1 /*
   2  * Copyright (c) 1994, 2013, 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.lang.annotation.Native;
  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 1.0
  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     @Native 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     @Native public static final int   MAX_VALUE = 0x7fffffff;
  64 
  65     /**
  66      * The {@code Class} instance representing the primitive type
  67      * {@code int}.
  68      *
  69      * @since   1.1
  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.toUnsignedString(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   1.0.2
 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   1.0.2
 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   1.0.2
 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 val, int shift) {
 310         // assert shift > 0 && shift <=5 : "Illegal shift value";
 311         int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
 312         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 313         char[] buf = new char[chars];
 314 
 315         formatUnsignedInt(val, shift, buf, 0, chars);
 316 
 317         // Use special constructor which takes over "buf".
 318         return new String(buf, true);
 319     }
 320 
 321     /**
 322      * Format an {@code int} (treated as unsigned) into a character buffer. If
 323      * {@code len} exceeds the formatted ASCII representation of {@code val},
 324      * {@code buf} will be padded with leading zeroes.
 325      *
 326      * @param val the unsigned int to format
 327      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 328      * @param buf the character buffer to write to
 329      * @param offset the offset in the destination buffer to start at
 330      * @param len the number of characters to write
 331      */
 332      static void formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
 333         // assert shift > 0 && shift <=5 : "Illegal shift value";
 334         // assert offset >= 0 && offset < buf.length : "illegal offset";
 335         // assert len > 0 && (offset + len) <= buf.length : "illegal length";
 336         int charPos = offset + len;
 337         int radix = 1 << shift;
 338         int mask = radix - 1;
 339         while (charPos > offset) {
 340             buf[--charPos] = Integer.digits[val & mask];
 341             val >>>= shift;
 342         }
 343     }
 344 
 345     final static char [] DigitTens = {
 346         '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
 347         '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
 348         '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
 349         '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
 350         '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
 351         '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
 352         '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
 353         '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
 354         '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
 355         '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
 356         } ;
 357 
 358     final static char [] DigitOnes = {
 359         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 360         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 361         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 362         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 363         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 364         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 365         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 366         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 367         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 368         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 369         } ;
 370 
 371         // I use the "invariant division by multiplication" trick to
 372         // accelerate Integer.toString.  In particular we want to
 373         // avoid division by 10.
 374         //
 375         // The "trick" has roughly the same performance characteristics
 376         // as the "classic" Integer.toString code on a non-JIT VM.
 377         // The trick avoids .rem and .div calls but has a longer code
 378         // path and is thus dominated by dispatch overhead.  In the
 379         // JIT case the dispatch overhead doesn't exist and the
 380         // "trick" is considerably faster than the classic code.
 381         //
 382         // RE:  Division by Invariant Integers using Multiplication
 383         //      T Gralund, P Montgomery
 384         //      ACM PLDI 1994
 385         //
 386 
 387     /**
 388      * Returns a {@code String} object representing the
 389      * specified integer. The argument is converted to signed decimal
 390      * representation and returned as a string, exactly as if the
 391      * argument and radix 10 were given as arguments to the {@link
 392      * #toString(int, int)} method.
 393      *
 394      * @param   i   an integer to be converted.
 395      * @return  a string representation of the argument in base&nbsp;10.
 396      */
 397     public static String toString(int i) {
 398         if (i == Integer.MIN_VALUE)
 399             return "-2147483648";
 400         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
 401         char[] buf = new char[size];
 402         getChars(i, size, buf);
 403         return new String(buf, true);
 404     }
 405 
 406     /**
 407      * Returns a string representation of the argument as an unsigned
 408      * decimal value.
 409      *
 410      * The argument is converted to unsigned decimal representation
 411      * and returned as a string exactly as if the argument and radix
 412      * 10 were given as arguments to the {@link #toUnsignedString(int,
 413      * int)} method.
 414      *
 415      * @param   i  an integer to be converted to an unsigned string.
 416      * @return  an unsigned string representation of the argument.
 417      * @see     #toUnsignedString(int, int)
 418      * @since 1.8
 419      */
 420     public static String toUnsignedString(int i) {
 421         return Long.toString(toUnsignedLong(i));
 422     }
 423 
 424     /**
 425      * Places characters representing the integer i into the
 426      * character array buf. The characters are placed into
 427      * the buffer backwards starting with the least significant
 428      * digit at the specified index (exclusive), and working
 429      * backwards from there.
 430      *
 431      * Will fail if i == Integer.MIN_VALUE
 432      */
 433     static void getChars(int i, int index, char[] buf) {
 434         int q, r;
 435         int charPos = index;
 436         char sign = 0;
 437 
 438         if (i < 0) {
 439             sign = '-';
 440             i = -i;
 441         }
 442 
 443         // Generate two digits per iteration
 444         while (i >= 65536) {
 445             q = i / 100;
 446         // really: r = i - (q * 100);
 447             r = i - ((q << 6) + (q << 5) + (q << 2));
 448             i = q;
 449             buf [--charPos] = DigitOnes[r];
 450             buf [--charPos] = DigitTens[r];
 451         }
 452 
 453         // Fall thru to fast mode for smaller numbers
 454         // assert(i <= 65536, i);
 455         for (;;) {
 456             q = (i * 52429) >>> (16+3);
 457             r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
 458             buf [--charPos] = digits [r];
 459             i = q;
 460             if (i == 0) break;
 461         }
 462         if (sign != 0) {
 463             buf [--charPos] = sign;
 464         }
 465     }
 466 
 467     final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
 468                                       99999999, 999999999, Integer.MAX_VALUE };
 469 
 470     // Requires positive x
 471     static int stringSize(int x) {
 472         for (int i=0; ; i++)
 473             if (x <= sizeTable[i])
 474                 return i+1;
 475     }
 476 
 477     /**
 478      * Parses the string argument as a signed integer in the radix
 479      * specified by the second argument. The characters in the string
 480      * must all be digits of the specified radix (as determined by
 481      * whether {@link java.lang.Character#digit(char, int)} returns a
 482      * nonnegative value), except that the first character may be an
 483      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 484      * indicate a negative value or an ASCII plus sign {@code '+'}
 485      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 486      * resulting integer value is returned.
 487      *
 488      * <p>An exception of type {@code NumberFormatException} is
 489      * thrown if any of the following situations occurs:
 490      * <ul>
 491      * <li>The first argument is {@code null} or is a string of
 492      * length zero.
 493      *
 494      * <li>The radix is either smaller than
 495      * {@link java.lang.Character#MIN_RADIX} or
 496      * larger than {@link java.lang.Character#MAX_RADIX}.
 497      *
 498      * <li>Any character of the string is not a digit of the specified
 499      * radix, except that the first character may be a minus sign
 500      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
 501      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 502      * string is longer than length 1.
 503      *
 504      * <li>The value represented by the string is not a value of type
 505      * {@code int}.
 506      * </ul>
 507      *
 508      * <p>Examples:
 509      * <blockquote><pre>
 510      * parseInt("0", 10) returns 0
 511      * parseInt("473", 10) returns 473
 512      * parseInt("+42", 10) returns 42
 513      * parseInt("-0", 10) returns 0
 514      * parseInt("-FF", 16) returns -255
 515      * parseInt("1100110", 2) returns 102
 516      * parseInt("2147483647", 10) returns 2147483647
 517      * parseInt("-2147483648", 10) returns -2147483648
 518      * parseInt("2147483648", 10) throws a NumberFormatException
 519      * parseInt("99", 8) throws a NumberFormatException
 520      * parseInt("Kona", 10) throws a NumberFormatException
 521      * parseInt("Kona", 27) returns 411787
 522      * </pre></blockquote>
 523      *
 524      * @param      s   the {@code String} containing the integer
 525      *                  representation to be parsed
 526      * @param      radix   the radix to be used while parsing {@code s}.
 527      * @return     the integer represented by the string argument in the
 528      *             specified radix.
 529      * @exception  NumberFormatException if the {@code String}
 530      *             does not contain a parsable {@code int}.
 531      */
 532     public static int parseInt(String s, int radix)
 533                 throws NumberFormatException
 534     {
 535         /*
 536          * WARNING: This method may be invoked early during VM initialization
 537          * before IntegerCache is initialized. Care must be taken to not use
 538          * the valueOf method.
 539          */
 540 
 541         if (s == null) {
 542             throw new NumberFormatException("null");
 543         }
 544 
 545         if (radix < Character.MIN_RADIX) {
 546             throw new NumberFormatException("radix " + radix +
 547                                             " less than Character.MIN_RADIX");
 548         }
 549 
 550         if (radix > Character.MAX_RADIX) {
 551             throw new NumberFormatException("radix " + radix +
 552                                             " greater than Character.MAX_RADIX");
 553         }
 554 
 555         int result = 0;
 556         boolean negative = false;
 557         int i = 0, len = s.length();
 558         int limit = -Integer.MAX_VALUE;
 559         int multmin;
 560         int digit;
 561 
 562         if (len > 0) {
 563             char firstChar = s.charAt(0);
 564             if (firstChar < '0') { // Possible leading "+" or "-"
 565                 if (firstChar == '-') {
 566                     negative = true;
 567                     limit = Integer.MIN_VALUE;
 568                 } else if (firstChar != '+')
 569                     throw NumberFormatException.forInputString(s);
 570 
 571                 if (len == 1) // Cannot have lone "+" or "-"
 572                     throw NumberFormatException.forInputString(s);
 573                 i++;
 574             }
 575             multmin = limit / radix;
 576             while (i < len) {
 577                 // Accumulating negatively avoids surprises near MAX_VALUE
 578                 digit = Character.digit(s.charAt(i++),radix);
 579                 if (digit < 0) {
 580                     throw NumberFormatException.forInputString(s);
 581                 }
 582                 if (result < multmin) {
 583                     throw NumberFormatException.forInputString(s);
 584                 }
 585                 result *= radix;
 586                 if (result < limit + digit) {
 587                     throw NumberFormatException.forInputString(s);
 588                 }
 589                 result -= digit;
 590             }
 591         } else {
 592             throw NumberFormatException.forInputString(s);
 593         }
 594         return negative ? result : -result;
 595     }
 596 
 597     /**
 598      * Parses the string argument as a signed decimal integer. The
 599      * characters in the string must all be decimal digits, except
 600      * that the first character may be an ASCII minus sign {@code '-'}
 601      * ({@code '\u005Cu002D'}) to indicate a negative value or an
 602      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 603      * indicate a positive value. The resulting integer value is
 604      * returned, exactly as if the argument and the radix 10 were
 605      * given as arguments to the {@link #parseInt(java.lang.String,
 606      * int)} method.
 607      *
 608      * @param s    a {@code String} containing the {@code int}
 609      *             representation to be parsed
 610      * @return     the integer value represented by the argument in decimal.
 611      * @exception  NumberFormatException  if the string does not contain a
 612      *               parsable integer.
 613      */
 614     public static int parseInt(String s) throws NumberFormatException {
 615         return parseInt(s,10);
 616     }
 617 
 618     /**
 619      * Parses the string argument as an unsigned integer in the radix
 620      * specified by the second argument.  An unsigned integer maps the
 621      * values usually associated with negative numbers to positive
 622      * numbers larger than {@code MAX_VALUE}.
 623      *
 624      * The characters in the string must all be digits of the
 625      * specified radix (as determined by whether {@link
 626      * java.lang.Character#digit(char, int)} returns a nonnegative
 627      * value), except that the first character may be an ASCII plus
 628      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 629      * integer value is returned.
 630      *
 631      * <p>An exception of type {@code NumberFormatException} is
 632      * thrown if any of the following situations occurs:
 633      * <ul>
 634      * <li>The first argument is {@code null} or is a string of
 635      * length zero.
 636      *
 637      * <li>The radix is either smaller than
 638      * {@link java.lang.Character#MIN_RADIX} or
 639      * larger than {@link java.lang.Character#MAX_RADIX}.
 640      *
 641      * <li>Any character of the string is not a digit of the specified
 642      * radix, except that the first character may be a plus sign
 643      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 644      * string is longer than length 1.
 645      *
 646      * <li>The value represented by the string is larger than the
 647      * largest unsigned {@code int}, 2<sup>32</sup>-1.
 648      *
 649      * </ul>
 650      *
 651      *
 652      * @param      s   the {@code String} containing the unsigned integer
 653      *                  representation to be parsed
 654      * @param      radix   the radix to be used while parsing {@code s}.
 655      * @return     the integer represented by the string argument in the
 656      *             specified radix.
 657      * @throws     NumberFormatException if the {@code String}
 658      *             does not contain a parsable {@code int}.
 659      * @since 1.8
 660      */
 661     public static int parseUnsignedInt(String s, int radix)
 662                 throws NumberFormatException {
 663         if (s == null)  {
 664             throw new NumberFormatException("null");
 665         }
 666 
 667         int len = s.length();
 668         if (len > 0) {
 669             char firstChar = s.charAt(0);
 670             if (firstChar == '-') {
 671                 throw new
 672                     NumberFormatException(String.format("Illegal leading minus sign " +
 673                                                        "on unsigned string %s.", s));
 674             } else {
 675                 if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
 676                     (radix == 10 && len <= 9) ) { // Integer.MAX_VALUE in base 10 is 10 digits
 677                     return parseInt(s, radix);
 678                 } else {
 679                     long ell = Long.parseLong(s, radix);
 680                     if ((ell & 0xffff_ffff_0000_0000L) == 0) {
 681                         return (int) ell;
 682                     } else {
 683                         throw new
 684                             NumberFormatException(String.format("String value %s exceeds " +
 685                                                                 "range of unsigned int.", s));
 686                     }
 687                 }
 688             }
 689         } else {
 690             throw NumberFormatException.forInputString(s);
 691         }
 692     }
 693 
 694     /**
 695      * Parses the string argument as an unsigned decimal integer. The
 696      * characters in the string must all be decimal digits, except
 697      * that the first character may be an an ASCII plus sign {@code
 698      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 699      * is returned, exactly as if the argument and the radix 10 were
 700      * given as arguments to the {@link
 701      * #parseUnsignedInt(java.lang.String, int)} method.
 702      *
 703      * @param s   a {@code String} containing the unsigned {@code int}
 704      *            representation to be parsed
 705      * @return    the unsigned integer value represented by the argument in decimal.
 706      * @throws    NumberFormatException  if the string does not contain a
 707      *            parsable unsigned integer.
 708      * @since 1.8
 709      */
 710     public static int parseUnsignedInt(String s) throws NumberFormatException {
 711         return parseUnsignedInt(s, 10);
 712     }
 713 
 714     /**
 715      * Returns an {@code Integer} object holding the value
 716      * extracted from the specified {@code String} when parsed
 717      * with the radix given by the second argument. The first argument
 718      * is interpreted as representing a signed integer in the radix
 719      * specified by the second argument, exactly as if the arguments
 720      * were given to the {@link #parseInt(java.lang.String, int)}
 721      * method. The result is an {@code Integer} object that
 722      * represents the integer value specified by the string.
 723      *
 724      * <p>In other words, this method returns an {@code Integer}
 725      * object equal to the value of:
 726      *
 727      * <blockquote>
 728      *  {@code new Integer(Integer.parseInt(s, radix))}
 729      * </blockquote>
 730      *
 731      * @param      s   the string to be parsed.
 732      * @param      radix the radix to be used in interpreting {@code s}
 733      * @return     an {@code Integer} object holding the value
 734      *             represented by the string argument in the specified
 735      *             radix.
 736      * @exception NumberFormatException if the {@code String}
 737      *            does not contain a parsable {@code int}.
 738      */
 739     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 740         return Integer.valueOf(parseInt(s,radix));
 741     }
 742 
 743     /**
 744      * Returns an {@code Integer} object holding the
 745      * value of the specified {@code String}. The argument is
 746      * interpreted as representing a signed decimal integer, exactly
 747      * as if the argument were given to the {@link
 748      * #parseInt(java.lang.String)} method. The result is an
 749      * {@code Integer} object that represents the integer value
 750      * specified by the string.
 751      *
 752      * <p>In other words, this method returns an {@code Integer}
 753      * object equal to the value of:
 754      *
 755      * <blockquote>
 756      *  {@code new Integer(Integer.parseInt(s))}
 757      * </blockquote>
 758      *
 759      * @param      s   the string to be parsed.
 760      * @return     an {@code Integer} object holding the value
 761      *             represented by the string argument.
 762      * @exception  NumberFormatException  if the string cannot be parsed
 763      *             as an integer.
 764      */
 765     public static Integer valueOf(String s) throws NumberFormatException {
 766         return Integer.valueOf(parseInt(s, 10));
 767     }
 768 
 769     /**
 770      * Cache to support the object identity semantics of autoboxing for values between
 771      * -128 and 127 (inclusive) as required by JLS.
 772      *
 773      * The cache is initialized on first usage.  The size of the cache
 774      * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
 775      * During VM initialization, java.lang.Integer.IntegerCache.high property
 776      * may be set and saved in the private system properties in the
 777      * sun.misc.VM class.
 778      */
 779 
 780     private static class IntegerCache {
 781         static final int low = -128;
 782         static final int high;
 783         static final Integer cache[];
 784 
 785         static {
 786             // high value may be configured by property
 787             int h = 127;
 788             String integerCacheHighPropValue =
 789                 sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 790             if (integerCacheHighPropValue != null) {
 791                 try {
 792                     int i = parseInt(integerCacheHighPropValue);
 793                     i = Math.max(i, 127);
 794                     // Maximum array size is Integer.MAX_VALUE
 795                     h = Math.min(i, Integer.MAX_VALUE - (-low) -1);
 796                 } catch( NumberFormatException nfe) {
 797                     // If the property cannot be parsed into an int, ignore it.
 798                 }
 799             }
 800             high = h;
 801 
 802             cache = new Integer[(high - low) + 1];
 803             int j = low;
 804             for(int k = 0; k < cache.length; k++)
 805                 cache[k] = new Integer(j++);
 806 
 807             // range [-128, 127] must be interned (JLS7 5.1.7)
 808             assert IntegerCache.high >= 127;
 809         }
 810 
 811         private IntegerCache() {}
 812     }
 813 
 814     /**
 815      * Returns an {@code Integer} instance representing the specified
 816      * {@code int} value.  If a new {@code Integer} instance is not
 817      * required, this method should generally be used in preference to
 818      * the constructor {@link #Integer(int)}, as this method is likely
 819      * to yield significantly better space and time performance by
 820      * caching frequently requested values.
 821      *
 822      * This method will always cache values in the range -128 to 127,
 823      * inclusive, and may cache other values outside of this range.
 824      *
 825      * @param  i an {@code int} value.
 826      * @return an {@code Integer} instance representing {@code i}.
 827      * @since  1.5
 828      */
 829     public static Integer valueOf(int i) {
 830         if (i >= IntegerCache.low && i <= IntegerCache.high)
 831             return IntegerCache.cache[i + (-IntegerCache.low)];
 832         return new Integer(i);
 833     }
 834 
 835     /**
 836      * The value of the {@code Integer}.
 837      *
 838      * @serial
 839      */
 840     private final int value;
 841 
 842     /**
 843      * Constructs a newly allocated {@code Integer} object that
 844      * represents the specified {@code int} value.
 845      *
 846      * @param   value   the value to be represented by the
 847      *                  {@code Integer} object.
 848      */
 849     public Integer(int value) {
 850         this.value = value;
 851     }
 852 
 853     /**
 854      * Constructs a newly allocated {@code Integer} object that
 855      * represents the {@code int} value indicated by the
 856      * {@code String} parameter. The string is converted to an
 857      * {@code int} value in exactly the manner used by the
 858      * {@code parseInt} method for radix 10.
 859      *
 860      * @param      s   the {@code String} to be converted to an
 861      *                 {@code Integer}.
 862      * @exception  NumberFormatException  if the {@code String} does not
 863      *               contain a parsable integer.
 864      * @see        java.lang.Integer#parseInt(java.lang.String, int)
 865      */
 866     public Integer(String s) throws NumberFormatException {
 867         this.value = parseInt(s, 10);
 868     }
 869 
 870     /**
 871      * Returns the value of this {@code Integer} as a {@code byte}
 872      * after a narrowing primitive conversion.
 873      * @jls 5.1.3 Narrowing Primitive Conversions
 874      */
 875     public byte byteValue() {
 876         return (byte)value;
 877     }
 878 
 879     /**
 880      * Returns the value of this {@code Integer} as a {@code short}
 881      * after a narrowing primitive conversion.
 882      * @jls 5.1.3 Narrowing Primitive Conversions
 883      */
 884     public short shortValue() {
 885         return (short)value;
 886     }
 887 
 888     /**
 889      * Returns the value of this {@code Integer} as an
 890      * {@code int}.
 891      */
 892     public int intValue() {
 893         return value;
 894     }
 895 
 896     /**
 897      * Returns the value of this {@code Integer} as a {@code long}
 898      * after a widening primitive conversion.
 899      * @jls 5.1.2 Widening Primitive Conversions
 900      * @see Integer#toUnsignedLong(int)
 901      */
 902     public long longValue() {
 903         return (long)value;
 904     }
 905 
 906     /**
 907      * Returns the value of this {@code Integer} as a {@code float}
 908      * after a widening primitive conversion.
 909      * @jls 5.1.2 Widening Primitive Conversions
 910      */
 911     public float floatValue() {
 912         return (float)value;
 913     }
 914 
 915     /**
 916      * Returns the value of this {@code Integer} as a {@code double}
 917      * after a widening primitive conversion.
 918      * @jls 5.1.2 Widening Primitive Conversions
 919      */
 920     public double doubleValue() {
 921         return (double)value;
 922     }
 923 
 924     /**
 925      * Returns a {@code String} object representing this
 926      * {@code Integer}'s value. The value is converted to signed
 927      * decimal representation and returned as a string, exactly as if
 928      * the integer value were given as an argument to the {@link
 929      * java.lang.Integer#toString(int)} method.
 930      *
 931      * @return  a string representation of the value of this object in
 932      *          base&nbsp;10.
 933      */
 934     public String toString() {
 935         return toString(value);
 936     }
 937 
 938     /**
 939      * Returns a hash code for this {@code Integer}.
 940      *
 941      * @return  a hash code value for this object, equal to the
 942      *          primitive {@code int} value represented by this
 943      *          {@code Integer} object.
 944      */
 945     @Override
 946     public int hashCode() {
 947         return Integer.hashCode(value);
 948     }
 949 
 950     /**
 951      * Returns a hash code for a {@code int} value; compatible with
 952      * {@code Integer.hashCode()}.
 953      *
 954      * @param value the value to hash
 955      * @since 1.8
 956      *
 957      * @return a hash code value for a {@code int} value.
 958      */
 959     public static int hashCode(int value) {
 960         return value;
 961     }
 962 
 963     /**
 964      * Compares this object to the specified object.  The result is
 965      * {@code true} if and only if the argument is not
 966      * {@code null} and is an {@code Integer} object that
 967      * contains the same {@code int} value as this object.
 968      *
 969      * @param   obj   the object to compare with.
 970      * @return  {@code true} if the objects are the same;
 971      *          {@code false} otherwise.
 972      */
 973     public boolean equals(Object obj) {
 974         if (obj instanceof Integer) {
 975             return value == ((Integer)obj).intValue();
 976         }
 977         return false;
 978     }
 979 
 980     /**
 981      * Determines the integer value of the system property with the
 982      * specified name.
 983      *
 984      * <p>The first argument is treated as the name of a system
 985      * property.  System properties are accessible through the {@link
 986      * java.lang.System#getProperty(java.lang.String)} method. The
 987      * string value of this property is then interpreted as an integer
 988      * value using the grammar supported by {@link Integer#decode decode} and
 989      * an {@code Integer} object representing this value is returned.
 990      *
 991      * <p>If there is no property with the specified name, if the
 992      * specified name is empty or {@code null}, or if the property
 993      * does not have the correct numeric format, then {@code null} is
 994      * returned.
 995      *
 996      * <p>In other words, this method returns an {@code Integer}
 997      * object equal to the value of:
 998      *
 999      * <blockquote>
1000      *  {@code getInteger(nm, null)}
1001      * </blockquote>
1002      *
1003      * @param   nm   property name.
1004      * @return  the {@code Integer} value of the property.
1005      * @throws  SecurityException for the same reasons as
1006      *          {@link System#getProperty(String) System.getProperty}
1007      * @see     java.lang.System#getProperty(java.lang.String)
1008      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1009      */
1010     public static Integer getInteger(String nm) {
1011         return getInteger(nm, null);
1012     }
1013 
1014     /**
1015      * Determines the integer value of the system property with the
1016      * specified name.
1017      *
1018      * <p>The first argument is treated as the name of a system
1019      * property.  System properties are accessible through the {@link
1020      * java.lang.System#getProperty(java.lang.String)} method. The
1021      * string value of this property is then interpreted as an integer
1022      * value using the grammar supported by {@link Integer#decode decode} and
1023      * an {@code Integer} object representing this value is returned.
1024      *
1025      * <p>The second argument is the default value. An {@code Integer} object
1026      * that represents the value of the second argument is returned if there
1027      * is no property of the specified name, if the property does not have
1028      * the correct numeric format, or if the specified name is empty or
1029      * {@code null}.
1030      *
1031      * <p>In other words, this method returns an {@code Integer} object
1032      * equal to the value of:
1033      *
1034      * <blockquote>
1035      *  {@code getInteger(nm, new Integer(val))}
1036      * </blockquote>
1037      *
1038      * but in practice it may be implemented in a manner such as:
1039      *
1040      * <blockquote><pre>
1041      * Integer result = getInteger(nm, null);
1042      * return (result == null) ? new Integer(val) : result;
1043      * </pre></blockquote>
1044      *
1045      * to avoid the unnecessary allocation of an {@code Integer}
1046      * object when the default value is not needed.
1047      *
1048      * @param   nm   property name.
1049      * @param   val   default value.
1050      * @return  the {@code Integer} value of the property.
1051      * @throws  SecurityException for the same reasons as
1052      *          {@link System#getProperty(String) System.getProperty}
1053      * @see     java.lang.System#getProperty(java.lang.String)
1054      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1055      */
1056     public static Integer getInteger(String nm, int val) {
1057         Integer result = getInteger(nm, null);
1058         return (result == null) ? Integer.valueOf(val) : result;
1059     }
1060 
1061     /**
1062      * Returns the integer value of the system property with the
1063      * specified name.  The first argument is treated as the name of a
1064      * system property.  System properties are accessible through the
1065      * {@link java.lang.System#getProperty(java.lang.String)} method.
1066      * The string value of this property is then interpreted as an
1067      * integer value, as per the {@link Integer#decode decode} method,
1068      * and an {@code Integer} object representing this value is
1069      * returned; in summary:
1070      *
1071      * <ul><li>If the property value begins with the two ASCII characters
1072      *         {@code 0x} or the ASCII character {@code #}, not
1073      *      followed by a minus sign, then the rest of it is parsed as a
1074      *      hexadecimal integer exactly as by the method
1075      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1076      * <li>If the property value begins with the ASCII character
1077      *     {@code 0} followed by another character, it is parsed as an
1078      *     octal integer exactly as by the method
1079      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1080      * <li>Otherwise, the property value is parsed as a decimal integer
1081      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1082      * with radix 10.
1083      * </ul>
1084      *
1085      * <p>The second argument is the default value. The default value is
1086      * returned if there is no property of the specified name, if the
1087      * property does not have the correct numeric format, or if the
1088      * specified name is empty or {@code null}.
1089      *
1090      * @param   nm   property name.
1091      * @param   val   default value.
1092      * @return  the {@code Integer} value of the property.
1093      * @throws  SecurityException for the same reasons as
1094      *          {@link System#getProperty(String) System.getProperty}
1095      * @see     System#getProperty(java.lang.String)
1096      * @see     System#getProperty(java.lang.String, java.lang.String)
1097      */
1098     public static Integer getInteger(String nm, Integer val) {
1099         String v = null;
1100         try {
1101             v = System.getProperty(nm);
1102         } catch (IllegalArgumentException | NullPointerException e) {
1103         }
1104         if (v != null) {
1105             try {
1106                 return Integer.decode(v);
1107             } catch (NumberFormatException e) {
1108             }
1109         }
1110         return val;
1111     }
1112 
1113     /**
1114      * Decodes a {@code String} into an {@code Integer}.
1115      * Accepts decimal, hexadecimal, and octal numbers given
1116      * by the following grammar:
1117      *
1118      * <blockquote>
1119      * <dl>
1120      * <dt><i>DecodableString:</i>
1121      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1122      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1123      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1124      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1125      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1126      *
1127      * <dt><i>Sign:</i>
1128      * <dd>{@code -}
1129      * <dd>{@code +}
1130      * </dl>
1131      * </blockquote>
1132      *
1133      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1134      * are as defined in section 3.10.1 of
1135      * <cite>The Java&trade; Language Specification</cite>,
1136      * except that underscores are not accepted between digits.
1137      *
1138      * <p>The sequence of characters following an optional
1139      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1140      * "{@code #}", or leading zero) is parsed as by the {@code
1141      * Integer.parseInt} method with the indicated radix (10, 16, or
1142      * 8).  This sequence of characters must represent a positive
1143      * value or a {@link NumberFormatException} will be thrown.  The
1144      * result is negated if first character of the specified {@code
1145      * String} is the minus sign.  No whitespace characters are
1146      * permitted in the {@code String}.
1147      *
1148      * @param     nm the {@code String} to decode.
1149      * @return    an {@code Integer} object holding the {@code int}
1150      *             value represented by {@code nm}
1151      * @exception NumberFormatException  if the {@code String} does not
1152      *            contain a parsable integer.
1153      * @see java.lang.Integer#parseInt(java.lang.String, int)
1154      */
1155     public static Integer decode(String nm) throws NumberFormatException {
1156         int radix = 10;
1157         int index = 0;
1158         boolean negative = false;
1159         Integer result;
1160 
1161         if (nm.length() == 0)
1162             throw new NumberFormatException("Zero length string");
1163         char firstChar = nm.charAt(0);
1164         // Handle sign, if present
1165         if (firstChar == '-') {
1166             negative = true;
1167             index++;
1168         } else if (firstChar == '+')
1169             index++;
1170 
1171         // Handle radix specifier, if present
1172         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1173             index += 2;
1174             radix = 16;
1175         }
1176         else if (nm.startsWith("#", index)) {
1177             index ++;
1178             radix = 16;
1179         }
1180         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1181             index ++;
1182             radix = 8;
1183         }
1184 
1185         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1186             throw new NumberFormatException("Sign character in wrong position");
1187 
1188         try {
1189             result = Integer.valueOf(nm.substring(index), radix);
1190             result = negative ? Integer.valueOf(-result.intValue()) : result;
1191         } catch (NumberFormatException e) {
1192             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1193             // handles this case, and causes any genuine format error to be
1194             // rethrown.
1195             String constant = negative ? ("-" + nm.substring(index))
1196                                        : nm.substring(index);
1197             result = Integer.valueOf(constant, radix);
1198         }
1199         return result;
1200     }
1201 
1202     /**
1203      * Compares two {@code Integer} objects numerically.
1204      *
1205      * @param   anotherInteger   the {@code Integer} to be compared.
1206      * @return  the value {@code 0} if this {@code Integer} is
1207      *          equal to the argument {@code Integer}; a value less than
1208      *          {@code 0} if this {@code Integer} is numerically less
1209      *          than the argument {@code Integer}; and a value greater
1210      *          than {@code 0} if this {@code Integer} is numerically
1211      *           greater than the argument {@code Integer} (signed
1212      *           comparison).
1213      * @since   1.2
1214      */
1215     public int compareTo(Integer anotherInteger) {
1216         return compare(this.value, anotherInteger.value);
1217     }
1218 
1219     /**
1220      * Compares two {@code int} values numerically.
1221      * The value returned is identical to what would be returned by:
1222      * <pre>
1223      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1224      * </pre>
1225      *
1226      * @param  x the first {@code int} to compare
1227      * @param  y the second {@code int} to compare
1228      * @return the value {@code 0} if {@code x == y};
1229      *         a value less than {@code 0} if {@code x < y}; and
1230      *         a value greater than {@code 0} if {@code x > y}
1231      * @since 1.7
1232      */
1233     public static int compare(int x, int y) {
1234         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1235     }
1236 
1237     /**
1238      * Compares two {@code int} values numerically treating the values
1239      * as unsigned.
1240      *
1241      * @param  x the first {@code int} to compare
1242      * @param  y the second {@code int} to compare
1243      * @return the value {@code 0} if {@code x == y}; a value less
1244      *         than {@code 0} if {@code x < y} as unsigned values; and
1245      *         a value greater than {@code 0} if {@code x > y} as
1246      *         unsigned values
1247      * @since 1.8
1248      */
1249     public static int compareUnsigned(int x, int y) {
1250         return compare(x + MIN_VALUE, y + MIN_VALUE);
1251     }
1252 
1253     /**
1254      * Converts the argument to a {@code long} by an unsigned
1255      * conversion.  In an unsigned conversion to a {@code long}, the
1256      * high-order 32 bits of the {@code long} are zero and the
1257      * low-order 32 bits are equal to the bits of the integer
1258      * argument.
1259      *
1260      * Consequently, zero and positive {@code int} values are mapped
1261      * to a numerically equal {@code long} value and negative {@code
1262      * int} values are mapped to a {@code long} value equal to the
1263      * input plus 2<sup>32</sup>.
1264      *
1265      * @param  x the value to convert to an unsigned {@code long}
1266      * @return the argument converted to {@code long} by an unsigned
1267      *         conversion
1268      * @since 1.8
1269      */
1270     public static long toUnsignedLong(int x) {
1271         return ((long) x) & 0xffffffffL;
1272     }
1273 
1274     /**
1275      * Returns the unsigned quotient of dividing the first argument by
1276      * the second where each argument and the result is interpreted as
1277      * an unsigned value.
1278      *
1279      * <p>Note that in two's complement arithmetic, the three other
1280      * basic arithmetic operations of add, subtract, and multiply are
1281      * bit-wise identical if the two operands are regarded as both
1282      * being signed or both being unsigned.  Therefore separate {@code
1283      * addUnsigned}, etc. methods are not provided.
1284      *
1285      * @param dividend the value to be divided
1286      * @param divisor the value doing the dividing
1287      * @return the unsigned quotient of the first argument divided by
1288      * the second argument
1289      * @see #remainderUnsigned
1290      * @since 1.8
1291      */
1292     public static int divideUnsigned(int dividend, int divisor) {
1293         // In lieu of tricky code, for now just use long arithmetic.
1294         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1295     }
1296 
1297     /**
1298      * Returns the unsigned remainder from dividing the first argument
1299      * by the second where each argument and the result is interpreted
1300      * as an unsigned value.
1301      *
1302      * @param dividend the value to be divided
1303      * @param divisor the value doing the dividing
1304      * @return the unsigned remainder of the first argument divided by
1305      * the second argument
1306      * @see #divideUnsigned
1307      * @since 1.8
1308      */
1309     public static int remainderUnsigned(int dividend, int divisor) {
1310         // In lieu of tricky code, for now just use long arithmetic.
1311         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1312     }
1313 
1314 
1315     // Bit twiddling
1316 
1317     /**
1318      * The number of bits used to represent an {@code int} value in two's
1319      * complement binary form.
1320      *
1321      * @since 1.5
1322      */
1323     @Native public static final int SIZE = 32;
1324 
1325     /**
1326      * The number of bytes used to represent a {@code int} value in two's
1327      * complement binary form.
1328      *
1329      * @since 1.8
1330      */
1331     public static final int BYTES = SIZE / Byte.SIZE;
1332 
1333     /**
1334      * Returns an {@code int} value with at most a single one-bit, in the
1335      * position of the highest-order ("leftmost") one-bit in the specified
1336      * {@code int} value.  Returns zero if the specified value has no
1337      * one-bits in its two's complement binary representation, that is, if it
1338      * is equal to zero.
1339      *
1340      * @param i the value whose highest one bit is to be computed
1341      * @return an {@code int} value with a single one-bit, in the position
1342      *     of the highest-order one-bit in the specified value, or zero if
1343      *     the specified value is itself equal to zero.
1344      * @since 1.5
1345      */
1346     public static int highestOneBit(int i) {
1347         // HD, Figure 3-1
1348         i |= (i >>  1);
1349         i |= (i >>  2);
1350         i |= (i >>  4);
1351         i |= (i >>  8);
1352         i |= (i >> 16);
1353         return i - (i >>> 1);
1354     }
1355 
1356     /**
1357      * Returns an {@code int} value with at most a single one-bit, in the
1358      * position of the lowest-order ("rightmost") one-bit in the specified
1359      * {@code int} value.  Returns zero if the specified value has no
1360      * one-bits in its two's complement binary representation, that is, if it
1361      * is equal to zero.
1362      *
1363      * @param i the value whose lowest one bit is to be computed
1364      * @return an {@code int} value with a single one-bit, in the position
1365      *     of the lowest-order one-bit in the specified value, or zero if
1366      *     the specified value is itself equal to zero.
1367      * @since 1.5
1368      */
1369     public static int lowestOneBit(int i) {
1370         // HD, Section 2-1
1371         return i & -i;
1372     }
1373 
1374     /**
1375      * Returns the number of zero bits preceding the highest-order
1376      * ("leftmost") one-bit in the two's complement binary representation
1377      * of the specified {@code int} value.  Returns 32 if the
1378      * specified value has no one-bits in its two's complement representation,
1379      * in other words if it is equal to zero.
1380      *
1381      * <p>Note that this method is closely related to the logarithm base 2.
1382      * For all positive {@code int} values x:
1383      * <ul>
1384      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1385      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1386      * </ul>
1387      *
1388      * @param i the value whose number of leading zeros is to be computed
1389      * @return the number of zero bits preceding the highest-order
1390      *     ("leftmost") one-bit in the two's complement binary representation
1391      *     of the specified {@code int} value, or 32 if the value
1392      *     is equal to zero.
1393      * @since 1.5
1394      */
1395     public static int numberOfLeadingZeros(int i) {
1396         // HD, Figure 5-6
1397         if (i == 0)
1398             return 32;
1399         int n = 1;
1400         if (i >>> 16 == 0) { n += 16; i <<= 16; }
1401         if (i >>> 24 == 0) { n +=  8; i <<=  8; }
1402         if (i >>> 28 == 0) { n +=  4; i <<=  4; }
1403         if (i >>> 30 == 0) { n +=  2; i <<=  2; }
1404         n -= i >>> 31;
1405         return n;
1406     }
1407 
1408     /**
1409      * Returns the number of zero bits following the lowest-order ("rightmost")
1410      * one-bit in the two's complement binary representation of the specified
1411      * {@code int} value.  Returns 32 if the specified value has no
1412      * one-bits in its two's complement representation, in other words if it is
1413      * equal to zero.
1414      *
1415      * @param i the value whose number of trailing zeros is to be computed
1416      * @return the number of zero bits following the lowest-order ("rightmost")
1417      *     one-bit in the two's complement binary representation of the
1418      *     specified {@code int} value, or 32 if the value is equal
1419      *     to zero.
1420      * @since 1.5
1421      */
1422     public static int numberOfTrailingZeros(int i) {
1423         // HD, Figure 5-14
1424         int y;
1425         if (i == 0) return 32;
1426         int n = 31;
1427         y = i <<16; if (y != 0) { n = n -16; i = y; }
1428         y = i << 8; if (y != 0) { n = n - 8; i = y; }
1429         y = i << 4; if (y != 0) { n = n - 4; i = y; }
1430         y = i << 2; if (y != 0) { n = n - 2; i = y; }
1431         return n - ((i << 1) >>> 31);
1432     }
1433 
1434     /**
1435      * Returns the number of one-bits in the two's complement binary
1436      * representation of the specified {@code int} value.  This function is
1437      * sometimes referred to as the <i>population count</i>.
1438      *
1439      * @param i the value whose bits are to be counted
1440      * @return the number of one-bits in the two's complement binary
1441      *     representation of the specified {@code int} value.
1442      * @since 1.5
1443      */
1444     public static int bitCount(int i) {
1445         // HD, Figure 5-2
1446         i = i - ((i >>> 1) & 0x55555555);
1447         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1448         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1449         i = i + (i >>> 8);
1450         i = i + (i >>> 16);
1451         return i & 0x3f;
1452     }
1453 
1454     /**
1455      * Returns the value obtained by rotating the two's complement binary
1456      * representation of the specified {@code int} value left by the
1457      * specified number of bits.  (Bits shifted out of the left hand, or
1458      * high-order, side reenter on the right, or low-order.)
1459      *
1460      * <p>Note that left rotation with a negative distance is equivalent to
1461      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1462      * distance)}.  Note also that rotation by any multiple of 32 is a
1463      * no-op, so all but the last five bits of the rotation distance can be
1464      * ignored, even if the distance is negative: {@code rotateLeft(val,
1465      * distance) == rotateLeft(val, distance & 0x1F)}.
1466      *
1467      * @param i the value whose bits are to be rotated left
1468      * @param distance the number of bit positions to rotate left
1469      * @return the value obtained by rotating the two's complement binary
1470      *     representation of the specified {@code int} value left by the
1471      *     specified number of bits.
1472      * @since 1.5
1473      */
1474     public static int rotateLeft(int i, int distance) {
1475         return (i << distance) | (i >>> -distance);
1476     }
1477 
1478     /**
1479      * Returns the value obtained by rotating the two's complement binary
1480      * representation of the specified {@code int} value right by the
1481      * specified number of bits.  (Bits shifted out of the right hand, or
1482      * low-order, side reenter on the left, or high-order.)
1483      *
1484      * <p>Note that right rotation with a negative distance is equivalent to
1485      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1486      * distance)}.  Note also that rotation by any multiple of 32 is a
1487      * no-op, so all but the last five bits of the rotation distance can be
1488      * ignored, even if the distance is negative: {@code rotateRight(val,
1489      * distance) == rotateRight(val, distance & 0x1F)}.
1490      *
1491      * @param i the value whose bits are to be rotated right
1492      * @param distance the number of bit positions to rotate right
1493      * @return the value obtained by rotating the two's complement binary
1494      *     representation of the specified {@code int} value right by the
1495      *     specified number of bits.
1496      * @since 1.5
1497      */
1498     public static int rotateRight(int i, int distance) {
1499         return (i >>> distance) | (i << -distance);
1500     }
1501 
1502     /**
1503      * Returns the value obtained by reversing the order of the bits in the
1504      * two's complement binary representation of the specified {@code int}
1505      * value.
1506      *
1507      * @param i the value to be reversed
1508      * @return the value obtained by reversing order of the bits in the
1509      *     specified {@code int} value.
1510      * @since 1.5
1511      */
1512     public static int reverse(int i) {
1513         // HD, Figure 7-1
1514         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1515         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1516         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1517         i = (i << 24) | ((i & 0xff00) << 8) |
1518             ((i >>> 8) & 0xff00) | (i >>> 24);
1519         return i;
1520     }
1521 
1522     /**
1523      * Returns the signum function of the specified {@code int} value.  (The
1524      * return value is -1 if the specified value is negative; 0 if the
1525      * specified value is zero; and 1 if the specified value is positive.)
1526      *
1527      * @param i the value whose signum is to be computed
1528      * @return the signum function of the specified {@code int} value.
1529      * @since 1.5
1530      */
1531     public static int signum(int i) {
1532         // HD, Section 2-7
1533         return (i >> 31) | (-i >>> 31);
1534     }
1535 
1536     /**
1537      * Returns the value obtained by reversing the order of the bytes in the
1538      * two's complement representation of the specified {@code int} value.
1539      *
1540      * @param i the value whose bytes are to be reversed
1541      * @return the value obtained by reversing the bytes in the specified
1542      *     {@code int} value.
1543      * @since 1.5
1544      */
1545     public static int reverseBytes(int i) {
1546         return ((i >>> 24)           ) |
1547                ((i >>   8) &   0xFF00) |
1548                ((i <<   8) & 0xFF0000) |
1549                ((i << 24));
1550     }
1551 
1552     /**
1553      * Adds two integers together as per the + operator.
1554      *
1555      * @param a the first operand
1556      * @param b the second operand
1557      * @return the sum of {@code a} and {@code b}
1558      * @see java.util.function.BinaryOperator
1559      * @since 1.8
1560      */
1561     public static int sum(int a, int b) {
1562         return a + b;
1563     }
1564 
1565     /**
1566      * Returns the greater of two {@code int} values
1567      * as if by calling {@link Math#max(int, int) Math.max}.
1568      *
1569      * @param a the first operand
1570      * @param b the second operand
1571      * @return the greater of {@code a} and {@code b}
1572      * @see java.util.function.BinaryOperator
1573      * @since 1.8
1574      */
1575     public static int max(int a, int b) {
1576         return Math.max(a, b);
1577     }
1578 
1579     /**
1580      * Returns the smaller of two {@code int} values
1581      * as if by calling {@link Math#min(int, int) Math.min}.
1582      *
1583      * @param a the first operand
1584      * @param b the second operand
1585      * @return the smaller of {@code a} and {@code b}
1586      * @see java.util.function.BinaryOperator
1587      * @since 1.8
1588      */
1589     public static int min(int a, int b) {
1590         return Math.min(a, b);
1591     }
1592 
1593     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1594     @Native private static final long serialVersionUID = 1360826667806852920L;
1595 }