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.VM;
  30 import jdk.internal.util.DecimalDigits;
  31 import jdk.internal.value.DeserializeConstructor;
  32 import jdk.internal.vm.annotation.ForceInline;
  33 import jdk.internal.vm.annotation.IntrinsicCandidate;
  34 import jdk.internal.vm.annotation.Stable;
  35 
  36 import java.lang.annotation.Native;
  37 import java.lang.constant.Constable;
  38 import java.lang.constant.ConstantDesc;
  39 import java.lang.invoke.MethodHandles;
  40 import java.util.Objects;
  41 import java.util.Optional;
  42 
  43 import static java.lang.Character.digit;
  44 import static java.lang.String.COMPACT_STRINGS;
  45 import static java.lang.String.LATIN1;
  46 import static java.lang.String.UTF16;
  47 
  48 /**
  49  * The {@code Integer} class is the {@linkplain
  50  * java.lang##wrapperClass wrapper class} for values of the primitive
  51  * type {@code int}. An object of type {@code Integer} contains a
  52  * single field whose type is {@code int}.
  53  *
  54  * <p>In addition, this class provides several methods for converting
  55  * an {@code int} to a {@code String} and a {@code String} to an
  56  * {@code int}, as well as other constants and methods useful when
  57  * dealing with an {@code int}.
  58  *
  59  * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
  60  * class; programmers should treat instances that are {@linkplain #equals(Object) equal}
  61  * as interchangeable and should not use instances for synchronization, mutexes, or
  62  * with {@linkplain java.lang.ref.Reference object references}.
  63  *
  64  * <div class="preview-block">
  65  *      <div class="preview-comment">
  66  *          When preview features are enabled, {@code Integer} is a {@linkplain Class#isValue value class}.
  67  *          Use of value class instances for synchronization, mutexes, or with
  68  *          {@linkplain java.lang.ref.Reference object references} result in
  69  *          {@link IdentityException}.
  70  *      </div>
  71  * </div>
  72  *
  73  * <p>Implementation note: The implementations of the "bit twiddling"
  74  * methods (such as {@link #highestOneBit(int) highestOneBit} and
  75  * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
  76  * based on material from Henry S. Warren, Jr.'s <cite>Hacker's
  77  * Delight</cite>, (Addison Wesley, 2002) and <cite>Hacker's
  78  * Delight, Second Edition</cite>, (Pearson Education, 2013).
  79  *
  80  * @author  Lee Boynton
  81  * @author  Arthur van Hoff
  82  * @author  Josh Bloch
  83  * @author  Joseph D. Darcy
  84  * @since 1.0
  85  */
  86 @jdk.internal.MigratedValueClass
  87 @jdk.internal.ValueBased
  88 public final class Integer extends Number
  89         implements Comparable<Integer>, Constable, ConstantDesc {
  90     /**
  91      * A constant holding the minimum value an {@code int} can
  92      * have, -2<sup>31</sup>.
  93      */
  94     @Native public static final int   MIN_VALUE = 0x80000000;
  95 
  96     /**
  97      * A constant holding the maximum value an {@code int} can
  98      * have, 2<sup>31</sup>-1.
  99      */
 100     @Native public static final int   MAX_VALUE = 0x7fffffff;
 101 
 102     /**
 103      * The {@code Class} instance representing the primitive type
 104      * {@code int}.
 105      *
 106      * @since   1.1
 107      */
 108     public static final Class<Integer> TYPE = Class.getPrimitiveClass("int");
 109 
 110     /**
 111      * All possible chars for representing a number as a String
 112      */
 113     @Stable
 114     static final byte[] digits = {
 115         '0' , '1' , '2' , '3' , '4' , '5' ,
 116         '6' , '7' , '8' , '9' , 'a' , 'b' ,
 117         'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
 118         'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
 119         'o' , 'p' , 'q' , 'r' , 's' , 't' ,
 120         'u' , 'v' , 'w' , 'x' , 'y' , 'z'
 121     };
 122 
 123     /**
 124      * Returns a string representation of the first argument in the
 125      * radix specified by the second argument.
 126      *
 127      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 128      * or larger than {@code Character.MAX_RADIX}, then the radix
 129      * {@code 10} is used instead.
 130      *
 131      * <p>If the first argument is negative, the first element of the
 132      * result is the ASCII minus character {@code '-'}
 133      * ({@code '\u005Cu002D'}). If the first argument is not
 134      * negative, no sign character appears in the result.
 135      *
 136      * <p>The remaining characters of the result represent the magnitude
 137      * of the first argument. If the magnitude is zero, it is
 138      * represented by a single zero character {@code '0'}
 139      * ({@code '\u005Cu0030'}); otherwise, the first character of
 140      * the representation of the magnitude will not be the zero
 141      * character.  The following ASCII characters are used as digits:
 142      *
 143      * <blockquote>
 144      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 145      * </blockquote>
 146      *
 147      * These are {@code '\u005Cu0030'} through
 148      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 149      * {@code '\u005Cu007A'}. If {@code radix} is
 150      * <var>N</var>, then the first <var>N</var> of these characters
 151      * are used as radix-<var>N</var> digits in the order shown. Thus,
 152      * the digits for hexadecimal (radix 16) are
 153      * {@code 0123456789abcdef}. If uppercase letters are
 154      * desired, the {@link java.lang.String#toUpperCase()} method may
 155      * be called on the result:
 156      *
 157      * <blockquote>
 158      *  {@code Integer.toString(n, 16).toUpperCase()}
 159      * </blockquote>
 160      *
 161      * @param   i       an integer to be converted to a string.
 162      * @param   radix   the radix to use in the string representation.
 163      * @return  a string representation of the argument in the specified radix.
 164      * @see     java.lang.Character#MAX_RADIX
 165      * @see     java.lang.Character#MIN_RADIX
 166      */
 167     public static String toString(int i, int radix) {
 168         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 169             radix = 10;
 170 
 171         /* Use the faster version */
 172         if (radix == 10) {
 173             return toString(i);
 174         }
 175 
 176         if (COMPACT_STRINGS) {
 177             byte[] buf = new byte[33];
 178             boolean negative = (i < 0);
 179             int charPos = 32;
 180 
 181             if (!negative) {
 182                 i = -i;
 183             }
 184 
 185             while (i <= -radix) {
 186                 buf[charPos--] = digits[-(i % radix)];
 187                 i = i / radix;
 188             }
 189             buf[charPos] = digits[-i];
 190 
 191             if (negative) {
 192                 buf[--charPos] = '-';
 193             }
 194 
 195             return StringLatin1.newString(buf, charPos, (33 - charPos));
 196         }
 197         return toStringUTF16(i, radix);
 198     }
 199 
 200     private static String toStringUTF16(int i, int radix) {
 201         byte[] buf = new byte[33 * 2];
 202         boolean negative = (i < 0);
 203         int charPos = 32;
 204         if (!negative) {
 205             i = -i;
 206         }
 207         while (i <= -radix) {
 208             StringUTF16.putChar(buf, charPos--, digits[-(i % radix)]);
 209             i = i / radix;
 210         }
 211         StringUTF16.putChar(buf, charPos, digits[-i]);
 212 
 213         if (negative) {
 214             StringUTF16.putChar(buf, --charPos, '-');
 215         }
 216         return StringUTF16.newString(buf, charPos, (33 - charPos));
 217     }
 218 
 219     /**
 220      * Returns a string representation of the first argument as an
 221      * unsigned integer value in the radix specified by the second
 222      * argument.
 223      *
 224      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 225      * or larger than {@code Character.MAX_RADIX}, then the radix
 226      * {@code 10} is used instead.
 227      *
 228      * <p>Note that since the first argument is treated as an unsigned
 229      * value, no leading sign character is printed.
 230      *
 231      * <p>If the magnitude is zero, it is represented by a single zero
 232      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 233      * the first character of the representation of the magnitude will
 234      * not be the zero character.
 235      *
 236      * <p>The behavior of radixes and the characters used as digits
 237      * are the same as {@link #toString(int, int) toString}.
 238      *
 239      * @param   i       an integer to be converted to an unsigned string.
 240      * @param   radix   the radix to use in the string representation.
 241      * @return  an unsigned string representation of the argument in the specified radix.
 242      * @see     #toString(int, int)
 243      * @since 1.8
 244      */
 245     public static String toUnsignedString(int i, int radix) {
 246         return Long.toUnsignedString(toUnsignedLong(i), radix);
 247     }
 248 
 249     /**
 250      * Returns a string representation of the integer argument as an
 251      * unsigned integer in base&nbsp;16.
 252      *
 253      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 254      * if the argument is negative; otherwise, it is equal to the
 255      * argument.  This value is converted to a string of ASCII digits
 256      * in hexadecimal (base&nbsp;16) with no extra leading
 257      * {@code 0}s.
 258      *
 259      * <p>The value of the argument can be recovered from the returned
 260      * string {@code s} by calling {@link
 261      * Integer#parseUnsignedInt(String, int)
 262      * Integer.parseUnsignedInt(s, 16)}.
 263      *
 264      * <p>If the unsigned magnitude is zero, it is represented by a
 265      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 266      * otherwise, the first character of the representation of the
 267      * unsigned magnitude will not be the zero character. The
 268      * following characters are used as hexadecimal digits:
 269      *
 270      * <blockquote>
 271      *  {@code 0123456789abcdef}
 272      * </blockquote>
 273      *
 274      * These are the characters {@code '\u005Cu0030'} through
 275      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 276      * {@code '\u005Cu0066'}. If uppercase letters are
 277      * desired, the {@link java.lang.String#toUpperCase()} method may
 278      * be called on the result:
 279      *
 280      * <blockquote>
 281      *  {@code Integer.toHexString(n).toUpperCase()}
 282      * </blockquote>
 283      *
 284      * @apiNote
 285      * The {@link java.util.HexFormat} class provides formatting and parsing
 286      * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
 287      * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
 288      * with leading zeros and for byte arrays includes for each byte
 289      * a delimiter, prefix, and suffix.
 290      *
 291      * @param   i   an integer to be converted to a string.
 292      * @return  the string representation of the unsigned integer value
 293      *          represented by the argument in hexadecimal (base&nbsp;16).
 294      * @see java.util.HexFormat
 295      * @see #parseUnsignedInt(String, int)
 296      * @see #toUnsignedString(int, int)
 297      * @since   1.0.2
 298      */
 299     public static String toHexString(int i) {
 300         return toUnsignedString0(i, 4);
 301     }
 302 
 303     /**
 304      * Returns a string representation of the integer argument as an
 305      * unsigned integer in base&nbsp;8.
 306      *
 307      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 308      * if the argument is negative; otherwise, it is equal to the
 309      * argument.  This value is converted to a string of ASCII digits
 310      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
 311      *
 312      * <p>The value of the argument can be recovered from the returned
 313      * string {@code s} by calling {@link
 314      * Integer#parseUnsignedInt(String, int)
 315      * Integer.parseUnsignedInt(s, 8)}.
 316      *
 317      * <p>If the unsigned magnitude is zero, it is represented by a
 318      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 319      * otherwise, the first character of the representation of the
 320      * unsigned magnitude will not be the zero character. The
 321      * following characters are used as octal digits:
 322      *
 323      * <blockquote>
 324      * {@code 01234567}
 325      * </blockquote>
 326      *
 327      * These are the characters {@code '\u005Cu0030'} through
 328      * {@code '\u005Cu0037'}.
 329      *
 330      * @param   i   an integer to be converted to a string.
 331      * @return  the string representation of the unsigned integer value
 332      *          represented by the argument in octal (base&nbsp;8).
 333      * @see #parseUnsignedInt(String, int)
 334      * @see #toUnsignedString(int, int)
 335      * @since   1.0.2
 336      */
 337     public static String toOctalString(int i) {
 338         return toUnsignedString0(i, 3);
 339     }
 340 
 341     /**
 342      * Returns a string representation of the integer argument as an
 343      * unsigned integer in base&nbsp;2.
 344      *
 345      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 346      * if the argument is negative; otherwise it is equal to the
 347      * argument.  This value is converted to a string of ASCII digits
 348      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
 349      *
 350      * <p>The value of the argument can be recovered from the returned
 351      * string {@code s} by calling {@link
 352      * Integer#parseUnsignedInt(String, int)
 353      * Integer.parseUnsignedInt(s, 2)}.
 354      *
 355      * <p>If the unsigned magnitude is zero, it is represented by a
 356      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 357      * otherwise, the first character of the representation of the
 358      * unsigned magnitude will not be the zero character. The
 359      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 360      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 361      *
 362      * @param   i   an integer to be converted to a string.
 363      * @return  the string representation of the unsigned integer value
 364      *          represented by the argument in binary (base&nbsp;2).
 365      * @see #parseUnsignedInt(String, int)
 366      * @see #toUnsignedString(int, int)
 367      * @since   1.0.2
 368      */
 369     public static String toBinaryString(int i) {
 370         return toUnsignedString0(i, 1);
 371     }
 372 
 373     /**
 374      * Convert the integer to an unsigned number.
 375      */
 376     private static String toUnsignedString0(int val, int shift) {
 377         // assert shift > 0 && shift <=5 : "Illegal shift value";
 378         int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
 379         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 380         if (COMPACT_STRINGS) {
 381             byte[] buf = new byte[chars];
 382             formatUnsignedInt(val, shift, buf, chars);
 383             return new String(buf, LATIN1);
 384         } else {
 385             byte[] buf = new byte[chars * 2];
 386             formatUnsignedIntUTF16(val, shift, buf, chars);
 387             return new String(buf, UTF16);
 388         }
 389     }
 390 
 391     /**
 392      * Format an {@code int} (treated as unsigned) into a byte buffer (LATIN1 version). If
 393      * {@code len} exceeds the formatted ASCII representation of {@code val},
 394      * {@code buf} will be padded with leading zeroes.
 395      *
 396      * @param val the unsigned int to format
 397      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 398      * @param buf the byte buffer to write to
 399      * @param len the number of characters to write
 400      */
 401     private static void formatUnsignedInt(int val, int shift, byte[] buf, int len) {
 402         int charPos = len;
 403         int radix = 1 << shift;
 404         int mask = radix - 1;
 405         do {
 406             buf[--charPos] = Integer.digits[val & mask];
 407             val >>>= shift;
 408         } while (charPos > 0);
 409     }
 410 
 411     /**
 412      * Format an {@code int} (treated as unsigned) into a byte buffer (UTF16 version). If
 413      * {@code len} exceeds the formatted ASCII representation of {@code val},
 414      * {@code buf} will be padded with leading zeroes.
 415      *
 416      * @param val the unsigned int to format
 417      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 418      * @param buf the byte buffer to write to
 419      * @param len the number of characters to write
 420      */
 421     private static void formatUnsignedIntUTF16(int val, int shift, byte[] buf, int len) {
 422         int charPos = len;
 423         int radix = 1 << shift;
 424         int mask = radix - 1;
 425         do {
 426             StringUTF16.putChar(buf, --charPos, Integer.digits[val & mask]);
 427             val >>>= shift;
 428         } while (charPos > 0);
 429     }
 430 
 431     /**
 432      * Returns a {@code String} object representing the
 433      * specified integer. The argument is converted to signed decimal
 434      * representation and returned as a string, exactly as if the
 435      * argument and radix 10 were given as arguments to the {@link
 436      * #toString(int, int)} method.
 437      *
 438      * @param   i   an integer to be converted.
 439      * @return  a string representation of the argument in base&nbsp;10.
 440      */
 441     @IntrinsicCandidate
 442     public static String toString(int i) {
 443         int size = DecimalDigits.stringSize(i);
 444         if (COMPACT_STRINGS) {
 445             byte[] buf = new byte[size];
 446             DecimalDigits.uncheckedGetCharsLatin1(i, size, buf);
 447             return new String(buf, LATIN1);
 448         } else {
 449             byte[] buf = new byte[size * 2];
 450             DecimalDigits.uncheckedGetCharsUTF16(i, size, buf);
 451             return new String(buf, UTF16);
 452         }
 453     }
 454 
 455     /**
 456      * Returns a string representation of the argument as an unsigned
 457      * decimal value.
 458      *
 459      * The argument is converted to unsigned decimal representation
 460      * and returned as a string exactly as if the argument and radix
 461      * 10 were given as arguments to the {@link #toUnsignedString(int,
 462      * int)} method.
 463      *
 464      * @param   i  an integer to be converted to an unsigned string.
 465      * @return  an unsigned string representation of the argument.
 466      * @see     #toUnsignedString(int, int)
 467      * @since 1.8
 468      */
 469     public static String toUnsignedString(int i) {
 470         return Long.toString(toUnsignedLong(i));
 471     }
 472 
 473     /**
 474      * Parses the string argument as a signed integer in the radix
 475      * specified by the second argument. The characters in the string
 476      * must all be digits of the specified radix (as determined by
 477      * whether {@link java.lang.Character#digit(char, int)} returns a
 478      * nonnegative value), except that the first character may be an
 479      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 480      * indicate a negative value or an ASCII plus sign {@code '+'}
 481      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 482      * resulting integer value is returned.
 483      *
 484      * <p>An exception of type {@code NumberFormatException} is
 485      * thrown if any of the following situations occurs:
 486      * <ul>
 487      * <li>The first argument is {@code null} or is a string of
 488      * length zero.
 489      *
 490      * <li>The radix is either smaller than
 491      * {@link java.lang.Character#MIN_RADIX} or
 492      * larger than {@link java.lang.Character#MAX_RADIX}.
 493      *
 494      * <li>Any character of the string is not a digit of the specified
 495      * radix, except that the first character may be a minus sign
 496      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
 497      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 498      * string is longer than length 1.
 499      *
 500      * <li>The value represented by the string is not a value of type
 501      * {@code int}.
 502      * </ul>
 503      *
 504      * <p>Examples:
 505      * <blockquote><pre>
 506      * parseInt("0", 10) returns 0
 507      * parseInt("473", 10) returns 473
 508      * parseInt("+42", 10) returns 42
 509      * parseInt("-0", 10) returns 0
 510      * parseInt("-FF", 16) returns -255
 511      * parseInt("1100110", 2) returns 102
 512      * parseInt("2147483647", 10) returns 2147483647
 513      * parseInt("-2147483648", 10) returns -2147483648
 514      * parseInt("2147483648", 10) throws a NumberFormatException
 515      * parseInt("99", 8) throws a NumberFormatException
 516      * parseInt("Kona", 10) throws a NumberFormatException
 517      * parseInt("Kona", 27) returns 411787
 518      * </pre></blockquote>
 519      *
 520      * @param      s   the {@code String} containing the integer
 521      *                  representation to be parsed
 522      * @param      radix   the radix to be used while parsing {@code s}.
 523      * @return     the integer represented by the string argument in the
 524      *             specified radix.
 525      * @throws     NumberFormatException if the {@code String}
 526      *             does not contain a parsable {@code int}.
 527      */
 528     public static int parseInt(String s, int radix)
 529                 throws NumberFormatException {
 530         /*
 531          * WARNING: This method may be invoked early during VM initialization
 532          * before IntegerCache is initialized. Care must be taken to not use
 533          * the valueOf method.
 534          */
 535 
 536         if (s == null) {
 537             throw new NumberFormatException("Cannot parse null string");
 538         }
 539 
 540         if (radix < Character.MIN_RADIX) {
 541             throw new NumberFormatException(String.format(
 542                 "radix %s less than Character.MIN_RADIX", radix));
 543         }
 544 
 545         if (radix > Character.MAX_RADIX) {
 546             throw new NumberFormatException(String.format(
 547                 "radix %s greater than Character.MAX_RADIX", radix));
 548         }
 549 
 550         int len = s.length();
 551         if (len == 0) {
 552             throw NumberFormatException.forInputString("", radix);
 553         }
 554         int digit = ~0xFF;
 555         int i = 0;
 556         char firstChar = s.charAt(i++);
 557         if (firstChar != '-' && firstChar != '+') {
 558             digit = digit(firstChar, radix);
 559         }
 560         if (digit >= 0 || digit == ~0xFF && len > 1) {
 561             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 562             int multmin = limit / radix;
 563             int result = -(digit & 0xFF);
 564             boolean inRange = true;
 565             /* Accumulating negatively avoids surprises near MAX_VALUE */
 566             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 567                     && (inRange = result > multmin
 568                         || result == multmin && digit <= radix * multmin - limit)) {
 569                 result = radix * result - digit;
 570             }
 571             if (inRange && i == len && digit >= 0) {
 572                 return firstChar != '-' ? -result : result;
 573             }
 574         }
 575         throw NumberFormatException.forInputString(s, radix);
 576     }
 577 
 578     /**
 579      * Parses the {@link CharSequence} argument as a signed {@code int} in the
 580      * specified {@code radix}, beginning at the specified {@code beginIndex}
 581      * and extending to {@code endIndex - 1}.
 582      *
 583      * <p>The method does not take steps to guard against the
 584      * {@code CharSequence} being mutated while parsing.
 585      *
 586      * @param      s   the {@code CharSequence} containing the {@code int}
 587      *                  representation to be parsed
 588      * @param      beginIndex   the beginning index, inclusive.
 589      * @param      endIndex     the ending index, exclusive.
 590      * @param      radix   the radix to be used while parsing {@code s}.
 591      * @return     the signed {@code int} represented by the subsequence in
 592      *             the specified radix.
 593      * @throws     NullPointerException  if {@code s} is null.
 594      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 595      *             negative, or if {@code beginIndex} is greater than
 596      *             {@code endIndex} or if {@code endIndex} is greater than
 597      *             {@code s.length()}.
 598      * @throws     NumberFormatException  if the {@code CharSequence} does not
 599      *             contain a parsable {@code int} in the specified
 600      *             {@code radix}, or if {@code radix} is either smaller than
 601      *             {@link java.lang.Character#MIN_RADIX} or larger than
 602      *             {@link java.lang.Character#MAX_RADIX}.
 603      * @since  9
 604      */
 605     public static int parseInt(CharSequence s, int beginIndex, int endIndex, int radix)
 606                 throws NumberFormatException {
 607         Objects.requireNonNull(s);
 608         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 609 
 610         if (radix < Character.MIN_RADIX) {
 611             throw new NumberFormatException(String.format(
 612                 "radix %s less than Character.MIN_RADIX", radix));
 613         }
 614 
 615         if (radix > Character.MAX_RADIX) {
 616             throw new NumberFormatException(String.format(
 617                 "radix %s greater than Character.MAX_RADIX", radix));
 618         }
 619 
 620         /*
 621          * While s can be concurrently modified, it is ensured that each
 622          * of its characters is read at most once, from lower to higher indices.
 623          * This is obtained by reading them using the pattern s.charAt(i++),
 624          * and by not updating i anywhere else.
 625          */
 626         if (beginIndex == endIndex) {
 627             throw NumberFormatException.forInputString("", radix);
 628         }
 629         int digit = ~0xFF;
 630         int i = beginIndex;
 631         char firstChar = s.charAt(i++);
 632         if (firstChar != '-' && firstChar != '+') {
 633             digit = digit(firstChar, radix);
 634         }
 635         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 636             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 637             int multmin = limit / radix;
 638             int result = -(digit & 0xFF);
 639             boolean inRange = true;
 640             /* Accumulating negatively avoids surprises near MAX_VALUE */
 641             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 642                     && (inRange = result > multmin
 643                         || result == multmin && digit <= radix * multmin - limit)) {
 644                 result = radix * result - digit;
 645             }
 646             if (inRange && i == endIndex && digit >= 0) {
 647                 return firstChar != '-' ? -result : result;
 648             }
 649         }
 650         throw NumberFormatException.forCharSequence(s, beginIndex,
 651             endIndex, i - (digit < -1 ? 0 : 1));
 652     }
 653 
 654     /**
 655      * Parses the string argument as a signed decimal integer. The
 656      * characters in the string must all be decimal digits, except
 657      * that the first character may be an ASCII minus sign {@code '-'}
 658      * ({@code '\u005Cu002D'}) to indicate a negative value or an
 659      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 660      * indicate a positive value. The resulting integer value is
 661      * returned, exactly as if the argument and the radix 10 were
 662      * given as arguments to the {@link #parseInt(java.lang.String,
 663      * int)} method.
 664      *
 665      * @param s    a {@code String} containing the {@code int}
 666      *             representation to be parsed
 667      * @return     the integer value represented by the argument in decimal.
 668      * @throws     NumberFormatException  if the string does not contain a
 669      *               parsable integer.
 670      */
 671     public static int parseInt(String s) throws NumberFormatException {
 672         return parseInt(s, 10);
 673     }
 674 
 675     /**
 676      * Parses the string argument as an unsigned integer in the radix
 677      * specified by the second argument.  An unsigned integer maps the
 678      * values usually associated with negative numbers to positive
 679      * numbers larger than {@code MAX_VALUE}.
 680      *
 681      * The characters in the string must all be digits of the
 682      * specified radix (as determined by whether {@link
 683      * java.lang.Character#digit(char, int)} returns a nonnegative
 684      * value), except that the first character may be an ASCII plus
 685      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 686      * integer value is returned.
 687      *
 688      * <p>An exception of type {@code NumberFormatException} is
 689      * thrown if any of the following situations occurs:
 690      * <ul>
 691      * <li>The first argument is {@code null} or is a string of
 692      * length zero.
 693      *
 694      * <li>The radix is either smaller than
 695      * {@link java.lang.Character#MIN_RADIX} or
 696      * larger than {@link java.lang.Character#MAX_RADIX}.
 697      *
 698      * <li>Any character of the string is not a digit of the specified
 699      * radix, except that the first character may be a plus sign
 700      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 701      * string is longer than length 1.
 702      *
 703      * <li>The value represented by the string is larger than the
 704      * largest unsigned {@code int}, 2<sup>32</sup>-1.
 705      *
 706      * </ul>
 707      *
 708      *
 709      * @param      s   the {@code String} containing the unsigned integer
 710      *                  representation to be parsed
 711      * @param      radix   the radix to be used while parsing {@code s}.
 712      * @return     the integer represented by the string argument in the
 713      *             specified radix.
 714      * @throws     NumberFormatException if the {@code String}
 715      *             does not contain a parsable {@code int}.
 716      * @since 1.8
 717      */
 718     public static int parseUnsignedInt(String s, int radix)
 719                 throws NumberFormatException {
 720         if (s == null)  {
 721             throw new NumberFormatException("Cannot parse null string");
 722         }
 723 
 724         if (radix < Character.MIN_RADIX) {
 725             throw new NumberFormatException(String.format(
 726                 "radix %s less than Character.MIN_RADIX", radix));
 727         }
 728 
 729         if (radix > Character.MAX_RADIX) {
 730             throw new NumberFormatException(String.format(
 731                 "radix %s greater than Character.MAX_RADIX", radix));
 732         }
 733 
 734         int len = s.length();
 735         if (len == 0) {
 736             throw NumberFormatException.forInputString(s, radix);
 737         }
 738         int i = 0;
 739         char firstChar = s.charAt(i++);
 740         if (firstChar == '-') {
 741             throw new NumberFormatException(String.format(
 742                 "Illegal leading minus sign on unsigned string %s.", s));
 743         }
 744         int digit = ~0xFF;
 745         if (firstChar != '+') {
 746             digit = digit(firstChar, radix);
 747         }
 748         if (digit >= 0 || digit == ~0xFF && len > 1) {
 749             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 750             int result = digit & 0xFF;
 751             boolean inRange = true;
 752             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 753                     && (inRange = compareUnsigned(result, multmax) < 0
 754                         || result == multmax && digit < -radix * multmax)) {
 755                 result = radix * result + digit;
 756             }
 757             if (inRange && i == len && digit >= 0) {
 758                 return result;
 759             }
 760         }
 761         if (digit < 0) {
 762             throw NumberFormatException.forInputString(s, radix);
 763         }
 764         throw new NumberFormatException(String.format(
 765             "String value %s exceeds range of unsigned int.", s));
 766     }
 767 
 768     /**
 769      * Parses the {@link CharSequence} argument as an unsigned {@code int} in
 770      * the specified {@code radix}, beginning at the specified
 771      * {@code beginIndex} and extending to {@code endIndex - 1}.
 772      *
 773      * <p>The method does not take steps to guard against the
 774      * {@code CharSequence} being mutated while parsing.
 775      *
 776      * @param      s   the {@code CharSequence} containing the unsigned
 777      *                 {@code int} representation to be parsed
 778      * @param      beginIndex   the beginning index, inclusive.
 779      * @param      endIndex     the ending index, exclusive.
 780      * @param      radix   the radix to be used while parsing {@code s}.
 781      * @return     the unsigned {@code int} represented by the subsequence in
 782      *             the specified radix.
 783      * @throws     NullPointerException  if {@code s} is null.
 784      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 785      *             negative, or if {@code beginIndex} is greater than
 786      *             {@code endIndex} or if {@code endIndex} is greater than
 787      *             {@code s.length()}.
 788      * @throws     NumberFormatException  if the {@code CharSequence} does not
 789      *             contain a parsable unsigned {@code int} in the specified
 790      *             {@code radix}, or if {@code radix} is either smaller than
 791      *             {@link java.lang.Character#MIN_RADIX} or larger than
 792      *             {@link java.lang.Character#MAX_RADIX}.
 793      * @since  9
 794      */
 795     public static int parseUnsignedInt(CharSequence s, int beginIndex, int endIndex, int radix)
 796                 throws NumberFormatException {
 797         Objects.requireNonNull(s);
 798         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 799 
 800         if (radix < Character.MIN_RADIX) {
 801             throw new NumberFormatException(String.format(
 802                 "radix %s less than Character.MIN_RADIX", radix));
 803         }
 804 
 805         if (radix > Character.MAX_RADIX) {
 806             throw new NumberFormatException(String.format(
 807                 "radix %s greater than Character.MAX_RADIX", radix));
 808         }
 809 
 810         /*
 811          * While s can be concurrently modified, it is ensured that each
 812          * of its characters is read at most once, from lower to higher indices.
 813          * This is obtained by reading them using the pattern s.charAt(i++),
 814          * and by not updating i anywhere else.
 815          */
 816         if (beginIndex == endIndex) {
 817             throw NumberFormatException.forInputString("", radix);
 818         }
 819         int i = beginIndex;
 820         char firstChar = s.charAt(i++);
 821         if (firstChar == '-') {
 822             throw new NumberFormatException(
 823                 "Illegal leading minus sign on unsigned string " + s + ".");
 824         }
 825         int digit = ~0xFF;
 826         if (firstChar != '+') {
 827             digit = digit(firstChar, radix);
 828         }
 829         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 830             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 831             int result = digit & 0xFF;
 832             boolean inRange = true;
 833             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 834                     && (inRange = compareUnsigned(result, multmax) < 0
 835                         || result == multmax && digit < -radix * multmax)) {
 836                 result = radix * result + digit;
 837             }
 838             if (inRange && i == endIndex && digit >= 0) {
 839                 return result;
 840             }
 841         }
 842         if (digit < 0) {
 843             throw NumberFormatException.forCharSequence(s, beginIndex,
 844                 endIndex, i - (digit < -1 ? 0 : 1));
 845         }
 846         throw new NumberFormatException(String.format(
 847             "String value %s exceeds range of unsigned int.", s));
 848     }
 849 
 850     /**
 851      * Parses the string argument as an unsigned decimal integer. The
 852      * characters in the string must all be decimal digits, except
 853      * that the first character may be an ASCII plus sign {@code
 854      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 855      * is returned, exactly as if the argument and the radix 10 were
 856      * given as arguments to the {@link
 857      * #parseUnsignedInt(java.lang.String, int)} method.
 858      *
 859      * @param s   a {@code String} containing the unsigned {@code int}
 860      *            representation to be parsed
 861      * @return    the unsigned integer value represented by the argument in decimal.
 862      * @throws    NumberFormatException  if the string does not contain a
 863      *            parsable unsigned integer.
 864      * @since 1.8
 865      */
 866     public static int parseUnsignedInt(String s) throws NumberFormatException {
 867         return parseUnsignedInt(s, 10);
 868     }
 869 
 870     /**
 871      * Returns an {@code Integer} object holding the value
 872      * extracted from the specified {@code String} when parsed
 873      * with the radix given by the second argument. The first argument
 874      * is interpreted as representing a signed integer in the radix
 875      * specified by the second argument, exactly as if the arguments
 876      * were given to the {@link #parseInt(java.lang.String, int)}
 877      * method. The result is an {@code Integer} object that
 878      * represents the integer value specified by the string.
 879      *
 880      * <p>In other words, this method returns an {@code Integer}
 881      * object equal to the value of:
 882      *
 883      * <blockquote>
 884      *  {@code Integer.valueOf(Integer.parseInt(s, radix))}
 885      * </blockquote>
 886      *
 887      * @param      s   the string to be parsed.
 888      * @param      radix the radix to be used in interpreting {@code s}
 889      * @return     an {@code Integer} object holding the value
 890      *             represented by the string argument in the specified
 891      *             radix.
 892      * @throws    NumberFormatException if the {@code String}
 893      *            does not contain a parsable {@code int}.
 894      */
 895     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 896         return Integer.valueOf(parseInt(s,radix));
 897     }
 898 
 899     /**
 900      * Returns an {@code Integer} object holding the
 901      * value of the specified {@code String}. The argument is
 902      * interpreted as representing a signed decimal integer, exactly
 903      * as if the argument were given to the {@link
 904      * #parseInt(java.lang.String)} method. The result is an
 905      * {@code Integer} object that represents the integer value
 906      * specified by the string.
 907      *
 908      * <p>In other words, this method returns an {@code Integer}
 909      * object equal to the value of:
 910      *
 911      * <blockquote>
 912      *  {@code Integer.valueOf(Integer.parseInt(s))}
 913      * </blockquote>
 914      *
 915      * @param      s   the string to be parsed.
 916      * @return     an {@code Integer} object holding the value
 917      *             represented by the string argument.
 918      * @throws     NumberFormatException  if the string cannot be parsed
 919      *             as an integer.
 920      */
 921     public static Integer valueOf(String s) throws NumberFormatException {
 922         return Integer.valueOf(parseInt(s, 10));
 923     }
 924 
 925     /**
 926      * Cache to support the object identity semantics of autoboxing for values between
 927      * -128 and 127 (inclusive) as required by JLS.
 928      *
 929      * The cache is initialized on first usage.  The size of the cache
 930      * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
 931      * During VM initialization, java.lang.Integer.IntegerCache.high property
 932      * may be set and saved in the private system properties in the
 933      * jdk.internal.misc.VM class.
 934      *
 935      * WARNING: The cache is archived with CDS and reloaded from the shared
 936      * archive at runtime. The archived cache (Integer[]) and Integer objects
 937      * reside in the closed archive heap regions. Care should be taken when
 938      * changing the implementation and the cache array should not be assigned
 939      * with new Integer object(s) after initialization.
 940      */
 941 
 942     private static final class IntegerCache {
 943         static final int low = -128;
 944         static final int high;
 945 
 946         @Stable
 947         static final Integer[] cache;
 948         static Integer[] archivedCache;
 949 
 950         static {
 951             // high value may be configured by property
 952             int h = 127;
 953             String integerCacheHighPropValue =
 954                 VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 955             if (integerCacheHighPropValue != null) {
 956                 try {
 957                     h = Math.max(parseInt(integerCacheHighPropValue), 127);
 958                     // Maximum array size is Integer.MAX_VALUE
 959                     h = Math.min(h, Integer.MAX_VALUE - (-low) -1);
 960                 } catch( NumberFormatException nfe) {
 961                     // If the property cannot be parsed into an int, ignore it.
 962                 }
 963             }
 964             high = h;
 965 
 966             // Load IntegerCache.archivedCache from archive, if possible
 967             CDS.initializeFromArchive(IntegerCache.class);
 968             int size = (high - low) + 1;
 969 
 970             // Use the archived cache if it exists and is large enough
 971             if (archivedCache == null || size > archivedCache.length) {
 972                 Integer[] c = new Integer[size];
 973                 int j = low;
 974                 // If archive has Integer cache, we must use all instances from it.
 975                 // Otherwise, the identity checks between archived Integers and
 976                 // runtime-cached Integers would fail.
 977                 int archivedSize = (archivedCache == null) ? 0 : archivedCache.length;
 978                 for (int i = 0; i < archivedSize; i++) {
 979                     c[i] = archivedCache[i];
 980                     assert j == archivedCache[i];
 981                     j++;
 982                 }
 983                 // Fill the rest of the cache.
 984                 for (int i = archivedSize; i < size; i++) {
 985                     c[i] = new Integer(j++);
 986                 }
 987                 archivedCache = c;
 988             }
 989             cache = archivedCache;
 990             // range [-128, 127] must be interned (JLS7 5.1.7)
 991             assert IntegerCache.high >= 127;
 992         }
 993 
 994         private IntegerCache() {}
 995     }
 996 
 997     /**
 998      * Returns an {@code Integer} instance representing the specified
 999      * {@code int} value.  If a new {@code Integer} instance is not
1000      * required, this method should generally be used in preference to
1001      * the constructor {@link #Integer(int)}, as this method is likely
1002      * to yield significantly better space and time performance by
1003      * caching frequently requested values.
1004      *
1005      * This method will always cache values in the range -128 to 127,
1006      * inclusive, and may cache other values outside of this range.
1007      *
1008      * @param  i an {@code int} value.
1009      * @return an {@code Integer} instance representing {@code i}.
1010      * @since  1.5
1011      */
1012     @IntrinsicCandidate
1013     @DeserializeConstructor
1014     public static Integer valueOf(int i) {
1015         if (i >= IntegerCache.low && i <= IntegerCache.high)
1016             return IntegerCache.cache[i + (-IntegerCache.low)];
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 }