1 /*
   2  * Copyright (c) 1994, 2025, 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 jdk.internal.misc.CDS;
  29 import jdk.internal.misc.PreviewFeatures;
  30 import jdk.internal.misc.VM;
  31 import jdk.internal.util.DecimalDigits;
  32 import jdk.internal.value.DeserializeConstructor;
  33 import jdk.internal.vm.annotation.AOTRuntimeSetup;
  34 import jdk.internal.vm.annotation.AOTSafeClassInitializer;
  35 import jdk.internal.vm.annotation.ForceInline;
  36 import jdk.internal.vm.annotation.IntrinsicCandidate;
  37 import jdk.internal.vm.annotation.Stable;
  38 
  39 import java.lang.annotation.Native;
  40 import java.lang.constant.Constable;
  41 import java.lang.constant.ConstantDesc;
  42 import java.lang.invoke.MethodHandles;
  43 import java.util.Objects;
  44 import java.util.Optional;
  45 
  46 import static java.lang.Character.digit;
  47 import static java.lang.String.COMPACT_STRINGS;
  48 
  49 /**
  50  * The {@code Integer} class is the {@linkplain
  51  * java.lang##wrapperClass wrapper class} for values of the primitive
  52  * type {@code int}. An object of type {@code Integer} contains a
  53  * single field whose type is {@code int}.
  54  *
  55  * <p>In addition, this class provides several methods for converting
  56  * an {@code int} to a {@code String} and a {@code String} to an
  57  * {@code int}, as well as other constants and methods useful when
  58  * dealing with an {@code int}.
  59  *
  60  * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
  61  * class; programmers should treat instances that are {@linkplain #equals(Object) equal}
  62  * as interchangeable and should not use instances for synchronization, mutexes, or
  63  * with {@linkplain java.lang.ref.Reference object references}.
  64  *
  65  * <div class="preview-block">
  66  *      <div class="preview-comment">
  67  *          When preview features are enabled, {@code Integer} is a {@linkplain Class#isValue value class}.
  68  *          Use of value class instances for synchronization, mutexes, or with
  69  *          {@linkplain java.lang.ref.Reference object references} result in
  70  *          {@link IdentityException}.
  71  *      </div>
  72  * </div>
  73  *
  74  * <p>Implementation note: The implementations of the "bit twiddling"
  75  * methods (such as {@link #highestOneBit(int) highestOneBit} and
  76  * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
  77  * based on material from Henry S. Warren, Jr.'s <cite>Hacker's
  78  * Delight</cite>, (Addison Wesley, 2002) and <cite>Hacker's
  79  * Delight, Second Edition</cite>, (Pearson Education, 2013).
  80  *
  81  * @since 1.0
  82  */
  83 @jdk.internal.MigratedValueClass
  84 @jdk.internal.ValueBased
  85 public final class Integer extends Number
  86         implements Comparable<Integer>, Constable, ConstantDesc {
  87     /**
  88      * A constant holding the minimum value an {@code int} can
  89      * have, -2<sup>31</sup>.
  90      */
  91     @Native public static final int   MIN_VALUE = 0x80000000;
  92 
  93     /**
  94      * A constant holding the maximum value an {@code int} can
  95      * have, 2<sup>31</sup>-1.
  96      */
  97     @Native public static final int   MAX_VALUE = 0x7fffffff;
  98 
  99     /**
 100      * The {@code Class} instance representing the primitive type
 101      * {@code int}.
 102      *
 103      * @since   1.1
 104      */
 105     public static final Class<Integer> TYPE = Class.getPrimitiveClass("int");
 106 
 107     /**
 108      * All possible chars for representing a number as a String
 109      */
 110     @Stable
 111     static final byte[] digits = {
 112         '0' , '1' , '2' , '3' , '4' , '5' ,
 113         '6' , '7' , '8' , '9' , 'a' , 'b' ,
 114         'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
 115         'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
 116         'o' , 'p' , 'q' , 'r' , 's' , 't' ,
 117         'u' , 'v' , 'w' , 'x' , 'y' , 'z'
 118     };
 119 
 120     /**
 121      * Returns a string representation of the first argument in the
 122      * radix specified by the second argument.
 123      *
 124      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 125      * or larger than {@code Character.MAX_RADIX}, then the radix
 126      * {@code 10} is used instead.
 127      *
 128      * <p>If the first argument is negative, the first element of the
 129      * result is the ASCII minus character {@code '-'}
 130      * ({@code '\u005Cu002D'}). If the first argument is not
 131      * negative, no sign character appears in the result.
 132      *
 133      * <p>The remaining characters of the result represent the magnitude
 134      * of the first argument. If the magnitude is zero, it is
 135      * represented by a single zero character {@code '0'}
 136      * ({@code '\u005Cu0030'}); otherwise, the first character of
 137      * the representation of the magnitude will not be the zero
 138      * character.  The following ASCII characters are used as digits:
 139      *
 140      * <blockquote>
 141      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 142      * </blockquote>
 143      *
 144      * These are {@code '\u005Cu0030'} through
 145      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 146      * {@code '\u005Cu007A'}. If {@code radix} is
 147      * <var>N</var>, then the first <var>N</var> of these characters
 148      * are used as radix-<var>N</var> digits in the order shown. Thus,
 149      * the digits for hexadecimal (radix 16) are
 150      * {@code 0123456789abcdef}. If uppercase letters are
 151      * desired, the {@link java.lang.String#toUpperCase()} method may
 152      * be called on the result:
 153      *
 154      * <blockquote>
 155      *  {@code Integer.toString(n, 16).toUpperCase()}
 156      * </blockquote>
 157      *
 158      * @param   i       an integer to be converted to a string.
 159      * @param   radix   the radix to use in the string representation.
 160      * @return  a string representation of the argument in the specified radix.
 161      * @see     java.lang.Character#MAX_RADIX
 162      * @see     java.lang.Character#MIN_RADIX
 163      */
 164     public static String toString(int i, int radix) {
 165         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 166             radix = 10;
 167 
 168         /* Use the faster version */
 169         if (radix == 10) {
 170             return toString(i);
 171         }
 172 
 173         if (COMPACT_STRINGS) {
 174             byte[] buf = new byte[33];
 175             boolean negative = (i < 0);
 176             int charPos = 32;
 177 
 178             if (!negative) {
 179                 i = -i;
 180             }
 181 
 182             while (i <= -radix) {
 183                 buf[charPos--] = digits[-(i % radix)];
 184                 i = i / radix;
 185             }
 186             buf[charPos] = digits[-i];
 187 
 188             if (negative) {
 189                 buf[--charPos] = '-';
 190             }
 191 
 192             return StringLatin1.newString(buf, charPos, (33 - charPos));
 193         }
 194         return toStringUTF16(i, radix);
 195     }
 196 
 197     private static String toStringUTF16(int i, int radix) {
 198         byte[] buf = new byte[33 * 2];
 199         boolean negative = (i < 0);
 200         int charPos = 32;
 201         if (!negative) {
 202             i = -i;
 203         }
 204         while (i <= -radix) {
 205             StringUTF16.putChar(buf, charPos--, digits[-(i % radix)]);
 206             i = i / radix;
 207         }
 208         StringUTF16.putChar(buf, charPos, digits[-i]);
 209 
 210         if (negative) {
 211             StringUTF16.putChar(buf, --charPos, '-');
 212         }
 213         return StringUTF16.newString(buf, charPos, (33 - charPos));
 214     }
 215 
 216     /**
 217      * Returns a string representation of the first argument as an
 218      * unsigned integer value in the radix specified by the second
 219      * argument.
 220      *
 221      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 222      * or larger than {@code Character.MAX_RADIX}, then the radix
 223      * {@code 10} is used instead.
 224      *
 225      * <p>Note that since the first argument is treated as an unsigned
 226      * value, no leading sign character is printed.
 227      *
 228      * <p>If the magnitude is zero, it is represented by a single zero
 229      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 230      * the first character of the representation of the magnitude will
 231      * not be the zero character.
 232      *
 233      * <p>The behavior of radixes and the characters used as digits
 234      * are the same as {@link #toString(int, int) toString}.
 235      *
 236      * @param   i       an integer to be converted to an unsigned string.
 237      * @param   radix   the radix to use in the string representation.
 238      * @return  an unsigned string representation of the argument in the specified radix.
 239      * @see     #toString(int, int)
 240      * @since 1.8
 241      */
 242     public static String toUnsignedString(int i, int radix) {
 243         return Long.toUnsignedString(toUnsignedLong(i), radix);
 244     }
 245 
 246     /**
 247      * Returns a string representation of the integer argument as an
 248      * unsigned integer in base&nbsp;16.
 249      *
 250      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 251      * if the argument is negative; otherwise, it is equal to the
 252      * argument.  This value is converted to a string of ASCII digits
 253      * in hexadecimal (base&nbsp;16) with no extra leading
 254      * {@code 0}s.
 255      *
 256      * <p>The value of the argument can be recovered from the returned
 257      * string {@code s} by calling {@link
 258      * Integer#parseUnsignedInt(String, int)
 259      * Integer.parseUnsignedInt(s, 16)}.
 260      *
 261      * <p>If the unsigned magnitude is zero, it is represented by a
 262      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 263      * otherwise, the first character of the representation of the
 264      * unsigned magnitude will not be the zero character. The
 265      * following characters are used as hexadecimal digits:
 266      *
 267      * <blockquote>
 268      *  {@code 0123456789abcdef}
 269      * </blockquote>
 270      *
 271      * These are the characters {@code '\u005Cu0030'} through
 272      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 273      * {@code '\u005Cu0066'}. If uppercase letters are
 274      * desired, the {@link java.lang.String#toUpperCase()} method may
 275      * be called on the result:
 276      *
 277      * <blockquote>
 278      *  {@code Integer.toHexString(n).toUpperCase()}
 279      * </blockquote>
 280      *
 281      * @apiNote
 282      * The {@link java.util.HexFormat} class provides formatting and parsing
 283      * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
 284      * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
 285      * with leading zeros and for byte arrays includes for each byte
 286      * a delimiter, prefix, and suffix.
 287      *
 288      * @param   i   an integer to be converted to a string.
 289      * @return  the string representation of the unsigned integer value
 290      *          represented by the argument in hexadecimal (base&nbsp;16).
 291      * @see java.util.HexFormat
 292      * @see #parseUnsignedInt(String, int)
 293      * @see #toUnsignedString(int, int)
 294      * @since   1.0.2
 295      */
 296     public static String toHexString(int i) {
 297         return toUnsignedString0(i, 4);
 298     }
 299 
 300     /**
 301      * Returns a string representation of the integer argument as an
 302      * unsigned integer in base&nbsp;8.
 303      *
 304      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 305      * if the argument is negative; otherwise, it is equal to the
 306      * argument.  This value is converted to a string of ASCII digits
 307      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
 308      *
 309      * <p>The value of the argument can be recovered from the returned
 310      * string {@code s} by calling {@link
 311      * Integer#parseUnsignedInt(String, int)
 312      * Integer.parseUnsignedInt(s, 8)}.
 313      *
 314      * <p>If the unsigned magnitude is zero, it is represented by a
 315      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 316      * otherwise, the first character of the representation of the
 317      * unsigned magnitude will not be the zero character. The
 318      * following characters are used as octal digits:
 319      *
 320      * <blockquote>
 321      * {@code 01234567}
 322      * </blockquote>
 323      *
 324      * These are the characters {@code '\u005Cu0030'} through
 325      * {@code '\u005Cu0037'}.
 326      *
 327      * @param   i   an integer to be converted to a string.
 328      * @return  the string representation of the unsigned integer value
 329      *          represented by the argument in octal (base&nbsp;8).
 330      * @see #parseUnsignedInt(String, int)
 331      * @see #toUnsignedString(int, int)
 332      * @since   1.0.2
 333      */
 334     public static String toOctalString(int i) {
 335         return toUnsignedString0(i, 3);
 336     }
 337 
 338     /**
 339      * Returns a string representation of the integer argument as an
 340      * unsigned integer in base&nbsp;2.
 341      *
 342      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 343      * if the argument is negative; otherwise it is equal to the
 344      * argument.  This value is converted to a string of ASCII digits
 345      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
 346      *
 347      * <p>The value of the argument can be recovered from the returned
 348      * string {@code s} by calling {@link
 349      * Integer#parseUnsignedInt(String, int)
 350      * Integer.parseUnsignedInt(s, 2)}.
 351      *
 352      * <p>If the unsigned magnitude is zero, it is represented by a
 353      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 354      * otherwise, the first character of the representation of the
 355      * unsigned magnitude will not be the zero character. The
 356      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 357      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 358      *
 359      * @param   i   an integer to be converted to a string.
 360      * @return  the string representation of the unsigned integer value
 361      *          represented by the argument in binary (base&nbsp;2).
 362      * @see #parseUnsignedInt(String, int)
 363      * @see #toUnsignedString(int, int)
 364      * @since   1.0.2
 365      */
 366     public static String toBinaryString(int i) {
 367         return toUnsignedString0(i, 1);
 368     }
 369 
 370     /**
 371      * Convert the integer to an unsigned number.
 372      */
 373     private static String toUnsignedString0(int val, int shift) {
 374         // assert shift > 0 && shift <=5 : "Illegal shift value";
 375         int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
 376         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 377         byte[] buf = new byte[chars];
 378         formatUnsignedInt(val, shift, buf, chars);
 379         return String.newStringWithLatin1Bytes(buf);
 380     }
 381 
 382     /**
 383      * Format an {@code int} (treated as unsigned) into a byte buffer (LATIN1 version). If
 384      * {@code len} exceeds the formatted ASCII representation of {@code val},
 385      * {@code buf} will be padded with leading zeroes.
 386      *
 387      * @param val the unsigned int to format
 388      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 389      * @param buf the byte buffer to write to
 390      * @param len the number of characters to write
 391      */
 392     private static void formatUnsignedInt(int val, int shift, byte[] buf, int len) {
 393         int charPos = len;
 394         int radix = 1 << shift;
 395         int mask = radix - 1;
 396         do {
 397             buf[--charPos] = Integer.digits[val & mask];
 398             val >>>= shift;
 399         } while (charPos > 0);
 400     }
 401 
 402     /**
 403      * Returns a {@code String} object representing the
 404      * specified integer. The argument is converted to signed decimal
 405      * representation and returned as a string, exactly as if the
 406      * argument and radix 10 were given as arguments to the {@link
 407      * #toString(int, int)} method.
 408      *
 409      * @param   i   an integer to be converted.
 410      * @return  a string representation of the argument in base&nbsp;10.
 411      */
 412     @IntrinsicCandidate
 413     public static String toString(int i) {
 414         int size = DecimalDigits.stringSize(i);
 415         byte[] buf = new byte[size];
 416         DecimalDigits.uncheckedGetCharsLatin1(i, size, buf);
 417         return String.newStringWithLatin1Bytes(buf);
 418     }
 419 
 420     /**
 421      * Returns a string representation of the argument as an unsigned
 422      * decimal value.
 423      *
 424      * The argument is converted to unsigned decimal representation
 425      * and returned as a string exactly as if the argument and radix
 426      * 10 were given as arguments to the {@link #toUnsignedString(int,
 427      * int)} method.
 428      *
 429      * @param   i  an integer to be converted to an unsigned string.
 430      * @return  an unsigned string representation of the argument.
 431      * @see     #toUnsignedString(int, int)
 432      * @since 1.8
 433      */
 434     public static String toUnsignedString(int i) {
 435         return Long.toString(toUnsignedLong(i));
 436     }
 437 
 438     /**
 439      * Parses the string argument as a signed integer in the radix
 440      * specified by the second argument. The characters in the string
 441      * must all be digits of the specified radix (as determined by
 442      * whether {@link java.lang.Character#digit(char, int)} returns a
 443      * nonnegative value), except that the first character may be an
 444      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 445      * indicate a negative value or an ASCII plus sign {@code '+'}
 446      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 447      * resulting integer value is returned.
 448      *
 449      * <p>An exception of type {@code NumberFormatException} is
 450      * thrown if any of the following situations occurs:
 451      * <ul>
 452      * <li>The first argument is {@code null} or is a string of
 453      * length zero.
 454      *
 455      * <li>The radix is either smaller than
 456      * {@link java.lang.Character#MIN_RADIX} or
 457      * larger than {@link java.lang.Character#MAX_RADIX}.
 458      *
 459      * <li>Any character of the string is not a digit of the specified
 460      * radix, except that the first character may be a minus sign
 461      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
 462      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 463      * string is longer than length 1.
 464      *
 465      * <li>The value represented by the string is not a value of type
 466      * {@code int}.
 467      * </ul>
 468      *
 469      * <p>Examples:
 470      * <blockquote><pre>
 471      * parseInt("0", 10) returns 0
 472      * parseInt("473", 10) returns 473
 473      * parseInt("+42", 10) returns 42
 474      * parseInt("-0", 10) returns 0
 475      * parseInt("-FF", 16) returns -255
 476      * parseInt("1100110", 2) returns 102
 477      * parseInt("2147483647", 10) returns 2147483647
 478      * parseInt("-2147483648", 10) returns -2147483648
 479      * parseInt("2147483648", 10) throws a NumberFormatException
 480      * parseInt("99", 8) throws a NumberFormatException
 481      * parseInt("Kona", 10) throws a NumberFormatException
 482      * parseInt("Kona", 27) returns 411787
 483      * </pre></blockquote>
 484      *
 485      * @param      s   the {@code String} containing the integer
 486      *                  representation to be parsed
 487      * @param      radix   the radix to be used while parsing {@code s}.
 488      * @return     the integer represented by the string argument in the
 489      *             specified radix.
 490      * @throws     NumberFormatException if the {@code String}
 491      *             does not contain a parsable {@code int}.
 492      */
 493     public static int parseInt(String s, int radix)
 494                 throws NumberFormatException {
 495         /*
 496          * WARNING: This method may be invoked early during VM initialization
 497          * before IntegerCache is initialized. Care must be taken to not use
 498          * the valueOf method.
 499          */
 500 
 501         if (s == null) {
 502             throw new NumberFormatException("Cannot parse null string");
 503         }
 504 
 505         if (radix < Character.MIN_RADIX) {
 506             throw new NumberFormatException(String.format(
 507                 "radix %s less than Character.MIN_RADIX", radix));
 508         }
 509 
 510         if (radix > Character.MAX_RADIX) {
 511             throw new NumberFormatException(String.format(
 512                 "radix %s greater than Character.MAX_RADIX", radix));
 513         }
 514 
 515         int len = s.length();
 516         if (len == 0) {
 517             throw NumberFormatException.forInputString("", radix);
 518         }
 519         int digit = ~0xFF;
 520         int i = 0;
 521         char firstChar = s.charAt(i++);
 522         if (firstChar != '-' && firstChar != '+') {
 523             digit = digit(firstChar, radix);
 524         }
 525         if (digit >= 0 || digit == ~0xFF && len > 1) {
 526             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 527             int multmin = limit / radix;
 528             int result = -(digit & 0xFF);
 529             boolean inRange = true;
 530             /* Accumulating negatively avoids surprises near MAX_VALUE */
 531             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 532                     && (inRange = result > multmin
 533                         || result == multmin && digit <= radix * multmin - limit)) {
 534                 result = radix * result - digit;
 535             }
 536             if (inRange && i == len && digit >= 0) {
 537                 return firstChar != '-' ? -result : result;
 538             }
 539         }
 540         throw NumberFormatException.forInputString(s, radix);
 541     }
 542 
 543     /**
 544      * Parses the {@link CharSequence} argument as a signed {@code int} in the
 545      * specified {@code radix}, beginning at the specified {@code beginIndex}
 546      * and extending to {@code endIndex - 1}.
 547      *
 548      * <p>The method does not take steps to guard against the
 549      * {@code CharSequence} being mutated while parsing.
 550      *
 551      * @param      s   the {@code CharSequence} containing the {@code int}
 552      *                  representation to be parsed
 553      * @param      beginIndex   the beginning index, inclusive.
 554      * @param      endIndex     the ending index, exclusive.
 555      * @param      radix   the radix to be used while parsing {@code s}.
 556      * @return     the signed {@code int} represented by the subsequence in
 557      *             the specified radix.
 558      * @throws     NullPointerException  if {@code s} is null.
 559      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 560      *             negative, or if {@code beginIndex} is greater than
 561      *             {@code endIndex} or if {@code endIndex} is greater than
 562      *             {@code s.length()}.
 563      * @throws     NumberFormatException  if the {@code CharSequence} does not
 564      *             contain a parsable {@code int} in the specified
 565      *             {@code radix}, or if {@code radix} is either smaller than
 566      *             {@link java.lang.Character#MIN_RADIX} or larger than
 567      *             {@link java.lang.Character#MAX_RADIX}.
 568      * @since  9
 569      */
 570     public static int parseInt(CharSequence s, int beginIndex, int endIndex, int radix)
 571                 throws NumberFormatException {
 572         Objects.requireNonNull(s);
 573         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 574 
 575         if (radix < Character.MIN_RADIX) {
 576             throw new NumberFormatException(String.format(
 577                 "radix %s less than Character.MIN_RADIX", radix));
 578         }
 579 
 580         if (radix > Character.MAX_RADIX) {
 581             throw new NumberFormatException(String.format(
 582                 "radix %s greater than Character.MAX_RADIX", radix));
 583         }
 584 
 585         /*
 586          * While s can be concurrently modified, it is ensured that each
 587          * of its characters is read at most once, from lower to higher indices.
 588          * This is obtained by reading them using the pattern s.charAt(i++),
 589          * and by not updating i anywhere else.
 590          */
 591         if (beginIndex == endIndex) {
 592             throw NumberFormatException.forInputString("", radix);
 593         }
 594         int digit = ~0xFF;
 595         int i = beginIndex;
 596         char firstChar = s.charAt(i++);
 597         if (firstChar != '-' && firstChar != '+') {
 598             digit = digit(firstChar, radix);
 599         }
 600         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 601             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 602             int multmin = limit / radix;
 603             int result = -(digit & 0xFF);
 604             boolean inRange = true;
 605             /* Accumulating negatively avoids surprises near MAX_VALUE */
 606             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 607                     && (inRange = result > multmin
 608                         || result == multmin && digit <= radix * multmin - limit)) {
 609                 result = radix * result - digit;
 610             }
 611             if (inRange && i == endIndex && digit >= 0) {
 612                 return firstChar != '-' ? -result : result;
 613             }
 614         }
 615         throw NumberFormatException.forCharSequence(s, beginIndex,
 616             endIndex, i - (digit < -1 ? 0 : 1));
 617     }
 618 
 619     /**
 620      * Parses the string argument as a signed decimal integer. The
 621      * characters in the string must all be decimal digits, except
 622      * that the first character may be an ASCII minus sign {@code '-'}
 623      * ({@code '\u005Cu002D'}) to indicate a negative value or an
 624      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 625      * indicate a positive value. The resulting integer value is
 626      * returned, exactly as if the argument and the radix 10 were
 627      * given as arguments to the {@link #parseInt(java.lang.String,
 628      * int)} method.
 629      *
 630      * @param s    a {@code String} containing the {@code int}
 631      *             representation to be parsed
 632      * @return     the integer value represented by the argument in decimal.
 633      * @throws     NumberFormatException  if the string does not contain a
 634      *               parsable integer.
 635      */
 636     public static int parseInt(String s) throws NumberFormatException {
 637         return parseInt(s, 10);
 638     }
 639 
 640     /**
 641      * Parses the string argument as an unsigned integer in the radix
 642      * specified by the second argument.  An unsigned integer maps the
 643      * values usually associated with negative numbers to positive
 644      * numbers larger than {@code MAX_VALUE}.
 645      *
 646      * The characters in the string must all be digits of the
 647      * specified radix (as determined by whether {@link
 648      * java.lang.Character#digit(char, int)} returns a nonnegative
 649      * value), except that the first character may be an ASCII plus
 650      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 651      * integer value is returned.
 652      *
 653      * <p>An exception of type {@code NumberFormatException} is
 654      * thrown if any of the following situations occurs:
 655      * <ul>
 656      * <li>The first argument is {@code null} or is a string of
 657      * length zero.
 658      *
 659      * <li>The radix is either smaller than
 660      * {@link java.lang.Character#MIN_RADIX} or
 661      * larger than {@link java.lang.Character#MAX_RADIX}.
 662      *
 663      * <li>Any character of the string is not a digit of the specified
 664      * radix, except that the first character may be a plus sign
 665      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 666      * string is longer than length 1.
 667      *
 668      * <li>The value represented by the string is larger than the
 669      * largest unsigned {@code int}, 2<sup>32</sup>-1.
 670      *
 671      * </ul>
 672      *
 673      *
 674      * @param      s   the {@code String} containing the unsigned integer
 675      *                  representation to be parsed
 676      * @param      radix   the radix to be used while parsing {@code s}.
 677      * @return     the integer represented by the string argument in the
 678      *             specified radix.
 679      * @throws     NumberFormatException if the {@code String}
 680      *             does not contain a parsable {@code int}.
 681      * @since 1.8
 682      */
 683     public static int parseUnsignedInt(String s, int radix)
 684                 throws NumberFormatException {
 685         if (s == null)  {
 686             throw new NumberFormatException("Cannot parse null string");
 687         }
 688 
 689         if (radix < Character.MIN_RADIX) {
 690             throw new NumberFormatException(String.format(
 691                 "radix %s less than Character.MIN_RADIX", radix));
 692         }
 693 
 694         if (radix > Character.MAX_RADIX) {
 695             throw new NumberFormatException(String.format(
 696                 "radix %s greater than Character.MAX_RADIX", radix));
 697         }
 698 
 699         int len = s.length();
 700         if (len == 0) {
 701             throw NumberFormatException.forInputString(s, radix);
 702         }
 703         int i = 0;
 704         char firstChar = s.charAt(i++);
 705         if (firstChar == '-') {
 706             throw new NumberFormatException(String.format(
 707                 "Illegal leading minus sign on unsigned string %s.", s));
 708         }
 709         int digit = ~0xFF;
 710         if (firstChar != '+') {
 711             digit = digit(firstChar, radix);
 712         }
 713         if (digit >= 0 || digit == ~0xFF && len > 1) {
 714             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 715             int result = digit & 0xFF;
 716             boolean inRange = true;
 717             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 718                     && (inRange = compareUnsigned(result, multmax) < 0
 719                         || result == multmax && digit < -radix * multmax)) {
 720                 result = radix * result + digit;
 721             }
 722             if (inRange && i == len && digit >= 0) {
 723                 return result;
 724             }
 725         }
 726         if (digit < 0) {
 727             throw NumberFormatException.forInputString(s, radix);
 728         }
 729         throw new NumberFormatException(String.format(
 730             "String value %s exceeds range of unsigned int.", s));
 731     }
 732 
 733     /**
 734      * Parses the {@link CharSequence} argument as an unsigned {@code int} in
 735      * the specified {@code radix}, beginning at the specified
 736      * {@code beginIndex} and extending to {@code endIndex - 1}.
 737      *
 738      * <p>The method does not take steps to guard against the
 739      * {@code CharSequence} being mutated while parsing.
 740      *
 741      * @param      s   the {@code CharSequence} containing the unsigned
 742      *                 {@code int} representation to be parsed
 743      * @param      beginIndex   the beginning index, inclusive.
 744      * @param      endIndex     the ending index, exclusive.
 745      * @param      radix   the radix to be used while parsing {@code s}.
 746      * @return     the unsigned {@code int} represented by the subsequence in
 747      *             the specified radix.
 748      * @throws     NullPointerException  if {@code s} is null.
 749      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 750      *             negative, or if {@code beginIndex} is greater than
 751      *             {@code endIndex} or if {@code endIndex} is greater than
 752      *             {@code s.length()}.
 753      * @throws     NumberFormatException  if the {@code CharSequence} does not
 754      *             contain a parsable unsigned {@code int} in the specified
 755      *             {@code radix}, or if {@code radix} is either smaller than
 756      *             {@link java.lang.Character#MIN_RADIX} or larger than
 757      *             {@link java.lang.Character#MAX_RADIX}.
 758      * @since  9
 759      */
 760     public static int parseUnsignedInt(CharSequence s, int beginIndex, int endIndex, int radix)
 761                 throws NumberFormatException {
 762         Objects.requireNonNull(s);
 763         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 764 
 765         if (radix < Character.MIN_RADIX) {
 766             throw new NumberFormatException(String.format(
 767                 "radix %s less than Character.MIN_RADIX", radix));
 768         }
 769 
 770         if (radix > Character.MAX_RADIX) {
 771             throw new NumberFormatException(String.format(
 772                 "radix %s greater than Character.MAX_RADIX", radix));
 773         }
 774 
 775         /*
 776          * While s can be concurrently modified, it is ensured that each
 777          * of its characters is read at most once, from lower to higher indices.
 778          * This is obtained by reading them using the pattern s.charAt(i++),
 779          * and by not updating i anywhere else.
 780          */
 781         if (beginIndex == endIndex) {
 782             throw NumberFormatException.forInputString("", radix);
 783         }
 784         int i = beginIndex;
 785         char firstChar = s.charAt(i++);
 786         if (firstChar == '-') {
 787             throw new NumberFormatException(
 788                 "Illegal leading minus sign on unsigned string " + s + ".");
 789         }
 790         int digit = ~0xFF;
 791         if (firstChar != '+') {
 792             digit = digit(firstChar, radix);
 793         }
 794         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 795             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 796             int result = digit & 0xFF;
 797             boolean inRange = true;
 798             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 799                     && (inRange = compareUnsigned(result, multmax) < 0
 800                         || result == multmax && digit < -radix * multmax)) {
 801                 result = radix * result + digit;
 802             }
 803             if (inRange && i == endIndex && digit >= 0) {
 804                 return result;
 805             }
 806         }
 807         if (digit < 0) {
 808             throw NumberFormatException.forCharSequence(s, beginIndex,
 809                 endIndex, i - (digit < -1 ? 0 : 1));
 810         }
 811         throw new NumberFormatException(String.format(
 812             "String value %s exceeds range of unsigned int.", s));
 813     }
 814 
 815     /**
 816      * Parses the string argument as an unsigned decimal integer. The
 817      * characters in the string must all be decimal digits, except
 818      * that the first character may be an ASCII plus sign {@code
 819      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 820      * is returned, exactly as if the argument and the radix 10 were
 821      * given as arguments to the {@link
 822      * #parseUnsignedInt(java.lang.String, int)} method.
 823      *
 824      * @param s   a {@code String} containing the unsigned {@code int}
 825      *            representation to be parsed
 826      * @return    the unsigned integer value represented by the argument in decimal.
 827      * @throws    NumberFormatException  if the string does not contain a
 828      *            parsable unsigned integer.
 829      * @since 1.8
 830      */
 831     public static int parseUnsignedInt(String s) throws NumberFormatException {
 832         return parseUnsignedInt(s, 10);
 833     }
 834 
 835     /**
 836      * Returns an {@code Integer} object holding the value
 837      * extracted from the specified {@code String} when parsed
 838      * with the radix given by the second argument. The first argument
 839      * is interpreted as representing a signed integer in the radix
 840      * specified by the second argument, exactly as if the arguments
 841      * were given to the {@link #parseInt(java.lang.String, int)}
 842      * method. The result is an {@code Integer} object that
 843      * represents the integer value specified by the string.
 844      *
 845      * <p>In other words, this method returns an {@code Integer}
 846      * object equal to the value of:
 847      *
 848      * <blockquote>
 849      *  {@code Integer.valueOf(Integer.parseInt(s, radix))}
 850      * </blockquote>
 851      *
 852      * @param      s   the string to be parsed.
 853      * @param      radix the radix to be used in interpreting {@code s}
 854      * @return     an {@code Integer} object holding the value
 855      *             represented by the string argument in the specified
 856      *             radix.
 857      * @throws    NumberFormatException if the {@code String}
 858      *            does not contain a parsable {@code int}.
 859      */
 860     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 861         return Integer.valueOf(parseInt(s,radix));
 862     }
 863 
 864     /**
 865      * Returns an {@code Integer} object holding the
 866      * value of the specified {@code String}. The argument is
 867      * interpreted as representing a signed decimal integer, exactly
 868      * as if the argument were given to the {@link
 869      * #parseInt(java.lang.String)} method. The result is an
 870      * {@code Integer} object that represents the integer value
 871      * specified by the string.
 872      *
 873      * <p>In other words, this method returns an {@code Integer}
 874      * object equal to the value of:
 875      *
 876      * <blockquote>
 877      *  {@code Integer.valueOf(Integer.parseInt(s))}
 878      * </blockquote>
 879      *
 880      * @param      s   the string to be parsed.
 881      * @return     an {@code Integer} object holding the value
 882      *             represented by the string argument.
 883      * @throws     NumberFormatException  if the string cannot be parsed
 884      *             as an integer.
 885      */
 886     public static Integer valueOf(String s) throws NumberFormatException {
 887         return Integer.valueOf(parseInt(s, 10));
 888     }
 889 
 890     /**
 891      * Cache to support the object identity semantics of autoboxing for values between
 892      * -128 and 127 (inclusive) as required by JLS.
 893      *
 894      * The cache is initialized on first usage.  The size of the cache
 895      * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
 896      * During VM initialization, java.lang.Integer.IntegerCache.high property
 897      * may be set and saved in the private system properties in the
 898      * jdk.internal.misc.VM class.
 899      *
 900      * WARNING: The cache is archived with CDS and reloaded from the shared
 901      * archive at runtime. The archived cache (Integer[]) and Integer objects
 902      * reside in the closed archive heap regions. Care should be taken when
 903      * changing the implementation and the cache array should not be assigned
 904      * with new Integer object(s) after initialization.
 905      */
 906 
 907     @AOTSafeClassInitializer
 908     private static final class IntegerCache {
 909         static final int low = -128;
 910         @Stable static int high;
 911 
 912         @Stable static Integer[] cache;
 913         static Integer[] archivedCache;
 914 
 915         static {
 916             runtimeSetup();
 917         }
 918 
 919         @AOTRuntimeSetup
 920         private static void runtimeSetup() {
 921             // high value may be configured by property
 922             int h = 127;
 923             String integerCacheHighPropValue =
 924                 VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 925             if (integerCacheHighPropValue != null) {
 926                 try {
 927                     h = Math.max(parseInt(integerCacheHighPropValue), 127);
 928                     // Maximum array size is Integer.MAX_VALUE
 929                     h = Math.min(h, Integer.MAX_VALUE - (-low) -1);
 930                 } catch( NumberFormatException nfe) {
 931                     // If the property cannot be parsed into an int, ignore it.
 932                 }
 933             }
 934             high = h;
 935 
 936             Integer[] precomputed = null;
 937             if (cache != null) {
 938                 // IntegerCache has been AOT-initialized.
 939                 precomputed = cache;
 940             } else {
 941                 // Legacy CDS archive support (to be deprecated):
 942                 // Load IntegerCache.archivedCache from archive, if possible
 943                 CDS.initializeFromArchive(IntegerCache.class);
 944                 precomputed = archivedCache;
 945             }
 946 
 947             cache = loadOrInitializeCache(precomputed);
 948             archivedCache = cache; // Legacy CDS archive support (to be deprecated)
 949             // range [-128, 127] must be interned (JLS7 5.1.7)
 950             assert IntegerCache.high >= 127;
 951         }
 952 
 953         private static Integer[] loadOrInitializeCache(Integer[] precomputed) {
 954             int size = (high - low) + 1;
 955 
 956             // Use the precomputed cache if it exists and is large enough
 957             if (precomputed != null && size <= precomputed.length) {
 958                 return precomputed;
 959             }
 960 
 961             Integer[] c = new Integer[size];
 962             int j = low;
 963             // If we loading a precomputed cache (from AOT cache or CDS archive),
 964             // we must use all instances from it.
 965             // Otherwise, the Integers from the AOT cache (or CDS archive) will not
 966             // have the same object identity as items in IntegerCache.cache[].
 967             int precomputedSize = (precomputed == null) ? 0 : precomputed.length;
 968             for (int i = 0; i < precomputedSize; i++) {
 969                 c[i] = precomputed[i];
 970                 assert j == precomputed[i];
 971                 j++;
 972             }
 973             // Fill the rest of the cache.
 974             for (int i = precomputedSize; i < size; i++) {
 975                 c[i] = new Integer(j++);
 976             }
 977             return c;
 978         }
 979 
 980         private IntegerCache() {}
 981     }
 982 
 983     /**
 984      * Returns an {@code Integer} instance representing the specified
 985      * {@code int} value.
 986      * <div class="preview-block">
 987      *      <div class="preview-comment">
 988      *          <p>
 989      *              - When preview features are NOT enabled, {@code Integer} is an identity class.
 990      *              If a new {@code Integer} instance is not
 991      *              required, this method should generally be used in preference to
 992      *              the constructor {@link #Integer(int)}, as this method is likely
 993      *              to yield significantly better space and time performance by
 994      *              caching frequently requested values.
 995      *              This method will always cache values in the range -128 to 127,
 996      *              inclusive, and may cache other values outside of this range.
 997      *          </p>
 998      *          <p>
 999      *              - When preview features are enabled, {@code Integer} is a {@linkplain Class#isValue value class}.
1000      *              The {@code valueOf} behavior is the same as invoking the constructor,
1001      *              whether cached or not.
1002      *          </p>
1003      *      </div>
1004      * </div>
1005      *
1006      * @param  i an {@code int} value.
1007      * @return an {@code Integer} instance representing {@code i}.
1008      * @since  1.5
1009      */
1010     @IntrinsicCandidate
1011     @DeserializeConstructor
1012     public static Integer valueOf(int i) {
1013         if (!PreviewFeatures.isEnabled()) {
1014             if (i >= IntegerCache.low && i <= IntegerCache.high)
1015                 return IntegerCache.cache[i + (-IntegerCache.low)];
1016         }
1017         return new Integer(i);
1018     }
1019 
1020     /**
1021      * The value of the {@code Integer}.
1022      *
1023      * @serial
1024      */
1025     private final int value;
1026 
1027     /**
1028      * Constructs a newly allocated {@code Integer} object that
1029      * represents the specified {@code int} value.
1030      *
1031      * @param   value   the value to be represented by the
1032      *                  {@code Integer} object.
1033      *
1034      * @deprecated
1035      * It is rarely appropriate to use this constructor. The static factory
1036      * {@link #valueOf(int)} is generally a better choice, as it is
1037      * likely to yield significantly better space and time performance.
1038      */
1039     @Deprecated(since="9")
1040     public Integer(int value) {
1041         this.value = value;
1042     }
1043 
1044     /**
1045      * Constructs a newly allocated {@code Integer} object that
1046      * represents the {@code int} value indicated by the
1047      * {@code String} parameter. The string is converted to an
1048      * {@code int} value in exactly the manner used by the
1049      * {@code parseInt} method for radix 10.
1050      *
1051      * @param   s   the {@code String} to be converted to an {@code Integer}.
1052      * @throws      NumberFormatException if the {@code String} does not
1053      *              contain a parsable integer.
1054      *
1055      * @deprecated
1056      * It is rarely appropriate to use this constructor.
1057      * Use {@link #parseInt(String)} to convert a string to a
1058      * {@code int} primitive, or use {@link #valueOf(String)}
1059      * to convert a string to an {@code Integer} object.
1060      */
1061     @Deprecated(since="9")
1062     public Integer(String s) throws NumberFormatException {
1063         this.value = parseInt(s, 10);
1064     }
1065 
1066     /**
1067      * Returns the value of this {@code Integer} as a {@code byte}
1068      * after a narrowing primitive conversion.
1069      * @jls 5.1.3 Narrowing Primitive Conversion
1070      */
1071     public byte byteValue() {
1072         return (byte)value;
1073     }
1074 
1075     /**
1076      * Returns the value of this {@code Integer} as a {@code short}
1077      * after a narrowing primitive conversion.
1078      * @jls 5.1.3 Narrowing Primitive Conversion
1079      */
1080     public short shortValue() {
1081         return (short)value;
1082     }
1083 
1084     /**
1085      * Returns the value of this {@code Integer} as an
1086      * {@code int}.
1087      */
1088     @IntrinsicCandidate
1089     public int intValue() {
1090         return value;
1091     }
1092 
1093     /**
1094      * Returns the value of this {@code Integer} as a {@code long}
1095      * after a widening primitive conversion.
1096      * @jls 5.1.2 Widening Primitive Conversion
1097      * @see Integer#toUnsignedLong(int)
1098      */
1099     public long longValue() {
1100         return (long)value;
1101     }
1102 
1103     /**
1104      * Returns the value of this {@code Integer} as a {@code float}
1105      * after a widening primitive conversion.
1106      * @jls 5.1.2 Widening Primitive Conversion
1107      */
1108     public float floatValue() {
1109         return (float)value;
1110     }
1111 
1112     /**
1113      * Returns the value of this {@code Integer} as a {@code double}
1114      * after a widening primitive conversion.
1115      * @jls 5.1.2 Widening Primitive Conversion
1116      */
1117     public double doubleValue() {
1118         return (double)value;
1119     }
1120 
1121     /**
1122      * Returns a {@code String} object representing this
1123      * {@code Integer}'s value. The value is converted to signed
1124      * decimal representation and returned as a string, exactly as if
1125      * the integer value were given as an argument to the {@link
1126      * java.lang.Integer#toString(int)} method.
1127      *
1128      * @return  a string representation of the value of this object in
1129      *          base&nbsp;10.
1130      */
1131     public String toString() {
1132         return toString(value);
1133     }
1134 
1135     /**
1136      * Returns a hash code for this {@code Integer}.
1137      *
1138      * @return  a hash code value for this object, equal to the
1139      *          primitive {@code int} value represented by this
1140      *          {@code Integer} object.
1141      */
1142     @Override
1143     public int hashCode() {
1144         return Integer.hashCode(value);
1145     }
1146 
1147     /**
1148      * Returns a hash code for an {@code int} value; compatible with
1149      * {@code Integer.hashCode()}.
1150      *
1151      * @param value the value to hash
1152      * @since 1.8
1153      *
1154      * @return a hash code value for an {@code int} value.
1155      */
1156     public static int hashCode(int value) {
1157         return value;
1158     }
1159 
1160     /**
1161      * Compares this object to the specified object.  The result is
1162      * {@code true} if and only if the argument is not
1163      * {@code null} and is an {@code Integer} object that
1164      * contains the same {@code int} value as this object.
1165      *
1166      * @param   obj   the object to compare with.
1167      * @return  {@code true} if the objects are the same;
1168      *          {@code false} otherwise.
1169      */
1170     public boolean equals(Object obj) {
1171         if (obj instanceof Integer i) {
1172             return value == i.intValue();
1173         }
1174         return false;
1175     }
1176 
1177     /**
1178      * Determines the integer value of the system property with the
1179      * specified name.
1180      *
1181      * <p>The first argument is treated as the name of a system
1182      * property.  System properties are accessible through the {@link
1183      * java.lang.System#getProperty(java.lang.String)} method. The
1184      * string value of this property is then interpreted as an integer
1185      * value using the grammar supported by {@link Integer#decode decode} and
1186      * an {@code Integer} object representing this value is returned.
1187      *
1188      * <p>If there is no property with the specified name, if the
1189      * specified name is empty or {@code null}, or if the property
1190      * does not have the correct numeric format, then {@code null} is
1191      * returned.
1192      *
1193      * <p>In other words, this method returns an {@code Integer}
1194      * object equal to the value of:
1195      *
1196      * <blockquote>
1197      *  {@code getInteger(nm, null)}
1198      * </blockquote>
1199      *
1200      * @param   nm   property name.
1201      * @return  the {@code Integer} value of the property.
1202      * @see     java.lang.System#getProperty(java.lang.String)
1203      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1204      */
1205     public static Integer getInteger(String nm) {
1206         return getInteger(nm, null);
1207     }
1208 
1209     /**
1210      * Determines the integer value of the system property with the
1211      * specified name.
1212      *
1213      * <p>The first argument is treated as the name of a system
1214      * property.  System properties are accessible through the {@link
1215      * java.lang.System#getProperty(java.lang.String)} method. The
1216      * string value of this property is then interpreted as an integer
1217      * value using the grammar supported by {@link Integer#decode decode} and
1218      * an {@code Integer} object representing this value is returned.
1219      *
1220      * <p>The second argument is the default value. An {@code Integer} object
1221      * that represents the value of the second argument is returned if there
1222      * is no property of the specified name, if the property does not have
1223      * the correct numeric format, or if the specified name is empty or
1224      * {@code null}.
1225      *
1226      * <p>In other words, this method returns an {@code Integer} object
1227      * equal to the value of:
1228      *
1229      * <blockquote>
1230      *  {@code getInteger(nm, Integer.valueOf(val))}
1231      * </blockquote>
1232      *
1233      * but in practice it may be implemented in a manner such as:
1234      *
1235      * <blockquote><pre>
1236      * Integer result = getInteger(nm, null);
1237      * return (result == null) ? Integer.valueOf(val) : result;
1238      * </pre></blockquote>
1239      *
1240      * to avoid the unnecessary allocation of an {@code Integer}
1241      * object when the default value is not needed.
1242      *
1243      * @param   nm   property name.
1244      * @param   val   default value.
1245      * @return  the {@code Integer} value of the property.
1246      * @see     java.lang.System#getProperty(java.lang.String)
1247      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1248      */
1249     public static Integer getInteger(String nm, int val) {
1250         Integer result = getInteger(nm, null);
1251         return (result == null) ? Integer.valueOf(val) : result;
1252     }
1253 
1254     /**
1255      * Returns the integer value of the system property with the
1256      * specified name.  The first argument is treated as the name of a
1257      * system property.  System properties are accessible through the
1258      * {@link java.lang.System#getProperty(java.lang.String)} method.
1259      * The string value of this property is then interpreted as an
1260      * integer value, as per the {@link Integer#decode decode} method,
1261      * and an {@code Integer} object representing this value is
1262      * returned; in summary:
1263      *
1264      * <ul><li>If the property value begins with the two ASCII characters
1265      *         {@code 0x} or the ASCII character {@code #}, not
1266      *      followed by a minus sign, then the rest of it is parsed as a
1267      *      hexadecimal integer exactly as by the method
1268      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1269      * <li>If the property value begins with the ASCII character
1270      *     {@code 0} followed by another character, it is parsed as an
1271      *     octal integer exactly as by the method
1272      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1273      * <li>Otherwise, the property value is parsed as a decimal integer
1274      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1275      * with radix 10.
1276      * </ul>
1277      *
1278      * <p>The second argument is the default value. The default value is
1279      * returned if there is no property of the specified name, if the
1280      * property does not have the correct numeric format, or if the
1281      * specified name is empty or {@code null}.
1282      *
1283      * @param   nm   property name.
1284      * @param   val   default value.
1285      * @return  the {@code Integer} value of the property.
1286      * @see     System#getProperty(java.lang.String)
1287      * @see     System#getProperty(java.lang.String, java.lang.String)
1288      */
1289     public static Integer getInteger(String nm, Integer val) {
1290         String v = nm != null && !nm.isEmpty() ? System.getProperty(nm) : null;
1291         if (v != null) {
1292             try {
1293                 return Integer.decode(v);
1294             } catch (NumberFormatException e) {
1295             }
1296         }
1297         return val;
1298     }
1299 
1300     /**
1301      * Decodes a {@code String} into an {@code Integer}.
1302      * Accepts decimal, hexadecimal, and octal numbers given
1303      * by the following grammar:
1304      *
1305      * <blockquote>
1306      * <dl>
1307      * <dt><i>DecodableString:</i>
1308      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1309      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1310      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1311      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1312      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1313      *
1314      * <dt><i>Sign:</i>
1315      * <dd>{@code -}
1316      * <dd>{@code +}
1317      * </dl>
1318      * </blockquote>
1319      *
1320      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1321      * are as defined in section {@jls 3.10.1} of
1322      * <cite>The Java Language Specification</cite>,
1323      * except that underscores are not accepted between digits.
1324      *
1325      * <p>The sequence of characters following an optional
1326      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1327      * "{@code #}", or leading zero) is parsed as by the {@code
1328      * Integer.parseInt} method with the indicated radix (10, 16, or
1329      * 8).  This sequence of characters must represent a positive
1330      * value or a {@link NumberFormatException} will be thrown.  The
1331      * result is negated if first character of the specified {@code
1332      * String} is the minus sign.  No whitespace characters are
1333      * permitted in the {@code String}.
1334      *
1335      * @param     nm the {@code String} to decode.
1336      * @return    an {@code Integer} object holding the {@code int}
1337      *             value represented by {@code nm}
1338      * @throws    NumberFormatException  if the {@code String} does not
1339      *            contain a parsable integer.
1340      * @see java.lang.Integer#parseInt(java.lang.String, int)
1341      */
1342     public static Integer decode(String nm) throws NumberFormatException {
1343         int radix = 10;
1344         int index = 0;
1345         boolean negative = false;
1346         int result;
1347 
1348         if (nm.isEmpty())
1349             throw new NumberFormatException("Zero length string");
1350         char firstChar = nm.charAt(0);
1351         // Handle sign, if present
1352         if (firstChar == '-') {
1353             negative = true;
1354             index++;
1355         } else if (firstChar == '+')
1356             index++;
1357 
1358         // Handle radix specifier, if present
1359         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1360             index += 2;
1361             radix = 16;
1362         }
1363         else if (nm.startsWith("#", index)) {
1364             index ++;
1365             radix = 16;
1366         }
1367         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1368             index ++;
1369             radix = 8;
1370         }
1371 
1372         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1373             throw new NumberFormatException("Sign character in wrong position");
1374 
1375         try {
1376             result = parseInt(nm, index, nm.length(), radix);
1377             result = negative ? -result : result;
1378         } catch (NumberFormatException e) {
1379             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1380             // handles this case, and causes any genuine format error to be
1381             // rethrown.
1382             String constant = negative ? ("-" + nm.substring(index))
1383                                        : nm.substring(index);
1384             result = parseInt(constant, radix);
1385         }
1386         return result;
1387     }
1388 
1389     /**
1390      * Compares two {@code Integer} objects numerically.
1391      *
1392      * @param   anotherInteger   the {@code Integer} to be compared.
1393      * @return  the value {@code 0} if this {@code Integer} is
1394      *          equal to the argument {@code Integer}; a value less than
1395      *          {@code 0} if this {@code Integer} is numerically less
1396      *          than the argument {@code Integer}; and a value greater
1397      *          than {@code 0} if this {@code Integer} is numerically
1398      *           greater than the argument {@code Integer} (signed
1399      *           comparison).
1400      * @since   1.2
1401      */
1402     public int compareTo(Integer anotherInteger) {
1403         return compare(this.value, anotherInteger.value);
1404     }
1405 
1406     /**
1407      * Compares two {@code int} values numerically.
1408      * The value returned is identical to what would be returned by:
1409      * <pre>
1410      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1411      * </pre>
1412      *
1413      * @param  x the first {@code int} to compare
1414      * @param  y the second {@code int} to compare
1415      * @return the value {@code 0} if {@code x == y};
1416      *         a value less than {@code 0} if {@code x < y}; and
1417      *         a value greater than {@code 0} if {@code x > y}
1418      * @since 1.7
1419      */
1420     public static int compare(int x, int y) {
1421         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1422     }
1423 
1424     /**
1425      * Compares two {@code int} values numerically treating the values
1426      * as unsigned.
1427      *
1428      * @param  x the first {@code int} to compare
1429      * @param  y the second {@code int} to compare
1430      * @return the value {@code 0} if {@code x == y}; a value less
1431      *         than {@code 0} if {@code x < y} as unsigned values; and
1432      *         a value greater than {@code 0} if {@code x > y} as
1433      *         unsigned values
1434      * @since 1.8
1435      */
1436     @IntrinsicCandidate
1437     public static int compareUnsigned(int x, int y) {
1438         return compare(x + MIN_VALUE, y + MIN_VALUE);
1439     }
1440 
1441     /**
1442      * Converts the argument to a {@code long} by an unsigned
1443      * conversion.  In an unsigned conversion to a {@code long}, the
1444      * high-order 32 bits of the {@code long} are zero and the
1445      * low-order 32 bits are equal to the bits of the integer
1446      * argument.
1447      *
1448      * Consequently, zero and positive {@code int} values are mapped
1449      * to a numerically equal {@code long} value and negative {@code
1450      * int} values are mapped to a {@code long} value equal to the
1451      * input plus 2<sup>32</sup>.
1452      *
1453      * @param  x the value to convert to an unsigned {@code long}
1454      * @return the argument converted to {@code long} by an unsigned
1455      *         conversion
1456      * @since 1.8
1457      */
1458     public static long toUnsignedLong(int x) {
1459         return ((long) x) & 0xffffffffL;
1460     }
1461 
1462     /**
1463      * Returns the unsigned quotient of dividing the first argument by
1464      * the second where each argument and the result is interpreted as
1465      * an unsigned value.
1466      *
1467      * <p>Note that in two's complement arithmetic, the three other
1468      * basic arithmetic operations of add, subtract, and multiply are
1469      * bit-wise identical if the two operands are regarded as both
1470      * being signed or both being unsigned.  Therefore separate {@code
1471      * addUnsigned}, etc. methods are not provided.
1472      *
1473      * @param dividend the value to be divided
1474      * @param divisor the value doing the dividing
1475      * @return the unsigned quotient of the first argument divided by
1476      * the second argument
1477      * @see #remainderUnsigned
1478      * @since 1.8
1479      */
1480     @IntrinsicCandidate
1481     public static int divideUnsigned(int dividend, int divisor) {
1482         // In lieu of tricky code, for now just use long arithmetic.
1483         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1484     }
1485 
1486     /**
1487      * Returns the unsigned remainder from dividing the first argument
1488      * by the second where each argument and the result is interpreted
1489      * as an unsigned value.
1490      *
1491      * @param dividend the value to be divided
1492      * @param divisor the value doing the dividing
1493      * @return the unsigned remainder of the first argument divided by
1494      * the second argument
1495      * @see #divideUnsigned
1496      * @since 1.8
1497      */
1498     @IntrinsicCandidate
1499     public static int remainderUnsigned(int dividend, int divisor) {
1500         // In lieu of tricky code, for now just use long arithmetic.
1501         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1502     }
1503 
1504 
1505     // Bit twiddling
1506 
1507     /**
1508      * The number of bits used to represent an {@code int} value in two's
1509      * complement binary form.
1510      *
1511      * @since 1.5
1512      */
1513     @Native public static final int SIZE = 32;
1514 
1515     /**
1516      * The number of bytes used to represent an {@code int} value in two's
1517      * complement binary form.
1518      *
1519      * @since 1.8
1520      */
1521     public static final int BYTES = SIZE / Byte.SIZE;
1522 
1523     /**
1524      * Returns an {@code int} value with at most a single one-bit, in the
1525      * position of the highest-order ("leftmost") one-bit in the specified
1526      * {@code int} value.  Returns zero if the specified value has no
1527      * one-bits in its two's complement binary representation, that is, if it
1528      * is equal to zero.
1529      *
1530      * @param i the value whose highest one bit is to be computed
1531      * @return an {@code int} value with a single one-bit, in the position
1532      *     of the highest-order one-bit in the specified value, or zero if
1533      *     the specified value is itself equal to zero.
1534      * @since 1.5
1535      */
1536     public static int highestOneBit(int i) {
1537         return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
1538     }
1539 
1540     /**
1541      * Returns an {@code int} value with at most a single one-bit, in the
1542      * position of the lowest-order ("rightmost") one-bit in the specified
1543      * {@code int} value.  Returns zero if the specified value has no
1544      * one-bits in its two's complement binary representation, that is, if it
1545      * is equal to zero.
1546      *
1547      * @param i the value whose lowest one bit is to be computed
1548      * @return an {@code int} value with a single one-bit, in the position
1549      *     of the lowest-order one-bit in the specified value, or zero if
1550      *     the specified value is itself equal to zero.
1551      * @since 1.5
1552      */
1553     public static int lowestOneBit(int i) {
1554         // HD, Section 2-1
1555         return i & -i;
1556     }
1557 
1558     /**
1559      * Returns the number of zero bits preceding the highest-order
1560      * ("leftmost") one-bit in the two's complement binary representation
1561      * of the specified {@code int} value.  Returns 32 if the
1562      * specified value has no one-bits in its two's complement representation,
1563      * in other words if it is equal to zero.
1564      *
1565      * <p>Note that this method is closely related to the logarithm base 2.
1566      * For all positive {@code int} values x:
1567      * <ul>
1568      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1569      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1570      * </ul>
1571      *
1572      * @param i the value whose number of leading zeros is to be computed
1573      * @return the number of zero bits preceding the highest-order
1574      *     ("leftmost") one-bit in the two's complement binary representation
1575      *     of the specified {@code int} value, or 32 if the value
1576      *     is equal to zero.
1577      * @since 1.5
1578      */
1579     @IntrinsicCandidate
1580     public static int numberOfLeadingZeros(int i) {
1581         // HD, Count leading 0's
1582         if (i <= 0)
1583             return i == 0 ? 32 : 0;
1584         int n = 31;
1585         if (i >= 1 << 16) { n -= 16; i >>>= 16; }
1586         if (i >= 1 <<  8) { n -=  8; i >>>=  8; }
1587         if (i >= 1 <<  4) { n -=  4; i >>>=  4; }
1588         if (i >= 1 <<  2) { n -=  2; i >>>=  2; }
1589         return n - (i >>> 1);
1590     }
1591 
1592     /**
1593      * Returns the number of zero bits following the lowest-order ("rightmost")
1594      * one-bit in the two's complement binary representation of the specified
1595      * {@code int} value.  Returns 32 if the specified value has no
1596      * one-bits in its two's complement representation, in other words if it is
1597      * equal to zero.
1598      *
1599      * @param i the value whose number of trailing zeros is to be computed
1600      * @return the number of zero bits following the lowest-order ("rightmost")
1601      *     one-bit in the two's complement binary representation of the
1602      *     specified {@code int} value, or 32 if the value is equal
1603      *     to zero.
1604      * @since 1.5
1605      */
1606     @IntrinsicCandidate
1607     public static int numberOfTrailingZeros(int i) {
1608         // HD, Count trailing 0's
1609         i = ~i & (i - 1);
1610         if (i <= 0) return i & 32;
1611         int n = 1;
1612         if (i > 1 << 16) { n += 16; i >>>= 16; }
1613         if (i > 1 <<  8) { n +=  8; i >>>=  8; }
1614         if (i > 1 <<  4) { n +=  4; i >>>=  4; }
1615         if (i > 1 <<  2) { n +=  2; i >>>=  2; }
1616         return n + (i >>> 1);
1617     }
1618 
1619     /**
1620      * Returns the number of one-bits in the two's complement binary
1621      * representation of the specified {@code int} value.  This function is
1622      * sometimes referred to as the <i>population count</i>.
1623      *
1624      * @param i the value whose bits are to be counted
1625      * @return the number of one-bits in the two's complement binary
1626      *     representation of the specified {@code int} value.
1627      * @since 1.5
1628      */
1629     @IntrinsicCandidate
1630     public static int bitCount(int i) {
1631         // HD, Figure 5-2
1632         i = i - ((i >>> 1) & 0x55555555);
1633         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1634         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1635         i = i + (i >>> 8);
1636         i = i + (i >>> 16);
1637         return i & 0x3f;
1638     }
1639 
1640     /**
1641      * Returns the value obtained by rotating the two's complement binary
1642      * representation of the specified {@code int} value left by the
1643      * specified number of bits.  (Bits shifted out of the left hand, or
1644      * high-order, side reenter on the right, or low-order.)
1645      *
1646      * <p>Note that left rotation with a negative distance is equivalent to
1647      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1648      * distance)}.  Note also that rotation by any multiple of 32 is a
1649      * no-op, so all but the last five bits of the rotation distance can be
1650      * ignored, even if the distance is negative: {@code rotateLeft(val,
1651      * distance) == rotateLeft(val, distance & 0x1F)}.
1652      *
1653      * @param i the value whose bits are to be rotated left
1654      * @param distance the number of bit positions to rotate left
1655      * @return the value obtained by rotating the two's complement binary
1656      *     representation of the specified {@code int} value left by the
1657      *     specified number of bits.
1658      * @since 1.5
1659      */
1660     public static int rotateLeft(int i, int distance) {
1661         return (i << distance) | (i >>> -distance);
1662     }
1663 
1664     /**
1665      * Returns the value obtained by rotating the two's complement binary
1666      * representation of the specified {@code int} value right by the
1667      * specified number of bits.  (Bits shifted out of the right hand, or
1668      * low-order, side reenter on the left, or high-order.)
1669      *
1670      * <p>Note that right rotation with a negative distance is equivalent to
1671      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1672      * distance)}.  Note also that rotation by any multiple of 32 is a
1673      * no-op, so all but the last five bits of the rotation distance can be
1674      * ignored, even if the distance is negative: {@code rotateRight(val,
1675      * distance) == rotateRight(val, distance & 0x1F)}.
1676      *
1677      * @param i the value whose bits are to be rotated right
1678      * @param distance the number of bit positions to rotate right
1679      * @return the value obtained by rotating the two's complement binary
1680      *     representation of the specified {@code int} value right by the
1681      *     specified number of bits.
1682      * @since 1.5
1683      */
1684     public static int rotateRight(int i, int distance) {
1685         return (i >>> distance) | (i << -distance);
1686     }
1687 
1688     /**
1689      * Returns the value obtained by reversing the order of the bits in the
1690      * two's complement binary representation of the specified {@code int}
1691      * value.
1692      *
1693      * @param i the value to be reversed
1694      * @return the value obtained by reversing order of the bits in the
1695      *     specified {@code int} value.
1696      * @since 1.5
1697      */
1698     @IntrinsicCandidate
1699     public static int reverse(int i) {
1700         // HD, Figure 7-1
1701         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1702         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1703         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1704 
1705         return reverseBytes(i);
1706     }
1707 
1708     /**
1709      * Returns the value obtained by compressing the bits of the
1710      * specified {@code int} value, {@code i}, in accordance with
1711      * the specified bit mask.
1712      * <p>
1713      * For each one-bit value {@code mb} of the mask, from least
1714      * significant to most significant, the bit value of {@code i} at
1715      * the same bit location as {@code mb} is assigned to the compressed
1716      * value contiguously starting from the least significant bit location.
1717      * All the upper remaining bits of the compressed value are set
1718      * to zero.
1719      *
1720      * @apiNote
1721      * Consider the simple case of compressing the digits of a hexadecimal
1722      * value:
1723      * {@snippet lang="java" :
1724      * // Compressing drink to food
1725      * compress(0xCAFEBABE, 0xFF00FFF0) == 0xCABAB
1726      * }
1727      * Starting from the least significant hexadecimal digit at position 0
1728      * from the right, the mask {@code 0xFF00FFF0} selects hexadecimal digits
1729      * at positions 1, 2, 3, 6 and 7 of {@code 0xCAFEBABE}. The selected digits
1730      * occur in the resulting compressed value contiguously from digit position
1731      * 0 in the same order.
1732      * <p>
1733      * The following identities all return {@code true} and are helpful to
1734      * understand the behaviour of {@code compress}:
1735      * {@snippet lang="java" :
1736      * // Returns 1 if the bit at position n is one
1737      * compress(x, 1 << n) == (x >> n & 1)
1738      *
1739      * // Logical shift right
1740      * compress(x, -1 << n) == x >>> n
1741      *
1742      * // Any bits not covered by the mask are ignored
1743      * compress(x, m) == compress(x & m, m)
1744      *
1745      * // Compressing a value by itself
1746      * compress(m, m) == (m == -1 || m == 0) ? m : (1 << bitCount(m)) - 1
1747      *
1748      * // Expanding then compressing with the same mask
1749      * compress(expand(x, m), m) == x & compress(m, m)
1750      * }
1751      * <p>
1752      * The Sheep And Goats (SAG) operation (see Hacker's Delight, Second Edition, section 7.7)
1753      * can be implemented as follows:
1754      * {@snippet lang="java" :
1755      * int compressLeft(int i, int mask) {
1756      *     // This implementation follows the description in Hacker's Delight which
1757      *     // is informative. A more optimal implementation is:
1758      *     //   Integer.compress(i, mask) << -Integer.bitCount(mask)
1759      *     return Integer.reverse(
1760      *         Integer.compress(Integer.reverse(i), Integer.reverse(mask)));
1761      * }
1762      *
1763      * int sag(int i, int mask) {
1764      *     return compressLeft(i, mask) | Integer.compress(i, ~mask);
1765      * }
1766      *
1767      * // Separate the sheep from the goats
1768      * sag(0xCAFEBABE, 0xFF00FFF0) == 0xCABABFEE
1769      * }
1770      *
1771      * @param i the value whose bits are to be compressed
1772      * @param mask the bit mask
1773      * @return the compressed value
1774      * @see #expand
1775      * @since 19
1776      */
1777     @IntrinsicCandidate
1778     public static int compress(int i, int mask) {
1779         // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract
1780 
1781         i = i & mask; // Clear irrelevant bits
1782         int maskCount = ~mask << 1; // Count 0's to right
1783 
1784         for (int j = 0; j < 5; j++) {
1785             // Parallel prefix
1786             // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
1787             int maskPrefix = parallelSuffix(maskCount);
1788             // Bits to move
1789             int maskMove = maskPrefix & mask;
1790             // Compress mask
1791             mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
1792             // Bits of i to be moved
1793             int t = i & maskMove;
1794             // Compress i
1795             i = (i ^ t) | (t >>> (1 << j));
1796             // Adjust the mask count by identifying bits that have 0 to the right
1797             maskCount = maskCount & ~maskPrefix;
1798         }
1799         return i;
1800     }
1801 
1802     /**
1803      * Returns the value obtained by expanding the bits of the
1804      * specified {@code int} value, {@code i}, in accordance with
1805      * the specified bit mask.
1806      * <p>
1807      * For each one-bit value {@code mb} of the mask, from least
1808      * significant to most significant, the next contiguous bit value
1809      * of {@code i} starting at the least significant bit is assigned
1810      * to the expanded value at the same bit location as {@code mb}.
1811      * All other remaining bits of the expanded value are set to zero.
1812      *
1813      * @apiNote
1814      * Consider the simple case of expanding the digits of a hexadecimal
1815      * value:
1816      * {@snippet lang="java" :
1817      * expand(0x0000CABAB, 0xFF00FFF0) == 0xCA00BAB0
1818      * }
1819      * Starting from the least significant hexadecimal digit at position 0
1820      * from the right, the mask {@code 0xFF00FFF0} selects the first five
1821      * hexadecimal digits of {@code 0x0000CABAB}. The selected digits occur
1822      * in the resulting expanded value in order at positions 1, 2, 3, 6, and 7.
1823      * <p>
1824      * The following identities all return {@code true} and are helpful to
1825      * understand the behaviour of {@code expand}:
1826      * {@snippet lang="java" :
1827      * // Logically shift right the bit at position 0
1828      * expand(x, 1 << n) == (x & 1) << n
1829      *
1830      * // Logically shift right
1831      * expand(x, -1 << n) == x << n
1832      *
1833      * // Expanding all bits returns the mask
1834      * expand(-1, m) == m
1835      *
1836      * // Any bits not covered by the mask are ignored
1837      * expand(x, m) == expand(x, m) & m
1838      *
1839      * // Compressing then expanding with the same mask
1840      * expand(compress(x, m), m) == x & m
1841      * }
1842      * <p>
1843      * The select operation for determining the position of the one-bit with
1844      * index {@code n} in a {@code int} value can be implemented as follows:
1845      * {@snippet lang="java" :
1846      * int select(int i, int n) {
1847      *     // the one-bit in i (the mask) with index n
1848      *     int nthBit = Integer.expand(1 << n, i);
1849      *     // the bit position of the one-bit with index n
1850      *     return Integer.numberOfTrailingZeros(nthBit);
1851      * }
1852      *
1853      * // The one-bit with index 0 is at bit position 1
1854      * select(0b10101010_10101010, 0) == 1
1855      * // The one-bit with index 3 is at bit position 7
1856      * select(0b10101010_10101010, 3) == 7
1857      * }
1858      *
1859      * @param i the value whose bits are to be expanded
1860      * @param mask the bit mask
1861      * @return the expanded value
1862      * @see #compress
1863      * @since 19
1864      */
1865     @IntrinsicCandidate
1866     public static int expand(int i, int mask) {
1867         // Save original mask
1868         int originalMask = mask;
1869         // Count 0's to right
1870         int maskCount = ~mask << 1;
1871         int maskPrefix = parallelSuffix(maskCount);
1872         // Bits to move
1873         int maskMove1 = maskPrefix & mask;
1874         // Compress mask
1875         mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
1876         maskCount = maskCount & ~maskPrefix;
1877 
1878         maskPrefix = parallelSuffix(maskCount);
1879         // Bits to move
1880         int maskMove2 = maskPrefix & mask;
1881         // Compress mask
1882         mask = (mask ^ maskMove2) | (maskMove2 >>> (1 << 1));
1883         maskCount = maskCount & ~maskPrefix;
1884 
1885         maskPrefix = parallelSuffix(maskCount);
1886         // Bits to move
1887         int maskMove3 = maskPrefix & mask;
1888         // Compress mask
1889         mask = (mask ^ maskMove3) | (maskMove3 >>> (1 << 2));
1890         maskCount = maskCount & ~maskPrefix;
1891 
1892         maskPrefix = parallelSuffix(maskCount);
1893         // Bits to move
1894         int maskMove4 = maskPrefix & mask;
1895         // Compress mask
1896         mask = (mask ^ maskMove4) | (maskMove4 >>> (1 << 3));
1897         maskCount = maskCount & ~maskPrefix;
1898 
1899         maskPrefix = parallelSuffix(maskCount);
1900         // Bits to move
1901         int maskMove5 = maskPrefix & mask;
1902 
1903         int t = i << (1 << 4);
1904         i = (i & ~maskMove5) | (t & maskMove5);
1905         t = i << (1 << 3);
1906         i = (i & ~maskMove4) | (t & maskMove4);
1907         t = i << (1 << 2);
1908         i = (i & ~maskMove3) | (t & maskMove3);
1909         t = i << (1 << 1);
1910         i = (i & ~maskMove2) | (t & maskMove2);
1911         t = i << (1 << 0);
1912         i = (i & ~maskMove1) | (t & maskMove1);
1913 
1914         // Clear irrelevant bits
1915         return i & originalMask;
1916     }
1917 
1918     @ForceInline
1919     private static int parallelSuffix(int maskCount) {
1920         int maskPrefix = maskCount ^ (maskCount << 1);
1921         maskPrefix = maskPrefix ^ (maskPrefix << 2);
1922         maskPrefix = maskPrefix ^ (maskPrefix << 4);
1923         maskPrefix = maskPrefix ^ (maskPrefix << 8);
1924         maskPrefix = maskPrefix ^ (maskPrefix << 16);
1925         return maskPrefix;
1926     }
1927 
1928     /**
1929      * Returns the signum function of the specified {@code int} value.  (The
1930      * return value is -1 if the specified value is negative; 0 if the
1931      * specified value is zero; and 1 if the specified value is positive.)
1932      *
1933      * @param i the value whose signum is to be computed
1934      * @return the signum function of the specified {@code int} value.
1935      * @since 1.5
1936      */
1937     public static int signum(int i) {
1938         // HD, Section 2-7
1939         return (i >> 31) | (-i >>> 31);
1940     }
1941 
1942     /**
1943      * Returns the value obtained by reversing the order of the bytes in the
1944      * two's complement representation of the specified {@code int} value.
1945      *
1946      * @param i the value whose bytes are to be reversed
1947      * @return the value obtained by reversing the bytes in the specified
1948      *     {@code int} value.
1949      * @since 1.5
1950      */
1951     @IntrinsicCandidate
1952     public static int reverseBytes(int i) {
1953         return (i << 24)            |
1954                ((i & 0xff00) << 8)  |
1955                ((i >>> 8) & 0xff00) |
1956                (i >>> 24);
1957     }
1958 
1959     /**
1960      * Adds two integers together as per the + operator.
1961      *
1962      * @param a the first operand
1963      * @param b the second operand
1964      * @return the sum of {@code a} and {@code b}
1965      * @see java.util.function.BinaryOperator
1966      * @since 1.8
1967      */
1968     public static int sum(int a, int b) {
1969         return a + b;
1970     }
1971 
1972     /**
1973      * Returns the greater of two {@code int} values
1974      * as if by calling {@link Math#max(int, int) Math.max}.
1975      *
1976      * @param a the first operand
1977      * @param b the second operand
1978      * @return the greater of {@code a} and {@code b}
1979      * @see java.util.function.BinaryOperator
1980      * @since 1.8
1981      */
1982     public static int max(int a, int b) {
1983         return Math.max(a, b);
1984     }
1985 
1986     /**
1987      * Returns the smaller of two {@code int} values
1988      * as if by calling {@link Math#min(int, int) Math.min}.
1989      *
1990      * @param a the first operand
1991      * @param b the second operand
1992      * @return the smaller of {@code a} and {@code b}
1993      * @see java.util.function.BinaryOperator
1994      * @since 1.8
1995      */
1996     public static int min(int a, int b) {
1997         return Math.min(a, b);
1998     }
1999 
2000     /**
2001      * Returns an {@link Optional} containing the nominal descriptor for this
2002      * instance, which is the instance itself.
2003      *
2004      * @return an {@link Optional} describing the {@linkplain Integer} instance
2005      * @since 12
2006      */
2007     @Override
2008     public Optional<Integer> describeConstable() {
2009         return Optional.of(this);
2010     }
2011 
2012     /**
2013      * Resolves this instance as a {@link ConstantDesc}, the result of which is
2014      * the instance itself.
2015      *
2016      * @param lookup ignored
2017      * @return the {@linkplain Integer} instance
2018      * @since 12
2019      */
2020     @Override
2021     public Integer resolveConstantDesc(MethodHandles.Lookup lookup) {
2022         return this;
2023     }
2024 
2025     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2026     @java.io.Serial
2027     @Native private static final long serialVersionUID = 1360826667806852920L;
2028 }