1 /*
   2  * Copyright (c) 1994, 2023, 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.vm.annotation.ForceInline;
  31 import jdk.internal.vm.annotation.IntrinsicCandidate;
  32 import jdk.internal.vm.annotation.Stable;
  33 
  34 import java.lang.annotation.Native;
  35 import java.lang.constant.Constable;
  36 import java.lang.constant.ConstantDesc;
  37 import java.lang.invoke.MethodHandles;
  38 import java.util.Objects;
  39 import java.util.Optional;
  40 
  41 import static java.lang.Character.digit;
  42 import static java.lang.String.COMPACT_STRINGS;
  43 import static java.lang.String.LATIN1;
  44 import static java.lang.String.UTF16;
  45 
  46 /**
  47  * The {@code Integer} class wraps a value of the primitive type
  48  * {@code int} in an object. An object of type {@code Integer}
  49  * contains a single field whose type is {@code int}.
  50  *
  51  * <p>In addition, this class provides several methods for converting
  52  * an {@code int} to a {@code String} and a {@code String} to an
  53  * {@code int}, as well as other constants and methods useful when
  54  * dealing with an {@code int}.
  55  *
  56  * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
  57  * class; programmers should treat instances that are
  58  * {@linkplain #equals(Object) equal} as interchangeable and should not
  59  * use instances for synchronization, or unpredictable behavior may
  60  * occur. For example, in a future release, synchronization may fail.
  61  *
  62  * <p>Implementation note: The implementations of the "bit twiddling"
  63  * methods (such as {@link #highestOneBit(int) highestOneBit} and
  64  * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
  65  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  66  * Delight</i>, (Addison Wesley, 2002).
  67  *
  68  * @author  Lee Boynton
  69  * @author  Arthur van Hoff
  70  * @author  Josh Bloch
  71  * @author  Joseph D. Darcy
  72  * @since 1.0
  73  */
  74 @jdk.internal.ValueBased
  75 public final class Integer extends Number
  76         implements Comparable<Integer>, Constable, ConstantDesc {
  77     /**
  78      * A constant holding the minimum value an {@code int} can
  79      * have, -2<sup>31</sup>.
  80      */
  81     @Native public static final int   MIN_VALUE = 0x80000000;
  82 
  83     /**
  84      * A constant holding the maximum value an {@code int} can
  85      * have, 2<sup>31</sup>-1.
  86      */
  87     @Native public static final int   MAX_VALUE = 0x7fffffff;
  88 
  89     /**
  90      * The {@code Class} instance representing the primitive type
  91      * {@code int}.
  92      *
  93      * @since   1.1
  94      */
  95     @SuppressWarnings("unchecked")
  96     public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
  97 
  98     /**
  99      * All possible chars for representing a number as a String
 100      */
 101     static final char[] digits = {
 102         '0' , '1' , '2' , '3' , '4' , '5' ,
 103         '6' , '7' , '8' , '9' , 'a' , 'b' ,
 104         'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
 105         'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
 106         'o' , 'p' , 'q' , 'r' , 's' , 't' ,
 107         'u' , 'v' , 'w' , 'x' , 'y' , 'z'
 108     };
 109 
 110     /**
 111      * Returns a string representation of the first argument in the
 112      * radix specified by the second argument.
 113      *
 114      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 115      * or larger than {@code Character.MAX_RADIX}, then the radix
 116      * {@code 10} is used instead.
 117      *
 118      * <p>If the first argument is negative, the first element of the
 119      * result is the ASCII minus character {@code '-'}
 120      * ({@code '\u005Cu002D'}). If the first argument is not
 121      * negative, no sign character appears in the result.
 122      *
 123      * <p>The remaining characters of the result represent the magnitude
 124      * of the first argument. If the magnitude is zero, it is
 125      * represented by a single zero character {@code '0'}
 126      * ({@code '\u005Cu0030'}); otherwise, the first character of
 127      * the representation of the magnitude will not be the zero
 128      * character.  The following ASCII characters are used as digits:
 129      *
 130      * <blockquote>
 131      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 132      * </blockquote>
 133      *
 134      * These are {@code '\u005Cu0030'} through
 135      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 136      * {@code '\u005Cu007A'}. If {@code radix} is
 137      * <var>N</var>, then the first <var>N</var> of these characters
 138      * are used as radix-<var>N</var> digits in the order shown. Thus,
 139      * the digits for hexadecimal (radix 16) are
 140      * {@code 0123456789abcdef}. If uppercase letters are
 141      * desired, the {@link java.lang.String#toUpperCase()} method may
 142      * be called on the result:
 143      *
 144      * <blockquote>
 145      *  {@code Integer.toString(n, 16).toUpperCase()}
 146      * </blockquote>
 147      *
 148      * @param   i       an integer to be converted to a string.
 149      * @param   radix   the radix to use in the string representation.
 150      * @return  a string representation of the argument in the specified radix.
 151      * @see     java.lang.Character#MAX_RADIX
 152      * @see     java.lang.Character#MIN_RADIX
 153      */
 154     public static String toString(int i, int radix) {
 155         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 156             radix = 10;
 157 
 158         /* Use the faster version */
 159         if (radix == 10) {
 160             return toString(i);
 161         }
 162 
 163         if (COMPACT_STRINGS) {
 164             byte[] buf = new byte[33];
 165             boolean negative = (i < 0);
 166             int charPos = 32;
 167 
 168             if (!negative) {
 169                 i = -i;
 170             }
 171 
 172             while (i <= -radix) {
 173                 buf[charPos--] = (byte)digits[-(i % radix)];
 174                 i = i / radix;
 175             }
 176             buf[charPos] = (byte)digits[-i];
 177 
 178             if (negative) {
 179                 buf[--charPos] = '-';
 180             }
 181 
 182             return StringLatin1.newString(buf, charPos, (33 - charPos));
 183         }
 184         return toStringUTF16(i, radix);
 185     }
 186 
 187     private static String toStringUTF16(int i, int radix) {
 188         byte[] buf = new byte[33 * 2];
 189         boolean negative = (i < 0);
 190         int charPos = 32;
 191         if (!negative) {
 192             i = -i;
 193         }
 194         while (i <= -radix) {
 195             StringUTF16.putChar(buf, charPos--, digits[-(i % radix)]);
 196             i = i / radix;
 197         }
 198         StringUTF16.putChar(buf, charPos, digits[-i]);
 199 
 200         if (negative) {
 201             StringUTF16.putChar(buf, --charPos, '-');
 202         }
 203         return StringUTF16.newString(buf, charPos, (33 - charPos));
 204     }
 205 
 206     /**
 207      * Returns a string representation of the first argument as an
 208      * unsigned integer value in the radix specified by the second
 209      * argument.
 210      *
 211      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 212      * or larger than {@code Character.MAX_RADIX}, then the radix
 213      * {@code 10} is used instead.
 214      *
 215      * <p>Note that since the first argument is treated as an unsigned
 216      * value, no leading sign character is printed.
 217      *
 218      * <p>If the magnitude is zero, it is represented by a single zero
 219      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 220      * the first character of the representation of the magnitude will
 221      * not be the zero character.
 222      *
 223      * <p>The behavior of radixes and the characters used as digits
 224      * are the same as {@link #toString(int, int) toString}.
 225      *
 226      * @param   i       an integer to be converted to an unsigned string.
 227      * @param   radix   the radix to use in the string representation.
 228      * @return  an unsigned string representation of the argument in the specified radix.
 229      * @see     #toString(int, int)
 230      * @since 1.8
 231      */
 232     public static String toUnsignedString(int i, int radix) {
 233         return Long.toUnsignedString(toUnsignedLong(i), radix);
 234     }
 235 
 236     /**
 237      * Returns a string representation of the integer argument as an
 238      * unsigned integer in base&nbsp;16.
 239      *
 240      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 241      * if the argument is negative; otherwise, it is equal to the
 242      * argument.  This value is converted to a string of ASCII digits
 243      * in hexadecimal (base&nbsp;16) with no extra leading
 244      * {@code 0}s.
 245      *
 246      * <p>The value of the argument can be recovered from the returned
 247      * string {@code s} by calling {@link
 248      * Integer#parseUnsignedInt(String, int)
 249      * Integer.parseUnsignedInt(s, 16)}.
 250      *
 251      * <p>If the unsigned magnitude is zero, it is represented by a
 252      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 253      * otherwise, the first character of the representation of the
 254      * unsigned magnitude will not be the zero character. The
 255      * following characters are used as hexadecimal digits:
 256      *
 257      * <blockquote>
 258      *  {@code 0123456789abcdef}
 259      * </blockquote>
 260      *
 261      * These are the characters {@code '\u005Cu0030'} through
 262      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 263      * {@code '\u005Cu0066'}. If uppercase letters are
 264      * desired, the {@link java.lang.String#toUpperCase()} method may
 265      * be called on the result:
 266      *
 267      * <blockquote>
 268      *  {@code Integer.toHexString(n).toUpperCase()}
 269      * </blockquote>
 270      *
 271      * @apiNote
 272      * The {@link java.util.HexFormat} class provides formatting and parsing
 273      * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
 274      * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
 275      * with leading zeros and for byte arrays includes for each byte
 276      * a delimiter, prefix, and suffix.
 277      *
 278      * @param   i   an integer to be converted to a string.
 279      * @return  the string representation of the unsigned integer value
 280      *          represented by the argument in hexadecimal (base&nbsp;16).
 281      * @see java.util.HexFormat
 282      * @see #parseUnsignedInt(String, int)
 283      * @see #toUnsignedString(int, int)
 284      * @since   1.0.2
 285      */
 286     public static String toHexString(int i) {
 287         return toUnsignedString0(i, 4);
 288     }
 289 
 290     /**
 291      * Returns a string representation of the integer argument as an
 292      * unsigned integer in base&nbsp;8.
 293      *
 294      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 295      * if the argument is negative; otherwise, it is equal to the
 296      * argument.  This value is converted to a string of ASCII digits
 297      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
 298      *
 299      * <p>The value of the argument can be recovered from the returned
 300      * string {@code s} by calling {@link
 301      * Integer#parseUnsignedInt(String, int)
 302      * Integer.parseUnsignedInt(s, 8)}.
 303      *
 304      * <p>If the unsigned magnitude is zero, it is represented by a
 305      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 306      * otherwise, the first character of the representation of the
 307      * unsigned magnitude will not be the zero character. The
 308      * following characters are used as octal digits:
 309      *
 310      * <blockquote>
 311      * {@code 01234567}
 312      * </blockquote>
 313      *
 314      * These are the characters {@code '\u005Cu0030'} through
 315      * {@code '\u005Cu0037'}.
 316      *
 317      * @param   i   an integer to be converted to a string.
 318      * @return  the string representation of the unsigned integer value
 319      *          represented by the argument in octal (base&nbsp;8).
 320      * @see #parseUnsignedInt(String, int)
 321      * @see #toUnsignedString(int, int)
 322      * @since   1.0.2
 323      */
 324     public static String toOctalString(int i) {
 325         return toUnsignedString0(i, 3);
 326     }
 327 
 328     /**
 329      * Returns a string representation of the integer argument as an
 330      * unsigned integer in base&nbsp;2.
 331      *
 332      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 333      * if the argument is negative; otherwise it is equal to the
 334      * argument.  This value is converted to a string of ASCII digits
 335      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
 336      *
 337      * <p>The value of the argument can be recovered from the returned
 338      * string {@code s} by calling {@link
 339      * Integer#parseUnsignedInt(String, int)
 340      * Integer.parseUnsignedInt(s, 2)}.
 341      *
 342      * <p>If the unsigned magnitude is zero, it is represented by a
 343      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 344      * otherwise, the first character of the representation of the
 345      * unsigned magnitude will not be the zero character. The
 346      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 347      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 348      *
 349      * @param   i   an integer to be converted to a string.
 350      * @return  the string representation of the unsigned integer value
 351      *          represented by the argument in binary (base&nbsp;2).
 352      * @see #parseUnsignedInt(String, int)
 353      * @see #toUnsignedString(int, int)
 354      * @since   1.0.2
 355      */
 356     public static String toBinaryString(int i) {
 357         return toUnsignedString0(i, 1);
 358     }
 359 
 360     /**
 361      * Convert the integer to an unsigned number.
 362      */
 363     private static String toUnsignedString0(int val, int shift) {
 364         // assert shift > 0 && shift <=5 : "Illegal shift value";
 365         int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
 366         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 367         if (COMPACT_STRINGS) {
 368             byte[] buf = new byte[chars];
 369             formatUnsignedInt(val, shift, buf, chars);
 370             return new String(buf, LATIN1);
 371         } else {
 372             byte[] buf = new byte[chars * 2];
 373             formatUnsignedIntUTF16(val, shift, buf, chars);
 374             return new String(buf, UTF16);
 375         }
 376     }
 377 
 378     /**
 379      * Format an {@code int} (treated as unsigned) into a byte buffer (LATIN1 version). If
 380      * {@code len} exceeds the formatted ASCII representation of {@code val},
 381      * {@code buf} will be padded with leading zeroes.
 382      *
 383      * @param val the unsigned int to format
 384      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 385      * @param buf the byte buffer to write to
 386      * @param len the number of characters to write
 387      */
 388     private static void formatUnsignedInt(int val, int shift, byte[] buf, int len) {
 389         int charPos = len;
 390         int radix = 1 << shift;
 391         int mask = radix - 1;
 392         do {
 393             buf[--charPos] = (byte)Integer.digits[val & mask];
 394             val >>>= shift;
 395         } while (charPos > 0);
 396     }
 397 
 398     /**
 399      * Format an {@code int} (treated as unsigned) into a byte buffer (UTF16 version). If
 400      * {@code len} exceeds the formatted ASCII representation of {@code val},
 401      * {@code buf} will be padded with leading zeroes.
 402      *
 403      * @param val the unsigned int to format
 404      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 405      * @param buf the byte buffer to write to
 406      * @param len the number of characters to write
 407      */
 408     private static void formatUnsignedIntUTF16(int val, int shift, byte[] buf, int len) {
 409         int charPos = len;
 410         int radix = 1 << shift;
 411         int mask = radix - 1;
 412         do {
 413             StringUTF16.putChar(buf, --charPos, Integer.digits[val & mask]);
 414             val >>>= shift;
 415         } while (charPos > 0);
 416     }
 417 
 418     /**
 419      * Returns a {@code String} object representing the
 420      * specified integer. The argument is converted to signed decimal
 421      * representation and returned as a string, exactly as if the
 422      * argument and radix 10 were given as arguments to the {@link
 423      * #toString(int, int)} method.
 424      *
 425      * @param   i   an integer to be converted.
 426      * @return  a string representation of the argument in base&nbsp;10.
 427      */
 428     @IntrinsicCandidate
 429     public static String toString(int i) {
 430         int size = stringSize(i);
 431         if (COMPACT_STRINGS) {
 432             byte[] buf = new byte[size];
 433             StringLatin1.getChars(i, size, buf);
 434             return new String(buf, LATIN1);
 435         } else {
 436             byte[] buf = new byte[size * 2];
 437             StringUTF16.getChars(i, size, buf);
 438             return new String(buf, UTF16);
 439         }
 440     }
 441 
 442     /**
 443      * Returns a string representation of the argument as an unsigned
 444      * decimal value.
 445      *
 446      * The argument is converted to unsigned decimal representation
 447      * and returned as a string exactly as if the argument and radix
 448      * 10 were given as arguments to the {@link #toUnsignedString(int,
 449      * int)} method.
 450      *
 451      * @param   i  an integer to be converted to an unsigned string.
 452      * @return  an unsigned string representation of the argument.
 453      * @see     #toUnsignedString(int, int)
 454      * @since 1.8
 455      */
 456     public static String toUnsignedString(int i) {
 457         return Long.toString(toUnsignedLong(i));
 458     }
 459 
 460     /**
 461      * Returns the string representation size for a given int value.
 462      *
 463      * @param x int value
 464      * @return string size
 465      *
 466      * @implNote There are other ways to compute this: e.g. binary search,
 467      * but values are biased heavily towards zero, and therefore linear search
 468      * wins. The iteration results are also routinely inlined in the generated
 469      * code after loop unrolling.
 470      */
 471     static int stringSize(int x) {
 472         int d = 1;
 473         if (x >= 0) {
 474             d = 0;
 475             x = -x;
 476         }
 477         int p = -10;
 478         for (int i = 1; i < 10; i++) {
 479             if (x > p)
 480                 return i + d;
 481             p = 10 * p;
 482         }
 483         return 10 + d;
 484     }
 485 
 486     /**
 487      * Parses the string argument as a signed integer in the radix
 488      * specified by the second argument. The characters in the string
 489      * must all be digits of the specified radix (as determined by
 490      * whether {@link java.lang.Character#digit(char, int)} returns a
 491      * nonnegative value), except that the first character may be an
 492      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 493      * indicate a negative value or an ASCII plus sign {@code '+'}
 494      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 495      * resulting integer value is returned.
 496      *
 497      * <p>An exception of type {@code NumberFormatException} is
 498      * thrown if any of the following situations occurs:
 499      * <ul>
 500      * <li>The first argument is {@code null} or is a string of
 501      * length zero.
 502      *
 503      * <li>The radix is either smaller than
 504      * {@link java.lang.Character#MIN_RADIX} or
 505      * larger than {@link java.lang.Character#MAX_RADIX}.
 506      *
 507      * <li>Any character of the string is not a digit of the specified
 508      * radix, except that the first character may be a minus sign
 509      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
 510      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 511      * string is longer than length 1.
 512      *
 513      * <li>The value represented by the string is not a value of type
 514      * {@code int}.
 515      * </ul>
 516      *
 517      * <p>Examples:
 518      * <blockquote><pre>
 519      * parseInt("0", 10) returns 0
 520      * parseInt("473", 10) returns 473
 521      * parseInt("+42", 10) returns 42
 522      * parseInt("-0", 10) returns 0
 523      * parseInt("-FF", 16) returns -255
 524      * parseInt("1100110", 2) returns 102
 525      * parseInt("2147483647", 10) returns 2147483647
 526      * parseInt("-2147483648", 10) returns -2147483648
 527      * parseInt("2147483648", 10) throws a NumberFormatException
 528      * parseInt("99", 8) throws a NumberFormatException
 529      * parseInt("Kona", 10) throws a NumberFormatException
 530      * parseInt("Kona", 27) returns 411787
 531      * </pre></blockquote>
 532      *
 533      * @param      s   the {@code String} containing the integer
 534      *                  representation to be parsed
 535      * @param      radix   the radix to be used while parsing {@code s}.
 536      * @return     the integer represented by the string argument in the
 537      *             specified radix.
 538      * @throws     NumberFormatException if the {@code String}
 539      *             does not contain a parsable {@code int}.
 540      */
 541     public static int parseInt(String s, int radix)
 542                 throws NumberFormatException {
 543         /*
 544          * WARNING: This method may be invoked early during VM initialization
 545          * before IntegerCache is initialized. Care must be taken to not use
 546          * the valueOf method.
 547          */
 548 
 549         if (s == null) {
 550             throw new NumberFormatException("Cannot parse null string");
 551         }
 552 
 553         if (radix < Character.MIN_RADIX) {
 554             throw new NumberFormatException(String.format(
 555                 "radix %s less than Character.MIN_RADIX", radix));
 556         }
 557 
 558         if (radix > Character.MAX_RADIX) {
 559             throw new NumberFormatException(String.format(
 560                 "radix %s greater than Character.MAX_RADIX", radix));
 561         }
 562 
 563         int len = s.length();
 564         if (len == 0) {
 565             throw NumberFormatException.forInputString("", radix);
 566         }
 567         int digit = ~0xFF;
 568         int i = 0;
 569         char firstChar = s.charAt(i++);
 570         if (firstChar != '-' && firstChar != '+') {
 571             digit = digit(firstChar, radix);
 572         }
 573         if (digit >= 0 || digit == ~0xFF && len > 1) {
 574             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 575             int multmin = limit / radix;
 576             int result = -(digit & 0xFF);
 577             boolean inRange = true;
 578             /* Accumulating negatively avoids surprises near MAX_VALUE */
 579             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 580                     && (inRange = result > multmin
 581                         || result == multmin && digit <= radix * multmin - limit)) {
 582                 result = radix * result - digit;
 583             }
 584             if (inRange && i == len && digit >= 0) {
 585                 return firstChar != '-' ? -result : result;
 586             }
 587         }
 588         throw NumberFormatException.forInputString(s, radix);
 589     }
 590 
 591     /**
 592      * Parses the {@link CharSequence} argument as a signed {@code int} in the
 593      * specified {@code radix}, beginning at the specified {@code beginIndex}
 594      * and extending to {@code endIndex - 1}.
 595      *
 596      * <p>The method does not take steps to guard against the
 597      * {@code CharSequence} being mutated while parsing.
 598      *
 599      * @param      s   the {@code CharSequence} containing the {@code int}
 600      *                  representation to be parsed
 601      * @param      beginIndex   the beginning index, inclusive.
 602      * @param      endIndex     the ending index, exclusive.
 603      * @param      radix   the radix to be used while parsing {@code s}.
 604      * @return     the signed {@code int} represented by the subsequence in
 605      *             the specified radix.
 606      * @throws     NullPointerException  if {@code s} is null.
 607      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 608      *             negative, or if {@code beginIndex} is greater than
 609      *             {@code endIndex} or if {@code endIndex} is greater than
 610      *             {@code s.length()}.
 611      * @throws     NumberFormatException  if the {@code CharSequence} does not
 612      *             contain a parsable {@code int} in the specified
 613      *             {@code radix}, or if {@code radix} is either smaller than
 614      *             {@link java.lang.Character#MIN_RADIX} or larger than
 615      *             {@link java.lang.Character#MAX_RADIX}.
 616      * @since  9
 617      */
 618     public static int parseInt(CharSequence s, int beginIndex, int endIndex, int radix)
 619                 throws NumberFormatException {
 620         Objects.requireNonNull(s);
 621         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 622 
 623         if (radix < Character.MIN_RADIX) {
 624             throw new NumberFormatException(String.format(
 625                 "radix %s less than Character.MIN_RADIX", radix));
 626         }
 627 
 628         if (radix > Character.MAX_RADIX) {
 629             throw new NumberFormatException(String.format(
 630                 "radix %s greater than Character.MAX_RADIX", radix));
 631         }
 632 
 633         /*
 634          * While s can be concurrently modified, it is ensured that each
 635          * of its characters is read at most once, from lower to higher indices.
 636          * This is obtained by reading them using the pattern s.charAt(i++),
 637          * and by not updating i anywhere else.
 638          */
 639         if (beginIndex == endIndex) {
 640             throw NumberFormatException.forInputString("", radix);
 641         }
 642         int digit = ~0xFF;
 643         int i = beginIndex;
 644         char firstChar = s.charAt(i++);
 645         if (firstChar != '-' && firstChar != '+') {
 646             digit = digit(firstChar, radix);
 647         }
 648         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 649             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 650             int multmin = limit / radix;
 651             int result = -(digit & 0xFF);
 652             boolean inRange = true;
 653             /* Accumulating negatively avoids surprises near MAX_VALUE */
 654             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 655                     && (inRange = result > multmin
 656                         || result == multmin && digit <= radix * multmin - limit)) {
 657                 result = radix * result - digit;
 658             }
 659             if (inRange && i == endIndex && digit >= 0) {
 660                 return firstChar != '-' ? -result : result;
 661             }
 662         }
 663         throw NumberFormatException.forCharSequence(s, beginIndex,
 664             endIndex, i - (digit < -1 ? 0 : 1));
 665     }
 666 
 667     /**
 668      * Parses the string argument as a signed decimal integer. The
 669      * characters in the string must all be decimal digits, except
 670      * that the first character may be an ASCII minus sign {@code '-'}
 671      * ({@code '\u005Cu002D'}) to indicate a negative value or an
 672      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 673      * indicate a positive value. The resulting integer value is
 674      * returned, exactly as if the argument and the radix 10 were
 675      * given as arguments to the {@link #parseInt(java.lang.String,
 676      * int)} method.
 677      *
 678      * @param s    a {@code String} containing the {@code int}
 679      *             representation to be parsed
 680      * @return     the integer value represented by the argument in decimal.
 681      * @throws     NumberFormatException  if the string does not contain a
 682      *               parsable integer.
 683      */
 684     public static int parseInt(String s) throws NumberFormatException {
 685         return parseInt(s, 10);
 686     }
 687 
 688     /**
 689      * Parses the string argument as an unsigned integer in the radix
 690      * specified by the second argument.  An unsigned integer maps the
 691      * values usually associated with negative numbers to positive
 692      * numbers larger than {@code MAX_VALUE}.
 693      *
 694      * The characters in the string must all be digits of the
 695      * specified radix (as determined by whether {@link
 696      * java.lang.Character#digit(char, int)} returns a nonnegative
 697      * value), except that the first character may be an ASCII plus
 698      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 699      * integer value is returned.
 700      *
 701      * <p>An exception of type {@code NumberFormatException} is
 702      * thrown if any of the following situations occurs:
 703      * <ul>
 704      * <li>The first argument is {@code null} or is a string of
 705      * length zero.
 706      *
 707      * <li>The radix is either smaller than
 708      * {@link java.lang.Character#MIN_RADIX} or
 709      * larger than {@link java.lang.Character#MAX_RADIX}.
 710      *
 711      * <li>Any character of the string is not a digit of the specified
 712      * radix, except that the first character may be a plus sign
 713      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 714      * string is longer than length 1.
 715      *
 716      * <li>The value represented by the string is larger than the
 717      * largest unsigned {@code int}, 2<sup>32</sup>-1.
 718      *
 719      * </ul>
 720      *
 721      *
 722      * @param      s   the {@code String} containing the unsigned integer
 723      *                  representation to be parsed
 724      * @param      radix   the radix to be used while parsing {@code s}.
 725      * @return     the integer represented by the string argument in the
 726      *             specified radix.
 727      * @throws     NumberFormatException if the {@code String}
 728      *             does not contain a parsable {@code int}.
 729      * @since 1.8
 730      */
 731     public static int parseUnsignedInt(String s, int radix)
 732                 throws NumberFormatException {
 733         if (s == null)  {
 734             throw new NumberFormatException("Cannot parse null string");
 735         }
 736 
 737         if (radix < Character.MIN_RADIX) {
 738             throw new NumberFormatException(String.format(
 739                 "radix %s less than Character.MIN_RADIX", radix));
 740         }
 741 
 742         if (radix > Character.MAX_RADIX) {
 743             throw new NumberFormatException(String.format(
 744                 "radix %s greater than Character.MAX_RADIX", radix));
 745         }
 746 
 747         int len = s.length();
 748         if (len == 0) {
 749             throw NumberFormatException.forInputString(s, radix);
 750         }
 751         int i = 0;
 752         char firstChar = s.charAt(i++);
 753         if (firstChar == '-') {
 754             throw new NumberFormatException(String.format(
 755                 "Illegal leading minus sign on unsigned string %s.", s));
 756         }
 757         int digit = ~0xFF;
 758         if (firstChar != '+') {
 759             digit = digit(firstChar, radix);
 760         }
 761         if (digit >= 0 || digit == ~0xFF && len > 1) {
 762             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 763             int result = digit & 0xFF;
 764             boolean inRange = true;
 765             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 766                     && (inRange = compareUnsigned(result, multmax) < 0
 767                         || result == multmax && digit < -radix * multmax)) {
 768                 result = radix * result + digit;
 769             }
 770             if (inRange && i == len && digit >= 0) {
 771                 return result;
 772             }
 773         }
 774         if (digit < 0) {
 775             throw NumberFormatException.forInputString(s, radix);
 776         }
 777         throw new NumberFormatException(String.format(
 778             "String value %s exceeds range of unsigned int.", s));
 779     }
 780 
 781     /**
 782      * Parses the {@link CharSequence} argument as an unsigned {@code int} in
 783      * the specified {@code radix}, beginning at the specified
 784      * {@code beginIndex} and extending to {@code endIndex - 1}.
 785      *
 786      * <p>The method does not take steps to guard against the
 787      * {@code CharSequence} being mutated while parsing.
 788      *
 789      * @param      s   the {@code CharSequence} containing the unsigned
 790      *                 {@code int} representation to be parsed
 791      * @param      beginIndex   the beginning index, inclusive.
 792      * @param      endIndex     the ending index, exclusive.
 793      * @param      radix   the radix to be used while parsing {@code s}.
 794      * @return     the unsigned {@code int} represented by the subsequence in
 795      *             the specified radix.
 796      * @throws     NullPointerException  if {@code s} is null.
 797      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 798      *             negative, or if {@code beginIndex} is greater than
 799      *             {@code endIndex} or if {@code endIndex} is greater than
 800      *             {@code s.length()}.
 801      * @throws     NumberFormatException  if the {@code CharSequence} does not
 802      *             contain a parsable unsigned {@code int} in the specified
 803      *             {@code radix}, or if {@code radix} is either smaller than
 804      *             {@link java.lang.Character#MIN_RADIX} or larger than
 805      *             {@link java.lang.Character#MAX_RADIX}.
 806      * @since  9
 807      */
 808     public static int parseUnsignedInt(CharSequence s, int beginIndex, int endIndex, int radix)
 809                 throws NumberFormatException {
 810         Objects.requireNonNull(s);
 811         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 812 
 813         if (radix < Character.MIN_RADIX) {
 814             throw new NumberFormatException(String.format(
 815                 "radix %s less than Character.MIN_RADIX", radix));
 816         }
 817 
 818         if (radix > Character.MAX_RADIX) {
 819             throw new NumberFormatException(String.format(
 820                 "radix %s greater than Character.MAX_RADIX", radix));
 821         }
 822 
 823         /*
 824          * While s can be concurrently modified, it is ensured that each
 825          * of its characters is read at most once, from lower to higher indices.
 826          * This is obtained by reading them using the pattern s.charAt(i++),
 827          * and by not updating i anywhere else.
 828          */
 829         if (beginIndex == endIndex) {
 830             throw NumberFormatException.forInputString("", radix);
 831         }
 832         int i = beginIndex;
 833         char firstChar = s.charAt(i++);
 834         if (firstChar == '-') {
 835             throw new NumberFormatException(
 836                 "Illegal leading minus sign on unsigned string " + s + ".");
 837         }
 838         int digit = ~0xFF;
 839         if (firstChar != '+') {
 840             digit = digit(firstChar, radix);
 841         }
 842         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 843             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 844             int result = digit & 0xFF;
 845             boolean inRange = true;
 846             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 847                     && (inRange = compareUnsigned(result, multmax) < 0
 848                         || result == multmax && digit < -radix * multmax)) {
 849                 result = radix * result + digit;
 850             }
 851             if (inRange && i == endIndex && digit >= 0) {
 852                 return result;
 853             }
 854         }
 855         if (digit < 0) {
 856             throw NumberFormatException.forCharSequence(s, beginIndex,
 857                 endIndex, i - (digit < -1 ? 0 : 1));
 858         }
 859         throw new NumberFormatException(String.format(
 860             "String value %s exceeds range of unsigned int.", s));
 861     }
 862 
 863     /**
 864      * Parses the string argument as an unsigned decimal integer. The
 865      * characters in the string must all be decimal digits, except
 866      * that the first character may be an ASCII plus sign {@code
 867      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 868      * is returned, exactly as if the argument and the radix 10 were
 869      * given as arguments to the {@link
 870      * #parseUnsignedInt(java.lang.String, int)} method.
 871      *
 872      * @param s   a {@code String} containing the unsigned {@code int}
 873      *            representation to be parsed
 874      * @return    the unsigned integer value represented by the argument in decimal.
 875      * @throws    NumberFormatException  if the string does not contain a
 876      *            parsable unsigned integer.
 877      * @since 1.8
 878      */
 879     public static int parseUnsignedInt(String s) throws NumberFormatException {
 880         return parseUnsignedInt(s, 10);
 881     }
 882 
 883     /**
 884      * Returns an {@code Integer} object holding the value
 885      * extracted from the specified {@code String} when parsed
 886      * with the radix given by the second argument. The first argument
 887      * is interpreted as representing a signed integer in the radix
 888      * specified by the second argument, exactly as if the arguments
 889      * were given to the {@link #parseInt(java.lang.String, int)}
 890      * method. The result is an {@code Integer} object that
 891      * represents the integer value specified by the string.
 892      *
 893      * <p>In other words, this method returns an {@code Integer}
 894      * object equal to the value of:
 895      *
 896      * <blockquote>
 897      *  {@code Integer.valueOf(Integer.parseInt(s, radix))}
 898      * </blockquote>
 899      *
 900      * @param      s   the string to be parsed.
 901      * @param      radix the radix to be used in interpreting {@code s}
 902      * @return     an {@code Integer} object holding the value
 903      *             represented by the string argument in the specified
 904      *             radix.
 905      * @throws    NumberFormatException if the {@code String}
 906      *            does not contain a parsable {@code int}.
 907      */
 908     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 909         return Integer.valueOf(parseInt(s,radix));
 910     }
 911 
 912     /**
 913      * Returns an {@code Integer} object holding the
 914      * value of the specified {@code String}. The argument is
 915      * interpreted as representing a signed decimal integer, exactly
 916      * as if the argument were given to the {@link
 917      * #parseInt(java.lang.String)} method. The result is an
 918      * {@code Integer} object that represents the integer value
 919      * specified by the string.
 920      *
 921      * <p>In other words, this method returns an {@code Integer}
 922      * object equal to the value of:
 923      *
 924      * <blockquote>
 925      *  {@code Integer.valueOf(Integer.parseInt(s))}
 926      * </blockquote>
 927      *
 928      * @param      s   the string to be parsed.
 929      * @return     an {@code Integer} object holding the value
 930      *             represented by the string argument.
 931      * @throws     NumberFormatException  if the string cannot be parsed
 932      *             as an integer.
 933      */
 934     public static Integer valueOf(String s) throws NumberFormatException {
 935         return Integer.valueOf(parseInt(s, 10));
 936     }
 937 
 938     /**
 939      * Cache to support the object identity semantics of autoboxing for values between
 940      * -128 and 127 (inclusive) as required by JLS.
 941      *
 942      * The cache is initialized on first usage.  The size of the cache
 943      * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
 944      * During VM initialization, java.lang.Integer.IntegerCache.high property
 945      * may be set and saved in the private system properties in the
 946      * jdk.internal.misc.VM class.
 947      *
 948      * WARNING: The cache is archived with CDS and reloaded from the shared
 949      * archive at runtime. The archived cache (Integer[]) and Integer objects
 950      * reside in the closed archive heap regions. Care should be taken when
 951      * changing the implementation and the cache array should not be assigned
 952      * with new Integer object(s) after initialization.
 953      */
 954 
 955     private static final class IntegerCache {
 956         static final int low = -128;
 957         static final int high;
 958 
 959         @Stable
 960         static final Integer[] cache;
 961         static Integer[] archivedCache;
 962 
 963         static {
 964             // high value may be configured by property
 965             int h = 127;
 966             String integerCacheHighPropValue =
 967                 VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 968             if (integerCacheHighPropValue != null) {
 969                 try {
 970                     h = Math.max(parseInt(integerCacheHighPropValue), 127);
 971                     // Maximum array size is Integer.MAX_VALUE
 972                     h = Math.min(h, Integer.MAX_VALUE - (-low) -1);
 973                 } catch( NumberFormatException nfe) {
 974                     // If the property cannot be parsed into an int, ignore it.
 975                 }
 976             }
 977             high = h;
 978 
 979             // Load IntegerCache.archivedCache from archive, if possible
 980             CDS.initializeFromArchive(IntegerCache.class);
 981             int size = (high - low) + 1;
 982 
 983             // Use the archived cache if it exists and is large enough
 984             if (archivedCache == null || size > archivedCache.length) {
 985                 Integer[] c = new Integer[size];
 986                 int j = low;
 987                 for(int i = 0; i < c.length; i++) {
 988                     c[i] = new Integer(j++);
 989                 }
 990                 archivedCache = c;
 991             }
 992             cache = archivedCache;
 993             // range [-128, 127] must be interned (JLS7 5.1.7)
 994             assert IntegerCache.high >= 127;
 995         }
 996 
 997         private IntegerCache() {}
 998     }
 999 
1000     /**
1001      * Returns an {@code Integer} instance representing the specified
1002      * {@code int} value.  If a new {@code Integer} instance is not
1003      * required, this method should generally be used in preference to
1004      * the constructor {@link #Integer(int)}, as this method is likely
1005      * to yield significantly better space and time performance by
1006      * caching frequently requested values.
1007      *
1008      * This method will always cache values in the range -128 to 127,
1009      * inclusive, and may cache other values outside of this range.
1010      *
1011      * @param  i an {@code int} value.
1012      * @return an {@code Integer} instance representing {@code i}.
1013      * @since  1.5
1014      */
1015     @IntrinsicCandidate
1016     public static Integer valueOf(int i) {
1017         if (i >= IntegerCache.low && i <= IntegerCache.high)
1018             return IntegerCache.cache[i + (-IntegerCache.low)];
1019         return new Integer(i);
1020     }
1021 
1022     /**
1023      * The value of the {@code Integer}.
1024      *
1025      * @serial
1026      */
1027     private final int value;
1028 
1029     /**
1030      * Constructs a newly allocated {@code Integer} object that
1031      * represents the specified {@code int} value.
1032      *
1033      * @param   value   the value to be represented by the
1034      *                  {@code Integer} object.
1035      *
1036      * @deprecated
1037      * It is rarely appropriate to use this constructor. The static factory
1038      * {@link #valueOf(int)} is generally a better choice, as it is
1039      * likely to yield significantly better space and time performance.
1040      */
1041     @Deprecated(since="9", forRemoval = true)
1042     public Integer(int value) {
1043         this.value = value;
1044     }
1045 
1046     /**
1047      * Constructs a newly allocated {@code Integer} object that
1048      * represents the {@code int} value indicated by the
1049      * {@code String} parameter. The string is converted to an
1050      * {@code int} value in exactly the manner used by the
1051      * {@code parseInt} method for radix 10.
1052      *
1053      * @param   s   the {@code String} to be converted to an {@code Integer}.
1054      * @throws      NumberFormatException if the {@code String} does not
1055      *              contain a parsable integer.
1056      *
1057      * @deprecated
1058      * It is rarely appropriate to use this constructor.
1059      * Use {@link #parseInt(String)} to convert a string to a
1060      * {@code int} primitive, or use {@link #valueOf(String)}
1061      * to convert a string to an {@code Integer} object.
1062      */
1063     @Deprecated(since="9", forRemoval = true)
1064     public Integer(String s) throws NumberFormatException {
1065         this.value = parseInt(s, 10);
1066     }
1067 
1068     /**
1069      * Returns the value of this {@code Integer} as a {@code byte}
1070      * after a narrowing primitive conversion.
1071      * @jls 5.1.3 Narrowing Primitive Conversion
1072      */
1073     public byte byteValue() {
1074         return (byte)value;
1075     }
1076 
1077     /**
1078      * Returns the value of this {@code Integer} as a {@code short}
1079      * after a narrowing primitive conversion.
1080      * @jls 5.1.3 Narrowing Primitive Conversion
1081      */
1082     public short shortValue() {
1083         return (short)value;
1084     }
1085 
1086     /**
1087      * Returns the value of this {@code Integer} as an
1088      * {@code int}.
1089      */
1090     @IntrinsicCandidate
1091     public int intValue() {
1092         return value;
1093     }
1094 
1095     /**
1096      * Returns the value of this {@code Integer} as a {@code long}
1097      * after a widening primitive conversion.
1098      * @jls 5.1.2 Widening Primitive Conversion
1099      * @see Integer#toUnsignedLong(int)
1100      */
1101     public long longValue() {
1102         return (long)value;
1103     }
1104 
1105     /**
1106      * Returns the value of this {@code Integer} as a {@code float}
1107      * after a widening primitive conversion.
1108      * @jls 5.1.2 Widening Primitive Conversion
1109      */
1110     public float floatValue() {
1111         return (float)value;
1112     }
1113 
1114     /**
1115      * Returns the value of this {@code Integer} as a {@code double}
1116      * after a widening primitive conversion.
1117      * @jls 5.1.2 Widening Primitive Conversion
1118      */
1119     public double doubleValue() {
1120         return (double)value;
1121     }
1122 
1123     /**
1124      * Returns a {@code String} object representing this
1125      * {@code Integer}'s value. The value is converted to signed
1126      * decimal representation and returned as a string, exactly as if
1127      * the integer value were given as an argument to the {@link
1128      * java.lang.Integer#toString(int)} method.
1129      *
1130      * @return  a string representation of the value of this object in
1131      *          base&nbsp;10.
1132      */
1133     public String toString() {
1134         return toString(value);
1135     }
1136 
1137     /**
1138      * Returns a hash code for this {@code Integer}.
1139      *
1140      * @return  a hash code value for this object, equal to the
1141      *          primitive {@code int} value represented by this
1142      *          {@code Integer} object.
1143      */
1144     @Override
1145     public int hashCode() {
1146         return Integer.hashCode(value);
1147     }
1148 
1149     /**
1150      * Returns a hash code for an {@code int} value; compatible with
1151      * {@code Integer.hashCode()}.
1152      *
1153      * @param value the value to hash
1154      * @since 1.8
1155      *
1156      * @return a hash code value for an {@code int} value.
1157      */
1158     public static int hashCode(int value) {
1159         return value;
1160     }
1161 
1162     /**
1163      * Compares this object to the specified object.  The result is
1164      * {@code true} if and only if the argument is not
1165      * {@code null} and is an {@code Integer} object that
1166      * contains the same {@code int} value as this object.
1167      *
1168      * @param   obj   the object to compare with.
1169      * @return  {@code true} if the objects are the same;
1170      *          {@code false} otherwise.
1171      */
1172     public boolean equals(Object obj) {
1173         if (obj instanceof Integer) {
1174             return value == ((Integer)obj).intValue();
1175         }
1176         return false;
1177     }
1178 
1179     /**
1180      * Determines the integer value of the system property with the
1181      * specified name.
1182      *
1183      * <p>The first argument is treated as the name of a system
1184      * property.  System properties are accessible through the {@link
1185      * java.lang.System#getProperty(java.lang.String)} method. The
1186      * string value of this property is then interpreted as an integer
1187      * value using the grammar supported by {@link Integer#decode decode} and
1188      * an {@code Integer} object representing this value is returned.
1189      *
1190      * <p>If there is no property with the specified name, if the
1191      * specified name is empty or {@code null}, or if the property
1192      * does not have the correct numeric format, then {@code null} is
1193      * returned.
1194      *
1195      * <p>In other words, this method returns an {@code Integer}
1196      * object equal to the value of:
1197      *
1198      * <blockquote>
1199      *  {@code getInteger(nm, null)}
1200      * </blockquote>
1201      *
1202      * @param   nm   property name.
1203      * @return  the {@code Integer} value of the property.
1204      * @throws  SecurityException for the same reasons as
1205      *          {@link System#getProperty(String) System.getProperty}
1206      * @see     java.lang.System#getProperty(java.lang.String)
1207      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1208      */
1209     public static Integer getInteger(String nm) {
1210         return getInteger(nm, null);
1211     }
1212 
1213     /**
1214      * Determines the integer value of the system property with the
1215      * specified name.
1216      *
1217      * <p>The first argument is treated as the name of a system
1218      * property.  System properties are accessible through the {@link
1219      * java.lang.System#getProperty(java.lang.String)} method. The
1220      * string value of this property is then interpreted as an integer
1221      * value using the grammar supported by {@link Integer#decode decode} and
1222      * an {@code Integer} object representing this value is returned.
1223      *
1224      * <p>The second argument is the default value. An {@code Integer} object
1225      * that represents the value of the second argument is returned if there
1226      * is no property of the specified name, if the property does not have
1227      * the correct numeric format, or if the specified name is empty or
1228      * {@code null}.
1229      *
1230      * <p>In other words, this method returns an {@code Integer} object
1231      * equal to the value of:
1232      *
1233      * <blockquote>
1234      *  {@code getInteger(nm, Integer.valueOf(val))}
1235      * </blockquote>
1236      *
1237      * but in practice it may be implemented in a manner such as:
1238      *
1239      * <blockquote><pre>
1240      * Integer result = getInteger(nm, null);
1241      * return (result == null) ? Integer.valueOf(val) : result;
1242      * </pre></blockquote>
1243      *
1244      * to avoid the unnecessary allocation of an {@code Integer}
1245      * object when the default value is not needed.
1246      *
1247      * @param   nm   property name.
1248      * @param   val   default value.
1249      * @return  the {@code Integer} value of the property.
1250      * @throws  SecurityException for the same reasons as
1251      *          {@link System#getProperty(String) System.getProperty}
1252      * @see     java.lang.System#getProperty(java.lang.String)
1253      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1254      */
1255     public static Integer getInteger(String nm, int val) {
1256         Integer result = getInteger(nm, null);
1257         return (result == null) ? Integer.valueOf(val) : result;
1258     }
1259 
1260     /**
1261      * Returns the integer value of the system property with the
1262      * specified name.  The first argument is treated as the name of a
1263      * system property.  System properties are accessible through the
1264      * {@link java.lang.System#getProperty(java.lang.String)} method.
1265      * The string value of this property is then interpreted as an
1266      * integer value, as per the {@link Integer#decode decode} method,
1267      * and an {@code Integer} object representing this value is
1268      * returned; in summary:
1269      *
1270      * <ul><li>If the property value begins with the two ASCII characters
1271      *         {@code 0x} or the ASCII character {@code #}, not
1272      *      followed by a minus sign, then the rest of it is parsed as a
1273      *      hexadecimal integer exactly as by the method
1274      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1275      * <li>If the property value begins with the ASCII character
1276      *     {@code 0} followed by another character, it is parsed as an
1277      *     octal integer exactly as by the method
1278      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1279      * <li>Otherwise, the property value is parsed as a decimal integer
1280      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1281      * with radix 10.
1282      * </ul>
1283      *
1284      * <p>The second argument is the default value. The default value is
1285      * returned if there is no property of the specified name, if the
1286      * property does not have the correct numeric format, or if the
1287      * specified name is empty or {@code null}.
1288      *
1289      * @param   nm   property name.
1290      * @param   val   default value.
1291      * @return  the {@code Integer} value of the property.
1292      * @throws  SecurityException for the same reasons as
1293      *          {@link System#getProperty(String) System.getProperty}
1294      * @see     System#getProperty(java.lang.String)
1295      * @see     System#getProperty(java.lang.String, java.lang.String)
1296      */
1297     public static Integer getInteger(String nm, Integer val) {
1298         String v = null;
1299         try {
1300             v = System.getProperty(nm);
1301         } catch (IllegalArgumentException | NullPointerException e) {
1302         }
1303         if (v != null) {
1304             try {
1305                 return Integer.decode(v);
1306             } catch (NumberFormatException e) {
1307             }
1308         }
1309         return val;
1310     }
1311 
1312     /**
1313      * Decodes a {@code String} into an {@code Integer}.
1314      * Accepts decimal, hexadecimal, and octal numbers given
1315      * by the following grammar:
1316      *
1317      * <blockquote>
1318      * <dl>
1319      * <dt><i>DecodableString:</i>
1320      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1321      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1322      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1323      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1324      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1325      *
1326      * <dt><i>Sign:</i>
1327      * <dd>{@code -}
1328      * <dd>{@code +}
1329      * </dl>
1330      * </blockquote>
1331      *
1332      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1333      * are as defined in section {@jls 3.10.1} of
1334      * <cite>The Java Language Specification</cite>,
1335      * except that underscores are not accepted between digits.
1336      *
1337      * <p>The sequence of characters following an optional
1338      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1339      * "{@code #}", or leading zero) is parsed as by the {@code
1340      * Integer.parseInt} method with the indicated radix (10, 16, or
1341      * 8).  This sequence of characters must represent a positive
1342      * value or a {@link NumberFormatException} will be thrown.  The
1343      * result is negated if first character of the specified {@code
1344      * String} is the minus sign.  No whitespace characters are
1345      * permitted in the {@code String}.
1346      *
1347      * @param     nm the {@code String} to decode.
1348      * @return    an {@code Integer} object holding the {@code int}
1349      *             value represented by {@code nm}
1350      * @throws    NumberFormatException  if the {@code String} does not
1351      *            contain a parsable integer.
1352      * @see java.lang.Integer#parseInt(java.lang.String, int)
1353      */
1354     public static Integer decode(String nm) throws NumberFormatException {
1355         int radix = 10;
1356         int index = 0;
1357         boolean negative = false;
1358         int result;
1359 
1360         if (nm.isEmpty())
1361             throw new NumberFormatException("Zero length string");
1362         char firstChar = nm.charAt(0);
1363         // Handle sign, if present
1364         if (firstChar == '-') {
1365             negative = true;
1366             index++;
1367         } else if (firstChar == '+')
1368             index++;
1369 
1370         // Handle radix specifier, if present
1371         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1372             index += 2;
1373             radix = 16;
1374         }
1375         else if (nm.startsWith("#", index)) {
1376             index ++;
1377             radix = 16;
1378         }
1379         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1380             index ++;
1381             radix = 8;
1382         }
1383 
1384         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1385             throw new NumberFormatException("Sign character in wrong position");
1386 
1387         try {
1388             result = parseInt(nm, index, nm.length(), radix);
1389             result = negative ? -result : result;
1390         } catch (NumberFormatException e) {
1391             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1392             // handles this case, and causes any genuine format error to be
1393             // rethrown.
1394             String constant = negative ? ("-" + nm.substring(index))
1395                                        : nm.substring(index);
1396             result = parseInt(constant, radix);
1397         }
1398         return result;
1399     }
1400 
1401     /**
1402      * Compares two {@code Integer} objects numerically.
1403      *
1404      * @param   anotherInteger   the {@code Integer} to be compared.
1405      * @return  the value {@code 0} if this {@code Integer} is
1406      *          equal to the argument {@code Integer}; a value less than
1407      *          {@code 0} if this {@code Integer} is numerically less
1408      *          than the argument {@code Integer}; and a value greater
1409      *          than {@code 0} if this {@code Integer} is numerically
1410      *           greater than the argument {@code Integer} (signed
1411      *           comparison).
1412      * @since   1.2
1413      */
1414     public int compareTo(Integer anotherInteger) {
1415         return compare(this.value, anotherInteger.value);
1416     }
1417 
1418     /**
1419      * Compares two {@code int} values numerically.
1420      * The value returned is identical to what would be returned by:
1421      * <pre>
1422      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1423      * </pre>
1424      *
1425      * @param  x the first {@code int} to compare
1426      * @param  y the second {@code int} to compare
1427      * @return the value {@code 0} if {@code x == y};
1428      *         a value less than {@code 0} if {@code x < y}; and
1429      *         a value greater than {@code 0} if {@code x > y}
1430      * @since 1.7
1431      */
1432     public static int compare(int x, int y) {
1433         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1434     }
1435 
1436     /**
1437      * Compares two {@code int} values numerically treating the values
1438      * as unsigned.
1439      *
1440      * @param  x the first {@code int} to compare
1441      * @param  y the second {@code int} to compare
1442      * @return the value {@code 0} if {@code x == y}; a value less
1443      *         than {@code 0} if {@code x < y} as unsigned values; and
1444      *         a value greater than {@code 0} if {@code x > y} as
1445      *         unsigned values
1446      * @since 1.8
1447      */
1448     @IntrinsicCandidate
1449     public static int compareUnsigned(int x, int y) {
1450         return compare(x + MIN_VALUE, y + MIN_VALUE);
1451     }
1452 
1453     /**
1454      * Converts the argument to a {@code long} by an unsigned
1455      * conversion.  In an unsigned conversion to a {@code long}, the
1456      * high-order 32 bits of the {@code long} are zero and the
1457      * low-order 32 bits are equal to the bits of the integer
1458      * argument.
1459      *
1460      * Consequently, zero and positive {@code int} values are mapped
1461      * to a numerically equal {@code long} value and negative {@code
1462      * int} values are mapped to a {@code long} value equal to the
1463      * input plus 2<sup>32</sup>.
1464      *
1465      * @param  x the value to convert to an unsigned {@code long}
1466      * @return the argument converted to {@code long} by an unsigned
1467      *         conversion
1468      * @since 1.8
1469      */
1470     public static long toUnsignedLong(int x) {
1471         return ((long) x) & 0xffffffffL;
1472     }
1473 
1474     /**
1475      * Returns the unsigned quotient of dividing the first argument by
1476      * the second where each argument and the result is interpreted as
1477      * an unsigned value.
1478      *
1479      * <p>Note that in two's complement arithmetic, the three other
1480      * basic arithmetic operations of add, subtract, and multiply are
1481      * bit-wise identical if the two operands are regarded as both
1482      * being signed or both being unsigned.  Therefore separate {@code
1483      * addUnsigned}, etc. methods are not provided.
1484      *
1485      * @param dividend the value to be divided
1486      * @param divisor the value doing the dividing
1487      * @return the unsigned quotient of the first argument divided by
1488      * the second argument
1489      * @see #remainderUnsigned
1490      * @since 1.8
1491      */
1492     @IntrinsicCandidate
1493     public static int divideUnsigned(int dividend, int divisor) {
1494         // In lieu of tricky code, for now just use long arithmetic.
1495         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1496     }
1497 
1498     /**
1499      * Returns the unsigned remainder from dividing the first argument
1500      * by the second where each argument and the result is interpreted
1501      * as an unsigned value.
1502      *
1503      * @param dividend the value to be divided
1504      * @param divisor the value doing the dividing
1505      * @return the unsigned remainder of the first argument divided by
1506      * the second argument
1507      * @see #divideUnsigned
1508      * @since 1.8
1509      */
1510     @IntrinsicCandidate
1511     public static int remainderUnsigned(int dividend, int divisor) {
1512         // In lieu of tricky code, for now just use long arithmetic.
1513         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1514     }
1515 
1516 
1517     // Bit twiddling
1518 
1519     /**
1520      * The number of bits used to represent an {@code int} value in two's
1521      * complement binary form.
1522      *
1523      * @since 1.5
1524      */
1525     @Native public static final int SIZE = 32;
1526 
1527     /**
1528      * The number of bytes used to represent an {@code int} value in two's
1529      * complement binary form.
1530      *
1531      * @since 1.8
1532      */
1533     public static final int BYTES = SIZE / Byte.SIZE;
1534 
1535     /**
1536      * Returns an {@code int} value with at most a single one-bit, in the
1537      * position of the highest-order ("leftmost") one-bit in the specified
1538      * {@code int} value.  Returns zero if the specified value has no
1539      * one-bits in its two's complement binary representation, that is, if it
1540      * is equal to zero.
1541      *
1542      * @param i the value whose highest one bit is to be computed
1543      * @return an {@code int} value with a single one-bit, in the position
1544      *     of the highest-order one-bit in the specified value, or zero if
1545      *     the specified value is itself equal to zero.
1546      * @since 1.5
1547      */
1548     public static int highestOneBit(int i) {
1549         return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
1550     }
1551 
1552     /**
1553      * Returns an {@code int} value with at most a single one-bit, in the
1554      * position of the lowest-order ("rightmost") one-bit in the specified
1555      * {@code int} value.  Returns zero if the specified value has no
1556      * one-bits in its two's complement binary representation, that is, if it
1557      * is equal to zero.
1558      *
1559      * @param i the value whose lowest one bit is to be computed
1560      * @return an {@code int} value with a single one-bit, in the position
1561      *     of the lowest-order one-bit in the specified value, or zero if
1562      *     the specified value is itself equal to zero.
1563      * @since 1.5
1564      */
1565     public static int lowestOneBit(int i) {
1566         // HD, Section 2-1
1567         return i & -i;
1568     }
1569 
1570     /**
1571      * Returns the number of zero bits preceding the highest-order
1572      * ("leftmost") one-bit in the two's complement binary representation
1573      * of the specified {@code int} value.  Returns 32 if the
1574      * specified value has no one-bits in its two's complement representation,
1575      * in other words if it is equal to zero.
1576      *
1577      * <p>Note that this method is closely related to the logarithm base 2.
1578      * For all positive {@code int} values x:
1579      * <ul>
1580      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1581      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1582      * </ul>
1583      *
1584      * @param i the value whose number of leading zeros is to be computed
1585      * @return the number of zero bits preceding the highest-order
1586      *     ("leftmost") one-bit in the two's complement binary representation
1587      *     of the specified {@code int} value, or 32 if the value
1588      *     is equal to zero.
1589      * @since 1.5
1590      */
1591     @IntrinsicCandidate
1592     public static int numberOfLeadingZeros(int i) {
1593         // HD, Count leading 0's
1594         if (i <= 0)
1595             return i == 0 ? 32 : 0;
1596         int n = 31;
1597         if (i >= 1 << 16) { n -= 16; i >>>= 16; }
1598         if (i >= 1 <<  8) { n -=  8; i >>>=  8; }
1599         if (i >= 1 <<  4) { n -=  4; i >>>=  4; }
1600         if (i >= 1 <<  2) { n -=  2; i >>>=  2; }
1601         return n - (i >>> 1);
1602     }
1603 
1604     /**
1605      * Returns the number of zero bits following the lowest-order ("rightmost")
1606      * one-bit in the two's complement binary representation of the specified
1607      * {@code int} value.  Returns 32 if the specified value has no
1608      * one-bits in its two's complement representation, in other words if it is
1609      * equal to zero.
1610      *
1611      * @param i the value whose number of trailing zeros is to be computed
1612      * @return the number of zero bits following the lowest-order ("rightmost")
1613      *     one-bit in the two's complement binary representation of the
1614      *     specified {@code int} value, or 32 if the value is equal
1615      *     to zero.
1616      * @since 1.5
1617      */
1618     @IntrinsicCandidate
1619     public static int numberOfTrailingZeros(int i) {
1620         // HD, Count trailing 0's
1621         i = ~i & (i - 1);
1622         if (i <= 0) return i & 32;
1623         int n = 1;
1624         if (i > 1 << 16) { n += 16; i >>>= 16; }
1625         if (i > 1 <<  8) { n +=  8; i >>>=  8; }
1626         if (i > 1 <<  4) { n +=  4; i >>>=  4; }
1627         if (i > 1 <<  2) { n +=  2; i >>>=  2; }
1628         return n + (i >>> 1);
1629     }
1630 
1631     /**
1632      * Returns the number of one-bits in the two's complement binary
1633      * representation of the specified {@code int} value.  This function is
1634      * sometimes referred to as the <i>population count</i>.
1635      *
1636      * @param i the value whose bits are to be counted
1637      * @return the number of one-bits in the two's complement binary
1638      *     representation of the specified {@code int} value.
1639      * @since 1.5
1640      */
1641     @IntrinsicCandidate
1642     public static int bitCount(int i) {
1643         // HD, Figure 5-2
1644         i = i - ((i >>> 1) & 0x55555555);
1645         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1646         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1647         i = i + (i >>> 8);
1648         i = i + (i >>> 16);
1649         return i & 0x3f;
1650     }
1651 
1652     /**
1653      * Returns the value obtained by rotating the two's complement binary
1654      * representation of the specified {@code int} value left by the
1655      * specified number of bits.  (Bits shifted out of the left hand, or
1656      * high-order, side reenter on the right, or low-order.)
1657      *
1658      * <p>Note that left rotation with a negative distance is equivalent to
1659      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1660      * distance)}.  Note also that rotation by any multiple of 32 is a
1661      * no-op, so all but the last five bits of the rotation distance can be
1662      * ignored, even if the distance is negative: {@code rotateLeft(val,
1663      * distance) == rotateLeft(val, distance & 0x1F)}.
1664      *
1665      * @param i the value whose bits are to be rotated left
1666      * @param distance the number of bit positions to rotate left
1667      * @return the value obtained by rotating the two's complement binary
1668      *     representation of the specified {@code int} value left by the
1669      *     specified number of bits.
1670      * @since 1.5
1671      */
1672     public static int rotateLeft(int i, int distance) {
1673         return (i << distance) | (i >>> -distance);
1674     }
1675 
1676     /**
1677      * Returns the value obtained by rotating the two's complement binary
1678      * representation of the specified {@code int} value right by the
1679      * specified number of bits.  (Bits shifted out of the right hand, or
1680      * low-order, side reenter on the left, or high-order.)
1681      *
1682      * <p>Note that right rotation with a negative distance is equivalent to
1683      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1684      * distance)}.  Note also that rotation by any multiple of 32 is a
1685      * no-op, so all but the last five bits of the rotation distance can be
1686      * ignored, even if the distance is negative: {@code rotateRight(val,
1687      * distance) == rotateRight(val, distance & 0x1F)}.
1688      *
1689      * @param i the value whose bits are to be rotated right
1690      * @param distance the number of bit positions to rotate right
1691      * @return the value obtained by rotating the two's complement binary
1692      *     representation of the specified {@code int} value right by the
1693      *     specified number of bits.
1694      * @since 1.5
1695      */
1696     public static int rotateRight(int i, int distance) {
1697         return (i >>> distance) | (i << -distance);
1698     }
1699 
1700     /**
1701      * Returns the value obtained by reversing the order of the bits in the
1702      * two's complement binary representation of the specified {@code int}
1703      * value.
1704      *
1705      * @param i the value to be reversed
1706      * @return the value obtained by reversing order of the bits in the
1707      *     specified {@code int} value.
1708      * @since 1.5
1709      */
1710     @IntrinsicCandidate
1711     public static int reverse(int i) {
1712         // HD, Figure 7-1
1713         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1714         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1715         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1716 
1717         return reverseBytes(i);
1718     }
1719 
1720     /**
1721      * Returns the value obtained by compressing the bits of the
1722      * specified {@code int} value, {@code i}, in accordance with
1723      * the specified bit mask.
1724      * <p>
1725      * For each one-bit value {@code mb} of the mask, from least
1726      * significant to most significant, the bit value of {@code i} at
1727      * the same bit location as {@code mb} is assigned to the compressed
1728      * value contiguously starting from the least significant bit location.
1729      * All the upper remaining bits of the compressed value are set
1730      * to zero.
1731      *
1732      * @apiNote
1733      * Consider the simple case of compressing the digits of a hexadecimal
1734      * value:
1735      * {@snippet lang="java" :
1736      * // Compressing drink to food
1737      * compress(0xCAFEBABE, 0xFF00FFF0) == 0xCABAB
1738      * }
1739      * Starting from the least significant hexadecimal digit at position 0
1740      * from the right, the mask {@code 0xFF00FFF0} selects hexadecimal digits
1741      * at positions 1, 2, 3, 6 and 7 of {@code 0xCAFEBABE}. The selected digits
1742      * occur in the resulting compressed value contiguously from digit position
1743      * 0 in the same order.
1744      * <p>
1745      * The following identities all return {@code true} and are helpful to
1746      * understand the behaviour of {@code compress}:
1747      * {@snippet lang="java" :
1748      * // Returns 1 if the bit at position n is one
1749      * compress(x, 1 << n) == (x >> n & 1)
1750      *
1751      * // Logical shift right
1752      * compress(x, -1 << n) == x >>> n
1753      *
1754      * // Any bits not covered by the mask are ignored
1755      * compress(x, m) == compress(x & m, m)
1756      *
1757      * // Compressing a value by itself
1758      * compress(m, m) == (m == -1 || m == 0) ? m : (1 << bitCount(m)) - 1
1759      *
1760      * // Expanding then compressing with the same mask
1761      * compress(expand(x, m), m) == x & compress(m, m)
1762      * }
1763      * <p>
1764      * The Sheep And Goats (SAG) operation (see Hacker's Delight, section 7.7)
1765      * can be implemented as follows:
1766      * {@snippet lang="java" :
1767      * int compressLeft(int i, int mask) {
1768      *     // This implementation follows the description in Hacker's Delight which
1769      *     // is informative. A more optimal implementation is:
1770      *     //   Integer.compress(i, mask) << -Integer.bitCount(mask)
1771      *     return Integer.reverse(
1772      *         Integer.compress(Integer.reverse(i), Integer.reverse(mask)));
1773      * }
1774      *
1775      * int sag(int i, int mask) {
1776      *     return compressLeft(i, mask) | Integer.compress(i, ~mask);
1777      * }
1778      *
1779      * // Separate the sheep from the goats
1780      * sag(0xCAFEBABE, 0xFF00FFF0) == 0xCABABFEE
1781      * }
1782      *
1783      * @param i the value whose bits are to be compressed
1784      * @param mask the bit mask
1785      * @return the compressed value
1786      * @see #expand
1787      * @since 19
1788      */
1789     @IntrinsicCandidate
1790     public static int compress(int i, int mask) {
1791         // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract
1792 
1793         i = i & mask; // Clear irrelevant bits
1794         int maskCount = ~mask << 1; // Count 0's to right
1795 
1796         for (int j = 0; j < 5; j++) {
1797             // Parallel prefix
1798             // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
1799             int maskPrefix = parallelSuffix(maskCount);
1800             // Bits to move
1801             int maskMove = maskPrefix & mask;
1802             // Compress mask
1803             mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
1804             // Bits of i to be moved
1805             int t = i & maskMove;
1806             // Compress i
1807             i = (i ^ t) | (t >>> (1 << j));
1808             // Adjust the mask count by identifying bits that have 0 to the right
1809             maskCount = maskCount & ~maskPrefix;
1810         }
1811         return i;
1812     }
1813 
1814     /**
1815      * Returns the value obtained by expanding the bits of the
1816      * specified {@code int} value, {@code i}, in accordance with
1817      * the specified bit mask.
1818      * <p>
1819      * For each one-bit value {@code mb} of the mask, from least
1820      * significant to most significant, the next contiguous bit value
1821      * of {@code i} starting at the least significant bit is assigned
1822      * to the expanded value at the same bit location as {@code mb}.
1823      * All other remaining bits of the expanded value are set to zero.
1824      *
1825      * @apiNote
1826      * Consider the simple case of expanding the digits of a hexadecimal
1827      * value:
1828      * {@snippet lang="java" :
1829      * expand(0x0000CABAB, 0xFF00FFF0) == 0xCA00BAB0
1830      * }
1831      * Starting from the least significant hexadecimal digit at position 0
1832      * from the right, the mask {@code 0xFF00FFF0} selects the first five
1833      * hexadecimal digits of {@code 0x0000CABAB}. The selected digits occur
1834      * in the resulting expanded value in order at positions 1, 2, 3, 6, and 7.
1835      * <p>
1836      * The following identities all return {@code true} and are helpful to
1837      * understand the behaviour of {@code expand}:
1838      * {@snippet lang="java" :
1839      * // Logically shift right the bit at position 0
1840      * expand(x, 1 << n) == (x & 1) << n
1841      *
1842      * // Logically shift right
1843      * expand(x, -1 << n) == x << n
1844      *
1845      * // Expanding all bits returns the mask
1846      * expand(-1, m) == m
1847      *
1848      * // Any bits not covered by the mask are ignored
1849      * expand(x, m) == expand(x, m) & m
1850      *
1851      * // Compressing then expanding with the same mask
1852      * expand(compress(x, m), m) == x & m
1853      * }
1854      * <p>
1855      * The select operation for determining the position of the one-bit with
1856      * index {@code n} in a {@code int} value can be implemented as follows:
1857      * {@snippet lang="java" :
1858      * int select(int i, int n) {
1859      *     // the one-bit in i (the mask) with index n
1860      *     int nthBit = Integer.expand(1 << n, i);
1861      *     // the bit position of the one-bit with index n
1862      *     return Integer.numberOfTrailingZeros(nthBit);
1863      * }
1864      *
1865      * // The one-bit with index 0 is at bit position 1
1866      * select(0b10101010_10101010, 0) == 1
1867      * // The one-bit with index 3 is at bit position 7
1868      * select(0b10101010_10101010, 3) == 7
1869      * }
1870      *
1871      * @param i the value whose bits are to be expanded
1872      * @param mask the bit mask
1873      * @return the expanded value
1874      * @see #compress
1875      * @since 19
1876      */
1877     @IntrinsicCandidate
1878     public static int expand(int i, int mask) {
1879         // Save original mask
1880         int originalMask = mask;
1881         // Count 0's to right
1882         int maskCount = ~mask << 1;
1883         int maskPrefix = parallelSuffix(maskCount);
1884         // Bits to move
1885         int maskMove1 = maskPrefix & mask;
1886         // Compress mask
1887         mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
1888         maskCount = maskCount & ~maskPrefix;
1889 
1890         maskPrefix = parallelSuffix(maskCount);
1891         // Bits to move
1892         int maskMove2 = maskPrefix & mask;
1893         // Compress mask
1894         mask = (mask ^ maskMove2) | (maskMove2 >>> (1 << 1));
1895         maskCount = maskCount & ~maskPrefix;
1896 
1897         maskPrefix = parallelSuffix(maskCount);
1898         // Bits to move
1899         int maskMove3 = maskPrefix & mask;
1900         // Compress mask
1901         mask = (mask ^ maskMove3) | (maskMove3 >>> (1 << 2));
1902         maskCount = maskCount & ~maskPrefix;
1903 
1904         maskPrefix = parallelSuffix(maskCount);
1905         // Bits to move
1906         int maskMove4 = maskPrefix & mask;
1907         // Compress mask
1908         mask = (mask ^ maskMove4) | (maskMove4 >>> (1 << 3));
1909         maskCount = maskCount & ~maskPrefix;
1910 
1911         maskPrefix = parallelSuffix(maskCount);
1912         // Bits to move
1913         int maskMove5 = maskPrefix & mask;
1914 
1915         int t = i << (1 << 4);
1916         i = (i & ~maskMove5) | (t & maskMove5);
1917         t = i << (1 << 3);
1918         i = (i & ~maskMove4) | (t & maskMove4);
1919         t = i << (1 << 2);
1920         i = (i & ~maskMove3) | (t & maskMove3);
1921         t = i << (1 << 1);
1922         i = (i & ~maskMove2) | (t & maskMove2);
1923         t = i << (1 << 0);
1924         i = (i & ~maskMove1) | (t & maskMove1);
1925 
1926         // Clear irrelevant bits
1927         return i & originalMask;
1928     }
1929 
1930     @ForceInline
1931     private static int parallelSuffix(int maskCount) {
1932         int maskPrefix = maskCount ^ (maskCount << 1);
1933         maskPrefix = maskPrefix ^ (maskPrefix << 2);
1934         maskPrefix = maskPrefix ^ (maskPrefix << 4);
1935         maskPrefix = maskPrefix ^ (maskPrefix << 8);
1936         maskPrefix = maskPrefix ^ (maskPrefix << 16);
1937         return maskPrefix;
1938     }
1939 
1940     /**
1941      * Returns the signum function of the specified {@code int} value.  (The
1942      * return value is -1 if the specified value is negative; 0 if the
1943      * specified value is zero; and 1 if the specified value is positive.)
1944      *
1945      * @param i the value whose signum is to be computed
1946      * @return the signum function of the specified {@code int} value.
1947      * @since 1.5
1948      */
1949     public static int signum(int i) {
1950         // HD, Section 2-7
1951         return (i >> 31) | (-i >>> 31);
1952     }
1953 
1954     /**
1955      * Returns the value obtained by reversing the order of the bytes in the
1956      * two's complement representation of the specified {@code int} value.
1957      *
1958      * @param i the value whose bytes are to be reversed
1959      * @return the value obtained by reversing the bytes in the specified
1960      *     {@code int} value.
1961      * @since 1.5
1962      */
1963     @IntrinsicCandidate
1964     public static int reverseBytes(int i) {
1965         return (i << 24)            |
1966                ((i & 0xff00) << 8)  |
1967                ((i >>> 8) & 0xff00) |
1968                (i >>> 24);
1969     }
1970 
1971     /**
1972      * Adds two integers together as per the + operator.
1973      *
1974      * @param a the first operand
1975      * @param b the second operand
1976      * @return the sum of {@code a} and {@code b}
1977      * @see java.util.function.BinaryOperator
1978      * @since 1.8
1979      */
1980     public static int sum(int a, int b) {
1981         return a + b;
1982     }
1983 
1984     /**
1985      * Returns the greater of two {@code int} values
1986      * as if by calling {@link Math#max(int, int) Math.max}.
1987      *
1988      * @param a the first operand
1989      * @param b the second operand
1990      * @return the greater of {@code a} and {@code b}
1991      * @see java.util.function.BinaryOperator
1992      * @since 1.8
1993      */
1994     public static int max(int a, int b) {
1995         return Math.max(a, b);
1996     }
1997 
1998     /**
1999      * Returns the smaller of two {@code int} values
2000      * as if by calling {@link Math#min(int, int) Math.min}.
2001      *
2002      * @param a the first operand
2003      * @param b the second operand
2004      * @return the smaller of {@code a} and {@code b}
2005      * @see java.util.function.BinaryOperator
2006      * @since 1.8
2007      */
2008     public static int min(int a, int b) {
2009         return Math.min(a, b);
2010     }
2011 
2012     /**
2013      * Returns an {@link Optional} containing the nominal descriptor for this
2014      * instance, which is the instance itself.
2015      *
2016      * @return an {@link Optional} describing the {@linkplain Integer} instance
2017      * @since 12
2018      */
2019     @Override
2020     public Optional<Integer> describeConstable() {
2021         return Optional.of(this);
2022     }
2023 
2024     /**
2025      * Resolves this instance as a {@link ConstantDesc}, the result of which is
2026      * the instance itself.
2027      *
2028      * @param lookup ignored
2029      * @return the {@linkplain Integer} instance
2030      * @since 12
2031      */
2032     @Override
2033     public Integer resolveConstantDesc(MethodHandles.Lookup lookup) {
2034         return this;
2035     }
2036 
2037     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2038     @java.io.Serial
2039     @Native private static final long serialVersionUID = 1360826667806852920L;
2040 }