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(0, size, buf);
 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 
 785         private IntegerCache() {}
 786     }
 787 
 788     /**
 789      * Returns an {@code Integer} instance representing the specified
 790      * {@code int} value.  If a new {@code Integer} instance is not
 791      * required, this method should generally be used in preference to
 792      * the constructor {@link #Integer(int)}, as this method is likely
 793      * to yield significantly better space and time performance by
 794      * caching frequently requested values.
 795      *
 796      * This method will always cache values in the range -128 to 127,
 797      * inclusive, and may cache other values outside of this range.
 798      *
 799      * @param  i an {@code int} value.
 800      * @return an {@code Integer} instance representing {@code i}.
 801      * @since  1.5
 802      */
 803     public static Integer valueOf(int i) {
 804         assert IntegerCache.high >= 127;
 805         if (i >= IntegerCache.low && i <= IntegerCache.high)
 806             return IntegerCache.cache[i + (-IntegerCache.low)];
 807         return new Integer(i);
 808     }
 809 
 810     /**
 811      * The value of the {@code Integer}.
 812      *
 813      * @serial
 814      */
 815     private final int value;
 816 
 817     /**
 818      * Constructs a newly allocated {@code Integer} object that
 819      * represents the specified {@code int} value.
 820      *
 821      * @param   value   the value to be represented by the
 822      *                  {@code Integer} object.
 823      */
 824     public Integer(int value) {
 825         this.value = value;
 826     }
 827 
 828     /**
 829      * Constructs a newly allocated {@code Integer} object that
 830      * represents the {@code int} value indicated by the
 831      * {@code String} parameter. The string is converted to an
 832      * {@code int} value in exactly the manner used by the
 833      * {@code parseInt} method for radix 10.
 834      *
 835      * @param      s   the {@code String} to be converted to an
 836      *                 {@code Integer}.
 837      * @exception  NumberFormatException  if the {@code String} does not
 838      *               contain a parsable integer.
 839      * @see        java.lang.Integer#parseInt(java.lang.String, int)
 840      */
 841     public Integer(String s) throws NumberFormatException {
 842         this.value = parseInt(s, 10);
 843     }
 844 
 845     /**
 846      * Returns the value of this {@code Integer} as a {@code byte}
 847      * after a narrowing primitive conversion.
 848      * @jls 5.1.3 Narrowing Primitive Conversions
 849      */
 850     public byte byteValue() {
 851         return (byte)value;
 852     }
 853 
 854     /**
 855      * Returns the value of this {@code Integer} as a {@code short}
 856      * after a narrowing primitive conversion.
 857      * @jls 5.1.3 Narrowing Primitive Conversions
 858      */
 859     public short shortValue() {
 860         return (short)value;
 861     }
 862 
 863     /**
 864      * Returns the value of this {@code Integer} as an
 865      * {@code int}.
 866      */
 867     public int intValue() {
 868         return value;
 869     }
 870 
 871     /**
 872      * Returns the value of this {@code Integer} as a {@code long}
 873      * after a widening primitive conversion.
 874      * @jls 5.1.2 Widening Primitive Conversions
 875      */
 876     public long longValue() {
 877         return (long)value;
 878     }
 879 
 880     /**
 881      * Returns the value of this {@code Integer} as a {@code float}
 882      * after a widening primitive conversion.
 883      * @jls 5.1.2 Widening Primitive Conversions
 884      */
 885     public float floatValue() {
 886         return (float)value;
 887     }
 888 
 889     /**
 890      * Returns the value of this {@code Integer} as a {@code double}
 891      * after a widening primitive conversion.
 892      * @jls 5.1.2 Widening Primitive Conversions
 893      */
 894     public double doubleValue() {
 895         return (double)value;
 896     }
 897 
 898     /**
 899      * Returns a {@code String} object representing this
 900      * {@code Integer}'s value. The value is converted to signed
 901      * decimal representation and returned as a string, exactly as if
 902      * the integer value were given as an argument to the {@link
 903      * java.lang.Integer#toString(int)} method.
 904      *
 905      * @return  a string representation of the value of this object in
 906      *          base&nbsp;10.
 907      */
 908     public String toString() {
 909         return toString(value);
 910     }
 911 
 912     /**
 913      * Returns a hash code for this {@code Integer}.
 914      *
 915      * @return  a hash code value for this object, equal to the
 916      *          primitive {@code int} value represented by this
 917      *          {@code Integer} object.
 918      */
 919     public int hashCode() {
 920         return value;
 921     }
 922 
 923     /**
 924      * Compares this object to the specified object.  The result is
 925      * {@code true} if and only if the argument is not
 926      * {@code null} and is an {@code Integer} object that
 927      * contains the same {@code int} value as this object.
 928      *
 929      * @param   obj   the object to compare with.
 930      * @return  {@code true} if the objects are the same;
 931      *          {@code false} otherwise.
 932      */
 933     public boolean equals(Object obj) {
 934         if (obj instanceof Integer) {
 935             return value == ((Integer)obj).intValue();
 936         }
 937         return false;
 938     }
 939 
 940     /**
 941      * Determines the integer value of the system property with the
 942      * specified name.
 943      *
 944      * <p>The first argument is treated as the name of a system
 945      * property.  System properties are accessible through the {@link
 946      * java.lang.System#getProperty(java.lang.String)} method. The
 947      * string value of this property is then interpreted as an integer
 948      * value using the grammar supported by {@link Integer#decode decode} and
 949      * an {@code Integer} object representing this value is returned.
 950      *
 951      * <p>If there is no property with the specified name, if the
 952      * specified name is empty or {@code null}, or if the property
 953      * does not have the correct numeric format, then {@code null} is
 954      * returned.
 955      *
 956      * <p>In other words, this method returns an {@code Integer}
 957      * object equal to the value of:
 958      *
 959      * <blockquote>
 960      *  {@code getInteger(nm, null)}
 961      * </blockquote>
 962      *
 963      * @param   nm   property name.
 964      * @return  the {@code Integer} value of the property.
 965      * @throws  SecurityException for the same reasons as
 966      *          {@link System#getProperty(String) System.getProperty}
 967      * @see     java.lang.System#getProperty(java.lang.String)
 968      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
 969      */
 970     public static Integer getInteger(String nm) {
 971         return getInteger(nm, null);
 972     }
 973 
 974     /**
 975      * Determines the integer value of the system property with the
 976      * specified name.
 977      *
 978      * <p>The first argument is treated as the name of a system
 979      * property.  System properties are accessible through the {@link
 980      * java.lang.System#getProperty(java.lang.String)} method. The
 981      * string value of this property is then interpreted as an integer
 982      * value using the grammar supported by {@link Integer#decode decode} and
 983      * an {@code Integer} object representing this value is returned.
 984      *
 985      * <p>The second argument is the default value. An {@code Integer} object
 986      * that represents the value of the second argument is returned if there
 987      * is no property of the specified name, if the property does not have
 988      * the correct numeric format, or if the specified name is empty or
 989      * {@code null}.
 990      *
 991      * <p>In other words, this method returns an {@code Integer} object
 992      * equal to the value of:
 993      *
 994      * <blockquote>
 995      *  {@code getInteger(nm, new Integer(val))}
 996      * </blockquote>
 997      *
 998      * but in practice it may be implemented in a manner such as:
 999      *
1000      * <blockquote><pre>
1001      * Integer result = getInteger(nm, null);
1002      * return (result == null) ? new Integer(val) : result;
1003      * </pre></blockquote>
1004      *
1005      * to avoid the unnecessary allocation of an {@code Integer}
1006      * object when the default value is not needed.
1007      *
1008      * @param   nm   property name.
1009      * @param   val   default value.
1010      * @return  the {@code Integer} value of the property.
1011      * @throws  SecurityException for the same reasons as
1012      *          {@link System#getProperty(String) System.getProperty}
1013      * @see     java.lang.System#getProperty(java.lang.String)
1014      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1015      */
1016     public static Integer getInteger(String nm, int val) {
1017         Integer result = getInteger(nm, null);
1018         return (result == null) ? Integer.valueOf(val) : result;
1019     }
1020 
1021     /**
1022      * Returns the integer value of the system property with the
1023      * specified name.  The first argument is treated as the name of a
1024      * system property.  System properties are accessible through the
1025      * {@link java.lang.System#getProperty(java.lang.String)} method.
1026      * The string value of this property is then interpreted as an
1027      * integer value, as per the {@link Integer#decode decode} method,
1028      * and an {@code Integer} object representing this value is
1029      * returned; in summary:
1030      *
1031      * <ul><li>If the property value begins with the two ASCII characters
1032      *         {@code 0x} or the ASCII character {@code #}, not
1033      *      followed by a minus sign, then the rest of it is parsed as a
1034      *      hexadecimal integer exactly as by the method
1035      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1036      * <li>If the property value begins with the ASCII character
1037      *     {@code 0} followed by another character, it is parsed as an
1038      *     octal integer exactly as by the method
1039      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1040      * <li>Otherwise, the property value is parsed as a decimal integer
1041      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1042      * with radix 10.
1043      * </ul>
1044      *
1045      * <p>The second argument is the default value. The default value is
1046      * returned if there is no property of the specified name, if the
1047      * property does not have the correct numeric format, or if the
1048      * specified name is empty or {@code null}.
1049      *
1050      * @param   nm   property name.
1051      * @param   val   default value.
1052      * @return  the {@code Integer} value of the property.
1053      * @throws  SecurityException for the same reasons as
1054      *          {@link System#getProperty(String) System.getProperty}
1055      * @see     System#getProperty(java.lang.String)
1056      * @see     System#getProperty(java.lang.String, java.lang.String)
1057      */
1058     public static Integer getInteger(String nm, Integer val) {
1059         String v = null;
1060         try {
1061             v = System.getProperty(nm);
1062         } catch (IllegalArgumentException | NullPointerException e) {
1063         }
1064         if (v != null) {
1065             try {
1066                 return Integer.decode(v);
1067             } catch (NumberFormatException e) {
1068             }
1069         }
1070         return val;
1071     }
1072 
1073     /**
1074      * Decodes a {@code String} into an {@code Integer}.
1075      * Accepts decimal, hexadecimal, and octal numbers given
1076      * by the following grammar:
1077      *
1078      * <blockquote>
1079      * <dl>
1080      * <dt><i>DecodableString:</i>
1081      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1082      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1083      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1084      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1085      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1086      * <p>
1087      * <dt><i>Sign:</i>
1088      * <dd>{@code -}
1089      * <dd>{@code +}
1090      * </dl>
1091      * </blockquote>
1092      *
1093      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1094      * are as defined in section 3.10.1 of
1095      * <cite>The Java&trade; Language Specification</cite>,
1096      * except that underscores are not accepted between digits.
1097      *
1098      * <p>The sequence of characters following an optional
1099      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1100      * "{@code #}", or leading zero) is parsed as by the {@code
1101      * Integer.parseInt} method with the indicated radix (10, 16, or
1102      * 8).  This sequence of characters must represent a positive
1103      * value or a {@link NumberFormatException} will be thrown.  The
1104      * result is negated if first character of the specified {@code
1105      * String} is the minus sign.  No whitespace characters are
1106      * permitted in the {@code String}.
1107      *
1108      * @param     nm the {@code String} to decode.
1109      * @return    an {@code Integer} object holding the {@code int}
1110      *             value represented by {@code nm}
1111      * @exception NumberFormatException  if the {@code String} does not
1112      *            contain a parsable integer.
1113      * @see java.lang.Integer#parseInt(java.lang.String, int)
1114      */
1115     public static Integer decode(String nm) throws NumberFormatException {
1116         int radix = 10;
1117         int index = 0;
1118         boolean negative = false;
1119         Integer result;
1120 
1121         if (nm.length() == 0)
1122             throw new NumberFormatException("Zero length string");
1123         char firstChar = nm.charAt(0);
1124         // Handle sign, if present
1125         if (firstChar == '-') {
1126             negative = true;
1127             index++;
1128         } else if (firstChar == '+')
1129             index++;
1130 
1131         // Handle radix specifier, if present
1132         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1133             index += 2;
1134             radix = 16;
1135         }
1136         else if (nm.startsWith("#", index)) {
1137             index ++;
1138             radix = 16;
1139         }
1140         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1141             index ++;
1142             radix = 8;
1143         }
1144 
1145         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1146             throw new NumberFormatException("Sign character in wrong position");
1147 
1148         try {
1149             result = Integer.valueOf(nm.substring(index), radix);
1150             result = negative ? Integer.valueOf(-result.intValue()) : result;
1151         } catch (NumberFormatException e) {
1152             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1153             // handles this case, and causes any genuine format error to be
1154             // rethrown.
1155             String constant = negative ? ("-" + nm.substring(index))
1156                                        : nm.substring(index);
1157             result = Integer.valueOf(constant, radix);
1158         }
1159         return result;
1160     }
1161 
1162     /**
1163      * Compares two {@code Integer} objects numerically.
1164      *
1165      * @param   anotherInteger   the {@code Integer} to be compared.
1166      * @return  the value {@code 0} if this {@code Integer} is
1167      *          equal to the argument {@code Integer}; a value less than
1168      *          {@code 0} if this {@code Integer} is numerically less
1169      *          than the argument {@code Integer}; and a value greater
1170      *          than {@code 0} if this {@code Integer} is numerically
1171      *           greater than the argument {@code Integer} (signed
1172      *           comparison).
1173      * @since   1.2
1174      */
1175     public int compareTo(Integer anotherInteger) {
1176         return compare(this.value, anotherInteger.value);
1177     }
1178 
1179     /**
1180      * Compares two {@code int} values numerically.
1181      * The value returned is identical to what would be returned by:
1182      * <pre>
1183      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1184      * </pre>
1185      *
1186      * @param  x the first {@code int} to compare
1187      * @param  y the second {@code int} to compare
1188      * @return the value {@code 0} if {@code x == y};
1189      *         a value less than {@code 0} if {@code x < y}; and
1190      *         a value greater than {@code 0} if {@code x > y}
1191      * @since 1.7
1192      */
1193     public static int compare(int x, int y) {
1194         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1195     }
1196 
1197     /**
1198      * Compares two {@code int} values numerically treating the values
1199      * as unsigned.
1200      *
1201      * @param  x the first {@code int} to compare
1202      * @param  y the second {@code int} to compare
1203      * @return the value {@code 0} if {@code x == y}; a value less
1204      *         than {@code 0} if {@code x < y} as unsigned values; and
1205      *         a value greater than {@code 0} if {@code x > y} as
1206      *         unsigned values
1207      * @since 1.8
1208      */
1209     public static int compareUnsigned(int x, int y) {
1210         return compare(x + MIN_VALUE, y + MIN_VALUE);
1211     }
1212 
1213     /**
1214      * Converts the argument to a {@code long} by an unsigned
1215      * conversion.  In an unsigned conversion to a {@code long}, the
1216      * high-order 32 bits of the {@code long} are zero and the
1217      * low-order 32 bits are equal to the bits of the integer
1218      * argument.
1219      *
1220      * Consequently, zero and positive {@code int} values are mapped
1221      * to a numerically equal {@code long} value and negative {@code
1222      * int} values are mapped to a {@code long} value equal to the
1223      * input plus 2<sup>32</sup>.
1224      *
1225      * @param  x the value to convert to an unsigned {@code long}
1226      * @return the argument converted to {@code long} by an unsigned
1227      *         conversion
1228      * @since 1.8
1229      */
1230     public static long toUnsignedLong(int x) {
1231         return ((long) x) & 0xffffffffL;
1232     }
1233 
1234     /**
1235      * Returns the unsigned quotient of dividing the first argument by
1236      * the second where each argument and the result is interpreted as
1237      * an unsigned value.
1238      *
1239      * <p>Note that in two's complement arithmetic, the three other
1240      * basic arithmetic operations of add, subtract, and multiply are
1241      * bit-wise identical if the two operands are regarded as both
1242      * being signed or both being unsigned.  Therefore separate {@code
1243      * addUnsigned}, etc. methods are not provided.
1244      *
1245      * @param dividend the value to be divided
1246      * @param divisor the value doing the dividing
1247      * @return the unsigned quotient of the first argument divided by
1248      * the second argument
1249      * @see #remainderUnsigned
1250      * @since 1.8
1251      */
1252     public static int divideUnsigned(int dividend, int divisor) {
1253         // In lieu of tricky code, for now just use long arithmetic.
1254         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1255     }
1256 
1257     /**
1258      * Returns the unsigned remainder from dividing the first argument
1259      * by the second where each argument and the result is interpreted
1260      * as an unsigned value.
1261      *
1262      * @param dividend the value to be divided
1263      * @param divisor the value doing the dividing
1264      * @return the unsigned remainder of the first argument divided by
1265      * the second argument
1266      * @see #divideUnsigned
1267      * @since 1.8
1268      */
1269     public static int remainderUnsigned(int dividend, int divisor) {
1270         // In lieu of tricky code, for now just use long arithmetic.
1271         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1272     }
1273 
1274 
1275     // Bit twiddling
1276 
1277     /**
1278      * The number of bits used to represent an {@code int} value in two's
1279      * complement binary form.
1280      *
1281      * @since 1.5
1282      */
1283     public static final int SIZE = 32;
1284 
1285     /**
1286      * Returns an {@code int} value with at most a single one-bit, in the
1287      * position of the highest-order ("leftmost") one-bit in the specified
1288      * {@code int} value.  Returns zero if the specified value has no
1289      * one-bits in its two's complement binary representation, that is, if it
1290      * is equal to zero.
1291      *
1292      * @return an {@code int} value with a single one-bit, in the position
1293      *     of the highest-order one-bit in the specified value, or zero if
1294      *     the specified value is itself equal to zero.
1295      * @since 1.5
1296      */
1297     public static int highestOneBit(int i) {
1298         // HD, Figure 3-1
1299         i |= (i >>  1);
1300         i |= (i >>  2);
1301         i |= (i >>  4);
1302         i |= (i >>  8);
1303         i |= (i >> 16);
1304         return i - (i >>> 1);
1305     }
1306 
1307     /**
1308      * Returns an {@code int} value with at most a single one-bit, in the
1309      * position of the lowest-order ("rightmost") one-bit in the specified
1310      * {@code int} value.  Returns zero if the specified value has no
1311      * one-bits in its two's complement binary representation, that is, if it
1312      * is equal to zero.
1313      *
1314      * @return an {@code int} value with a single one-bit, in the position
1315      *     of the lowest-order one-bit in the specified value, or zero if
1316      *     the specified value is itself equal to zero.
1317      * @since 1.5
1318      */
1319     public static int lowestOneBit(int i) {
1320         // HD, Section 2-1
1321         return i & -i;
1322     }
1323 
1324     /**
1325      * Returns the number of zero bits preceding the highest-order
1326      * ("leftmost") one-bit in the two's complement binary representation
1327      * of the specified {@code int} value.  Returns 32 if the
1328      * specified value has no one-bits in its two's complement representation,
1329      * in other words if it is equal to zero.
1330      *
1331      * <p>Note that this method is closely related to the logarithm base 2.
1332      * For all positive {@code int} values x:
1333      * <ul>
1334      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1335      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1336      * </ul>
1337      *
1338      * @return the number of zero bits preceding the highest-order
1339      *     ("leftmost") one-bit in the two's complement binary representation
1340      *     of the specified {@code int} value, or 32 if the value
1341      *     is equal to zero.
1342      * @since 1.5
1343      */
1344     public static int numberOfLeadingZeros(int i) {
1345         // HD, Figure 5-6
1346         if (i == 0)
1347             return 32;
1348         int n = 1;
1349         if (i >>> 16 == 0) { n += 16; i <<= 16; }
1350         if (i >>> 24 == 0) { n +=  8; i <<=  8; }
1351         if (i >>> 28 == 0) { n +=  4; i <<=  4; }
1352         if (i >>> 30 == 0) { n +=  2; i <<=  2; }
1353         n -= i >>> 31;
1354         return n;
1355     }
1356 
1357     /**
1358      * Returns the number of zero bits following the lowest-order ("rightmost")
1359      * one-bit in the two's complement binary representation of the specified
1360      * {@code int} value.  Returns 32 if the specified value has no
1361      * one-bits in its two's complement representation, in other words if it is
1362      * equal to zero.
1363      *
1364      * @return the number of zero bits following the lowest-order ("rightmost")
1365      *     one-bit in the two's complement binary representation of the
1366      *     specified {@code int} value, or 32 if the value is equal
1367      *     to zero.
1368      * @since 1.5
1369      */
1370     public static int numberOfTrailingZeros(int i) {
1371         // HD, Figure 5-14
1372         int y;
1373         if (i == 0) return 32;
1374         int n = 31;
1375         y = i <<16; if (y != 0) { n = n -16; i = y; }
1376         y = i << 8; if (y != 0) { n = n - 8; i = y; }
1377         y = i << 4; if (y != 0) { n = n - 4; i = y; }
1378         y = i << 2; if (y != 0) { n = n - 2; i = y; }
1379         return n - ((i << 1) >>> 31);
1380     }
1381 
1382     /**
1383      * Returns the number of one-bits in the two's complement binary
1384      * representation of the specified {@code int} value.  This function is
1385      * sometimes referred to as the <i>population count</i>.
1386      *
1387      * @return the number of one-bits in the two's complement binary
1388      *     representation of the specified {@code int} value.
1389      * @since 1.5
1390      */
1391     public static int bitCount(int i) {
1392         // HD, Figure 5-2
1393         i = i - ((i >>> 1) & 0x55555555);
1394         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1395         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1396         i = i + (i >>> 8);
1397         i = i + (i >>> 16);
1398         return i & 0x3f;
1399     }
1400 
1401     /**
1402      * Returns the value obtained by rotating the two's complement binary
1403      * representation of the specified {@code int} value left by the
1404      * specified number of bits.  (Bits shifted out of the left hand, or
1405      * high-order, side reenter on the right, or low-order.)
1406      *
1407      * <p>Note that left rotation with a negative distance is equivalent to
1408      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1409      * distance)}.  Note also that rotation by any multiple of 32 is a
1410      * no-op, so all but the last five bits of the rotation distance can be
1411      * ignored, even if the distance is negative: {@code rotateLeft(val,
1412      * distance) == rotateLeft(val, distance & 0x1F)}.
1413      *
1414      * @return the value obtained by rotating the two's complement binary
1415      *     representation of the specified {@code int} value left by the
1416      *     specified number of bits.
1417      * @since 1.5
1418      */
1419     public static int rotateLeft(int i, int distance) {
1420         return (i << distance) | (i >>> -distance);
1421     }
1422 
1423     /**
1424      * Returns the value obtained by rotating the two's complement binary
1425      * representation of the specified {@code int} value right by the
1426      * specified number of bits.  (Bits shifted out of the right hand, or
1427      * low-order, side reenter on the left, or high-order.)
1428      *
1429      * <p>Note that right rotation with a negative distance is equivalent to
1430      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1431      * distance)}.  Note also that rotation by any multiple of 32 is a
1432      * no-op, so all but the last five bits of the rotation distance can be
1433      * ignored, even if the distance is negative: {@code rotateRight(val,
1434      * distance) == rotateRight(val, distance & 0x1F)}.
1435      *
1436      * @return the value obtained by rotating the two's complement binary
1437      *     representation of the specified {@code int} value right by the
1438      *     specified number of bits.
1439      * @since 1.5
1440      */
1441     public static int rotateRight(int i, int distance) {
1442         return (i >>> distance) | (i << -distance);
1443     }
1444 
1445     /**
1446      * Returns the value obtained by reversing the order of the bits in the
1447      * two's complement binary representation of the specified {@code int}
1448      * value.
1449      *
1450      * @return the value obtained by reversing order of the bits in the
1451      *     specified {@code int} value.
1452      * @since 1.5
1453      */
1454     public static int reverse(int i) {
1455         // HD, Figure 7-1
1456         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1457         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1458         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1459         i = (i << 24) | ((i & 0xff00) << 8) |
1460             ((i >>> 8) & 0xff00) | (i >>> 24);
1461         return i;
1462     }
1463 
1464     /**
1465      * Returns the signum function of the specified {@code int} value.  (The
1466      * return value is -1 if the specified value is negative; 0 if the
1467      * specified value is zero; and 1 if the specified value is positive.)
1468      *
1469      * @return the signum function of the specified {@code int} value.
1470      * @since 1.5
1471      */
1472     public static int signum(int i) {
1473         // HD, Section 2-7
1474         return (i >> 31) | (-i >>> 31);
1475     }
1476 
1477     /**
1478      * Returns the value obtained by reversing the order of the bytes in the
1479      * two's complement representation of the specified {@code int} value.
1480      *
1481      * @return the value obtained by reversing the bytes in the specified
1482      *     {@code int} value.
1483      * @since 1.5
1484      */
1485     public static int reverseBytes(int i) {
1486         return ((i >>> 24)           ) |
1487                ((i >>   8) &   0xFF00) |
1488                ((i <<   8) & 0xFF0000) |
1489                ((i << 24));
1490     }
1491 
1492     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1493     private static final long serialVersionUID = 1360826667806852920L;
1494 }