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