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.MigratedValueClass
  75 @jdk.internal.ValueBased
  76 public final class Integer extends Number
  77         implements Comparable<Integer>, Constable, ConstantDesc {
  78     /**
  79      * A constant holding the minimum value an {@code int} can
  80      * have, -2<sup>31</sup>.
  81      */
  82     @Native public static final int   MIN_VALUE = 0x80000000;
  83 
  84     /**
  85      * A constant holding the maximum value an {@code int} can
  86      * have, 2<sup>31</sup>-1.
  87      */
  88     @Native public static final int   MAX_VALUE = 0x7fffffff;
  89 
  90     /**
  91      * The {@code Class} instance representing the primitive type
  92      * {@code int}.
  93      *
  94      * @since   1.1
  95      */
  96     @SuppressWarnings("unchecked")
  97     public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
  98 
  99     /**
 100      * All possible chars for representing a number as a String
 101      */
 102     static final char[] digits = {
 103         '0' , '1' , '2' , '3' , '4' , '5' ,
 104         '6' , '7' , '8' , '9' , 'a' , 'b' ,
 105         'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
 106         'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
 107         'o' , 'p' , 'q' , 'r' , 's' , 't' ,
 108         'u' , 'v' , 'w' , 'x' , 'y' , 'z'
 109     };
 110 
 111     /**
 112      * Returns a string representation of the first argument in the
 113      * radix specified by the second argument.
 114      *
 115      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 116      * or larger than {@code Character.MAX_RADIX}, then the radix
 117      * {@code 10} is used instead.
 118      *
 119      * <p>If the first argument is negative, the first element of the
 120      * result is the ASCII minus character {@code '-'}
 121      * ({@code '\u005Cu002D'}). If the first argument is not
 122      * negative, no sign character appears in the result.
 123      *
 124      * <p>The remaining characters of the result represent the magnitude
 125      * of the first argument. If the magnitude is zero, it is
 126      * represented by a single zero character {@code '0'}
 127      * ({@code '\u005Cu0030'}); otherwise, the first character of
 128      * the representation of the magnitude will not be the zero
 129      * character.  The following ASCII characters are used as digits:
 130      *
 131      * <blockquote>
 132      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 133      * </blockquote>
 134      *
 135      * These are {@code '\u005Cu0030'} through
 136      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 137      * {@code '\u005Cu007A'}. If {@code radix} is
 138      * <var>N</var>, then the first <var>N</var> of these characters
 139      * are used as radix-<var>N</var> digits in the order shown. Thus,
 140      * the digits for hexadecimal (radix 16) are
 141      * {@code 0123456789abcdef}. If uppercase letters are
 142      * desired, the {@link java.lang.String#toUpperCase()} method may
 143      * be called on the result:
 144      *
 145      * <blockquote>
 146      *  {@code Integer.toString(n, 16).toUpperCase()}
 147      * </blockquote>
 148      *
 149      * @param   i       an integer to be converted to a string.
 150      * @param   radix   the radix to use in the string representation.
 151      * @return  a string representation of the argument in the specified radix.
 152      * @see     java.lang.Character#MAX_RADIX
 153      * @see     java.lang.Character#MIN_RADIX
 154      */
 155     public static String toString(int i, int radix) {
 156         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 157             radix = 10;
 158 
 159         /* Use the faster version */
 160         if (radix == 10) {
 161             return toString(i);
 162         }
 163 
 164         if (COMPACT_STRINGS) {
 165             byte[] buf = new byte[33];
 166             boolean negative = (i < 0);
 167             int charPos = 32;
 168 
 169             if (!negative) {
 170                 i = -i;
 171             }
 172 
 173             while (i <= -radix) {
 174                 buf[charPos--] = (byte)digits[-(i % radix)];
 175                 i = i / radix;
 176             }
 177             buf[charPos] = (byte)digits[-i];
 178 
 179             if (negative) {
 180                 buf[--charPos] = '-';
 181             }
 182 
 183             return StringLatin1.newString(buf, charPos, (33 - charPos));
 184         }
 185         return toStringUTF16(i, radix);
 186     }
 187 
 188     private static String toStringUTF16(int i, int radix) {
 189         byte[] buf = new byte[33 * 2];
 190         boolean negative = (i < 0);
 191         int charPos = 32;
 192         if (!negative) {
 193             i = -i;
 194         }
 195         while (i <= -radix) {
 196             StringUTF16.putChar(buf, charPos--, digits[-(i % radix)]);
 197             i = i / radix;
 198         }
 199         StringUTF16.putChar(buf, charPos, digits[-i]);
 200 
 201         if (negative) {
 202             StringUTF16.putChar(buf, --charPos, '-');
 203         }
 204         return StringUTF16.newString(buf, charPos, (33 - charPos));
 205     }
 206 
 207     /**
 208      * Returns a string representation of the first argument as an
 209      * unsigned integer value in the radix specified by the second
 210      * argument.
 211      *
 212      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 213      * or larger than {@code Character.MAX_RADIX}, then the radix
 214      * {@code 10} is used instead.
 215      *
 216      * <p>Note that since the first argument is treated as an unsigned
 217      * value, no leading sign character is printed.
 218      *
 219      * <p>If the magnitude is zero, it is represented by a single zero
 220      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 221      * the first character of the representation of the magnitude will
 222      * not be the zero character.
 223      *
 224      * <p>The behavior of radixes and the characters used as digits
 225      * are the same as {@link #toString(int, int) toString}.
 226      *
 227      * @param   i       an integer to be converted to an unsigned string.
 228      * @param   radix   the radix to use in the string representation.
 229      * @return  an unsigned string representation of the argument in the specified radix.
 230      * @see     #toString(int, int)
 231      * @since 1.8
 232      */
 233     public static String toUnsignedString(int i, int radix) {
 234         return Long.toUnsignedString(toUnsignedLong(i), radix);
 235     }
 236 
 237     /**
 238      * Returns a string representation of the integer argument as an
 239      * unsigned integer in base&nbsp;16.
 240      *
 241      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 242      * if the argument is negative; otherwise, it is equal to the
 243      * argument.  This value is converted to a string of ASCII digits
 244      * in hexadecimal (base&nbsp;16) with no extra leading
 245      * {@code 0}s.
 246      *
 247      * <p>The value of the argument can be recovered from the returned
 248      * string {@code s} by calling {@link
 249      * Integer#parseUnsignedInt(String, int)
 250      * Integer.parseUnsignedInt(s, 16)}.
 251      *
 252      * <p>If the unsigned magnitude is zero, it is represented by a
 253      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 254      * otherwise, the first character of the representation of the
 255      * unsigned magnitude will not be the zero character. The
 256      * following characters are used as hexadecimal digits:
 257      *
 258      * <blockquote>
 259      *  {@code 0123456789abcdef}
 260      * </blockquote>
 261      *
 262      * These are the characters {@code '\u005Cu0030'} through
 263      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 264      * {@code '\u005Cu0066'}. If uppercase letters are
 265      * desired, the {@link java.lang.String#toUpperCase()} method may
 266      * be called on the result:
 267      *
 268      * <blockquote>
 269      *  {@code Integer.toHexString(n).toUpperCase()}
 270      * </blockquote>
 271      *
 272      * @apiNote
 273      * The {@link java.util.HexFormat} class provides formatting and parsing
 274      * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
 275      * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
 276      * with leading zeros and for byte arrays includes for each byte
 277      * a delimiter, prefix, and suffix.
 278      *
 279      * @param   i   an integer to be converted to a string.
 280      * @return  the string representation of the unsigned integer value
 281      *          represented by the argument in hexadecimal (base&nbsp;16).
 282      * @see java.util.HexFormat
 283      * @see #parseUnsignedInt(String, int)
 284      * @see #toUnsignedString(int, int)
 285      * @since   1.0.2
 286      */
 287     public static String toHexString(int i) {
 288         return toUnsignedString0(i, 4);
 289     }
 290 
 291     /**
 292      * Returns a string representation of the integer argument as an
 293      * unsigned integer in base&nbsp;8.
 294      *
 295      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 296      * if the argument is negative; otherwise, it is equal to the
 297      * argument.  This value is converted to a string of ASCII digits
 298      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
 299      *
 300      * <p>The value of the argument can be recovered from the returned
 301      * string {@code s} by calling {@link
 302      * Integer#parseUnsignedInt(String, int)
 303      * Integer.parseUnsignedInt(s, 8)}.
 304      *
 305      * <p>If the unsigned magnitude is zero, it is represented by a
 306      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 307      * otherwise, the first character of the representation of the
 308      * unsigned magnitude will not be the zero character. The
 309      * following characters are used as octal digits:
 310      *
 311      * <blockquote>
 312      * {@code 01234567}
 313      * </blockquote>
 314      *
 315      * These are the characters {@code '\u005Cu0030'} through
 316      * {@code '\u005Cu0037'}.
 317      *
 318      * @param   i   an integer to be converted to a string.
 319      * @return  the string representation of the unsigned integer value
 320      *          represented by the argument in octal (base&nbsp;8).
 321      * @see #parseUnsignedInt(String, int)
 322      * @see #toUnsignedString(int, int)
 323      * @since   1.0.2
 324      */
 325     public static String toOctalString(int i) {
 326         return toUnsignedString0(i, 3);
 327     }
 328 
 329     /**
 330      * Returns a string representation of the integer argument as an
 331      * unsigned integer in base&nbsp;2.
 332      *
 333      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
 334      * if the argument is negative; otherwise it is equal to the
 335      * argument.  This value is converted to a string of ASCII digits
 336      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
 337      *
 338      * <p>The value of the argument can be recovered from the returned
 339      * string {@code s} by calling {@link
 340      * Integer#parseUnsignedInt(String, int)
 341      * Integer.parseUnsignedInt(s, 2)}.
 342      *
 343      * <p>If the unsigned magnitude is zero, it is represented by a
 344      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 345      * otherwise, the first character of the representation of the
 346      * unsigned magnitude will not be the zero character. The
 347      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 348      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 349      *
 350      * @param   i   an integer to be converted to a string.
 351      * @return  the string representation of the unsigned integer value
 352      *          represented by the argument in binary (base&nbsp;2).
 353      * @see #parseUnsignedInt(String, int)
 354      * @see #toUnsignedString(int, int)
 355      * @since   1.0.2
 356      */
 357     public static String toBinaryString(int i) {
 358         return toUnsignedString0(i, 1);
 359     }
 360 
 361     /**
 362      * Convert the integer to an unsigned number.
 363      */
 364     private static String toUnsignedString0(int val, int shift) {
 365         // assert shift > 0 && shift <=5 : "Illegal shift value";
 366         int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
 367         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 368         if (COMPACT_STRINGS) {
 369             byte[] buf = new byte[chars];
 370             formatUnsignedInt(val, shift, buf, chars);
 371             return new String(buf, LATIN1);
 372         } else {
 373             byte[] buf = new byte[chars * 2];
 374             formatUnsignedIntUTF16(val, shift, buf, chars);
 375             return new String(buf, UTF16);
 376         }
 377     }
 378 
 379     /**
 380      * Format an {@code int} (treated as unsigned) into a byte buffer (LATIN1 version). If
 381      * {@code len} exceeds the formatted ASCII representation of {@code val},
 382      * {@code buf} will be padded with leading zeroes.
 383      *
 384      * @param val the unsigned int to format
 385      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 386      * @param buf the byte buffer to write to
 387      * @param len the number of characters to write
 388      */
 389     private static void formatUnsignedInt(int val, int shift, byte[] buf, int len) {
 390         int charPos = len;
 391         int radix = 1 << shift;
 392         int mask = radix - 1;
 393         do {
 394             buf[--charPos] = (byte)Integer.digits[val & mask];
 395             val >>>= shift;
 396         } while (charPos > 0);
 397     }
 398 
 399     /**
 400      * Format an {@code int} (treated as unsigned) into a byte buffer (UTF16 version). If
 401      * {@code len} exceeds the formatted ASCII representation of {@code val},
 402      * {@code buf} will be padded with leading zeroes.
 403      *
 404      * @param val the unsigned int to format
 405      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 406      * @param buf the byte buffer to write to
 407      * @param len the number of characters to write
 408      */
 409     private static void formatUnsignedIntUTF16(int val, int shift, byte[] buf, int len) {
 410         int charPos = len;
 411         int radix = 1 << shift;
 412         int mask = radix - 1;
 413         do {
 414             StringUTF16.putChar(buf, --charPos, Integer.digits[val & mask]);
 415             val >>>= shift;
 416         } while (charPos > 0);
 417     }
 418 
 419     /**
 420      * Returns a {@code String} object representing the
 421      * specified integer. The argument is converted to signed decimal
 422      * representation and returned as a string, exactly as if the
 423      * argument and radix 10 were given as arguments to the {@link
 424      * #toString(int, int)} method.
 425      *
 426      * @param   i   an integer to be converted.
 427      * @return  a string representation of the argument in base&nbsp;10.
 428      */
 429     @IntrinsicCandidate
 430     public static String toString(int i) {
 431         int size = stringSize(i);
 432         if (COMPACT_STRINGS) {
 433             byte[] buf = new byte[size];
 434             StringLatin1.getChars(i, size, buf);
 435             return new String(buf, LATIN1);
 436         } else {
 437             byte[] buf = new byte[size * 2];
 438             StringUTF16.getChars(i, size, buf);
 439             return new String(buf, UTF16);
 440         }
 441     }
 442 
 443     /**
 444      * Returns a string representation of the argument as an unsigned
 445      * decimal value.
 446      *
 447      * The argument is converted to unsigned decimal representation
 448      * and returned as a string exactly as if the argument and radix
 449      * 10 were given as arguments to the {@link #toUnsignedString(int,
 450      * int)} method.
 451      *
 452      * @param   i  an integer to be converted to an unsigned string.
 453      * @return  an unsigned string representation of the argument.
 454      * @see     #toUnsignedString(int, int)
 455      * @since 1.8
 456      */
 457     public static String toUnsignedString(int i) {
 458         return Long.toString(toUnsignedLong(i));
 459     }
 460 
 461     /**
 462      * Returns the string representation size for a given int value.
 463      *
 464      * @param x int value
 465      * @return string size
 466      *
 467      * @implNote There are other ways to compute this: e.g. binary search,
 468      * but values are biased heavily towards zero, and therefore linear search
 469      * wins. The iteration results are also routinely inlined in the generated
 470      * code after loop unrolling.
 471      */
 472     static int stringSize(int x) {
 473         int d = 1;
 474         if (x >= 0) {
 475             d = 0;
 476             x = -x;
 477         }
 478         int p = -10;
 479         for (int i = 1; i < 10; i++) {
 480             if (x > p)
 481                 return i + d;
 482             p = 10 * p;
 483         }
 484         return 10 + d;
 485     }
 486 
 487     /**
 488      * Parses the string argument as a signed integer in the radix
 489      * specified by the second argument. The characters in the string
 490      * must all be digits of the specified radix (as determined by
 491      * whether {@link java.lang.Character#digit(char, int)} returns a
 492      * nonnegative value), except that the first character may be an
 493      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 494      * indicate a negative value or an ASCII plus sign {@code '+'}
 495      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 496      * resulting integer value is returned.
 497      *
 498      * <p>An exception of type {@code NumberFormatException} is
 499      * thrown if any of the following situations occurs:
 500      * <ul>
 501      * <li>The first argument is {@code null} or is a string of
 502      * length zero.
 503      *
 504      * <li>The radix is either smaller than
 505      * {@link java.lang.Character#MIN_RADIX} or
 506      * larger than {@link java.lang.Character#MAX_RADIX}.
 507      *
 508      * <li>Any character of the string is not a digit of the specified
 509      * radix, except that the first character may be a minus sign
 510      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
 511      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 512      * string is longer than length 1.
 513      *
 514      * <li>The value represented by the string is not a value of type
 515      * {@code int}.
 516      * </ul>
 517      *
 518      * <p>Examples:
 519      * <blockquote><pre>
 520      * parseInt("0", 10) returns 0
 521      * parseInt("473", 10) returns 473
 522      * parseInt("+42", 10) returns 42
 523      * parseInt("-0", 10) returns 0
 524      * parseInt("-FF", 16) returns -255
 525      * parseInt("1100110", 2) returns 102
 526      * parseInt("2147483647", 10) returns 2147483647
 527      * parseInt("-2147483648", 10) returns -2147483648
 528      * parseInt("2147483648", 10) throws a NumberFormatException
 529      * parseInt("99", 8) throws a NumberFormatException
 530      * parseInt("Kona", 10) throws a NumberFormatException
 531      * parseInt("Kona", 27) returns 411787
 532      * </pre></blockquote>
 533      *
 534      * @param      s   the {@code String} containing the integer
 535      *                  representation to be parsed
 536      * @param      radix   the radix to be used while parsing {@code s}.
 537      * @return     the integer represented by the string argument in the
 538      *             specified radix.
 539      * @throws     NumberFormatException if the {@code String}
 540      *             does not contain a parsable {@code int}.
 541      */
 542     public static int parseInt(String s, int radix)
 543                 throws NumberFormatException {
 544         /*
 545          * WARNING: This method may be invoked early during VM initialization
 546          * before IntegerCache is initialized. Care must be taken to not use
 547          * the valueOf method.
 548          */
 549 
 550         if (s == null) {
 551             throw new NumberFormatException("Cannot parse null string");
 552         }
 553 
 554         if (radix < Character.MIN_RADIX) {
 555             throw new NumberFormatException(String.format(
 556                 "radix %s less than Character.MIN_RADIX", radix));
 557         }
 558 
 559         if (radix > Character.MAX_RADIX) {
 560             throw new NumberFormatException(String.format(
 561                 "radix %s greater than Character.MAX_RADIX", radix));
 562         }
 563 
 564         int len = s.length();
 565         if (len == 0) {
 566             throw NumberFormatException.forInputString("", radix);
 567         }
 568         int digit = ~0xFF;
 569         int i = 0;
 570         char firstChar = s.charAt(i++);
 571         if (firstChar != '-' && firstChar != '+') {
 572             digit = digit(firstChar, radix);
 573         }
 574         if (digit >= 0 || digit == ~0xFF && len > 1) {
 575             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 576             int multmin = limit / radix;
 577             int result = -(digit & 0xFF);
 578             boolean inRange = true;
 579             /* Accumulating negatively avoids surprises near MAX_VALUE */
 580             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 581                     && (inRange = result > multmin
 582                         || result == multmin && digit <= radix * multmin - limit)) {
 583                 result = radix * result - digit;
 584             }
 585             if (inRange && i == len && digit >= 0) {
 586                 return firstChar != '-' ? -result : result;
 587             }
 588         }
 589         throw NumberFormatException.forInputString(s, radix);
 590     }
 591 
 592     /**
 593      * Parses the {@link CharSequence} argument as a signed {@code int} in the
 594      * specified {@code radix}, beginning at the specified {@code beginIndex}
 595      * and extending to {@code endIndex - 1}.
 596      *
 597      * <p>The method does not take steps to guard against the
 598      * {@code CharSequence} being mutated while parsing.
 599      *
 600      * @param      s   the {@code CharSequence} containing the {@code int}
 601      *                  representation to be parsed
 602      * @param      beginIndex   the beginning index, inclusive.
 603      * @param      endIndex     the ending index, exclusive.
 604      * @param      radix   the radix to be used while parsing {@code s}.
 605      * @return     the signed {@code int} represented by the subsequence in
 606      *             the specified radix.
 607      * @throws     NullPointerException  if {@code s} is null.
 608      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 609      *             negative, or if {@code beginIndex} is greater than
 610      *             {@code endIndex} or if {@code endIndex} is greater than
 611      *             {@code s.length()}.
 612      * @throws     NumberFormatException  if the {@code CharSequence} does not
 613      *             contain a parsable {@code int} in the specified
 614      *             {@code radix}, or if {@code radix} is either smaller than
 615      *             {@link java.lang.Character#MIN_RADIX} or larger than
 616      *             {@link java.lang.Character#MAX_RADIX}.
 617      * @since  9
 618      */
 619     public static int parseInt(CharSequence s, int beginIndex, int endIndex, int radix)
 620                 throws NumberFormatException {
 621         Objects.requireNonNull(s);
 622         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 623 
 624         if (radix < Character.MIN_RADIX) {
 625             throw new NumberFormatException(String.format(
 626                 "radix %s less than Character.MIN_RADIX", radix));
 627         }
 628 
 629         if (radix > Character.MAX_RADIX) {
 630             throw new NumberFormatException(String.format(
 631                 "radix %s greater than Character.MAX_RADIX", radix));
 632         }
 633 
 634         /*
 635          * While s can be concurrently modified, it is ensured that each
 636          * of its characters is read at most once, from lower to higher indices.
 637          * This is obtained by reading them using the pattern s.charAt(i++),
 638          * and by not updating i anywhere else.
 639          */
 640         if (beginIndex == endIndex) {
 641             throw NumberFormatException.forInputString("", radix);
 642         }
 643         int digit = ~0xFF;
 644         int i = beginIndex;
 645         char firstChar = s.charAt(i++);
 646         if (firstChar != '-' && firstChar != '+') {
 647             digit = digit(firstChar, radix);
 648         }
 649         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 650             int limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 651             int multmin = limit / radix;
 652             int result = -(digit & 0xFF);
 653             boolean inRange = true;
 654             /* Accumulating negatively avoids surprises near MAX_VALUE */
 655             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 656                     && (inRange = result > multmin
 657                         || result == multmin && digit <= radix * multmin - limit)) {
 658                 result = radix * result - digit;
 659             }
 660             if (inRange && i == endIndex && digit >= 0) {
 661                 return firstChar != '-' ? -result : result;
 662             }
 663         }
 664         throw NumberFormatException.forCharSequence(s, beginIndex,
 665             endIndex, i - (digit < -1 ? 0 : 1));
 666     }
 667 
 668     /**
 669      * Parses the string argument as a signed decimal integer. The
 670      * characters in the string must all be decimal digits, except
 671      * that the first character may be an ASCII minus sign {@code '-'}
 672      * ({@code '\u005Cu002D'}) to indicate a negative value or an
 673      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 674      * indicate a positive value. The resulting integer value is
 675      * returned, exactly as if the argument and the radix 10 were
 676      * given as arguments to the {@link #parseInt(java.lang.String,
 677      * int)} method.
 678      *
 679      * @param s    a {@code String} containing the {@code int}
 680      *             representation to be parsed
 681      * @return     the integer value represented by the argument in decimal.
 682      * @throws     NumberFormatException  if the string does not contain a
 683      *               parsable integer.
 684      */
 685     public static int parseInt(String s) throws NumberFormatException {
 686         return parseInt(s, 10);
 687     }
 688 
 689     /**
 690      * Parses the string argument as an unsigned integer in the radix
 691      * specified by the second argument.  An unsigned integer maps the
 692      * values usually associated with negative numbers to positive
 693      * numbers larger than {@code MAX_VALUE}.
 694      *
 695      * The characters in the string must all be digits of the
 696      * specified radix (as determined by whether {@link
 697      * java.lang.Character#digit(char, int)} returns a nonnegative
 698      * value), except that the first character may be an ASCII plus
 699      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 700      * integer value is returned.
 701      *
 702      * <p>An exception of type {@code NumberFormatException} is
 703      * thrown if any of the following situations occurs:
 704      * <ul>
 705      * <li>The first argument is {@code null} or is a string of
 706      * length zero.
 707      *
 708      * <li>The radix is either smaller than
 709      * {@link java.lang.Character#MIN_RADIX} or
 710      * larger than {@link java.lang.Character#MAX_RADIX}.
 711      *
 712      * <li>Any character of the string is not a digit of the specified
 713      * radix, except that the first character may be a plus sign
 714      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 715      * string is longer than length 1.
 716      *
 717      * <li>The value represented by the string is larger than the
 718      * largest unsigned {@code int}, 2<sup>32</sup>-1.
 719      *
 720      * </ul>
 721      *
 722      *
 723      * @param      s   the {@code String} containing the unsigned integer
 724      *                  representation to be parsed
 725      * @param      radix   the radix to be used while parsing {@code s}.
 726      * @return     the integer represented by the string argument in the
 727      *             specified radix.
 728      * @throws     NumberFormatException if the {@code String}
 729      *             does not contain a parsable {@code int}.
 730      * @since 1.8
 731      */
 732     public static int parseUnsignedInt(String s, int radix)
 733                 throws NumberFormatException {
 734         if (s == null)  {
 735             throw new NumberFormatException("Cannot parse null string");
 736         }
 737 
 738         if (radix < Character.MIN_RADIX) {
 739             throw new NumberFormatException(String.format(
 740                 "radix %s less than Character.MIN_RADIX", radix));
 741         }
 742 
 743         if (radix > Character.MAX_RADIX) {
 744             throw new NumberFormatException(String.format(
 745                 "radix %s greater than Character.MAX_RADIX", radix));
 746         }
 747 
 748         int len = s.length();
 749         if (len == 0) {
 750             throw NumberFormatException.forInputString(s, radix);
 751         }
 752         int i = 0;
 753         char firstChar = s.charAt(i++);
 754         if (firstChar == '-') {
 755             throw new NumberFormatException(String.format(
 756                 "Illegal leading minus sign on unsigned string %s.", s));
 757         }
 758         int digit = ~0xFF;
 759         if (firstChar != '+') {
 760             digit = digit(firstChar, radix);
 761         }
 762         if (digit >= 0 || digit == ~0xFF && len > 1) {
 763             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 764             int result = digit & 0xFF;
 765             boolean inRange = true;
 766             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 767                     && (inRange = compareUnsigned(result, multmax) < 0
 768                         || result == multmax && digit < -radix * multmax)) {
 769                 result = radix * result + digit;
 770             }
 771             if (inRange && i == len && digit >= 0) {
 772                 return result;
 773             }
 774         }
 775         if (digit < 0) {
 776             throw NumberFormatException.forInputString(s, radix);
 777         }
 778         throw new NumberFormatException(String.format(
 779             "String value %s exceeds range of unsigned int.", s));
 780     }
 781 
 782     /**
 783      * Parses the {@link CharSequence} argument as an unsigned {@code int} in
 784      * the specified {@code radix}, beginning at the specified
 785      * {@code beginIndex} and extending to {@code endIndex - 1}.
 786      *
 787      * <p>The method does not take steps to guard against the
 788      * {@code CharSequence} being mutated while parsing.
 789      *
 790      * @param      s   the {@code CharSequence} containing the unsigned
 791      *                 {@code int} representation to be parsed
 792      * @param      beginIndex   the beginning index, inclusive.
 793      * @param      endIndex     the ending index, exclusive.
 794      * @param      radix   the radix to be used while parsing {@code s}.
 795      * @return     the unsigned {@code int} represented by the subsequence in
 796      *             the specified radix.
 797      * @throws     NullPointerException  if {@code s} is null.
 798      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 799      *             negative, or if {@code beginIndex} is greater than
 800      *             {@code endIndex} or if {@code endIndex} is greater than
 801      *             {@code s.length()}.
 802      * @throws     NumberFormatException  if the {@code CharSequence} does not
 803      *             contain a parsable unsigned {@code int} in the specified
 804      *             {@code radix}, or if {@code radix} is either smaller than
 805      *             {@link java.lang.Character#MIN_RADIX} or larger than
 806      *             {@link java.lang.Character#MAX_RADIX}.
 807      * @since  9
 808      */
 809     public static int parseUnsignedInt(CharSequence s, int beginIndex, int endIndex, int radix)
 810                 throws NumberFormatException {
 811         Objects.requireNonNull(s);
 812         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 813 
 814         if (radix < Character.MIN_RADIX) {
 815             throw new NumberFormatException(String.format(
 816                 "radix %s less than Character.MIN_RADIX", radix));
 817         }
 818 
 819         if (radix > Character.MAX_RADIX) {
 820             throw new NumberFormatException(String.format(
 821                 "radix %s greater than Character.MAX_RADIX", radix));
 822         }
 823 
 824         /*
 825          * While s can be concurrently modified, it is ensured that each
 826          * of its characters is read at most once, from lower to higher indices.
 827          * This is obtained by reading them using the pattern s.charAt(i++),
 828          * and by not updating i anywhere else.
 829          */
 830         if (beginIndex == endIndex) {
 831             throw NumberFormatException.forInputString("", radix);
 832         }
 833         int i = beginIndex;
 834         char firstChar = s.charAt(i++);
 835         if (firstChar == '-') {
 836             throw new NumberFormatException(
 837                 "Illegal leading minus sign on unsigned string " + s + ".");
 838         }
 839         int digit = ~0xFF;
 840         if (firstChar != '+') {
 841             digit = digit(firstChar, radix);
 842         }
 843         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 844             int multmax = divideUnsigned(-1, radix);  // -1 is max unsigned int
 845             int result = digit & 0xFF;
 846             boolean inRange = true;
 847             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 848                     && (inRange = compareUnsigned(result, multmax) < 0
 849                         || result == multmax && digit < -radix * multmax)) {
 850                 result = radix * result + digit;
 851             }
 852             if (inRange && i == endIndex && digit >= 0) {
 853                 return result;
 854             }
 855         }
 856         if (digit < 0) {
 857             throw NumberFormatException.forCharSequence(s, beginIndex,
 858                 endIndex, i - (digit < -1 ? 0 : 1));
 859         }
 860         throw new NumberFormatException(String.format(
 861             "String value %s exceeds range of unsigned int.", s));
 862     }
 863 
 864     /**
 865      * Parses the string argument as an unsigned decimal integer. The
 866      * characters in the string must all be decimal digits, except
 867      * that the first character may be an ASCII plus sign {@code
 868      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 869      * is returned, exactly as if the argument and the radix 10 were
 870      * given as arguments to the {@link
 871      * #parseUnsignedInt(java.lang.String, int)} method.
 872      *
 873      * @param s   a {@code String} containing the unsigned {@code int}
 874      *            representation to be parsed
 875      * @return    the unsigned integer value represented by the argument in decimal.
 876      * @throws    NumberFormatException  if the string does not contain a
 877      *            parsable unsigned integer.
 878      * @since 1.8
 879      */
 880     public static int parseUnsignedInt(String s) throws NumberFormatException {
 881         return parseUnsignedInt(s, 10);
 882     }
 883 
 884     /**
 885      * Returns an {@code Integer} object holding the value
 886      * extracted from the specified {@code String} when parsed
 887      * with the radix given by the second argument. The first argument
 888      * is interpreted as representing a signed integer in the radix
 889      * specified by the second argument, exactly as if the arguments
 890      * were given to the {@link #parseInt(java.lang.String, int)}
 891      * method. The result is an {@code Integer} object that
 892      * represents the integer value specified by the string.
 893      *
 894      * <p>In other words, this method returns an {@code Integer}
 895      * object equal to the value of:
 896      *
 897      * <blockquote>
 898      *  {@code Integer.valueOf(Integer.parseInt(s, radix))}
 899      * </blockquote>
 900      *
 901      * @param      s   the string to be parsed.
 902      * @param      radix the radix to be used in interpreting {@code s}
 903      * @return     an {@code Integer} object holding the value
 904      *             represented by the string argument in the specified
 905      *             radix.
 906      * @throws    NumberFormatException if the {@code String}
 907      *            does not contain a parsable {@code int}.
 908      */
 909     public static Integer valueOf(String s, int radix) throws NumberFormatException {
 910         return Integer.valueOf(parseInt(s,radix));
 911     }
 912 
 913     /**
 914      * Returns an {@code Integer} object holding the
 915      * value of the specified {@code String}. The argument is
 916      * interpreted as representing a signed decimal integer, exactly
 917      * as if the argument were given to the {@link
 918      * #parseInt(java.lang.String)} method. The result is an
 919      * {@code Integer} object that represents the integer value
 920      * specified by the string.
 921      *
 922      * <p>In other words, this method returns an {@code Integer}
 923      * object equal to the value of:
 924      *
 925      * <blockquote>
 926      *  {@code Integer.valueOf(Integer.parseInt(s))}
 927      * </blockquote>
 928      *
 929      * @param      s   the string to be parsed.
 930      * @return     an {@code Integer} object holding the value
 931      *             represented by the string argument.
 932      * @throws     NumberFormatException  if the string cannot be parsed
 933      *             as an integer.
 934      */
 935     public static Integer valueOf(String s) throws NumberFormatException {
 936         return Integer.valueOf(parseInt(s, 10));
 937     }
 938 
 939     /**
 940      * Cache to support the object identity semantics of autoboxing for values between
 941      * -128 and 127 (inclusive) as required by JLS.
 942      *
 943      * The cache is initialized on first usage.  The size of the cache
 944      * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
 945      * During VM initialization, java.lang.Integer.IntegerCache.high property
 946      * may be set and saved in the private system properties in the
 947      * jdk.internal.misc.VM class.
 948      *
 949      * WARNING: The cache is archived with CDS and reloaded from the shared
 950      * archive at runtime. The archived cache (Integer[]) and Integer objects
 951      * reside in the closed archive heap regions. Care should be taken when
 952      * changing the implementation and the cache array should not be assigned
 953      * with new Integer object(s) after initialization.
 954      */
 955 
 956     private static final class IntegerCache {
 957         static final int low = -128;
 958         static final int high;
 959 
 960         @Stable
 961         static final Integer[] cache;
 962         static Integer[] archivedCache;
 963 
 964         static {
 965             // high value may be configured by property
 966             int h = 127;
 967             String integerCacheHighPropValue =
 968                 VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
 969             if (integerCacheHighPropValue != null) {
 970                 try {
 971                     h = Math.max(parseInt(integerCacheHighPropValue), 127);
 972                     // Maximum array size is Integer.MAX_VALUE
 973                     h = Math.min(h, Integer.MAX_VALUE - (-low) -1);
 974                 } catch( NumberFormatException nfe) {
 975                     // If the property cannot be parsed into an int, ignore it.
 976                 }
 977             }
 978             high = h;
 979 
 980             // Load IntegerCache.archivedCache from archive, if possible
 981             CDS.initializeFromArchive(IntegerCache.class);
 982             int size = (high - low) + 1;
 983 
 984             // Use the archived cache if it exists and is large enough
 985             if (archivedCache == null || size > archivedCache.length) {
 986                 Integer[] c = new Integer[size];
 987                 int j = low;
 988                 for(int i = 0; i < c.length; i++) {
 989                     c[i] = new Integer(j++);
 990                 }
 991                 archivedCache = c;
 992             }
 993             cache = archivedCache;
 994             // range [-128, 127] must be interned (JLS7 5.1.7)
 995             assert IntegerCache.high >= 127;
 996         }
 997 
 998         private IntegerCache() {}
 999     }
1000 
1001     /**
1002      * Returns an {@code Integer} instance representing the specified
1003      * {@code int} value.  If a new {@code Integer} instance is not
1004      * required, this method should generally be used in preference to
1005      * the constructor {@link #Integer(int)}, as this method is likely
1006      * to yield significantly better space and time performance by
1007      * caching frequently requested values.
1008      *
1009      * This method will always cache values in the range -128 to 127,
1010      * inclusive, and may cache other values outside of this range.
1011      *
1012      * @param  i an {@code int} value.
1013      * @return an {@code Integer} instance representing {@code i}.
1014      * @since  1.5
1015      */
1016     @IntrinsicCandidate
1017     public static Integer valueOf(int i) {
1018         if (i >= IntegerCache.low && i <= IntegerCache.high)
1019             return IntegerCache.cache[i + (-IntegerCache.low)];
1020         return new Integer(i);
1021     }
1022 
1023     /**
1024      * The value of the {@code Integer}.
1025      *
1026      * @serial
1027      */
1028     private final int value;
1029 
1030     /**
1031      * Constructs a newly allocated {@code Integer} object that
1032      * represents the specified {@code int} value.
1033      *
1034      * @param   value   the value to be represented by the
1035      *                  {@code Integer} object.
1036      *
1037      * @deprecated
1038      * It is rarely appropriate to use this constructor. The static factory
1039      * {@link #valueOf(int)} is generally a better choice, as it is
1040      * likely to yield significantly better space and time performance.
1041      */
1042     @Deprecated(since="9", forRemoval = true)
1043     public Integer(int value) {
1044         this.value = value;
1045     }
1046 
1047     /**
1048      * Constructs a newly allocated {@code Integer} object that
1049      * represents the {@code int} value indicated by the
1050      * {@code String} parameter. The string is converted to an
1051      * {@code int} value in exactly the manner used by the
1052      * {@code parseInt} method for radix 10.
1053      *
1054      * @param   s   the {@code String} to be converted to an {@code Integer}.
1055      * @throws      NumberFormatException if the {@code String} does not
1056      *              contain a parsable integer.
1057      *
1058      * @deprecated
1059      * It is rarely appropriate to use this constructor.
1060      * Use {@link #parseInt(String)} to convert a string to a
1061      * {@code int} primitive, or use {@link #valueOf(String)}
1062      * to convert a string to an {@code Integer} object.
1063      */
1064     @Deprecated(since="9", forRemoval = true)
1065     public Integer(String s) throws NumberFormatException {
1066         this.value = parseInt(s, 10);
1067     }
1068 
1069     /**
1070      * Returns the value of this {@code Integer} as a {@code byte}
1071      * after a narrowing primitive conversion.
1072      * @jls 5.1.3 Narrowing Primitive Conversion
1073      */
1074     public byte byteValue() {
1075         return (byte)value;
1076     }
1077 
1078     /**
1079      * Returns the value of this {@code Integer} as a {@code short}
1080      * after a narrowing primitive conversion.
1081      * @jls 5.1.3 Narrowing Primitive Conversion
1082      */
1083     public short shortValue() {
1084         return (short)value;
1085     }
1086 
1087     /**
1088      * Returns the value of this {@code Integer} as an
1089      * {@code int}.
1090      */
1091     @IntrinsicCandidate
1092     public int intValue() {
1093         return value;
1094     }
1095 
1096     /**
1097      * Returns the value of this {@code Integer} as a {@code long}
1098      * after a widening primitive conversion.
1099      * @jls 5.1.2 Widening Primitive Conversion
1100      * @see Integer#toUnsignedLong(int)
1101      */
1102     public long longValue() {
1103         return (long)value;
1104     }
1105 
1106     /**
1107      * Returns the value of this {@code Integer} as a {@code float}
1108      * after a widening primitive conversion.
1109      * @jls 5.1.2 Widening Primitive Conversion
1110      */
1111     public float floatValue() {
1112         return (float)value;
1113     }
1114 
1115     /**
1116      * Returns the value of this {@code Integer} as a {@code double}
1117      * after a widening primitive conversion.
1118      * @jls 5.1.2 Widening Primitive Conversion
1119      */
1120     public double doubleValue() {
1121         return (double)value;
1122     }
1123 
1124     /**
1125      * Returns a {@code String} object representing this
1126      * {@code Integer}'s value. The value is converted to signed
1127      * decimal representation and returned as a string, exactly as if
1128      * the integer value were given as an argument to the {@link
1129      * java.lang.Integer#toString(int)} method.
1130      *
1131      * @return  a string representation of the value of this object in
1132      *          base&nbsp;10.
1133      */
1134     public String toString() {
1135         return toString(value);
1136     }
1137 
1138     /**
1139      * Returns a hash code for this {@code Integer}.
1140      *
1141      * @return  a hash code value for this object, equal to the
1142      *          primitive {@code int} value represented by this
1143      *          {@code Integer} object.
1144      */
1145     @Override
1146     public int hashCode() {
1147         return Integer.hashCode(value);
1148     }
1149 
1150     /**
1151      * Returns a hash code for an {@code int} value; compatible with
1152      * {@code Integer.hashCode()}.
1153      *
1154      * @param value the value to hash
1155      * @since 1.8
1156      *
1157      * @return a hash code value for an {@code int} value.
1158      */
1159     public static int hashCode(int value) {
1160         return value;
1161     }
1162 
1163     /**
1164      * Compares this object to the specified object.  The result is
1165      * {@code true} if and only if the argument is not
1166      * {@code null} and is an {@code Integer} object that
1167      * contains the same {@code int} value as this object.
1168      *
1169      * @param   obj   the object to compare with.
1170      * @return  {@code true} if the objects are the same;
1171      *          {@code false} otherwise.
1172      */
1173     public boolean equals(Object obj) {
1174         if (obj instanceof Integer) {
1175             return value == ((Integer)obj).intValue();
1176         }
1177         return false;
1178     }
1179 
1180     /**
1181      * Determines the integer value of the system property with the
1182      * specified name.
1183      *
1184      * <p>The first argument is treated as the name of a system
1185      * property.  System properties are accessible through the {@link
1186      * java.lang.System#getProperty(java.lang.String)} method. The
1187      * string value of this property is then interpreted as an integer
1188      * value using the grammar supported by {@link Integer#decode decode} and
1189      * an {@code Integer} object representing this value is returned.
1190      *
1191      * <p>If there is no property with the specified name, if the
1192      * specified name is empty or {@code null}, or if the property
1193      * does not have the correct numeric format, then {@code null} is
1194      * returned.
1195      *
1196      * <p>In other words, this method returns an {@code Integer}
1197      * object equal to the value of:
1198      *
1199      * <blockquote>
1200      *  {@code getInteger(nm, null)}
1201      * </blockquote>
1202      *
1203      * @param   nm   property name.
1204      * @return  the {@code Integer} value of the property.
1205      * @throws  SecurityException for the same reasons as
1206      *          {@link System#getProperty(String) System.getProperty}
1207      * @see     java.lang.System#getProperty(java.lang.String)
1208      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1209      */
1210     public static Integer getInteger(String nm) {
1211         return getInteger(nm, null);
1212     }
1213 
1214     /**
1215      * Determines the integer value of the system property with the
1216      * specified name.
1217      *
1218      * <p>The first argument is treated as the name of a system
1219      * property.  System properties are accessible through the {@link
1220      * java.lang.System#getProperty(java.lang.String)} method. The
1221      * string value of this property is then interpreted as an integer
1222      * value using the grammar supported by {@link Integer#decode decode} and
1223      * an {@code Integer} object representing this value is returned.
1224      *
1225      * <p>The second argument is the default value. An {@code Integer} object
1226      * that represents the value of the second argument is returned if there
1227      * is no property of the specified name, if the property does not have
1228      * the correct numeric format, or if the specified name is empty or
1229      * {@code null}.
1230      *
1231      * <p>In other words, this method returns an {@code Integer} object
1232      * equal to the value of:
1233      *
1234      * <blockquote>
1235      *  {@code getInteger(nm, Integer.valueOf(val))}
1236      * </blockquote>
1237      *
1238      * but in practice it may be implemented in a manner such as:
1239      *
1240      * <blockquote><pre>
1241      * Integer result = getInteger(nm, null);
1242      * return (result == null) ? Integer.valueOf(val) : result;
1243      * </pre></blockquote>
1244      *
1245      * to avoid the unnecessary allocation of an {@code Integer}
1246      * object when the default value is not needed.
1247      *
1248      * @param   nm   property name.
1249      * @param   val   default value.
1250      * @return  the {@code Integer} value of the property.
1251      * @throws  SecurityException for the same reasons as
1252      *          {@link System#getProperty(String) System.getProperty}
1253      * @see     java.lang.System#getProperty(java.lang.String)
1254      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1255      */
1256     public static Integer getInteger(String nm, int val) {
1257         Integer result = getInteger(nm, null);
1258         return (result == null) ? Integer.valueOf(val) : result;
1259     }
1260 
1261     /**
1262      * Returns the integer value of the system property with the
1263      * specified name.  The first argument is treated as the name of a
1264      * system property.  System properties are accessible through the
1265      * {@link java.lang.System#getProperty(java.lang.String)} method.
1266      * The string value of this property is then interpreted as an
1267      * integer value, as per the {@link Integer#decode decode} method,
1268      * and an {@code Integer} object representing this value is
1269      * returned; in summary:
1270      *
1271      * <ul><li>If the property value begins with the two ASCII characters
1272      *         {@code 0x} or the ASCII character {@code #}, not
1273      *      followed by a minus sign, then the rest of it is parsed as a
1274      *      hexadecimal integer exactly as by the method
1275      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1276      * <li>If the property value begins with the ASCII character
1277      *     {@code 0} followed by another character, it is parsed as an
1278      *     octal integer exactly as by the method
1279      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1280      * <li>Otherwise, the property value is parsed as a decimal integer
1281      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1282      * with radix 10.
1283      * </ul>
1284      *
1285      * <p>The second argument is the default value. The default value is
1286      * returned if there is no property of the specified name, if the
1287      * property does not have the correct numeric format, or if the
1288      * specified name is empty or {@code null}.
1289      *
1290      * @param   nm   property name.
1291      * @param   val   default value.
1292      * @return  the {@code Integer} value of the property.
1293      * @throws  SecurityException for the same reasons as
1294      *          {@link System#getProperty(String) System.getProperty}
1295      * @see     System#getProperty(java.lang.String)
1296      * @see     System#getProperty(java.lang.String, java.lang.String)
1297      */
1298     public static Integer getInteger(String nm, Integer val) {
1299         String v = null;
1300         try {
1301             v = System.getProperty(nm);
1302         } catch (IllegalArgumentException | NullPointerException e) {
1303         }
1304         if (v != null) {
1305             try {
1306                 return Integer.decode(v);
1307             } catch (NumberFormatException e) {
1308             }
1309         }
1310         return val;
1311     }
1312 
1313     /**
1314      * Decodes a {@code String} into an {@code Integer}.
1315      * Accepts decimal, hexadecimal, and octal numbers given
1316      * by the following grammar:
1317      *
1318      * <blockquote>
1319      * <dl>
1320      * <dt><i>DecodableString:</i>
1321      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1322      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1323      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1324      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1325      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1326      *
1327      * <dt><i>Sign:</i>
1328      * <dd>{@code -}
1329      * <dd>{@code +}
1330      * </dl>
1331      * </blockquote>
1332      *
1333      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1334      * are as defined in section {@jls 3.10.1} of
1335      * <cite>The Java Language Specification</cite>,
1336      * except that underscores are not accepted between digits.
1337      *
1338      * <p>The sequence of characters following an optional
1339      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1340      * "{@code #}", or leading zero) is parsed as by the {@code
1341      * Integer.parseInt} method with the indicated radix (10, 16, or
1342      * 8).  This sequence of characters must represent a positive
1343      * value or a {@link NumberFormatException} will be thrown.  The
1344      * result is negated if first character of the specified {@code
1345      * String} is the minus sign.  No whitespace characters are
1346      * permitted in the {@code String}.
1347      *
1348      * @param     nm the {@code String} to decode.
1349      * @return    an {@code Integer} object holding the {@code int}
1350      *             value represented by {@code nm}
1351      * @throws    NumberFormatException  if the {@code String} does not
1352      *            contain a parsable integer.
1353      * @see java.lang.Integer#parseInt(java.lang.String, int)
1354      */
1355     public static Integer decode(String nm) throws NumberFormatException {
1356         int radix = 10;
1357         int index = 0;
1358         boolean negative = false;
1359         int result;
1360 
1361         if (nm.isEmpty())
1362             throw new NumberFormatException("Zero length string");
1363         char firstChar = nm.charAt(0);
1364         // Handle sign, if present
1365         if (firstChar == '-') {
1366             negative = true;
1367             index++;
1368         } else if (firstChar == '+')
1369             index++;
1370 
1371         // Handle radix specifier, if present
1372         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1373             index += 2;
1374             radix = 16;
1375         }
1376         else if (nm.startsWith("#", index)) {
1377             index ++;
1378             radix = 16;
1379         }
1380         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1381             index ++;
1382             radix = 8;
1383         }
1384 
1385         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1386             throw new NumberFormatException("Sign character in wrong position");
1387 
1388         try {
1389             result = parseInt(nm, index, nm.length(), radix);
1390             result = negative ? -result : result;
1391         } catch (NumberFormatException e) {
1392             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1393             // handles this case, and causes any genuine format error to be
1394             // rethrown.
1395             String constant = negative ? ("-" + nm.substring(index))
1396                                        : nm.substring(index);
1397             result = parseInt(constant, radix);
1398         }
1399         return result;
1400     }
1401 
1402     /**
1403      * Compares two {@code Integer} objects numerically.
1404      *
1405      * @param   anotherInteger   the {@code Integer} to be compared.
1406      * @return  the value {@code 0} if this {@code Integer} is
1407      *          equal to the argument {@code Integer}; a value less than
1408      *          {@code 0} if this {@code Integer} is numerically less
1409      *          than the argument {@code Integer}; and a value greater
1410      *          than {@code 0} if this {@code Integer} is numerically
1411      *           greater than the argument {@code Integer} (signed
1412      *           comparison).
1413      * @since   1.2
1414      */
1415     public int compareTo(Integer anotherInteger) {
1416         return compare(this.value, anotherInteger.value);
1417     }
1418 
1419     /**
1420      * Compares two {@code int} values numerically.
1421      * The value returned is identical to what would be returned by:
1422      * <pre>
1423      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1424      * </pre>
1425      *
1426      * @param  x the first {@code int} to compare
1427      * @param  y the second {@code int} to compare
1428      * @return the value {@code 0} if {@code x == y};
1429      *         a value less than {@code 0} if {@code x < y}; and
1430      *         a value greater than {@code 0} if {@code x > y}
1431      * @since 1.7
1432      */
1433     public static int compare(int x, int y) {
1434         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1435     }
1436 
1437     /**
1438      * Compares two {@code int} values numerically treating the values
1439      * as unsigned.
1440      *
1441      * @param  x the first {@code int} to compare
1442      * @param  y the second {@code int} to compare
1443      * @return the value {@code 0} if {@code x == y}; a value less
1444      *         than {@code 0} if {@code x < y} as unsigned values; and
1445      *         a value greater than {@code 0} if {@code x > y} as
1446      *         unsigned values
1447      * @since 1.8
1448      */
1449     @IntrinsicCandidate
1450     public static int compareUnsigned(int x, int y) {
1451         return compare(x + MIN_VALUE, y + MIN_VALUE);
1452     }
1453 
1454     /**
1455      * Converts the argument to a {@code long} by an unsigned
1456      * conversion.  In an unsigned conversion to a {@code long}, the
1457      * high-order 32 bits of the {@code long} are zero and the
1458      * low-order 32 bits are equal to the bits of the integer
1459      * argument.
1460      *
1461      * Consequently, zero and positive {@code int} values are mapped
1462      * to a numerically equal {@code long} value and negative {@code
1463      * int} values are mapped to a {@code long} value equal to the
1464      * input plus 2<sup>32</sup>.
1465      *
1466      * @param  x the value to convert to an unsigned {@code long}
1467      * @return the argument converted to {@code long} by an unsigned
1468      *         conversion
1469      * @since 1.8
1470      */
1471     public static long toUnsignedLong(int x) {
1472         return ((long) x) & 0xffffffffL;
1473     }
1474 
1475     /**
1476      * Returns the unsigned quotient of dividing the first argument by
1477      * the second where each argument and the result is interpreted as
1478      * an unsigned value.
1479      *
1480      * <p>Note that in two's complement arithmetic, the three other
1481      * basic arithmetic operations of add, subtract, and multiply are
1482      * bit-wise identical if the two operands are regarded as both
1483      * being signed or both being unsigned.  Therefore separate {@code
1484      * addUnsigned}, etc. methods are not provided.
1485      *
1486      * @param dividend the value to be divided
1487      * @param divisor the value doing the dividing
1488      * @return the unsigned quotient of the first argument divided by
1489      * the second argument
1490      * @see #remainderUnsigned
1491      * @since 1.8
1492      */
1493     @IntrinsicCandidate
1494     public static int divideUnsigned(int dividend, int divisor) {
1495         // In lieu of tricky code, for now just use long arithmetic.
1496         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1497     }
1498 
1499     /**
1500      * Returns the unsigned remainder from dividing the first argument
1501      * by the second where each argument and the result is interpreted
1502      * as an unsigned value.
1503      *
1504      * @param dividend the value to be divided
1505      * @param divisor the value doing the dividing
1506      * @return the unsigned remainder of the first argument divided by
1507      * the second argument
1508      * @see #divideUnsigned
1509      * @since 1.8
1510      */
1511     @IntrinsicCandidate
1512     public static int remainderUnsigned(int dividend, int divisor) {
1513         // In lieu of tricky code, for now just use long arithmetic.
1514         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1515     }
1516 
1517 
1518     // Bit twiddling
1519 
1520     /**
1521      * The number of bits used to represent an {@code int} value in two's
1522      * complement binary form.
1523      *
1524      * @since 1.5
1525      */
1526     @Native public static final int SIZE = 32;
1527 
1528     /**
1529      * The number of bytes used to represent an {@code int} value in two's
1530      * complement binary form.
1531      *
1532      * @since 1.8
1533      */
1534     public static final int BYTES = SIZE / Byte.SIZE;
1535 
1536     /**
1537      * Returns an {@code int} value with at most a single one-bit, in the
1538      * position of the highest-order ("leftmost") one-bit in the specified
1539      * {@code int} value.  Returns zero if the specified value has no
1540      * one-bits in its two's complement binary representation, that is, if it
1541      * is equal to zero.
1542      *
1543      * @param i the value whose highest one bit is to be computed
1544      * @return an {@code int} value with a single one-bit, in the position
1545      *     of the highest-order one-bit in the specified value, or zero if
1546      *     the specified value is itself equal to zero.
1547      * @since 1.5
1548      */
1549     public static int highestOneBit(int i) {
1550         return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
1551     }
1552 
1553     /**
1554      * Returns an {@code int} value with at most a single one-bit, in the
1555      * position of the lowest-order ("rightmost") one-bit in the specified
1556      * {@code int} value.  Returns zero if the specified value has no
1557      * one-bits in its two's complement binary representation, that is, if it
1558      * is equal to zero.
1559      *
1560      * @param i the value whose lowest one bit is to be computed
1561      * @return an {@code int} value with a single one-bit, in the position
1562      *     of the lowest-order one-bit in the specified value, or zero if
1563      *     the specified value is itself equal to zero.
1564      * @since 1.5
1565      */
1566     public static int lowestOneBit(int i) {
1567         // HD, Section 2-1
1568         return i & -i;
1569     }
1570 
1571     /**
1572      * Returns the number of zero bits preceding the highest-order
1573      * ("leftmost") one-bit in the two's complement binary representation
1574      * of the specified {@code int} value.  Returns 32 if the
1575      * specified value has no one-bits in its two's complement representation,
1576      * in other words if it is equal to zero.
1577      *
1578      * <p>Note that this method is closely related to the logarithm base 2.
1579      * For all positive {@code int} values x:
1580      * <ul>
1581      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1582      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1583      * </ul>
1584      *
1585      * @param i the value whose number of leading zeros is to be computed
1586      * @return the number of zero bits preceding the highest-order
1587      *     ("leftmost") one-bit in the two's complement binary representation
1588      *     of the specified {@code int} value, or 32 if the value
1589      *     is equal to zero.
1590      * @since 1.5
1591      */
1592     @IntrinsicCandidate
1593     public static int numberOfLeadingZeros(int i) {
1594         // HD, Count leading 0's
1595         if (i <= 0)
1596             return i == 0 ? 32 : 0;
1597         int n = 31;
1598         if (i >= 1 << 16) { n -= 16; i >>>= 16; }
1599         if (i >= 1 <<  8) { n -=  8; i >>>=  8; }
1600         if (i >= 1 <<  4) { n -=  4; i >>>=  4; }
1601         if (i >= 1 <<  2) { n -=  2; i >>>=  2; }
1602         return n - (i >>> 1);
1603     }
1604 
1605     /**
1606      * Returns the number of zero bits following the lowest-order ("rightmost")
1607      * one-bit in the two's complement binary representation of the specified
1608      * {@code int} value.  Returns 32 if the specified value has no
1609      * one-bits in its two's complement representation, in other words if it is
1610      * equal to zero.
1611      *
1612      * @param i the value whose number of trailing zeros is to be computed
1613      * @return the number of zero bits following the lowest-order ("rightmost")
1614      *     one-bit in the two's complement binary representation of the
1615      *     specified {@code int} value, or 32 if the value is equal
1616      *     to zero.
1617      * @since 1.5
1618      */
1619     @IntrinsicCandidate
1620     public static int numberOfTrailingZeros(int i) {
1621         // HD, Count trailing 0's
1622         i = ~i & (i - 1);
1623         if (i <= 0) return i & 32;
1624         int n = 1;
1625         if (i > 1 << 16) { n += 16; i >>>= 16; }
1626         if (i > 1 <<  8) { n +=  8; i >>>=  8; }
1627         if (i > 1 <<  4) { n +=  4; i >>>=  4; }
1628         if (i > 1 <<  2) { n +=  2; i >>>=  2; }
1629         return n + (i >>> 1);
1630     }
1631 
1632     /**
1633      * Returns the number of one-bits in the two's complement binary
1634      * representation of the specified {@code int} value.  This function is
1635      * sometimes referred to as the <i>population count</i>.
1636      *
1637      * @param i the value whose bits are to be counted
1638      * @return the number of one-bits in the two's complement binary
1639      *     representation of the specified {@code int} value.
1640      * @since 1.5
1641      */
1642     @IntrinsicCandidate
1643     public static int bitCount(int i) {
1644         // HD, Figure 5-2
1645         i = i - ((i >>> 1) & 0x55555555);
1646         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1647         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1648         i = i + (i >>> 8);
1649         i = i + (i >>> 16);
1650         return i & 0x3f;
1651     }
1652 
1653     /**
1654      * Returns the value obtained by rotating the two's complement binary
1655      * representation of the specified {@code int} value left by the
1656      * specified number of bits.  (Bits shifted out of the left hand, or
1657      * high-order, side reenter on the right, or low-order.)
1658      *
1659      * <p>Note that left rotation with a negative distance is equivalent to
1660      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1661      * distance)}.  Note also that rotation by any multiple of 32 is a
1662      * no-op, so all but the last five bits of the rotation distance can be
1663      * ignored, even if the distance is negative: {@code rotateLeft(val,
1664      * distance) == rotateLeft(val, distance & 0x1F)}.
1665      *
1666      * @param i the value whose bits are to be rotated left
1667      * @param distance the number of bit positions to rotate left
1668      * @return the value obtained by rotating the two's complement binary
1669      *     representation of the specified {@code int} value left by the
1670      *     specified number of bits.
1671      * @since 1.5
1672      */
1673     public static int rotateLeft(int i, int distance) {
1674         return (i << distance) | (i >>> -distance);
1675     }
1676 
1677     /**
1678      * Returns the value obtained by rotating the two's complement binary
1679      * representation of the specified {@code int} value right by the
1680      * specified number of bits.  (Bits shifted out of the right hand, or
1681      * low-order, side reenter on the left, or high-order.)
1682      *
1683      * <p>Note that right rotation with a negative distance is equivalent to
1684      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1685      * distance)}.  Note also that rotation by any multiple of 32 is a
1686      * no-op, so all but the last five bits of the rotation distance can be
1687      * ignored, even if the distance is negative: {@code rotateRight(val,
1688      * distance) == rotateRight(val, distance & 0x1F)}.
1689      *
1690      * @param i the value whose bits are to be rotated right
1691      * @param distance the number of bit positions to rotate right
1692      * @return the value obtained by rotating the two's complement binary
1693      *     representation of the specified {@code int} value right by the
1694      *     specified number of bits.
1695      * @since 1.5
1696      */
1697     public static int rotateRight(int i, int distance) {
1698         return (i >>> distance) | (i << -distance);
1699     }
1700 
1701     /**
1702      * Returns the value obtained by reversing the order of the bits in the
1703      * two's complement binary representation of the specified {@code int}
1704      * value.
1705      *
1706      * @param i the value to be reversed
1707      * @return the value obtained by reversing order of the bits in the
1708      *     specified {@code int} value.
1709      * @since 1.5
1710      */
1711     @IntrinsicCandidate
1712     public static int reverse(int i) {
1713         // HD, Figure 7-1
1714         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1715         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1716         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1717 
1718         return reverseBytes(i);
1719     }
1720 
1721     /**
1722      * Returns the value obtained by compressing the bits of the
1723      * specified {@code int} value, {@code i}, in accordance with
1724      * the specified bit mask.
1725      * <p>
1726      * For each one-bit value {@code mb} of the mask, from least
1727      * significant to most significant, the bit value of {@code i} at
1728      * the same bit location as {@code mb} is assigned to the compressed
1729      * value contiguously starting from the least significant bit location.
1730      * All the upper remaining bits of the compressed value are set
1731      * to zero.
1732      *
1733      * @apiNote
1734      * Consider the simple case of compressing the digits of a hexadecimal
1735      * value:
1736      * {@snippet lang="java" :
1737      * // Compressing drink to food
1738      * compress(0xCAFEBABE, 0xFF00FFF0) == 0xCABAB
1739      * }
1740      * Starting from the least significant hexadecimal digit at position 0
1741      * from the right, the mask {@code 0xFF00FFF0} selects hexadecimal digits
1742      * at positions 1, 2, 3, 6 and 7 of {@code 0xCAFEBABE}. The selected digits
1743      * occur in the resulting compressed value contiguously from digit position
1744      * 0 in the same order.
1745      * <p>
1746      * The following identities all return {@code true} and are helpful to
1747      * understand the behaviour of {@code compress}:
1748      * {@snippet lang="java" :
1749      * // Returns 1 if the bit at position n is one
1750      * compress(x, 1 << n) == (x >> n & 1)
1751      *
1752      * // Logical shift right
1753      * compress(x, -1 << n) == x >>> n
1754      *
1755      * // Any bits not covered by the mask are ignored
1756      * compress(x, m) == compress(x & m, m)
1757      *
1758      * // Compressing a value by itself
1759      * compress(m, m) == (m == -1 || m == 0) ? m : (1 << bitCount(m)) - 1
1760      *
1761      * // Expanding then compressing with the same mask
1762      * compress(expand(x, m), m) == x & compress(m, m)
1763      * }
1764      * <p>
1765      * The Sheep And Goats (SAG) operation (see Hacker's Delight, section 7.7)
1766      * can be implemented as follows:
1767      * {@snippet lang="java" :
1768      * int compressLeft(int i, int mask) {
1769      *     // This implementation follows the description in Hacker's Delight which
1770      *     // is informative. A more optimal implementation is:
1771      *     //   Integer.compress(i, mask) << -Integer.bitCount(mask)
1772      *     return Integer.reverse(
1773      *         Integer.compress(Integer.reverse(i), Integer.reverse(mask)));
1774      * }
1775      *
1776      * int sag(int i, int mask) {
1777      *     return compressLeft(i, mask) | Integer.compress(i, ~mask);
1778      * }
1779      *
1780      * // Separate the sheep from the goats
1781      * sag(0xCAFEBABE, 0xFF00FFF0) == 0xCABABFEE
1782      * }
1783      *
1784      * @param i the value whose bits are to be compressed
1785      * @param mask the bit mask
1786      * @return the compressed value
1787      * @see #expand
1788      * @since 19
1789      */
1790     @IntrinsicCandidate
1791     public static int compress(int i, int mask) {
1792         // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract
1793 
1794         i = i & mask; // Clear irrelevant bits
1795         int maskCount = ~mask << 1; // Count 0's to right
1796 
1797         for (int j = 0; j < 5; j++) {
1798             // Parallel prefix
1799             // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
1800             int maskPrefix = parallelSuffix(maskCount);
1801             // Bits to move
1802             int maskMove = maskPrefix & mask;
1803             // Compress mask
1804             mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
1805             // Bits of i to be moved
1806             int t = i & maskMove;
1807             // Compress i
1808             i = (i ^ t) | (t >>> (1 << j));
1809             // Adjust the mask count by identifying bits that have 0 to the right
1810             maskCount = maskCount & ~maskPrefix;
1811         }
1812         return i;
1813     }
1814 
1815     /**
1816      * Returns the value obtained by expanding the bits of the
1817      * specified {@code int} value, {@code i}, in accordance with
1818      * the specified bit mask.
1819      * <p>
1820      * For each one-bit value {@code mb} of the mask, from least
1821      * significant to most significant, the next contiguous bit value
1822      * of {@code i} starting at the least significant bit is assigned
1823      * to the expanded value at the same bit location as {@code mb}.
1824      * All other remaining bits of the expanded value are set to zero.
1825      *
1826      * @apiNote
1827      * Consider the simple case of expanding the digits of a hexadecimal
1828      * value:
1829      * {@snippet lang="java" :
1830      * expand(0x0000CABAB, 0xFF00FFF0) == 0xCA00BAB0
1831      * }
1832      * Starting from the least significant hexadecimal digit at position 0
1833      * from the right, the mask {@code 0xFF00FFF0} selects the first five
1834      * hexadecimal digits of {@code 0x0000CABAB}. The selected digits occur
1835      * in the resulting expanded value in order at positions 1, 2, 3, 6, and 7.
1836      * <p>
1837      * The following identities all return {@code true} and are helpful to
1838      * understand the behaviour of {@code expand}:
1839      * {@snippet lang="java" :
1840      * // Logically shift right the bit at position 0
1841      * expand(x, 1 << n) == (x & 1) << n
1842      *
1843      * // Logically shift right
1844      * expand(x, -1 << n) == x << n
1845      *
1846      * // Expanding all bits returns the mask
1847      * expand(-1, m) == m
1848      *
1849      * // Any bits not covered by the mask are ignored
1850      * expand(x, m) == expand(x, m) & m
1851      *
1852      * // Compressing then expanding with the same mask
1853      * expand(compress(x, m), m) == x & m
1854      * }
1855      * <p>
1856      * The select operation for determining the position of the one-bit with
1857      * index {@code n} in a {@code int} value can be implemented as follows:
1858      * {@snippet lang="java" :
1859      * int select(int i, int n) {
1860      *     // the one-bit in i (the mask) with index n
1861      *     int nthBit = Integer.expand(1 << n, i);
1862      *     // the bit position of the one-bit with index n
1863      *     return Integer.numberOfTrailingZeros(nthBit);
1864      * }
1865      *
1866      * // The one-bit with index 0 is at bit position 1
1867      * select(0b10101010_10101010, 0) == 1
1868      * // The one-bit with index 3 is at bit position 7
1869      * select(0b10101010_10101010, 3) == 7
1870      * }
1871      *
1872      * @param i the value whose bits are to be expanded
1873      * @param mask the bit mask
1874      * @return the expanded value
1875      * @see #compress
1876      * @since 19
1877      */
1878     @IntrinsicCandidate
1879     public static int expand(int i, int mask) {
1880         // Save original mask
1881         int originalMask = mask;
1882         // Count 0's to right
1883         int maskCount = ~mask << 1;
1884         int maskPrefix = parallelSuffix(maskCount);
1885         // Bits to move
1886         int maskMove1 = maskPrefix & mask;
1887         // Compress mask
1888         mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
1889         maskCount = maskCount & ~maskPrefix;
1890 
1891         maskPrefix = parallelSuffix(maskCount);
1892         // Bits to move
1893         int maskMove2 = maskPrefix & mask;
1894         // Compress mask
1895         mask = (mask ^ maskMove2) | (maskMove2 >>> (1 << 1));
1896         maskCount = maskCount & ~maskPrefix;
1897 
1898         maskPrefix = parallelSuffix(maskCount);
1899         // Bits to move
1900         int maskMove3 = maskPrefix & mask;
1901         // Compress mask
1902         mask = (mask ^ maskMove3) | (maskMove3 >>> (1 << 2));
1903         maskCount = maskCount & ~maskPrefix;
1904 
1905         maskPrefix = parallelSuffix(maskCount);
1906         // Bits to move
1907         int maskMove4 = maskPrefix & mask;
1908         // Compress mask
1909         mask = (mask ^ maskMove4) | (maskMove4 >>> (1 << 3));
1910         maskCount = maskCount & ~maskPrefix;
1911 
1912         maskPrefix = parallelSuffix(maskCount);
1913         // Bits to move
1914         int maskMove5 = maskPrefix & mask;
1915 
1916         int t = i << (1 << 4);
1917         i = (i & ~maskMove5) | (t & maskMove5);
1918         t = i << (1 << 3);
1919         i = (i & ~maskMove4) | (t & maskMove4);
1920         t = i << (1 << 2);
1921         i = (i & ~maskMove3) | (t & maskMove3);
1922         t = i << (1 << 1);
1923         i = (i & ~maskMove2) | (t & maskMove2);
1924         t = i << (1 << 0);
1925         i = (i & ~maskMove1) | (t & maskMove1);
1926 
1927         // Clear irrelevant bits
1928         return i & originalMask;
1929     }
1930 
1931     @ForceInline
1932     private static int parallelSuffix(int maskCount) {
1933         int maskPrefix = maskCount ^ (maskCount << 1);
1934         maskPrefix = maskPrefix ^ (maskPrefix << 2);
1935         maskPrefix = maskPrefix ^ (maskPrefix << 4);
1936         maskPrefix = maskPrefix ^ (maskPrefix << 8);
1937         maskPrefix = maskPrefix ^ (maskPrefix << 16);
1938         return maskPrefix;
1939     }
1940 
1941     /**
1942      * Returns the signum function of the specified {@code int} value.  (The
1943      * return value is -1 if the specified value is negative; 0 if the
1944      * specified value is zero; and 1 if the specified value is positive.)
1945      *
1946      * @param i the value whose signum is to be computed
1947      * @return the signum function of the specified {@code int} value.
1948      * @since 1.5
1949      */
1950     public static int signum(int i) {
1951         // HD, Section 2-7
1952         return (i >> 31) | (-i >>> 31);
1953     }
1954 
1955     /**
1956      * Returns the value obtained by reversing the order of the bytes in the
1957      * two's complement representation of the specified {@code int} value.
1958      *
1959      * @param i the value whose bytes are to be reversed
1960      * @return the value obtained by reversing the bytes in the specified
1961      *     {@code int} value.
1962      * @since 1.5
1963      */
1964     @IntrinsicCandidate
1965     public static int reverseBytes(int i) {
1966         return (i << 24)            |
1967                ((i & 0xff00) << 8)  |
1968                ((i >>> 8) & 0xff00) |
1969                (i >>> 24);
1970     }
1971 
1972     /**
1973      * Adds two integers together as per the + operator.
1974      *
1975      * @param a the first operand
1976      * @param b the second operand
1977      * @return the sum of {@code a} and {@code b}
1978      * @see java.util.function.BinaryOperator
1979      * @since 1.8
1980      */
1981     public static int sum(int a, int b) {
1982         return a + b;
1983     }
1984 
1985     /**
1986      * Returns the greater of two {@code int} values
1987      * as if by calling {@link Math#max(int, int) Math.max}.
1988      *
1989      * @param a the first operand
1990      * @param b the second operand
1991      * @return the greater of {@code a} and {@code b}
1992      * @see java.util.function.BinaryOperator
1993      * @since 1.8
1994      */
1995     public static int max(int a, int b) {
1996         return Math.max(a, b);
1997     }
1998 
1999     /**
2000      * Returns the smaller of two {@code int} values
2001      * as if by calling {@link Math#min(int, int) Math.min}.
2002      *
2003      * @param a the first operand
2004      * @param b the second operand
2005      * @return the smaller of {@code a} and {@code b}
2006      * @see java.util.function.BinaryOperator
2007      * @since 1.8
2008      */
2009     public static int min(int a, int b) {
2010         return Math.min(a, b);
2011     }
2012 
2013     /**
2014      * Returns an {@link Optional} containing the nominal descriptor for this
2015      * instance, which is the instance itself.
2016      *
2017      * @return an {@link Optional} describing the {@linkplain Integer} instance
2018      * @since 12
2019      */
2020     @Override
2021     public Optional<Integer> describeConstable() {
2022         return Optional.of(this);
2023     }
2024 
2025     /**
2026      * Resolves this instance as a {@link ConstantDesc}, the result of which is
2027      * the instance itself.
2028      *
2029      * @param lookup ignored
2030      * @return the {@linkplain Integer} instance
2031      * @since 12
2032      */
2033     @Override
2034     public Integer resolveConstantDesc(MethodHandles.Lookup lookup) {
2035         return this;
2036     }
2037 
2038     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2039     @java.io.Serial
2040     @Native private static final long serialVersionUID = 1360826667806852920L;
2041 }