @param  x the first {@code int} to compare
1204      * @param  y the second {@code int} to compare
1205      * @return the value {@code 0} if {@code x == y}; a value less
1206      *         than {@code 0} if {@code x < y} as unsigned values; and
1207      *         a value greater than {@code 0} if {@code x > y} as
1208      *         unsigned values
1209      * @since 1.8
1210      */
1211     public static int compareUnsigned(int x, int y) {
1212         return compare(x + MIN_VALUE, y + MIN_VALUE);
1213     }
1214 
1215     /**
1216      * Converts the argument to a {@code long} by an unsigned
1217      * conversion.  In an unsigned conversion to a {@code long}, the
1218      * high-order 32 bits of the {@code long} are zero and the
1219      * low-order 32 bits are equal to the bits of the integer
1220      * argument.
1221      *
1222      * Consequently, zero and positive {@code int} values are mapped
1223      * to a numerically equal {@code long} value and negative {@code
1224      * int} values are mapped to a {@code long} value equal to the
1225      * input plus 2<sup>32</sup>.
1226      *
1227      * @param  x the value to convert to an unsigned {@code long}
1228      * @return the argument converted to {@code long} by an unsigned
1229      *         conversion
1230      * @since 1.8
1231      */
1232     public static long toUnsignedLong(int x) {
1233         return ((long) x) & 0xffffffffL;
1234     }
1235 
1236     /**
1237      * Returns the unsigned quotient of dividing the first argument by
1238      * the second where each argument and the result is interpreted as
1239      * an unsigned value.
1240      *
1241      * <p>Note that in two's complement arithmetic, the three other
1242      * basic arithmetic operations of add, subtract, and multiply are
1243      * bit-wise identical if the two operands are regarded as both
1244      * being signed or both being unsigned.  Therefore separate {@code
1245      * addUnsigned}, etc. methods are not provided.
1246      *
1247      * @param dividend the value to be divided
1248      * @param divisor the value doing the dividing
1249      * @return the unsigned quotient of the first argument divided by
1250      * the second argument
1251      * @see #remainderUnsigned
1252      * @since 1.8
1253      */
1254     public static int divideUnsigned(int dividend, int divisor) {
1255         // In lieu of tricky code, for now just use long arithmetic.
1256         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1257     }
1258 
1259     /**
1260      * Returns the unsigned remainder from dividing the first argument
1261      * by the second where each argument and the result is interpreted
1262      * as an unsigned value.
1263      *
1264      * @param dividend the value to be divided
1265      * @param divisor the value doing the dividing
1266      * @return the unsigned remainder of the first argument divided by
1267      * the second argument
1268      * @see #divideUnsigned
1269      * @since 1.8
1270      */
1271     public static int remainderUnsigned(int dividend, int divisor) {
1272         // In lieu of tricky code, for now just use long arithmetic.
1273         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1274     }
1275 
1276 
1277     // Bit twiddling
1278 
1279     /**
1280      * The number of bits used to represent an {@code int} value in two's
1281      * complement binary form.
1282      *
1283      * @since 1.5
1284      */
1285     public static final int SIZE = 32;
1286 
1287     /**
1288      * Returns an {@code int} value with at most a single one-bit, in the
1289      * position of the highest-order ("leftmost") one-bit in the specified
1290      * {@code int} value.  Returns zero if the specified value has no
1291      * one-bits in its two's complement binary representation, that is, if it
1292      * is equal to zero.
1293      *
1294      * @return an {@code int} value with a single one-bit, in the position
1295      *     of the highest-order one-bit in the specified value, or zero if
1296      *     the specified value is itself equal to zero.
1297      * @since 1.5
1298      */
1299     public static int highestOneBit(int i) {
1300         // HD, Figure 3-1
1301         i |= (i >>  1);
1302         i |= (i >>  2);
1303         i |= (i >>  4);
1304         i |= (i >>  8);
1305         i |= (i >> 16);
1306         return i - (i >>> 1);
1307     }
1308 
1309     /**
1310      * Returns an {@code int} value with at most a single one-bit, in the
1311      * position of the lowest-order ("rightmost") one-bit in the specified
1312      * {@code int} value.  Returns zero if the specified value has no
1313      * one-bits in its two's complement binary representation, that is, if it
1314      * is equal to zero.
1315      *
1316      * @return an {@code int} value with a single one-bit, in the position
1317      *     of the lowest-order one-bit in the specified value, or zero if
1318      *     the specified value is itself equal to zero.
1319      * @since 1.5
1320      */
1321     public static int lowestOneBit(int i) {
1322         // HD, Section 2-1
1323         return i & -i;
1324     }
1325 
1326     /**
1327      * Returns the number of zero bits preceding the highest-order
1328      * ("leftmost") one-bit in the two's complement binary representation
1329      * of the specified {@code int} value.  Returns 32 if the
1330      * specified value has no one-bits in its two's complement representation,
1331      * in other words if it is equal to zero.
1332      *
1333      * <p>Note that this method is closely related to the logarithm base 2.
1334      * For all positive {@code int} values x:
1335      * <ul>
1336      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1337      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1338      * </ul>
1339      *
1340      * @return the number of zero bits preceding the highest-order
1341      *     ("leftmost") one-bit in the two's complement binary representation
1342      *     of the specified {@code int} value, or 32 if the value
1343      *     is equal to zero.
1344      * @since 1.5
1345      */
1346     public static int numberOfLeadingZeros(int i) {
1347         // HD, Figure 5-6
1348         if (i == 0)
1349             return 32;
1350         int n = 1;
1351         if (i >>> 16 == 0) { n += 16; i <<= 16; }
1352         if (i >>> 24 == 0) { n +=  8; i <<=  8; }
1353         if (i >>> 28 == 0) { n +=  4; i <<=  4; }
1354         if (i >>> 30 == 0) { n +=  2; i <<=  2; }
1355         n -= i >>> 31;
1356         return n;
1357     }
1358 
1359     /**
1360      * Returns the number of zero bits following the lowest-order ("rightmost")
1361      * one-bit in the two's complement binary representation of the specified
1362      * {@code int} value.  Returns 32 if the specified value has no
1363      * one-bits in its two's complement representation, in other words if it is
1364      * equal to zero.
1365      *
1366      * @return the number of zero bits following the lowest-order ("rightmost")
1367      *     one-bit in the two's complement binary representation of the
1368      *     specified {@code int} value, or 32 if the value is equal
1369      *     to zero.
1370      * @since 1.5
1371      */
1372     public static int numberOfTrailingZeros(int i) {
1373         // HD, Figure 5-14
1374         int y;
1375         if (i == 0) return 32;
1376         int n = 31;
1377         y = i <<16; if (y != 0) { n = n -16; i = y; }
1378         y = i << 8; if (y != 0) { n = n - 8; i = y; }
1379         y = i << 4; if (y != 0) { n = n - 4; i = y; }
1380         y = i << 2; if (y != 0) { n = n - 2; i = y; }
1381         return n - ((i << 1) >>> 31);
1382     }
1383 
1384     /**
1385      * Returns the number of one-bits in the two's complement binary
1386      * representation of the specified {@code int} value.  This function is
1387      * sometimes referred to as the <i>population count</i>.
1388      *
1389      * @return the number of one-bits in the two's complement binary
1390      *     representation of the specified {@code int} value.
1391      * @since 1.5
1392      */
1393     public static int bitCount(int i) {
1394         // HD, Figure 5-2
1395         i = i - ((i >>> 1) & 0x55555555);
1396         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1397         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1398         i = i + (i >>> 8);
1399         i = i + (i >>> 16);
1400         return i & 0x3f;
1401     }
1402 
1403     /**
1404      * Returns the value obtained by rotating the two's complement binary
1405      * representation of the specified {@code int} value left by the
1406      * specified number of bits.  (Bits shifted out of the left hand, or
1407      * high-order, side reenter on the right, or low-order.)
1408      *
1409      * <p>Note that left rotation with a negative distance is equivalent to
1410      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1411      * distance)}.  Note also that rotation by any multiple of 32 is a
1412      * no-op, so all but the last five bits of the rotation distance can be
1413      * ignored, even if the distance is negative: {@code rotateLeft(val,
1414      * distance) == rotateLeft(val, distance & 0x1F)}.
1415      *
1416      * @return the value obtained by rotating the two's complement binary
1417      *     representation of the specified {@code int} value left by the
1418      *     specified number of bits.
1419      * @since 1.5
1420      */
1421     public static int rotateLeft(int i, int distance) {
1422         return (i << distance) | (i >>> -distance);
1423     }
1424 
1425     /**
1426      * Returns the value obtained by rotating the two's complement binary
1427      * representation of the specified {@code int} value right by the
1428      * specified number of bits.  (Bits shifted out of the right hand, or
1429      * low-order, side reenter on the left, or high-order.)
1430      *
1431      * <p>Note that right rotation with a negative distance is equivalent to
1432      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1433      * distance)}.  Note also that rotation by any multiple of 32 is a
1434      * no-op, so all but the last five bits of the rotation distance can be
1435      * ignored, even if the distance is negative: {@code rotateRight(val,
1436      * distance) == rotateRight(val, distance & 0x1F)}.
1437      *
1438      * @return the value obtained by rotating the two's complement binary
1439      *     representation of the specified {@code int} value right by the
1440      *     specified number of bits.
1441      * @since 1.5
1442      */
1443     public static int rotateRight(int i, int distance) {
1444         return (i >>> distance) | (i << -distance);
1445     }
1446 
1447     /**
1448      * Returns the value obtained by reversing the order of the bits in the
1449      * two's complement binary representation of the specified {@code int}
1450      * value.
1451      *
1452      * @return the value obtained by reversing order of the bits in the
1453      *     specified {@code int} value.
1454      * @since 1.5
1455      */
1456     public static int reverse(int i) {
1457         // HD, Figure 7-1
1458         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1459         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1460         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1461         i = (i << 24) | ((i & 0xff00) << 8) |
1462             ((i >>> 8) & 0xff00) | (i >>> 24);
1463         return i;
1464     }
1465 
1466     /**
1467      * Returns the signum function of the specified {@code int} value.  (The
1468      * return value is -1 if the specified value is negative; 0 if the
1469      * specified value is zero; and 1 if the specified value is positive.)
1470      *
1471      * @return the signum function of the specified {@code int} value.
1472      * @since 1.5
1473      */
1474     public static int signum(int i) {
1475         // HD, Section 2-7
1476         return (i >> 31) | (-i >>> 31);
1477     }
1478 
1479     /**
1480      * Returns the value obtained by reversing the order of the bytes in the
1481      * two's complement representation of the specified {@code int} value.
1482      *
1483      * @return the value obtained by reversing the bytes in the specified
1484      *     {@code int} value.
1485      * @since 1.5
1486      */
1487     public static int reverseBytes(int i) {
1488         return ((i >>> 24)           ) |
1489                ((i >>   8) &   0xFF00) |
1490                ((i <<   8) & 0xFF0000) |
1491                ((i << 24));
1492     }
1493 
1494     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1495     private static final long serialVersionUID = 1360826667806852920L;
1496 }