1 /*
   2  * Copyright (c) 1994, 2011, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.lang;
  27 
  28 import java.util.Properties;
  29 
  30 /**
  31  * The {@code Integer} class wraps a value of the primitive type
  32  * {@code int} in an object. An object of type {@code Integer}
  33  * contains a single field whose type is {@code int}.
  34  *
  35  * <p>In addition, this class provides several methods for converting
  36  * an {@code int} to a {@code String} and a {@code String} to an
  37  * {@code int}, as well as other constants and methods useful when
  38  * dealing with an {@code int}.
  39  *
  40  * <p>Implementation note: The implementations of the "bit twiddling"
  41  * methods (such as {@link #highestOneBit(int) highestOneBit} and
  42  * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
  43  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  44  * Delight</i>, (Addison Wesley, 2002).
  45  *
  46  * @author  Lee Boynton
  47  * @author  Arthur van Hoff
  48  * @author  Josh Bloch
  49  * @author  Joseph D. Darcy
  50  * @since JDK1.0
  51  */
  52 public final class Integer extends Number implements Comparable<Integer> {
  53     /**
  54      * A constant holding the minimum value an {@code int} can
  55      * have, -2<sup>31</sup>.
  56      */
  57     public static final int   MIN_VALUE = 0x80000000;
  58 
  59     /**
  60      * A constant holding the maximum value an {@code int} can
  61      * have, 2<sup>31</sup>-1.
  62      */
  63     public static final int   MAX_VALUE = 0x7fffffff;
  64 
  65     /**
  66      * The {@code Class} instance representing the primitive type
  67      * {@code int}.
  68      *
  69      * @since   JDK1.1
  70      */
  71     public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
  72 
  73     /**
  74      * All possible chars for representing a number as a String
  75      */
  76     final static char[] digits = {
  77         '0' , '1' , '2' , '3' , '4' , '5' ,
  78         '6' , '7' , '8' , '9' , 'a' , 'b' ,
  79         'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
  80         'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
  81         'o' , 'p' , 'q' , 'r' , 's' , 't' ,
  82         'u' , 'v' , 'w' , 'x' , 'y' , 'z'
  83     };
  84 
  85     /**
  86      * Returns a string representation of the first argument in the
  87      * radix specified by the second argument.
  88      *
  89      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  90      * or larger than {@code Character.MAX_RADIX}, then the radix
  91      * {@code 10} is used instead.
  92      *
  93      * <p>If the first argument is negative, the first element of the
  94      * result is the ASCII minus character {@code '-'}
  95      * (<code>'&#92;u002D'</code>). If the first argument is not
  96      * negative, no sign character appears in the result.
  97      *
  98      * <p>The remaining characters of the result represent the magnitude
  99      * of the first argument. If the magnitude is zero, it is
 100      * represented by a single zero character {@code '0'}
 101      * (<code>'&#92;u0030'</code>); otherwise, the first character of
 102      * the representation of the magnitude will not be the zero
 103      * character.  The following ASCII characters are used as digits:
 104      *
 105      * <blockquote>
 106      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 107      * </blockquote>
 108      *
 109      * These are <code>'&#92;u0030'</code> through
 110      * <code>'&#92;u0039'</code> and <code>'&#92;u0061'</code> through
 111      * <code>'&#92;u007A'</code>. If {@code radix} is
 112      * <var>N</var>, then the first <var>N</var> of these characters
 113      * are used as radix-<var>N</var> digits in the order shown. Thus,
 114      * the digits for hexadecimal (radix 16) are
 115      * {@code 0123456789abcdef}. If uppercase letters are
 116      * desired, the {@link java.lang.String#toUpperCase()} method may
 117      * be called on the result:
 118      *
 119      * <blockquote>
 120      *  {@code Integer.toString(n, 16).toUpperCase()}
 121      * </blockquote>
 122      *
 123      * @param   i       an integer to be converted to a string.
 124      * @param   radix   the radix to use in the string representation.
 125      * @return  a string representation of the argument in the specified radix.
 126      * @see     java.lang.Character#MAX_RADIX
 127      * @see     java.lang.Character#MIN_RADIX
 128      */
 129     public static String toString(int i, int radix) {
 130 
 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 integer argument as an
 162      * unsigned integer in base&nbsp;16.
 163      *
 164      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 165      * if the argument is negative; otherwise, it is equal to the
 166      * argument.  This value is converted to a string of ASCII digits
 167      * in hexadecimal (base&nbsp;16) with no extra leading
 168      * {@code 0}s. If the unsigned magnitude is zero, it is
 169      * represented by a single zero character {@code '0'}
 170      * (<code>'&#92;u0030'</code>); otherwise, the first character of
 171      * the representation of the unsigned magnitude will not be the
 172      * zero character. The following characters are used as
 173      * hexadecimal digits:
 174      *
 175      * <blockquote>
 176      *  {@code 0123456789abcdef}
 177      * </blockquote>
 178      *
 179      * These are the characters <code>'&#92;u0030'</code> through
 180      * <code>'&#92;u0039'</code> and <code>'&#92;u0061'</code> through
 181      * <code>'&#92;u0066'</code>. If uppercase letters are
 182      * desired, the {@link java.lang.String#toUpperCase()} method may
 183      * be called on the result:
 184      *
 185      * <blockquote>
 186      *  {@code Integer.toHexString(n).toUpperCase()}
 187      * </blockquote>
 188      *
 189      * @param   i   an integer to be converted to a string.
 190      * @return  the string representation of the unsigned integer value
 191      *          represented by the argument in hexadecimal (base&nbsp;16).
 192      * @since   JDK1.0.2
 193      */
 194     public static String toHexString(int i) {
 195         return toUnsignedString(i, 4);
 196     }
 197 
 198     /**
 199      * Returns a string representation of the integer argument as an
 200      * unsigned integer in base&nbsp;8.
 201      *
 202      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 203      * if the argument is negative; otherwise, it is equal to the
 204      * argument.  This value is converted to a string of ASCII digits
 205      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
 206      *
 207      * <p>If the unsigned magnitude is zero, it is represented by a
 208      * single zero character {@code '0'}
 209      * (<code>'&#92;u0030'</code>); otherwise, the first character of
 210      * the representation of the unsigned magnitude will not be the
 211      * zero character. The following characters are used as octal
 212      * digits:
 213      *
 214      * <blockquote>
 215      * {@code 01234567}
 216      * </blockquote>
 217      *
 218      * These are the characters <code>'&#92;u0030'</code> through
 219      * <code>'&#92;u0037'</code>.
 220      *
 221      * @param   i   an integer to be converted to a string.
 222      * @return  the string representation of the unsigned integer value
 223      *          represented by the argument in octal (base&nbsp;8).
 224      * @since   JDK1.0.2
 225      */
 226     public static String toOctalString(int i) {
 227         return toUnsignedString(i, 3);
 228     }
 229 
 230     /**
 231      * Returns a string representation of the integer argument as an
 232      * unsigned integer in base&nbsp;2.
 233      *
 234      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 235      * if the argument is negative; otherwise it is equal to the
 236      * argument.  This value is converted to a string of ASCII digits
 237      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
 238      * If the unsigned magnitude is zero, it is represented by a
 239      * single zero character {@code '0'}
 240      * (<code>'&#92;u0030'</code>); otherwise, the first character of
 241      * the representation of the unsigned magnitude will not be the
 242      * zero character. The characters {@code '0'}
 243      * (<code>'&#92;u0030'</code>) and {@code '1'}
 244      * (<code>'&#92;u0031'</code>) are used as binary digits.
 245      *
 246      * @param   i   an integer to be converted to a string.
 247      * @return  the string representation of the unsigned integer value
 248      *          represented by the argument in binary (base&nbsp;2).
 249      * @since   JDK1.0.2
 250      */
 251     public static String toBinaryString(int i) {
 252         return toUnsignedString(i, 1);
 253     }
 254 
 255     /**
 256      * Convert the integer to an unsigned number.
 257      */
 258     private static String toUnsignedString(int i, int shift) {
 259         char[] buf = new char[32];
 260         int charPos = 32;
 261         int radix = 1 << shift;
 262         int mask = radix - 1;
 263         do {
 264             buf[--charPos] = digits[i & mask];
 265             i >>>= shift;
 266         } while (i != 0);
 267 
 268         return new String(buf, charPos, (32 - charPos));
 269     }
 270 
 271 
 272     final static char [] DigitTens = {
 273         '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
 274         '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
 275         '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
 276         '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
 277         '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
 278         '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
 279         '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
 280         '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
 281         '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
 282         '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
 283         } ;
 284 
 285     final static char [] DigitOnes = {
 286         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 287         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 288         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 289         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 290         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 291         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 292         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 293         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 294         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 295         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
 296         } ;
 297 
 298         // I use the "invariant division by multiplication" trick to
 299         // accelerate Integer.toString.  In particular we want to
 300         // avoid division by 10.
 301         //
 302         // The "trick" has roughly the same performance characteristics
 303         // as the "classic" Integer.toString code on a non-JIT VM.
 304         // The trick avoids .rem and .div calls but has a longer code
 305         // path and is thus dominated by dispatch overhead.  In the
 306         // JIT case the dispatch overhead doesn't exist and the
 307         // "trick" is considerably faster than the classic code.
 308         //
 309         // TODO-FIXME: convert (x * 52429) into the equiv shift-add
 310         // sequence.
 311         //
 312         // RE:  Division by Invariant Integers using Multiplication
 313         //      T Gralund, P Montgomery
 314         //      ACM PLDI 1994
 315         //
 316 
 317     /**
 318      * Returns a {@code String} object representing the
 319      * specified integer. The argument is converted to signed decimal
 320      * representation and returned as a string, exactly as if the
 321      * argument and radix 10 were given as arguments to the {@link
 322      * #toString(int, int)} method.
 323      *
 324      * @param   i   an integer to be converted.
 325      * @return  a string representation of the argument in base&nbsp;10.
 326      */
 327     public static String toString(int i) {
 328         if (i == Integer.MIN_VALUE)
 329             return "-2147483648";
 330         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
 331         char[] buf = new char[size];
 332         getChars(i, size, buf);
 333         return new String(0, size, buf);
 334     }
 335 
 336     /**
 337      * Places characters representing the integer i into the
 338      * character array buf. The characters are placed into
 339      * the buffer backwards starting with the least significant
 340      * digit at the specified index (exclusive), and working
 341      * backwards from there.
 342      *
 343      * Will fail if i == Integer.MIN_VALUE
 344      */
 345     static void getChars(int i, int index, char[] buf) {
 346         int q, r;
 347         int charPos = index;
 348         char sign = 0;
 349 
 350         if (i < 0) {
 351             sign = '-';
 352             i = -i;
 353         }
 354 
 355         // Generate two digits per iteration
 356         while (i >= 65536) {
 357             q = i / 100;
 358         // really: r = i - (q * 100);
 359             r = i - ((q << 6) + (q << 5) + (q << 2));
 360             i = q;
 361             buf [--charPos] = DigitOnes[r];
 362             buf [--charPos] = DigitTens[r];
 363         }
 364 
 365         // Fall thru to fast mode for smaller numbers
 366         // assert(i <= 65536, i);
 367         for (;;) {
 368             q = (i * 52429) >>> (16+3);
 369             r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
 370             buf [--charPos] = digits [r];
 371             i = q;
 372             if (i == 0) break;
 373         }
 374         if (sign != 0) {
 375             buf [--charPos] = sign;
 376         }
 377     }
 378 
 379     final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
 380                                       99999999, 999999999, Integer.MAX_VALUE };
 381 
 382     // Requires positive x
 383     static int stringSize(int x) {
 384         for (int i=0; ; i++)
 385             if (x <= sizeTable[i])
 386                 return i+1;
 387     }
 388 
 389     /**
 390      * Parses the string argument as a signed integer in the radix
 391      * specified by the second argument. The characters in the string
 392      * must all be digits of the specified radix (as determined by
 393      * whether {@link java.lang.Character#digit(char, int)} returns a
 394      * nonnegative value), except that the first character may be an
 395      * ASCII minus sign {@code '-'} (<code>'&#92;u002D'</code>) to
 396      * indicate a negative value or an ASCII plus sign {@code '+'}
 397      * (<code>'&#92;u002B'</code>) to indicate a positive value. The
 398      * resulting integer value is returned.
 399      *
 400      * <p>An exception of type {@code NumberFormatException} is
 401      * thrown if any of the following situations occurs:
 402      * <ul>
 403      * <li>The first argument is {@code null} or is a string of
 404      * length zero.
 405      *
 406      * <li>The radix is either smaller than
 407      * {@link java.lang.Character#MIN_RADIX} or
 408      * larger than {@link java.lang.Character#MAX_RADIX}.
 409      *
 410      * <li>Any character of the string is not a digit of the specified
 411      * radix, except that the first character may be a minus sign
 412      * {@code '-'} (<code>'&#92;u002D'</code>) or plus sign
 413      * {@code '+'} (<code>'&#92;u002B'</code>) provided that the
 414      * string is longer than length 1.
 415      *
 416      * <li>The value represented by the string is not a value of type
 417      * {@code int}.
 418      * </ul>
 419      *
 420      * <p>Examples:
 421      * <blockquote><pre>
 422      * parseInt("0", 10) returns 0
 423      * parseInt("473", 10) returns 473
 424      * parseInt("+42", 10) returns 42
 425      * parseInt("-0", 10) returns 0
 426      * parseInt("-FF", 16) returns -255
 427      * parseInt("1100110", 2) returns 102
 428      * parseInt("2147483647", 10) returns 2147483647
 429      * parseInt("-2147483648", 10) returns -2147483648
 430      * parseInt("2147483648", 10) throws a NumberFormatException
 431      * parseInt("99", 8) throws a NumberFormatException
 432      * parseInt("Kona", 10) throws a NumberFormatException
 433      * parseInt("Kona", 27) returns 411787
 434      * </pre></blockquote>
 435      *
 436      * @param      s   the {@code String} containing the integer
 437      *                  representation to be parsed
 438      * @param      radix   the radix to be used while parsing {@code s}.
 439      * @return     the integer represented by the string argument in the
 440      *             specified radix.
 441      * @exception  NumberFormatException if the {@code String}
 442      *             does not contain a parsable {@code int}.
 443      */
 444     public static int parseInt(String s, int radix)
 445                 throws NumberFormatException
 446     {
 447         /*
 448          * WARNING: This method may be invoked early during VM initialization
 449          * before IntegerCache is initialized. Care must be taken to not use
 450          * the valueOf method.
 451          */
 452 
 453         if (s == null) {
 454             throw new NumberFormatException("null");
 455         }
 456 
 457         if (radix < Character.MIN_RADIX) {
 458             throw new NumberFormatException("radix " + radix +
 459                                             " less than Character.MIN_RADIX");
 460         }
 461 
 462         if (radix > Character.MAX_RADIX) {
 463             throw new NumberFormatException("radix " + radix +
 464                                             " greater than Character.MAX_RADIX");
 465         }
 466 
 467         int result = 0;
 468         boolean negative = false;
 469         int i = 0, len = s.length();
 470         int limit = -Integer.MAX_VALUE;
 471         int multmin;
 472         int digit;
 473 
 474         if (len > 0) {
 475             char firstChar = s.charAt(0);
 476             if (firstChar < '0') { // Possible leading "+" or "-"
 477                 if (firstChar == '-') {
 478                     negative = true;
 479                     limit = Integer.MIN_VALUE;
 480                 } else if (firstChar != '+')
 481                     throw NumberFormatException.forInputString(s);
 482 
 483                 if (len == 1) // Cannot have lone "+" or "-"
 484                     throw NumberFormatException.forInputString(s);
 485                 i++;
 486             }
 487             multmin = limit / radix;
 488             while (i < len) {
 489                 // Accumulating negatively avoids surprises near MAX_VALUE
 490                 digit = Character.digit(s.charAt(i++),radix);
 491                 if (digit < 0) {
 492                     throw NumberFormatException.forInputString(s);
 493                 }
 494                 if (result < multmin) {
 495                     throw NumberFormatException.forInputString(s);
 496                 }
 497                 result *= radix;
 498                 if (result < limit + digit) {
 499                     throw NumberFormatException.forInputString(s);
 500                 }
 501                 result -= digit;
 502             }
 503         } else {
 504             throw NumberFormatException.forInputString(s);
 505         }
 506         return negative ? result : -result;
 507     }
 508 
 509     /**
 510      * Parses the string argument as a signed decimal integer. The
 511      * characters in the string must all be decimal digits, except
 512      * that the first character may be an ASCII minus sign {@code '-'}
 513      * (<code>'&#92;u002D'</code>) to indicate a negative value or an
 514      * ASCII plus sign {@code '+'} (<code>'&#92;u002B'</code>) to
 515      * indicate a positive value. The resulting integer value is
 516      * returned, exactly as if the argument and the radix 10 were
 517      * given as arguments to the {@link #parseInt(java.lang.String,
 518      * int)} method.
 519      *
 520      * @param s    a {@code String} containing the {@code int}
 521      *             representation to be parsed
 522      * @return     the integer value represented by the argument in decimal.
 523      * @exception  NumberFormatException  if the string does not contain a
 524      *               parsable integer.
 525      */
 526     public static int parseInt(String s) throws NumberFormatException {
 527         return parseInt(s,10);
 528     }
 529 
 530     /**
 531      * Returns an {@code Integer} object holding the value
 532      * extracted from the specified {@code String} when parsed
 533      * with the radix given by the second argument. The first argument
 534      * is interpreted as representing a signed integer in the radix
 535      * specified by the second argument, exactly as if the arguments
 536      * were given to the {@link #parseInt(java.lang.String, int)}
 537      * method. The result is an {@code Integer} object that
 538      * represents the integer value specified by the string.
 539      *
 540      * <p>In other words, this method returns an {@code Integer}
 541      * object equal to the value of:
 542      *
 543      * <blockquote>
 544      *  {@code new Integer(Integer.parseInt(s, radix))}
 545      * </blockquote>
 546      *
 547      * @param      s   the string to be parsed.
 548      * @param      radix the radix to be used in interpreting {@code s}
 549      * @return     an {@code Integer} object holding the value
 550      *             represented by the string argument in the specified
 551      *             radix.
 552      * @exception NumberFormatException if the {@code String}
 553      *            does not contain a parsable {@code int}.
 554      */
 555     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 556         return Integer.valueOf(parseInt(s,radix));
 557     }
 558 
 559     /**
 560      * Returns an {@code Integer} object holding the
 561      * value of the specified {@code String}. The argument is
 562      * interpreted as representing a signed decimal integer, exactly
 563      * as if the argument were given to the {@link
 564      * #parseInt(java.lang.String)} method. The result is an
 565      * {@code Integer} object that represents the integer value
 566      * specified by the string.
 567      *
 568      * <p>In other words, this method returns an {@code Integer}
 569      * object equal to the value of:
 570      *
 571      * <blockquote>
 572      *  {@code new Integer(Integer.parseInt(s))}
 573      * </blockquote>
 574      *
 575      * @param      s   the string to be parsed.
 576      * @return     an {@code Integer} object holding the value
 577      *             represented by the string argument.
 578      * @exception  NumberFormatException  if the string cannot be parsed
 579      *             as an integer.
 580      */
 581     public static Integer valueOf(String s) throws NumberFormatException {
 582         return Integer.valueOf(parseInt(s, 10));
 583     }
 584 
 585     /**
 586      * Cache to support the object identity semantics of autoboxing for values between
 587      * -128 and 127 (inclusive) as required by JLS.
 588      *
 589      * The cache is initialized on first usage.  The size of the cache
 590      * may be controlled by the -XX:AutoBoxCacheMax=<size> option.
 591      * During VM initialization, java.lang.Integer.IntegerCache.high property
 592      * may be set and saved in the private system properties in the
 593      * sun.misc.VM class.
 594      */
 595 
 596     private static class IntegerCache {
 597         static final int low = -128;
 598         static final int high;
 599         static final Integer cache[];
 600 
 601         static {
 602             // high value may be configured by property
 603             int h = 127;
 604             String integerCacheHighPropValue =
 605                 sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 606             if (integerCacheHighPropValue != null) {
 607                 int i = parseInt(integerCacheHighPropValue);
 608                 i = Math.max(i, 127);
 609                 // Maximum array size is Integer.MAX_VALUE
 610                 h = Math.min(i, Integer.MAX_VALUE - (-low));
 611             }
 612             high = h;
 613 
 614             cache = new Integer[(high - low) + 1];
 615             int j = low;
 616             for(int k = 0; k < cache.length; k++)
 617                 cache[k] = new Integer(j++);
 618         }
 619 
 620         private IntegerCache() {}
 621     }
 622 
 623     /**
 624      * Returns an {@code Integer} instance representing the specified
 625      * {@code int} value.  If a new {@code Integer} instance is not
 626      * required, this method should generally be used in preference to
 627      * the constructor {@link #Integer(int)}, as this method is likely
 628      * to yield significantly better space and time performance by
 629      * caching frequently requested values.
 630      *
 631      * This method will always cache values in the range -128 to 127,
 632      * inclusive, and may cache other values outside of this range.
 633      *
 634      * @param  i an {@code int} value.
 635      * @return an {@code Integer} instance representing {@code i}.
 636      * @since  1.5
 637      */
 638     public static Integer valueOf(int i) {
 639         assert IntegerCache.high >= 127;
 640         if (i >= IntegerCache.low && i <= IntegerCache.high)
 641             return IntegerCache.cache[i + (-IntegerCache.low)];
 642         return new Integer(i);
 643     }
 644 
 645     /**
 646      * The value of the {@code Integer}.
 647      *
 648      * @serial
 649      */
 650     private final int value;
 651 
 652     /**
 653      * Constructs a newly allocated {@code Integer} object that
 654      * represents the specified {@code int} value.
 655      *
 656      * @param   value   the value to be represented by the
 657      *                  {@code Integer} object.
 658      */
 659     public Integer(int value) {
 660         this.value = value;
 661     }
 662 
 663     /**
 664      * Constructs a newly allocated {@code Integer} object that
 665      * represents the {@code int} value indicated by the
 666      * {@code String} parameter. The string is converted to an
 667      * {@code int} value in exactly the manner used by the
 668      * {@code parseInt} method for radix 10.
 669      *
 670      * @param      s   the {@code String} to be converted to an
 671      *                 {@code Integer}.
 672      * @exception  NumberFormatException  if the {@code String} does not
 673      *               contain a parsable integer.
 674      * @see        java.lang.Integer#parseInt(java.lang.String, int)
 675      */
 676     public Integer(String s) throws NumberFormatException {
 677         this.value = parseInt(s, 10);
 678     }
 679 
 680     /**
 681      * Returns the value of this {@code Integer} as a {@code byte}
 682      * after a narrowing primitive conversion.
 683      * @jls 5.1.3 Narrowing Primitive Conversions
 684      */
 685     public byte byteValue() {
 686         return (byte)value;
 687     }
 688 
 689     /**
 690      * Returns the value of this {@code Integer} as a {@code short}
 691      * after a narrowing primitive conversion.
 692      * @jls 5.1.3 Narrowing Primitive Conversions
 693      */
 694     public short shortValue() {
 695         return (short)value;
 696     }
 697 
 698     /**
 699      * Returns the value of this {@code Integer} as an
 700      * {@code int}.
 701      */
 702     public int intValue() {
 703         return value;
 704     }
 705 
 706     /**
 707      * Returns the value of this {@code Integer} as a {@code long}
 708      * after a widening primitive conversion.
 709      * @jls 5.1.2 Widening Primitive Conversions
 710      */
 711     public long longValue() {
 712         return (long)value;
 713     }
 714 
 715     /**
 716      * Returns the value of this {@code Integer} as a {@code float}
 717      * after a widening primitive conversion.
 718      * @jls 5.1.2 Widening Primitive Conversions
 719      */
 720     public float floatValue() {
 721         return (float)value;
 722     }
 723 
 724     /**
 725      * Returns the value of this {@code Integer} as a {@code double}
 726      * after a widening primitive conversion.
 727      * @jls 5.1.2 Widening Primitive Conversions
 728      */
 729     public double doubleValue() {
 730         return (double)value;
 731     }
 732 
 733     /**
 734      * Returns a {@code String} object representing this
 735      * {@code Integer}'s value. The value is converted to signed
 736      * decimal representation and returned as a string, exactly as if
 737      * the integer value were given as an argument to the {@link
 738      * java.lang.Integer#toString(int)} method.
 739      *
 740      * @return  a string representation of the value of this object in
 741      *          base&nbsp;10.
 742      */
 743     public String toString() {
 744         return toString(value);
 745     }
 746 
 747     /**
 748      * Returns a hash code for this {@code Integer}.
 749      *
 750      * @return  a hash code value for this object, equal to the
 751      *          primitive {@code int} value represented by this
 752      *          {@code Integer} object.
 753      */
 754     public int hashCode() {
 755         return value;
 756     }
 757 
 758     /**
 759      * Returns a hash code for a {@code int} value; compatible with
 760      * {@code Integer.hashCode()}.
 761      *  
 762      * @since 1.8
 763      *
 764      * @return a hash code value for a {@code int} value.
 765      */
 766     public static int hashCode(int value) {
 767         return value;
 768     }
 769 
 770     /**
 771      * Compares this object to the specified object.  The result is
 772      * {@code true} if and only if the argument is not
 773      * {@code null} and is an {@code Integer} object that
 774      * contains the same {@code int} value as this object.
 775      *
 776      * @param   obj   the object to compare with.
 777      * @return  {@code true} if the objects are the same;
 778      *          {@code false} otherwise.
 779      */
 780     public boolean equals(Object obj) {
 781         if (obj instanceof Integer) {
 782             return value == ((Integer)obj).intValue();
 783         }
 784         return false;
 785     }
 786 
 787     /**
 788      * Determines the integer value of the system property with the
 789      * specified name.
 790      *
 791      * <p>The first argument is treated as the name of a system
 792      * property.  System properties are accessible through the {@link
 793      * java.lang.System#getProperty(java.lang.String)} method. The
 794      * string value of this property is then interpreted as an integer
 795      * value using the grammar supported by {@link Integer#decode decode} and
 796      * an {@code Integer} object representing this value is returned.
 797      *
 798      * <p>If there is no property with the specified name, if the
 799      * specified name is empty or {@code null}, or if the property
 800      * does not have the correct numeric format, then {@code null} is
 801      * returned.
 802      *
 803      * <p>In other words, this method returns an {@code Integer}
 804      * object equal to the value of:
 805      *
 806      * <blockquote>
 807      *  {@code getInteger(nm, null)}
 808      * </blockquote>
 809      *
 810      * @param   nm   property name.
 811      * @return  the {@code Integer} value of the property.
 812      * @see     java.lang.System#getProperty(java.lang.String)
 813      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
 814      */
 815     public static Integer getInteger(String nm) {
 816         return getInteger(nm, null);
 817     }
 818 
 819     /**
 820      * Determines the integer value of the system property with the
 821      * specified name.
 822      *
 823      * <p>The first argument is treated as the name of a system
 824      * property.  System properties are accessible through the {@link
 825      * java.lang.System#getProperty(java.lang.String)} method. The
 826      * string value of this property is then interpreted as an integer
 827      * value using the grammar supported by {@link Integer#decode decode} and
 828      * an {@code Integer} object representing this value is returned.
 829      *
 830      * <p>The second argument is the default value. An {@code Integer} object
 831      * that represents the value of the second argument is returned if there
 832      * is no property of the specified name, if the property does not have
 833      * the correct numeric format, or if the specified name is empty or
 834      * {@code null}.
 835      *
 836      * <p>In other words, this method returns an {@code Integer} object
 837      * equal to the value of:
 838      *
 839      * <blockquote>
 840      *  {@code getInteger(nm, new Integer(val))}
 841      * </blockquote>
 842      *
 843      * but in practice it may be implemented in a manner such as:
 844      *
 845      * <blockquote><pre>
 846      * Integer result = getInteger(nm, null);
 847      * return (result == null) ? new Integer(val) : result;
 848      * </pre></blockquote>
 849      *
 850      * to avoid the unnecessary allocation of an {@code Integer}
 851      * object when the default value is not needed.
 852      *
 853      * @param   nm   property name.
 854      * @param   val   default value.
 855      * @return  the {@code Integer} value of the property.
 856      * @see     java.lang.System#getProperty(java.lang.String)
 857      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
 858      */
 859     public static Integer getInteger(String nm, int val) {
 860         Integer result = getInteger(nm, null);
 861         return (result == null) ? Integer.valueOf(val) : result;
 862     }
 863 
 864     /**
 865      * Returns the integer value of the system property with the
 866      * specified name.  The first argument is treated as the name of a
 867      * system property.  System properties are accessible through the
 868      * {@link java.lang.System#getProperty(java.lang.String)} method.
 869      * The string value of this property is then interpreted as an
 870      * integer value, as per the {@link Integer#decode decode} method,
 871      * and an {@code Integer} object representing this value is
 872      * returned; in summary:
 873      *
 874      * <ul><li>If the property value begins with the two ASCII characters
 875      *         {@code 0x} or the ASCII character {@code #}, not
 876      *      followed by a minus sign, then the rest of it is parsed as a
 877      *      hexadecimal integer exactly as by the method
 878      *      {@link #valueOf(java.lang.String, int)} with radix 16.
 879      * <li>If the property value begins with the ASCII character
 880      *     {@code 0} followed by another character, it is parsed as an
 881      *     octal integer exactly as by the method
 882      *     {@link #valueOf(java.lang.String, int)} with radix 8.
 883      * <li>Otherwise, the property value is parsed as a decimal integer
 884      * exactly as by the method {@link #valueOf(java.lang.String, int)}
 885      * with radix 10.
 886      * </ul>
 887      *
 888      * <p>The second argument is the default value. The default value is
 889      * returned if there is no property of the specified name, if the
 890      * property does not have the correct numeric format, or if the
 891      * specified name is empty or {@code null}.
 892      *
 893      * @param   nm   property name.
 894      * @param   val   default value.
 895      * @return  the {@code Integer} value of the property.
 896      * @see     System#getProperty(java.lang.String)
 897      * @see     System#getProperty(java.lang.String, java.lang.String)
 898      */
 899     public static Integer getInteger(String nm, Integer val) {
 900         String v = null;
 901         try {
 902             v = System.getProperty(nm);
 903         } catch (IllegalArgumentException | NullPointerException e) {
 904         }
 905         if (v != null) {
 906             try {
 907                 return Integer.decode(v);
 908             } catch (NumberFormatException e) {
 909             }
 910         }
 911         return val;
 912     }
 913 
 914     /**
 915      * Decodes a {@code String} into an {@code Integer}.
 916      * Accepts decimal, hexadecimal, and octal numbers given
 917      * by the following grammar:
 918      *
 919      * <blockquote>
 920      * <dl>
 921      * <dt><i>DecodableString:</i>
 922      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
 923      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
 924      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
 925      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
 926      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
 927      * <p>
 928      * <dt><i>Sign:</i>
 929      * <dd>{@code -}
 930      * <dd>{@code +}
 931      * </dl>
 932      * </blockquote>
 933      *
 934      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
 935      * are as defined in section 3.10.1 of
 936      * <cite>The Java&trade; Language Specification</cite>,
 937      * except that underscores are not accepted between digits.
 938      *
 939      * <p>The sequence of characters following an optional
 940      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
 941      * "{@code #}", or leading zero) is parsed as by the {@code
 942      * Integer.parseInt} method with the indicated radix (10, 16, or
 943      * 8).  This sequence of characters must represent a positive
 944      * value or a {@link NumberFormatException} will be thrown.  The
 945      * result is negated if first character of the specified {@code
 946      * String} is the minus sign.  No whitespace characters are
 947      * permitted in the {@code String}.
 948      *
 949      * @param     nm the {@code String} to decode.
 950      * @return    an {@code Integer} object holding the {@code int}
 951      *             value represented by {@code nm}
 952      * @exception NumberFormatException  if the {@code String} does not
 953      *            contain a parsable integer.
 954      * @see java.lang.Integer#parseInt(java.lang.String, int)
 955      */
 956     public static Integer decode(String nm) throws NumberFormatException {
 957         int radix = 10;
 958         int index = 0;
 959         boolean negative = false;
 960         Integer result;
 961 
 962         if (nm.length() == 0)
 963             throw new NumberFormatException("Zero length string");
 964         char firstChar = nm.charAt(0);
 965         // Handle sign, if present
 966         if (firstChar == '-') {
 967             negative = true;
 968             index++;
 969         } else if (firstChar == '+')
 970             index++;
 971 
 972         // Handle radix specifier, if present
 973         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
 974             index += 2;
 975             radix = 16;
 976         }
 977         else if (nm.startsWith("#", index)) {
 978             index ++;
 979             radix = 16;
 980         }
 981         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
 982             index ++;
 983             radix = 8;
 984         }
 985 
 986         if (nm.startsWith("-", index) || nm.startsWith("+", index))
 987             throw new NumberFormatException("Sign character in wrong position");
 988 
 989         try {
 990             result = Integer.valueOf(nm.substring(index), radix);
 991             result = negative ? Integer.valueOf(-result.intValue()) : result;
 992         } catch (NumberFormatException e) {
 993             // If number is Integer.MIN_VALUE, we'll end up here. The next line
 994             // handles this case, and causes any genuine format error to be
 995             // rethrown.
 996             String constant = negative ? ("-" + nm.substring(index))
 997                                        : nm.substring(index);
 998             result = Integer.valueOf(constant, radix);
 999         }
1000         return result;
1001     }
1002 
1003     /**
1004      * Compares two {@code Integer} objects numerically.
1005      *
1006      * @param   anotherInteger   the {@code Integer} to be compared.
1007      * @return  the value {@code 0} if this {@code Integer} is
1008      *          equal to the argument {@code Integer}; a value less than
1009      *          {@code 0} if this {@code Integer} is numerically less
1010      *          than the argument {@code Integer}; and a value greater
1011      *          than {@code 0} if this {@code Integer} is numerically
1012      *           greater than the argument {@code Integer} (signed
1013      *           comparison).
1014      * @since   1.2
1015      */
1016     public int compareTo(Integer anotherInteger) {
1017         return compare(this.value, anotherInteger.value);
1018     }
1019 
1020     /**
1021      * Compares two {@code int} values numerically.
1022      * The value returned is identical to what would be returned by:
1023      * <pre>
1024      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1025      * </pre>
1026      *
1027      * @param  x the first {@code int} to compare
1028      * @param  y the second {@code int} to compare
1029      * @return the value {@code 0} if {@code x == y};
1030      *         a value less than {@code 0} if {@code x < y}; and
1031      *         a value greater than {@code 0} if {@code x > y}
1032      * @since 1.7
1033      */
1034     public static int compare(int x, int y) {
1035         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1036     }
1037 
1038 
1039     // Bit twiddling
1040 
1041     /**
1042      * The number of bits used to represent an {@code int} value in two's
1043      * complement binary form.
1044      *
1045      * @since 1.5
1046      */
1047     public static final int SIZE = 32;
1048 
1049     /**
1050      * The number of bytes used to represent a {@code int} value in two's
1051      * complement binary form.
1052      *
1053      * @since 1.8
1054      */
1055     public static final int BYTES = SIZE / Byte.SIZE;
1056 
1057     /**
1058      * Returns an {@code int} value with at most a single one-bit, in the
1059      * position of the highest-order ("leftmost") one-bit in the specified
1060      * {@code int} value.  Returns zero if the specified value has no
1061      * one-bits in its two's complement binary representation, that is, if it
1062      * is equal to zero.
1063      *
1064      * @return an {@code int} value with a single one-bit, in the position
1065      *     of the highest-order one-bit in the specified value, or zero if
1066      *     the specified value is itself equal to zero.
1067      * @since 1.5
1068      */
1069     public static int highestOneBit(int i) {
1070         // HD, Figure 3-1
1071         i |= (i >>  1);
1072         i |= (i >>  2);
1073         i |= (i >>  4);
1074         i |= (i >>  8);
1075         i |= (i >> 16);
1076         return i - (i >>> 1);
1077     }
1078 
1079     /**
1080      * Returns an {@code int} value with at most a single one-bit, in the
1081      * position of the lowest-order ("rightmost") one-bit in the specified
1082      * {@code int} value.  Returns zero if the specified value has no
1083      * one-bits in its two's complement binary representation, that is, if it
1084      * is equal to zero.
1085      *
1086      * @return an {@code int} value with a single one-bit, in the position
1087      *     of the lowest-order one-bit in the specified value, or zero if
1088      *     the specified value is itself equal to zero.
1089      * @since 1.5
1090      */
1091     public static int lowestOneBit(int i) {
1092         // HD, Section 2-1
1093         return i & -i;
1094     }
1095 
1096     /**
1097      * Returns the number of zero bits preceding the highest-order
1098      * ("leftmost") one-bit in the two's complement binary representation
1099      * of the specified {@code int} value.  Returns 32 if the
1100      * specified value has no one-bits in its two's complement representation,
1101      * in other words if it is equal to zero.
1102      *
1103      * <p>Note that this method is closely related to the logarithm base 2.
1104      * For all positive {@code int} values x:
1105      * <ul>
1106      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1107      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1108      * </ul>
1109      *
1110      * @return the number of zero bits preceding the highest-order
1111      *     ("leftmost") one-bit in the two's complement binary representation
1112      *     of the specified {@code int} value, or 32 if the value
1113      *     is equal to zero.
1114      * @since 1.5
1115      */
1116     public static int numberOfLeadingZeros(int i) {
1117         // HD, Figure 5-6
1118         if (i == 0)
1119             return 32;
1120         int n = 1;
1121         if (i >>> 16 == 0) { n += 16; i <<= 16; }
1122         if (i >>> 24 == 0) { n +=  8; i <<=  8; }
1123         if (i >>> 28 == 0) { n +=  4; i <<=  4; }
1124         if (i >>> 30 == 0) { n +=  2; i <<=  2; }
1125         n -= i >>> 31;
1126         return n;
1127     }
1128 
1129     /**
1130      * Returns the number of zero bits following the lowest-order ("rightmost")
1131      * one-bit in the two's complement binary representation of the specified
1132      * {@code int} value.  Returns 32 if the specified value has no
1133      * one-bits in its two's complement representation, in other words if it is
1134      * equal to zero.
1135      *
1136      * @return the number of zero bits following the lowest-order ("rightmost")
1137      *     one-bit in the two's complement binary representation of the
1138      *     specified {@code int} value, or 32 if the value is equal
1139      *     to zero.
1140      * @since 1.5
1141      */
1142     public static int numberOfTrailingZeros(int i) {
1143         // HD, Figure 5-14
1144         int y;
1145         if (i == 0) return 32;
1146         int n = 31;
1147         y = i <<16; if (y != 0) { n = n -16; i = y; }
1148         y = i << 8; if (y != 0) { n = n - 8; i = y; }
1149         y = i << 4; if (y != 0) { n = n - 4; i = y; }
1150         y = i << 2; if (y != 0) { n = n - 2; i = y; }
1151         return n - ((i << 1) >>> 31);
1152     }
1153 
1154     /**
1155      * Returns the number of one-bits in the two's complement binary
1156      * representation of the specified {@code int} value.  This function is
1157      * sometimes referred to as the <i>population count</i>.
1158      *
1159      * @return the number of one-bits in the two's complement binary
1160      *     representation of the specified {@code int} value.
1161      * @since 1.5
1162      */
1163     public static int bitCount(int i) {
1164         // HD, Figure 5-2
1165         i = i - ((i >>> 1) & 0x55555555);
1166         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1167         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1168         i = i + (i >>> 8);
1169         i = i + (i >>> 16);
1170         return i & 0x3f;
1171     }
1172 
1173     /**
1174      * Returns the value obtained by rotating the two's complement binary
1175      * representation of the specified {@code int} value left by the
1176      * specified number of bits.  (Bits shifted out of the left hand, or
1177      * high-order, side reenter on the right, or low-order.)
1178      *
1179      * <p>Note that left rotation with a negative distance is equivalent to
1180      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1181      * distance)}.  Note also that rotation by any multiple of 32 is a
1182      * no-op, so all but the last five bits of the rotation distance can be
1183      * ignored, even if the distance is negative: {@code rotateLeft(val,
1184      * distance) == rotateLeft(val, distance & 0x1F)}.
1185      *
1186      * @return the value obtained by rotating the two's complement binary
1187      *     representation of the specified {@code int} value left by the
1188      *     specified number of bits.
1189      * @since 1.5
1190      */
1191     public static int rotateLeft(int i, int distance) {
1192         return (i << distance) | (i >>> -distance);
1193     }
1194 
1195     /**
1196      * Returns the value obtained by rotating the two's complement binary
1197      * representation of the specified {@code int} value right by the
1198      * specified number of bits.  (Bits shifted out of the right hand, or
1199      * low-order, side reenter on the left, or high-order.)
1200      *
1201      * <p>Note that right rotation with a negative distance is equivalent to
1202      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1203      * distance)}.  Note also that rotation by any multiple of 32 is a
1204      * no-op, so all but the last five bits of the rotation distance can be
1205      * ignored, even if the distance is negative: {@code rotateRight(val,
1206      * distance) == rotateRight(val, distance & 0x1F)}.
1207      *
1208      * @return the value obtained by rotating the two's complement binary
1209      *     representation of the specified {@code int} value right by the
1210      *     specified number of bits.
1211      * @since 1.5
1212      */
1213     public static int rotateRight(int i, int distance) {
1214         return (i >>> distance) | (i << -distance);
1215     }
1216 
1217     /**
1218      * Returns the value obtained by reversing the order of the bits in the
1219      * two's complement binary representation of the specified {@code int}
1220      * value.
1221      *
1222      * @return the value obtained by reversing order of the bits in the
1223      *     specified {@code int} value.
1224      * @since 1.5
1225      */
1226     public static int reverse(int i) {
1227         // HD, Figure 7-1
1228         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1229         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1230         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1231         i = (i << 24) | ((i & 0xff00) << 8) |
1232             ((i >>> 8) & 0xff00) | (i >>> 24);
1233         return i;
1234     }
1235 
1236     /**
1237      * Returns the signum function of the specified {@code int} value.  (The
1238      * return value is -1 if the specified value is negative; 0 if the
1239      * specified value is zero; and 1 if the specified value is positive.)
1240      *
1241      * @return the signum function of the specified {@code int} value.
1242      * @since 1.5
1243      */
1244     public static int signum(int i) {
1245         // HD, Section 2-7
1246         return (i >> 31) | (-i >>> 31);
1247     }
1248 
1249     /**
1250      * Returns the value obtained by reversing the order of the bytes in the
1251      * two's complement representation of the specified {@code int} value.
1252      *
1253      * @return the value obtained by reversing the bytes in the specified
1254      *     {@code int} value.
1255      * @since 1.5
1256      */
1257     public static int reverseBytes(int i) {
1258         return ((i >>> 24)           ) |
1259                ((i >>   8) &   0xFF00) |
1260                ((i <<   8) & 0xFF0000) |
1261                ((i << 24));
1262     }
1263 
1264     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1265     private static final long serialVersionUID = 1360826667806852920L;
1266 }