1 /*
   2  * Copyright (c) 1994, 2024, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.lang;
  27 
  28 import java.lang.annotation.Native;
  29 import java.lang.invoke.MethodHandles;
  30 import java.lang.constant.Constable;
  31 import java.lang.constant.ConstantDesc;
  32 import java.math.*;
  33 import java.util.Objects;
  34 import java.util.Optional;
  35 
  36 import jdk.internal.misc.CDS;
  37 import jdk.internal.value.DeserializeConstructor;
  38 import jdk.internal.util.DecimalDigits;
  39 import jdk.internal.vm.annotation.ForceInline;
  40 import jdk.internal.vm.annotation.IntrinsicCandidate;
  41 import jdk.internal.vm.annotation.Stable;
  42 
  43 import static java.lang.Character.digit;
  44 import static java.lang.String.COMPACT_STRINGS;
  45 import static java.lang.String.LATIN1;
  46 import static java.lang.String.UTF16;
  47 
  48 /**
  49  * The {@code Long} class is the {@linkplain
  50  * java.lang##wrapperClass wrapper class} for values of the primitive
  51  * type {@code long}. An object of type {@code Long} contains a
  52  * single field whose type is {@code long}.
  53  *
  54  * <p> In addition, this class provides several methods for converting
  55  * a {@code long} to a {@code String} and a {@code String} to a {@code
  56  * long}, as well as other constants and methods useful when dealing
  57  * with a {@code long}.
  58  *
  59  * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
  60  * class; programmers should treat instances that are
  61  * {@linkplain #equals(Object) equal} as interchangeable and should not
  62  * use instances for synchronization, or unpredictable behavior may
  63  * occur. For example, in a future release, synchronization may fail.
  64  *
  65  * <p>Implementation note: The implementations of the "bit twiddling"
  66  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  67  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  68  * based on material from Henry S. Warren, Jr.'s <cite>Hacker's
  69  * Delight</cite>, (Addison Wesley, 2002) and <cite>Hacker's
  70  * Delight, Second Edition</cite>, (Pearson Education, 2013).
  71  *
  72  * @author  Lee Boynton
  73  * @author  Arthur van Hoff
  74  * @author  Josh Bloch
  75  * @author  Joseph D. Darcy
  76  * @since   1.0
  77  */
  78 @jdk.internal.MigratedValueClass
  79 @jdk.internal.ValueBased
  80 public final class Long extends Number
  81         implements Comparable<Long>, Constable, ConstantDesc {
  82     /**
  83      * A constant holding the minimum value a {@code long} can
  84      * have, -2<sup>63</sup>.
  85      */
  86     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  87 
  88     /**
  89      * A constant holding the maximum value a {@code long} can
  90      * have, 2<sup>63</sup>-1.
  91      */
  92     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  93 
  94     /**
  95      * The {@code Class} instance representing the primitive type
  96      * {@code long}.
  97      *
  98      * @since   1.1
  99      */
 100     public static final Class<Long> TYPE = Class.getPrimitiveClass("long");
 101 
 102     /**
 103      * Returns a string representation of the first argument in the
 104      * radix specified by the second argument.
 105      *
 106      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 107      * or larger than {@code Character.MAX_RADIX}, then the radix
 108      * {@code 10} is used instead.
 109      *
 110      * <p>If the first argument is negative, the first element of the
 111      * result is the ASCII minus sign {@code '-'}
 112      * ({@code '\u005Cu002d'}). If the first argument is not
 113      * negative, no sign character appears in the result.
 114      *
 115      * <p>The remaining characters of the result represent the magnitude
 116      * of the first argument. If the magnitude is zero, it is
 117      * represented by a single zero character {@code '0'}
 118      * ({@code '\u005Cu0030'}); otherwise, the first character of
 119      * the representation of the magnitude will not be the zero
 120      * character.  The following ASCII characters are used as digits:
 121      *
 122      * <blockquote>
 123      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 124      * </blockquote>
 125      *
 126      * These are {@code '\u005Cu0030'} through
 127      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 128      * {@code '\u005Cu007a'}. If {@code radix} is
 129      * <var>N</var>, then the first <var>N</var> of these characters
 130      * are used as radix-<var>N</var> digits in the order shown. Thus,
 131      * the digits for hexadecimal (radix 16) are
 132      * {@code 0123456789abcdef}. If uppercase letters are
 133      * desired, the {@link java.lang.String#toUpperCase()} method may
 134      * be called on the result:
 135      *
 136      * <blockquote>
 137      *  {@code Long.toString(n, 16).toUpperCase()}
 138      * </blockquote>
 139      *
 140      * @param   i       a {@code long} to be converted to a string.
 141      * @param   radix   the radix to use in the string representation.
 142      * @return  a string representation of the argument in the specified radix.
 143      * @see     java.lang.Character#MAX_RADIX
 144      * @see     java.lang.Character#MIN_RADIX
 145      */
 146     public static String toString(long i, int radix) {
 147         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 148             radix = 10;
 149         if (radix == 10)
 150             return toString(i);
 151 
 152         if (COMPACT_STRINGS) {
 153             byte[] buf = new byte[65];
 154             int charPos = 64;
 155             boolean negative = (i < 0);
 156 
 157             if (!negative) {
 158                 i = -i;
 159             }
 160 
 161             while (i <= -radix) {
 162                 buf[charPos--] = (byte)Integer.digits[(int)(-(i % radix))];
 163                 i = i / radix;
 164             }
 165             buf[charPos] = (byte)Integer.digits[(int)(-i)];
 166 
 167             if (negative) {
 168                 buf[--charPos] = '-';
 169             }
 170             return StringLatin1.newString(buf, charPos, (65 - charPos));
 171         }
 172         return toStringUTF16(i, radix);
 173     }
 174 
 175     private static String toStringUTF16(long i, int radix) {
 176         byte[] buf = new byte[65 * 2];
 177         int charPos = 64;
 178         boolean negative = (i < 0);
 179         if (!negative) {
 180             i = -i;
 181         }
 182         while (i <= -radix) {
 183             StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 184             i = i / radix;
 185         }
 186         StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 187         if (negative) {
 188             StringUTF16.putChar(buf, --charPos, '-');
 189         }
 190         return StringUTF16.newString(buf, charPos, (65 - charPos));
 191     }
 192 
 193     /**
 194      * Returns a string representation of the first argument as an
 195      * unsigned integer value in the radix specified by the second
 196      * argument.
 197      *
 198      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 199      * or larger than {@code Character.MAX_RADIX}, then the radix
 200      * {@code 10} is used instead.
 201      *
 202      * <p>Note that since the first argument is treated as an unsigned
 203      * value, no leading sign character is printed.
 204      *
 205      * <p>If the magnitude is zero, it is represented by a single zero
 206      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 207      * the first character of the representation of the magnitude will
 208      * not be the zero character.
 209      *
 210      * <p>The behavior of radixes and the characters used as digits
 211      * are the same as {@link #toString(long, int) toString}.
 212      *
 213      * @param   i       an integer to be converted to an unsigned string.
 214      * @param   radix   the radix to use in the string representation.
 215      * @return  an unsigned string representation of the argument in the specified radix.
 216      * @see     #toString(long, int)
 217      * @since 1.8
 218      */
 219     public static String toUnsignedString(long i, int radix) {
 220         if (i >= 0)
 221             return toString(i, radix);
 222         else {
 223             return switch (radix) {
 224                 case 2  -> toBinaryString(i);
 225                 case 4  -> toUnsignedString0(i, 2);
 226                 case 8  -> toOctalString(i);
 227                 case 10 -> {
 228                     /*
 229                      * We can get the effect of an unsigned division by 10
 230                      * on a long value by first shifting right, yielding a
 231                      * positive value, and then dividing by 5.  This
 232                      * allows the last digit and preceding digits to be
 233                      * isolated more quickly than by an initial conversion
 234                      * to BigInteger.
 235                      */
 236                     long quot = (i >>> 1) / 5;
 237                     long rem = i - quot * 10;
 238                     yield toString(quot) + rem;
 239                 }
 240                 case 16 -> toHexString(i);
 241                 case 32 -> toUnsignedString0(i, 5);
 242                 default -> toUnsignedBigInteger(i).toString(radix);
 243             };
 244         }
 245     }
 246 
 247     /**
 248      * Return a BigInteger equal to the unsigned value of the
 249      * argument.
 250      */
 251     private static BigInteger toUnsignedBigInteger(long i) {
 252         if (i >= 0L)
 253             return BigInteger.valueOf(i);
 254         else {
 255             int upper = (int) (i >>> 32);
 256             int lower = (int) i;
 257 
 258             // return (upper << 32) + lower
 259             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 260                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 261         }
 262     }
 263 
 264     /**
 265      * Returns a string representation of the {@code long}
 266      * argument as an unsigned integer in base&nbsp;16.
 267      *
 268      * <p>The unsigned {@code long} value is the argument plus
 269      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 270      * equal to the argument.  This value is converted to a string of
 271      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 272      * leading {@code 0}s.
 273      *
 274      * <p>The value of the argument can be recovered from the returned
 275      * string {@code s} by calling {@link
 276      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 277      * 16)}.
 278      *
 279      * <p>If the unsigned magnitude is zero, it is represented by a
 280      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 281      * otherwise, the first character of the representation of the
 282      * unsigned magnitude will not be the zero character. The
 283      * following characters are used as hexadecimal digits:
 284      *
 285      * <blockquote>
 286      *  {@code 0123456789abcdef}
 287      * </blockquote>
 288      *
 289      * These are the characters {@code '\u005Cu0030'} through
 290      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 291      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 292      * the {@link java.lang.String#toUpperCase()} method may be called
 293      * on the result:
 294      *
 295      * <blockquote>
 296      *  {@code Long.toHexString(n).toUpperCase()}
 297      * </blockquote>
 298      *
 299      * @apiNote
 300      * The {@link java.util.HexFormat} class provides formatting and parsing
 301      * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
 302      * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
 303      * with leading zeros and for byte arrays includes for each byte
 304      * a delimiter, prefix, and suffix.
 305      *
 306      * @param   i   a {@code long} to be converted to a string.
 307      * @return  the string representation of the unsigned {@code long}
 308      *          value represented by the argument in hexadecimal
 309      *          (base&nbsp;16).
 310      * @see java.util.HexFormat
 311      * @see #parseUnsignedLong(String, int)
 312      * @see #toUnsignedString(long, int)
 313      * @since   1.0.2
 314      */
 315     public static String toHexString(long i) {
 316         return toUnsignedString0(i, 4);
 317     }
 318 
 319     /**
 320      * Returns a string representation of the {@code long}
 321      * argument as an unsigned integer in base&nbsp;8.
 322      *
 323      * <p>The unsigned {@code long} value is the argument plus
 324      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 325      * equal to the argument.  This value is converted to a string of
 326      * ASCII digits in octal (base&nbsp;8) with no extra leading
 327      * {@code 0}s.
 328      *
 329      * <p>The value of the argument can be recovered from the returned
 330      * string {@code s} by calling {@link
 331      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 332      * 8)}.
 333      *
 334      * <p>If the unsigned magnitude is zero, it is represented by a
 335      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 336      * otherwise, the first character of the representation of the
 337      * unsigned magnitude will not be the zero character. The
 338      * following characters are used as octal digits:
 339      *
 340      * <blockquote>
 341      *  {@code 01234567}
 342      * </blockquote>
 343      *
 344      * These are the characters {@code '\u005Cu0030'} through
 345      * {@code '\u005Cu0037'}.
 346      *
 347      * @param   i   a {@code long} to be converted to a string.
 348      * @return  the string representation of the unsigned {@code long}
 349      *          value represented by the argument in octal (base&nbsp;8).
 350      * @see #parseUnsignedLong(String, int)
 351      * @see #toUnsignedString(long, int)
 352      * @since   1.0.2
 353      */
 354     public static String toOctalString(long i) {
 355         return toUnsignedString0(i, 3);
 356     }
 357 
 358     /**
 359      * Returns a string representation of the {@code long}
 360      * argument as an unsigned integer in base&nbsp;2.
 361      *
 362      * <p>The unsigned {@code long} value is the argument plus
 363      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 364      * equal to the argument.  This value is converted to a string of
 365      * ASCII digits in binary (base&nbsp;2) with no extra leading
 366      * {@code 0}s.
 367      *
 368      * <p>The value of the argument can be recovered from the returned
 369      * string {@code s} by calling {@link
 370      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 371      * 2)}.
 372      *
 373      * <p>If the unsigned magnitude is zero, it is represented by a
 374      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 375      * otherwise, the first character of the representation of the
 376      * unsigned magnitude will not be the zero character. The
 377      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 378      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 379      *
 380      * @param   i   a {@code long} to be converted to a string.
 381      * @return  the string representation of the unsigned {@code long}
 382      *          value represented by the argument in binary (base&nbsp;2).
 383      * @see #parseUnsignedLong(String, int)
 384      * @see #toUnsignedString(long, int)
 385      * @since   1.0.2
 386      */
 387     public static String toBinaryString(long i) {
 388         return toUnsignedString0(i, 1);
 389     }
 390 
 391     /**
 392      * Format a long (treated as unsigned) into a String.
 393      * @param val the value to format
 394      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 395      */
 396     static String toUnsignedString0(long val, int shift) {
 397         // assert shift > 0 && shift <=5 : "Illegal shift value";
 398         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 399         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 400         if (COMPACT_STRINGS) {
 401             byte[] buf = new byte[chars];
 402             formatUnsignedLong0(val, shift, buf, 0, chars);
 403             return new String(buf, LATIN1);
 404         } else {
 405             byte[] buf = new byte[chars * 2];
 406             formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
 407             return new String(buf, UTF16);
 408         }
 409     }
 410 
 411     /**
 412      * Format a long (treated as unsigned) into a byte buffer (LATIN1 version). If
 413      * {@code len} exceeds the formatted ASCII representation of {@code val},
 414      * {@code buf} will be padded with leading zeroes.
 415      *
 416      * @param val the unsigned long to format
 417      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 418      * @param buf the byte buffer to write to
 419      * @param offset the offset in the destination buffer to start at
 420      * @param len the number of characters to write
 421      */
 422     private static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
 423         int charPos = offset + len;
 424         int radix = 1 << shift;
 425         int mask = radix - 1;
 426         do {
 427             buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
 428             val >>>= shift;
 429         } while (charPos > offset);
 430     }
 431 
 432     /**
 433      * Format a long (treated as unsigned) into a byte buffer (UTF16 version). If
 434      * {@code len} exceeds the formatted ASCII representation of {@code val},
 435      * {@code buf} will be padded with leading zeroes.
 436      *
 437      * @param val the unsigned long to format
 438      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 439      * @param buf the byte buffer to write to
 440      * @param offset the offset in the destination buffer to start at
 441      * @param len the number of characters to write
 442      */
 443     private static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
 444         int charPos = offset + len;
 445         int radix = 1 << shift;
 446         int mask = radix - 1;
 447         do {
 448             StringUTF16.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
 449             val >>>= shift;
 450         } while (charPos > offset);
 451     }
 452 
 453     /**
 454      * Returns a {@code String} object representing the specified
 455      * {@code long}.  The argument is converted to signed decimal
 456      * representation and returned as a string, exactly as if the
 457      * argument and the radix 10 were given as arguments to the {@link
 458      * #toString(long, int)} method.
 459      *
 460      * @param   i   a {@code long} to be converted.
 461      * @return  a string representation of the argument in base&nbsp;10.
 462      */
 463     public static String toString(long i) {
 464         int size = DecimalDigits.stringSize(i);
 465         if (COMPACT_STRINGS) {
 466             byte[] buf = new byte[size];
 467             StringLatin1.getChars(i, size, buf);
 468             return new String(buf, LATIN1);
 469         } else {
 470             byte[] buf = new byte[size * 2];
 471             StringUTF16.getChars(i, size, buf);
 472             return new String(buf, UTF16);
 473         }
 474     }
 475 
 476     /**
 477      * Returns a string representation of the argument as an unsigned
 478      * decimal value.
 479      *
 480      * The argument is converted to unsigned decimal representation
 481      * and returned as a string exactly as if the argument and radix
 482      * 10 were given as arguments to the {@link #toUnsignedString(long,
 483      * int)} method.
 484      *
 485      * @param   i  an integer to be converted to an unsigned string.
 486      * @return  an unsigned string representation of the argument.
 487      * @see     #toUnsignedString(long, int)
 488      * @since 1.8
 489      */
 490     public static String toUnsignedString(long i) {
 491         return toUnsignedString(i, 10);
 492     }
 493 
 494     /**
 495      * Parses the string argument as a signed {@code long} in the
 496      * radix specified by the second argument. The characters in the
 497      * string must all be digits of the specified radix (as determined
 498      * by whether {@link java.lang.Character#digit(char, int)} returns
 499      * a nonnegative value), except that the first character may be an
 500      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 501      * indicate a negative value or an ASCII plus sign {@code '+'}
 502      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 503      * resulting {@code long} value is returned.
 504      *
 505      * <p>Note that neither the character {@code L}
 506      * ({@code '\u005Cu004C'}) nor {@code l}
 507      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 508      * of the string as a type indicator, as would be permitted in
 509      * Java programming language source code - except that either
 510      * {@code L} or {@code l} may appear as a digit for a
 511      * radix greater than or equal to 22.
 512      *
 513      * <p>An exception of type {@code NumberFormatException} is
 514      * thrown if any of the following situations occurs:
 515      * <ul>
 516      *
 517      * <li>The first argument is {@code null} or is a string of
 518      * length zero.
 519      *
 520      * <li>The {@code radix} is either smaller than {@link
 521      * java.lang.Character#MIN_RADIX} or larger than {@link
 522      * java.lang.Character#MAX_RADIX}.
 523      *
 524      * <li>Any character of the string is not a digit of the specified
 525      * radix, except that the first character may be a minus sign
 526      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 527      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 528      * longer than length 1.
 529      *
 530      * <li>The value represented by the string is not a value of type
 531      *      {@code long}.
 532      * </ul>
 533      *
 534      * <p>Examples:
 535      * <blockquote><pre>
 536      * parseLong("0", 10) returns 0L
 537      * parseLong("473", 10) returns 473L
 538      * parseLong("+42", 10) returns 42L
 539      * parseLong("-0", 10) returns 0L
 540      * parseLong("-FF", 16) returns -255L
 541      * parseLong("1100110", 2) returns 102L
 542      * parseLong("99", 8) throws a NumberFormatException
 543      * parseLong("Hazelnut", 10) throws a NumberFormatException
 544      * parseLong("Hazelnut", 36) returns 1356099454469L
 545      * </pre></blockquote>
 546      *
 547      * @param      s       the {@code String} containing the
 548      *                     {@code long} representation to be parsed.
 549      * @param      radix   the radix to be used while parsing {@code s}.
 550      * @return     the {@code long} represented by the string argument in
 551      *             the specified radix.
 552      * @throws     NumberFormatException  if the string does not contain a
 553      *             parsable {@code long}.
 554      */
 555     public static long parseLong(String s, int radix)
 556                 throws NumberFormatException {
 557         if (s == null) {
 558             throw new NumberFormatException("Cannot parse null string");
 559         }
 560 
 561         if (radix < Character.MIN_RADIX) {
 562             throw new NumberFormatException(String.format(
 563                 "radix %s less than Character.MIN_RADIX", radix));
 564         }
 565 
 566         if (radix > Character.MAX_RADIX) {
 567             throw new NumberFormatException(String.format(
 568                 "radix %s greater than Character.MAX_RADIX", radix));
 569         }
 570 
 571         int len = s.length();
 572         if (len == 0) {
 573             throw NumberFormatException.forInputString("", radix);
 574         }
 575         int digit = ~0xFF;
 576         int i = 0;
 577         char firstChar = s.charAt(i++);
 578         if (firstChar != '-' && firstChar != '+') {
 579             digit = digit(firstChar, radix);
 580         }
 581         if (digit >= 0 || digit == ~0xFF && len > 1) {
 582             long limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 583             long multmin = limit / radix;
 584             long result = -(digit & 0xFF);
 585             boolean inRange = true;
 586             /* Accumulating negatively avoids surprises near MAX_VALUE */
 587             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 588                     && (inRange = result > multmin
 589                         || result == multmin && digit <= (int) (radix * multmin - limit))) {
 590                 result = radix * result - digit;
 591             }
 592             if (inRange && i == len && digit >= 0) {
 593                 return firstChar != '-' ? -result : result;
 594             }
 595         }
 596         throw NumberFormatException.forInputString(s, radix);
 597     }
 598 
 599     /**
 600      * Parses the {@link CharSequence} argument as a signed {@code long} in
 601      * the specified {@code radix}, beginning at the specified
 602      * {@code beginIndex} and extending to {@code endIndex - 1}.
 603      *
 604      * <p>The method does not take steps to guard against the
 605      * {@code CharSequence} being mutated while parsing.
 606      *
 607      * @param      s   the {@code CharSequence} containing the {@code long}
 608      *                  representation to be parsed
 609      * @param      beginIndex   the beginning index, inclusive.
 610      * @param      endIndex     the ending index, exclusive.
 611      * @param      radix   the radix to be used while parsing {@code s}.
 612      * @return     the signed {@code long} represented by the subsequence in
 613      *             the specified radix.
 614      * @throws     NullPointerException  if {@code s} is null.
 615      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 616      *             negative, or if {@code beginIndex} is greater than
 617      *             {@code endIndex} or if {@code endIndex} is greater than
 618      *             {@code s.length()}.
 619      * @throws     NumberFormatException  if the {@code CharSequence} does not
 620      *             contain a parsable {@code long} in the specified
 621      *             {@code radix}, or if {@code radix} is either smaller than
 622      *             {@link java.lang.Character#MIN_RADIX} or larger than
 623      *             {@link java.lang.Character#MAX_RADIX}.
 624      * @since  9
 625      */
 626     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 627                 throws NumberFormatException {
 628         Objects.requireNonNull(s);
 629         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 630 
 631         if (radix < Character.MIN_RADIX) {
 632             throw new NumberFormatException(String.format(
 633                 "radix %s less than Character.MIN_RADIX", radix));
 634         }
 635 
 636         if (radix > Character.MAX_RADIX) {
 637             throw new NumberFormatException(String.format(
 638                 "radix %s greater than Character.MAX_RADIX", radix));
 639         }
 640 
 641         /*
 642          * While s can be concurrently modified, it is ensured that each
 643          * of its characters is read at most once, from lower to higher indices.
 644          * This is obtained by reading them using the pattern s.charAt(i++),
 645          * and by not updating i anywhere else.
 646          */
 647         if (beginIndex == endIndex) {
 648             throw NumberFormatException.forInputString("", radix);
 649         }
 650         int digit = ~0xFF;  // ~0xFF means firstChar char is sign
 651         int i = beginIndex;
 652         char firstChar = s.charAt(i++);
 653         if (firstChar != '-' && firstChar != '+') {
 654             digit = digit(firstChar, radix);
 655         }
 656         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 657             long limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 658             long multmin = limit / radix;
 659             long result = -(digit & 0xFF);
 660             boolean inRange = true;
 661             /* Accumulating negatively avoids surprises near MAX_VALUE */
 662             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 663                     && (inRange = result > multmin
 664                         || result == multmin && digit <= (int) (radix * multmin - limit))) {
 665                 result = radix * result - digit;
 666             }
 667             if (inRange && i == endIndex && digit >= 0) {
 668                 return firstChar != '-' ? -result : result;
 669             }
 670         }
 671         throw NumberFormatException.forCharSequence(s, beginIndex,
 672             endIndex, i - (digit < -1 ? 0 : 1));
 673     }
 674 
 675     /**
 676      * Parses the string argument as a signed decimal {@code long}.
 677      * The characters in the string must all be decimal digits, except
 678      * that the first character may be an ASCII minus sign {@code '-'}
 679      * ({@code \u005Cu002D'}) to indicate a negative value or an
 680      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 681      * indicate a positive value. The resulting {@code long} value is
 682      * returned, exactly as if the argument and the radix {@code 10}
 683      * were given as arguments to the {@link
 684      * #parseLong(java.lang.String, int)} method.
 685      *
 686      * <p>Note that neither the character {@code L}
 687      * ({@code '\u005Cu004C'}) nor {@code l}
 688      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 689      * of the string as a type indicator, as would be permitted in
 690      * Java programming language source code.
 691      *
 692      * @param      s   a {@code String} containing the {@code long}
 693      *             representation to be parsed
 694      * @return     the {@code long} represented by the argument in
 695      *             decimal.
 696      * @throws     NumberFormatException  if the string does not contain a
 697      *             parsable {@code long}.
 698      */
 699     public static long parseLong(String s) throws NumberFormatException {
 700         return parseLong(s, 10);
 701     }
 702 
 703     /**
 704      * Parses the string argument as an unsigned {@code long} in the
 705      * radix specified by the second argument.  An unsigned integer
 706      * maps the values usually associated with negative numbers to
 707      * positive numbers larger than {@code MAX_VALUE}.
 708      *
 709      * The characters in the string must all be digits of the
 710      * specified radix (as determined by whether {@link
 711      * java.lang.Character#digit(char, int)} returns a nonnegative
 712      * value), except that the first character may be an ASCII plus
 713      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 714      * integer value is returned.
 715      *
 716      * <p>An exception of type {@code NumberFormatException} is
 717      * thrown if any of the following situations occurs:
 718      * <ul>
 719      * <li>The first argument is {@code null} or is a string of
 720      * length zero.
 721      *
 722      * <li>The radix is either smaller than
 723      * {@link java.lang.Character#MIN_RADIX} or
 724      * larger than {@link java.lang.Character#MAX_RADIX}.
 725      *
 726      * <li>Any character of the string is not a digit of the specified
 727      * radix, except that the first character may be a plus sign
 728      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 729      * string is longer than length 1.
 730      *
 731      * <li>The value represented by the string is larger than the
 732      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 733      *
 734      * </ul>
 735      *
 736      *
 737      * @param      s   the {@code String} containing the unsigned integer
 738      *                  representation to be parsed
 739      * @param      radix   the radix to be used while parsing {@code s}.
 740      * @return     the unsigned {@code long} represented by the string
 741      *             argument in the specified radix.
 742      * @throws     NumberFormatException if the {@code String}
 743      *             does not contain a parsable {@code long}.
 744      * @since 1.8
 745      */
 746     public static long parseUnsignedLong(String s, int radix)
 747                 throws NumberFormatException {
 748         if (s == null)  {
 749             throw new NumberFormatException("Cannot parse null string");
 750         }
 751 
 752         if (radix < Character.MIN_RADIX) {
 753             throw new NumberFormatException(String.format(
 754                 "radix %s less than Character.MIN_RADIX", radix));
 755         }
 756 
 757         if (radix > Character.MAX_RADIX) {
 758             throw new NumberFormatException(String.format(
 759                 "radix %s greater than Character.MAX_RADIX", radix));
 760         }
 761 
 762         int len = s.length();
 763         if (len == 0) {
 764             throw NumberFormatException.forInputString(s, radix);
 765         }
 766         int i = 0;
 767         char firstChar = s.charAt(i++);
 768         if (firstChar == '-') {
 769             throw new NumberFormatException(String.format(
 770                 "Illegal leading minus sign on unsigned string %s.", s));
 771         }
 772         int digit = ~0xFF;
 773         if (firstChar != '+') {
 774             digit = digit(firstChar, radix);
 775         }
 776         if (digit >= 0 || digit == ~0xFF && len > 1) {
 777             long multmax = divideUnsigned(-1L, radix);  // -1L is max unsigned long
 778             long result = digit & 0xFF;
 779             boolean inRange = true;
 780             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 781                     && (inRange = compareUnsigned(result, multmax) < 0
 782                         || result == multmax && digit < (int) (-radix * multmax))) {
 783                 result = radix * result + digit;
 784             }
 785             if (inRange && i == len && digit >= 0) {
 786                 return result;
 787             }
 788         }
 789         if (digit < 0) {
 790             throw NumberFormatException.forInputString(s, radix);
 791         }
 792         throw new NumberFormatException(String.format(
 793             "String value %s exceeds range of unsigned long.", s));
 794     }
 795 
 796     /**
 797      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 798      * the specified {@code radix}, beginning at the specified
 799      * {@code beginIndex} and extending to {@code endIndex - 1}.
 800      *
 801      * <p>The method does not take steps to guard against the
 802      * {@code CharSequence} being mutated while parsing.
 803      *
 804      * @param      s   the {@code CharSequence} containing the unsigned
 805      *                 {@code long} representation to be parsed
 806      * @param      beginIndex   the beginning index, inclusive.
 807      * @param      endIndex     the ending index, exclusive.
 808      * @param      radix   the radix to be used while parsing {@code s}.
 809      * @return     the unsigned {@code long} represented by the subsequence in
 810      *             the specified radix.
 811      * @throws     NullPointerException  if {@code s} is null.
 812      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 813      *             negative, or if {@code beginIndex} is greater than
 814      *             {@code endIndex} or if {@code endIndex} is greater than
 815      *             {@code s.length()}.
 816      * @throws     NumberFormatException  if the {@code CharSequence} does not
 817      *             contain a parsable unsigned {@code long} in the specified
 818      *             {@code radix}, or if {@code radix} is either smaller than
 819      *             {@link java.lang.Character#MIN_RADIX} or larger than
 820      *             {@link java.lang.Character#MAX_RADIX}.
 821      * @since  9
 822      */
 823     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
 824                 throws NumberFormatException {
 825         Objects.requireNonNull(s);
 826         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 827 
 828         if (radix < Character.MIN_RADIX) {
 829             throw new NumberFormatException(String.format(
 830                 "radix %s less than Character.MIN_RADIX", radix));
 831         }
 832 
 833         if (radix > Character.MAX_RADIX) {
 834             throw new NumberFormatException(String.format(
 835                 "radix %s greater than Character.MAX_RADIX", radix));
 836         }
 837 
 838         /*
 839          * While s can be concurrently modified, it is ensured that each
 840          * of its characters is read at most once, from lower to higher indices.
 841          * This is obtained by reading them using the pattern s.charAt(i++),
 842          * and by not updating i anywhere else.
 843          */
 844         if (beginIndex == endIndex) {
 845             throw NumberFormatException.forInputString("", radix);
 846         }
 847         int i = beginIndex;
 848         char firstChar = s.charAt(i++);
 849         if (firstChar == '-') {
 850             throw new NumberFormatException(
 851                 "Illegal leading minus sign on unsigned string " + s + ".");
 852         }
 853         int digit = ~0xFF;
 854         if (firstChar != '+') {
 855             digit = digit(firstChar, radix);
 856         }
 857         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 858             long multmax = divideUnsigned(-1L, radix);  // -1L is max unsigned long
 859             long result = digit & 0xFF;
 860             boolean inRange = true;
 861             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 862                     && (inRange = compareUnsigned(result, multmax) < 0
 863                         || result == multmax && digit < (int) (-radix * multmax))) {
 864                 result = radix * result + digit;
 865             }
 866             if (inRange && i == endIndex && digit >= 0) {
 867                 return result;
 868             }
 869         }
 870         if (digit < 0) {
 871             throw NumberFormatException.forCharSequence(s, beginIndex,
 872                 endIndex, i - (digit < -1 ? 0 : 1));
 873         }
 874         throw new NumberFormatException(String.format(
 875             "String value %s exceeds range of unsigned long.", s));
 876     }
 877 
 878     /**
 879      * Parses the string argument as an unsigned decimal {@code long}. The
 880      * characters in the string must all be decimal digits, except
 881      * that the first character may be an ASCII plus sign {@code
 882      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 883      * is returned, exactly as if the argument and the radix 10 were
 884      * given as arguments to the {@link
 885      * #parseUnsignedLong(java.lang.String, int)} method.
 886      *
 887      * @param s   a {@code String} containing the unsigned {@code long}
 888      *            representation to be parsed
 889      * @return    the unsigned {@code long} value represented by the decimal string argument
 890      * @throws    NumberFormatException  if the string does not contain a
 891      *            parsable unsigned integer.
 892      * @since 1.8
 893      */
 894     public static long parseUnsignedLong(String s) throws NumberFormatException {
 895         return parseUnsignedLong(s, 10);
 896     }
 897 
 898     /**
 899      * Returns a {@code Long} object holding the value
 900      * extracted from the specified {@code String} when parsed
 901      * with the radix given by the second argument.  The first
 902      * argument is interpreted as representing a signed
 903      * {@code long} in the radix specified by the second
 904      * argument, exactly as if the arguments were given to the {@link
 905      * #parseLong(java.lang.String, int)} method. The result is a
 906      * {@code Long} object that represents the {@code long}
 907      * value specified by the string.
 908      *
 909      * <p>In other words, this method returns a {@code Long} object equal
 910      * to the value of:
 911      *
 912      * <blockquote>
 913      *  {@code Long.valueOf(Long.parseLong(s, radix))}
 914      * </blockquote>
 915      *
 916      * @param      s       the string to be parsed
 917      * @param      radix   the radix to be used in interpreting {@code s}
 918      * @return     a {@code Long} object holding the value
 919      *             represented by the string argument in the specified
 920      *             radix.
 921      * @throws     NumberFormatException  If the {@code String} does not
 922      *             contain a parsable {@code long}.
 923      */
 924     public static Long valueOf(String s, int radix) throws NumberFormatException {
 925         return Long.valueOf(parseLong(s, radix));
 926     }
 927 
 928     /**
 929      * Returns a {@code Long} object holding the value
 930      * of the specified {@code String}. The argument is
 931      * interpreted as representing a signed decimal {@code long},
 932      * exactly as if the argument were given to the {@link
 933      * #parseLong(java.lang.String)} method. The result is a
 934      * {@code Long} object that represents the integer value
 935      * specified by the string.
 936      *
 937      * <p>In other words, this method returns a {@code Long} object
 938      * equal to the value of:
 939      *
 940      * <blockquote>
 941      *  {@code Long.valueOf(Long.parseLong(s))}
 942      * </blockquote>
 943      *
 944      * @param      s   the string to be parsed.
 945      * @return     a {@code Long} object holding the value
 946      *             represented by the string argument.
 947      * @throws     NumberFormatException  If the string cannot be parsed
 948      *             as a {@code long}.
 949      */
 950     public static Long valueOf(String s) throws NumberFormatException
 951     {
 952         return Long.valueOf(parseLong(s, 10));
 953     }
 954 
 955     private static final class LongCache {
 956         private LongCache() {}
 957 
 958         @Stable
 959         static final Long[] cache;
 960         static Long[] archivedCache;
 961 
 962         static {
 963             int size = -(-128) + 127 + 1;
 964 
 965             // Load and use the archived cache if it exists
 966             CDS.initializeFromArchive(LongCache.class);
 967             if (archivedCache == null) {
 968                 Long[] c = new Long[size];
 969                 long value = -128;
 970                 for(int i = 0; i < size; i++) {
 971                     c[i] = new Long(value++);
 972                 }
 973                 archivedCache = c;
 974             }
 975             cache = archivedCache;
 976             assert cache.length == size;
 977         }
 978     }
 979 
 980     /**
 981      * Returns a {@code Long} instance representing the specified
 982      * {@code long} value.
 983      * If a new {@code Long} instance is not required, this method
 984      * should generally be used in preference to the constructor
 985      * {@link #Long(long)}, as this method is likely to yield
 986      * significantly better space and time performance by caching
 987      * frequently requested values.
 988      *
 989      * This method will always cache values in the range -128 to 127,
 990      * inclusive, and may cache other values outside of this range.
 991      *
 992      * @param  l a long value.
 993      * @return a {@code Long} instance representing {@code l}.
 994      * @since  1.5
 995      */
 996     @IntrinsicCandidate
 997     @DeserializeConstructor
 998     public static Long valueOf(long l) {
 999         final int offset = 128;
1000         if (l >= -128 && l <= 127) { // will cache
1001             return LongCache.cache[(int)l + offset];
1002         }
1003         return new Long(l);
1004     }
1005 
1006     /**
1007      * Decodes a {@code String} into a {@code Long}.
1008      * Accepts decimal, hexadecimal, and octal numbers given by the
1009      * following grammar:
1010      *
1011      * <blockquote>
1012      * <dl>
1013      * <dt><i>DecodableString:</i>
1014      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1015      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1016      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1017      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1018      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1019      *
1020      * <dt><i>Sign:</i>
1021      * <dd>{@code -}
1022      * <dd>{@code +}
1023      * </dl>
1024      * </blockquote>
1025      *
1026      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1027      * are as defined in section {@jls 3.10.1} of
1028      * <cite>The Java Language Specification</cite>,
1029      * except that underscores are not accepted between digits.
1030      *
1031      * <p>The sequence of characters following an optional
1032      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1033      * "{@code #}", or leading zero) is parsed as by the {@code
1034      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1035      * This sequence of characters must represent a positive value or
1036      * a {@link NumberFormatException} will be thrown.  The result is
1037      * negated if first character of the specified {@code String} is
1038      * the minus sign.  No whitespace characters are permitted in the
1039      * {@code String}.
1040      *
1041      * @param     nm the {@code String} to decode.
1042      * @return    a {@code Long} object holding the {@code long}
1043      *            value represented by {@code nm}
1044      * @throws    NumberFormatException  if the {@code String} does not
1045      *            contain a parsable {@code long}.
1046      * @see java.lang.Long#parseLong(String, int)
1047      * @since 1.2
1048      */
1049     public static Long decode(String nm) throws NumberFormatException {
1050         int radix = 10;
1051         int index = 0;
1052         boolean negative = false;
1053         long result;
1054 
1055         if (nm.isEmpty())
1056             throw new NumberFormatException("Zero length string");
1057         char firstChar = nm.charAt(0);
1058         // Handle sign, if present
1059         if (firstChar == '-') {
1060             negative = true;
1061             index++;
1062         } else if (firstChar == '+')
1063             index++;
1064 
1065         // Handle radix specifier, if present
1066         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1067             index += 2;
1068             radix = 16;
1069         }
1070         else if (nm.startsWith("#", index)) {
1071             index ++;
1072             radix = 16;
1073         }
1074         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1075             index ++;
1076             radix = 8;
1077         }
1078 
1079         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1080             throw new NumberFormatException("Sign character in wrong position");
1081 
1082         try {
1083             result = parseLong(nm, index, nm.length(), radix);
1084             result = negative ? -result : result;
1085         } catch (NumberFormatException e) {
1086             // If number is Long.MIN_VALUE, we'll end up here. The next line
1087             // handles this case, and causes any genuine format error to be
1088             // rethrown.
1089             String constant = negative ? ("-" + nm.substring(index))
1090                                        : nm.substring(index);
1091             result = parseLong(constant, radix);
1092         }
1093         return result;
1094     }
1095 
1096     /**
1097      * The value of the {@code Long}.
1098      *
1099      * @serial
1100      */
1101     private final long value;
1102 
1103     /**
1104      * Constructs a newly allocated {@code Long} object that
1105      * represents the specified {@code long} argument.
1106      *
1107      * @param   value   the value to be represented by the
1108      *          {@code Long} object.
1109      *
1110      * @deprecated
1111      * It is rarely appropriate to use this constructor. The static factory
1112      * {@link #valueOf(long)} is generally a better choice, as it is
1113      * likely to yield significantly better space and time performance.
1114      */
1115     @Deprecated(since="9", forRemoval = true)
1116     public Long(long value) {
1117         this.value = value;
1118     }
1119 
1120     /**
1121      * Constructs a newly allocated {@code Long} object that
1122      * represents the {@code long} value indicated by the
1123      * {@code String} parameter. The string is converted to a
1124      * {@code long} value in exactly the manner used by the
1125      * {@code parseLong} method for radix 10.
1126      *
1127      * @param      s   the {@code String} to be converted to a
1128      *             {@code Long}.
1129      * @throws     NumberFormatException  if the {@code String} does not
1130      *             contain a parsable {@code long}.
1131      *
1132      * @deprecated
1133      * It is rarely appropriate to use this constructor.
1134      * Use {@link #parseLong(String)} to convert a string to a
1135      * {@code long} primitive, or use {@link #valueOf(String)}
1136      * to convert a string to a {@code Long} object.
1137      */
1138     @Deprecated(since="9", forRemoval = true)
1139     public Long(String s) throws NumberFormatException {
1140         this.value = parseLong(s, 10);
1141     }
1142 
1143     /**
1144      * Returns the value of this {@code Long} as a {@code byte} after
1145      * a narrowing primitive conversion.
1146      * @jls 5.1.3 Narrowing Primitive Conversion
1147      */
1148     public byte byteValue() {
1149         return (byte)value;
1150     }
1151 
1152     /**
1153      * Returns the value of this {@code Long} as a {@code short} after
1154      * a narrowing primitive conversion.
1155      * @jls 5.1.3 Narrowing Primitive Conversion
1156      */
1157     public short shortValue() {
1158         return (short)value;
1159     }
1160 
1161     /**
1162      * Returns the value of this {@code Long} as an {@code int} after
1163      * a narrowing primitive conversion.
1164      * @jls 5.1.3 Narrowing Primitive Conversion
1165      */
1166     public int intValue() {
1167         return (int)value;
1168     }
1169 
1170     /**
1171      * Returns the value of this {@code Long} as a
1172      * {@code long} value.
1173      */
1174     @IntrinsicCandidate
1175     public long longValue() {
1176         return value;
1177     }
1178 
1179     /**
1180      * Returns the value of this {@code Long} as a {@code float} after
1181      * a widening primitive conversion.
1182      * @jls 5.1.2 Widening Primitive Conversion
1183      */
1184     public float floatValue() {
1185         return (float)value;
1186     }
1187 
1188     /**
1189      * Returns the value of this {@code Long} as a {@code double}
1190      * after a widening primitive conversion.
1191      * @jls 5.1.2 Widening Primitive Conversion
1192      */
1193     public double doubleValue() {
1194         return (double)value;
1195     }
1196 
1197     /**
1198      * Returns a {@code String} object representing this
1199      * {@code Long}'s value.  The value is converted to signed
1200      * decimal representation and returned as a string, exactly as if
1201      * the {@code long} value were given as an argument to the
1202      * {@link java.lang.Long#toString(long)} method.
1203      *
1204      * @return  a string representation of the value of this object in
1205      *          base&nbsp;10.
1206      */
1207     public String toString() {
1208         return toString(value);
1209     }
1210 
1211     /**
1212      * Returns a hash code for this {@code Long}. The result is
1213      * the exclusive OR of the two halves of the primitive
1214      * {@code long} value held by this {@code Long}
1215      * object. That is, the hashcode is the value of the expression:
1216      *
1217      * <blockquote>
1218      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1219      * </blockquote>
1220      *
1221      * @return  a hash code value for this object.
1222      */
1223     @Override
1224     public int hashCode() {
1225         return Long.hashCode(value);
1226     }
1227 
1228     /**
1229      * Returns a hash code for a {@code long} value; compatible with
1230      * {@code Long.hashCode()}.
1231      *
1232      * @param value the value to hash
1233      * @return a hash code value for a {@code long} value.
1234      * @since 1.8
1235      */
1236     public static int hashCode(long value) {
1237         return (int)(value ^ (value >>> 32));
1238     }
1239 
1240     /**
1241      * Compares this object to the specified object.  The result is
1242      * {@code true} if and only if the argument is not
1243      * {@code null} and is a {@code Long} object that
1244      * contains the same {@code long} value as this object.
1245      *
1246      * @param   obj   the object to compare with.
1247      * @return  {@code true} if the objects are the same;
1248      *          {@code false} otherwise.
1249      */
1250     public boolean equals(Object obj) {
1251         if (obj instanceof Long ell) {
1252             return value == ell.longValue();
1253         }
1254         return false;
1255     }
1256 
1257     /**
1258      * Determines the {@code long} value of the system property
1259      * with the specified name.
1260      *
1261      * <p>The first argument is treated as the name of a system
1262      * property.  System properties are accessible through the {@link
1263      * java.lang.System#getProperty(java.lang.String)} method. The
1264      * string value of this property is then interpreted as a {@code
1265      * long} value using the grammar supported by {@link Long#decode decode}
1266      * and a {@code Long} object representing this value is returned.
1267      *
1268      * <p>If there is no property with the specified name, if the
1269      * specified name is empty or {@code null}, or if the property
1270      * does not have the correct numeric format, then {@code null} is
1271      * returned.
1272      *
1273      * <p>In other words, this method returns a {@code Long} object
1274      * equal to the value of:
1275      *
1276      * <blockquote>
1277      *  {@code getLong(nm, null)}
1278      * </blockquote>
1279      *
1280      * @param   nm   property name.
1281      * @return  the {@code Long} value of the property.
1282      * @throws  SecurityException for the same reasons as
1283      *          {@link System#getProperty(String) System.getProperty}
1284      * @see     java.lang.System#getProperty(java.lang.String)
1285      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1286      */
1287     public static Long getLong(String nm) {
1288         return getLong(nm, null);
1289     }
1290 
1291     /**
1292      * Determines the {@code long} value of the system property
1293      * with the specified name.
1294      *
1295      * <p>The first argument is treated as the name of a system
1296      * property.  System properties are accessible through the {@link
1297      * java.lang.System#getProperty(java.lang.String)} method. The
1298      * string value of this property is then interpreted as a {@code
1299      * long} value using the grammar supported by {@link Long#decode decode}
1300      * and a {@code Long} object representing this value is returned.
1301      *
1302      * <p>The second argument is the default value. A {@code Long} object
1303      * that represents the value of the second argument is returned if there
1304      * is no property of the specified name, if the property does not have
1305      * the correct numeric format, or if the specified name is empty or null.
1306      *
1307      * <p>In other words, this method returns a {@code Long} object equal
1308      * to the value of:
1309      *
1310      * <blockquote>
1311      *  {@code getLong(nm, Long.valueOf(val))}
1312      * </blockquote>
1313      *
1314      * but in practice it may be implemented in a manner such as:
1315      *
1316      * <blockquote><pre>
1317      * Long result = getLong(nm, null);
1318      * return (result == null) ? Long.valueOf(val) : result;
1319      * </pre></blockquote>
1320      *
1321      * to avoid the unnecessary allocation of a {@code Long} object when
1322      * the default value is not needed.
1323      *
1324      * @param   nm    property name.
1325      * @param   val   default value.
1326      * @return  the {@code Long} value of the property.
1327      * @throws  SecurityException for the same reasons as
1328      *          {@link System#getProperty(String) System.getProperty}
1329      * @see     java.lang.System#getProperty(java.lang.String)
1330      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1331      */
1332     public static Long getLong(String nm, long val) {
1333         Long result = Long.getLong(nm, null);
1334         return (result == null) ? Long.valueOf(val) : result;
1335     }
1336 
1337     /**
1338      * Returns the {@code long} value of the system property with
1339      * the specified name.  The first argument is treated as the name
1340      * of a system property.  System properties are accessible through
1341      * the {@link java.lang.System#getProperty(java.lang.String)}
1342      * method. The string value of this property is then interpreted
1343      * as a {@code long} value, as per the
1344      * {@link Long#decode decode} method, and a {@code Long} object
1345      * representing this value is returned; in summary:
1346      *
1347      * <ul>
1348      * <li>If the property value begins with the two ASCII characters
1349      * {@code 0x} or the ASCII character {@code #}, not followed by
1350      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1351      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1352      * with radix 16.
1353      * <li>If the property value begins with the ASCII character
1354      * {@code 0} followed by another character, it is parsed as
1355      * an octal integer exactly as by the method {@link
1356      * #valueOf(java.lang.String, int)} with radix 8.
1357      * <li>Otherwise the property value is parsed as a decimal
1358      * integer exactly as by the method
1359      * {@link #valueOf(java.lang.String, int)} with radix 10.
1360      * </ul>
1361      *
1362      * <p>Note that, in every case, neither {@code L}
1363      * ({@code '\u005Cu004C'}) nor {@code l}
1364      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1365      * of the property value as a type indicator, as would be
1366      * permitted in Java programming language source code.
1367      *
1368      * <p>The second argument is the default value. The default value is
1369      * returned if there is no property of the specified name, if the
1370      * property does not have the correct numeric format, or if the
1371      * specified name is empty or {@code null}.
1372      *
1373      * @param   nm   property name.
1374      * @param   val   default value.
1375      * @return  the {@code Long} value of the property.
1376      * @throws  SecurityException for the same reasons as
1377      *          {@link System#getProperty(String) System.getProperty}
1378      * @see     System#getProperty(java.lang.String)
1379      * @see     System#getProperty(java.lang.String, java.lang.String)
1380      */
1381     public static Long getLong(String nm, Long val) {
1382         String v = null;
1383         try {
1384             v = System.getProperty(nm);
1385         } catch (IllegalArgumentException | NullPointerException e) {
1386         }
1387         if (v != null) {
1388             try {
1389                 return Long.decode(v);
1390             } catch (NumberFormatException e) {
1391             }
1392         }
1393         return val;
1394     }
1395 
1396     /**
1397      * Compares two {@code Long} objects numerically.
1398      *
1399      * @param   anotherLong   the {@code Long} to be compared.
1400      * @return  the value {@code 0} if this {@code Long} is
1401      *          equal to the argument {@code Long}; a value less than
1402      *          {@code 0} if this {@code Long} is numerically less
1403      *          than the argument {@code Long}; and a value greater
1404      *          than {@code 0} if this {@code Long} is numerically
1405      *           greater than the argument {@code Long} (signed
1406      *           comparison).
1407      * @since   1.2
1408      */
1409     public int compareTo(Long anotherLong) {
1410         return compare(this.value, anotherLong.value);
1411     }
1412 
1413     /**
1414      * Compares two {@code long} values numerically.
1415      * The value returned is identical to what would be returned by:
1416      * <pre>
1417      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1418      * </pre>
1419      *
1420      * @param  x the first {@code long} to compare
1421      * @param  y the second {@code long} to compare
1422      * @return the value {@code 0} if {@code x == y};
1423      *         a value less than {@code 0} if {@code x < y}; and
1424      *         a value greater than {@code 0} if {@code x > y}
1425      * @since 1.7
1426      */
1427     public static int compare(long x, long y) {
1428         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1429     }
1430 
1431     /**
1432      * Compares two {@code long} values numerically treating the values
1433      * as unsigned.
1434      *
1435      * @param  x the first {@code long} to compare
1436      * @param  y the second {@code long} to compare
1437      * @return the value {@code 0} if {@code x == y}; a value less
1438      *         than {@code 0} if {@code x < y} as unsigned values; and
1439      *         a value greater than {@code 0} if {@code x > y} as
1440      *         unsigned values
1441      * @since 1.8
1442      */
1443     @IntrinsicCandidate
1444     public static int compareUnsigned(long x, long y) {
1445         return compare(x + MIN_VALUE, y + MIN_VALUE);
1446     }
1447 
1448 
1449     /**
1450      * Returns the unsigned quotient of dividing the first argument by
1451      * the second where each argument and the result is interpreted as
1452      * an unsigned value.
1453      *
1454      * <p>Note that in two's complement arithmetic, the three other
1455      * basic arithmetic operations of add, subtract, and multiply are
1456      * bit-wise identical if the two operands are regarded as both
1457      * being signed or both being unsigned.  Therefore separate {@code
1458      * addUnsigned}, etc. methods are not provided.
1459      *
1460      * @param dividend the value to be divided
1461      * @param divisor the value doing the dividing
1462      * @return the unsigned quotient of the first argument divided by
1463      * the second argument
1464      * @see #remainderUnsigned
1465      * @since 1.8
1466      */
1467     @IntrinsicCandidate
1468     public static long divideUnsigned(long dividend, long divisor) {
1469         /* See Hacker's Delight (2nd ed), section 9.3 */
1470         if (divisor >= 0) {
1471             final long q = (dividend >>> 1) / divisor << 1;
1472             final long r = dividend - q * divisor;
1473             return q + ((r | ~(r - divisor)) >>> (Long.SIZE - 1));
1474         }
1475         return (dividend & ~(dividend - divisor)) >>> (Long.SIZE - 1);
1476     }
1477 
1478     /**
1479      * Returns the unsigned remainder from dividing the first argument
1480      * by the second where each argument and the result is interpreted
1481      * as an unsigned value.
1482      *
1483      * @param dividend the value to be divided
1484      * @param divisor the value doing the dividing
1485      * @return the unsigned remainder of the first argument divided by
1486      * the second argument
1487      * @see #divideUnsigned
1488      * @since 1.8
1489      */
1490     @IntrinsicCandidate
1491     public static long remainderUnsigned(long dividend, long divisor) {
1492         /* See Hacker's Delight (2nd ed), section 9.3 */
1493         if (divisor >= 0) {
1494             final long q = (dividend >>> 1) / divisor << 1;
1495             final long r = dividend - q * divisor;
1496             /*
1497              * Here, 0 <= r < 2 * divisor
1498              * (1) When 0 <= r < divisor, the remainder is simply r.
1499              * (2) Otherwise the remainder is r - divisor.
1500              *
1501              * In case (1), r - divisor < 0. Applying ~ produces a long with
1502              * sign bit 0, so >> produces 0. The returned value is thus r.
1503              *
1504              * In case (2), a similar reasoning shows that >> produces -1,
1505              * so the returned value is r - divisor.
1506              */
1507             return r - ((~(r - divisor) >> (Long.SIZE - 1)) & divisor);
1508         }
1509         /*
1510          * (1) When dividend >= 0, the remainder is dividend.
1511          * (2) Otherwise
1512          *      (2.1) When dividend < divisor, the remainder is dividend.
1513          *      (2.2) Otherwise the remainder is dividend - divisor
1514          *
1515          * A reasoning similar to the above shows that the returned value
1516          * is as expected.
1517          */
1518         return dividend - (((dividend & ~(dividend - divisor)) >> (Long.SIZE - 1)) & divisor);
1519     }
1520 
1521     // Bit Twiddling
1522 
1523     /**
1524      * The number of bits used to represent a {@code long} value in two's
1525      * complement binary form.
1526      *
1527      * @since 1.5
1528      */
1529     @Native public static final int SIZE = 64;
1530 
1531     /**
1532      * The number of bytes used to represent a {@code long} value in two's
1533      * complement binary form.
1534      *
1535      * @since 1.8
1536      */
1537     public static final int BYTES = SIZE / Byte.SIZE;
1538 
1539     /**
1540      * Returns a {@code long} value with at most a single one-bit, in the
1541      * position of the highest-order ("leftmost") one-bit in the specified
1542      * {@code long} value.  Returns zero if the specified value has no
1543      * one-bits in its two's complement binary representation, that is, if it
1544      * is equal to zero.
1545      *
1546      * @param i the value whose highest one bit is to be computed
1547      * @return a {@code long} value with a single one-bit, in the position
1548      *     of the highest-order one-bit in the specified value, or zero if
1549      *     the specified value is itself equal to zero.
1550      * @since 1.5
1551      */
1552     public static long highestOneBit(long i) {
1553         return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
1554     }
1555 
1556     /**
1557      * Returns a {@code long} value with at most a single one-bit, in the
1558      * position of the lowest-order ("rightmost") one-bit in the specified
1559      * {@code long} value.  Returns zero if the specified value has no
1560      * one-bits in its two's complement binary representation, that is, if it
1561      * is equal to zero.
1562      *
1563      * @param i the value whose lowest one bit is to be computed
1564      * @return a {@code long} value with a single one-bit, in the position
1565      *     of the lowest-order one-bit in the specified value, or zero if
1566      *     the specified value is itself equal to zero.
1567      * @since 1.5
1568      */
1569     public static long lowestOneBit(long i) {
1570         // HD, Section 2-1
1571         return i & -i;
1572     }
1573 
1574     /**
1575      * Returns the number of zero bits preceding the highest-order
1576      * ("leftmost") one-bit in the two's complement binary representation
1577      * of the specified {@code long} value.  Returns 64 if the
1578      * specified value has no one-bits in its two's complement representation,
1579      * in other words if it is equal to zero.
1580      *
1581      * <p>Note that this method is closely related to the logarithm base 2.
1582      * For all positive {@code long} values x:
1583      * <ul>
1584      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1585      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1586      * </ul>
1587      *
1588      * @param i the value whose number of leading zeros is to be computed
1589      * @return the number of zero bits preceding the highest-order
1590      *     ("leftmost") one-bit in the two's complement binary representation
1591      *     of the specified {@code long} value, or 64 if the value
1592      *     is equal to zero.
1593      * @since 1.5
1594      */
1595     @IntrinsicCandidate
1596     public static int numberOfLeadingZeros(long i) {
1597         int x = (int)(i >>> 32);
1598         return x == 0 ? 32 + Integer.numberOfLeadingZeros((int)i)
1599                 : Integer.numberOfLeadingZeros(x);
1600     }
1601 
1602     /**
1603      * Returns the number of zero bits following the lowest-order ("rightmost")
1604      * one-bit in the two's complement binary representation of the specified
1605      * {@code long} value.  Returns 64 if the specified value has no
1606      * one-bits in its two's complement representation, in other words if it is
1607      * equal to zero.
1608      *
1609      * @param i the value whose number of trailing zeros is to be computed
1610      * @return the number of zero bits following the lowest-order ("rightmost")
1611      *     one-bit in the two's complement binary representation of the
1612      *     specified {@code long} value, or 64 if the value is equal
1613      *     to zero.
1614      * @since 1.5
1615      */
1616     @IntrinsicCandidate
1617     public static int numberOfTrailingZeros(long i) {
1618         int x = (int)i;
1619         return x == 0 ? 32 + Integer.numberOfTrailingZeros((int)(i >>> 32))
1620                 : Integer.numberOfTrailingZeros(x);
1621     }
1622 
1623     /**
1624      * Returns the number of one-bits in the two's complement binary
1625      * representation of the specified {@code long} value.  This function is
1626      * sometimes referred to as the <i>population count</i>.
1627      *
1628      * @param i the value whose bits are to be counted
1629      * @return the number of one-bits in the two's complement binary
1630      *     representation of the specified {@code long} value.
1631      * @since 1.5
1632      */
1633      @IntrinsicCandidate
1634      public static int bitCount(long i) {
1635         // HD, Figure 5-2
1636         i = i - ((i >>> 1) & 0x5555555555555555L);
1637         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1638         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1639         i = i + (i >>> 8);
1640         i = i + (i >>> 16);
1641         i = i + (i >>> 32);
1642         return (int)i & 0x7f;
1643      }
1644 
1645     /**
1646      * Returns the value obtained by rotating the two's complement binary
1647      * representation of the specified {@code long} value left by the
1648      * specified number of bits.  (Bits shifted out of the left hand, or
1649      * high-order, side reenter on the right, or low-order.)
1650      *
1651      * <p>Note that left rotation with a negative distance is equivalent to
1652      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1653      * distance)}.  Note also that rotation by any multiple of 64 is a
1654      * no-op, so all but the last six bits of the rotation distance can be
1655      * ignored, even if the distance is negative: {@code rotateLeft(val,
1656      * distance) == rotateLeft(val, distance & 0x3F)}.
1657      *
1658      * @param i the value whose bits are to be rotated left
1659      * @param distance the number of bit positions to rotate left
1660      * @return the value obtained by rotating the two's complement binary
1661      *     representation of the specified {@code long} value left by the
1662      *     specified number of bits.
1663      * @since 1.5
1664      */
1665     public static long rotateLeft(long i, int distance) {
1666         return (i << distance) | (i >>> -distance);
1667     }
1668 
1669     /**
1670      * Returns the value obtained by rotating the two's complement binary
1671      * representation of the specified {@code long} value right by the
1672      * specified number of bits.  (Bits shifted out of the right hand, or
1673      * low-order, side reenter on the left, or high-order.)
1674      *
1675      * <p>Note that right rotation with a negative distance is equivalent to
1676      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1677      * distance)}.  Note also that rotation by any multiple of 64 is a
1678      * no-op, so all but the last six bits of the rotation distance can be
1679      * ignored, even if the distance is negative: {@code rotateRight(val,
1680      * distance) == rotateRight(val, distance & 0x3F)}.
1681      *
1682      * @param i the value whose bits are to be rotated right
1683      * @param distance the number of bit positions to rotate right
1684      * @return the value obtained by rotating the two's complement binary
1685      *     representation of the specified {@code long} value right by the
1686      *     specified number of bits.
1687      * @since 1.5
1688      */
1689     public static long rotateRight(long i, int distance) {
1690         return (i >>> distance) | (i << -distance);
1691     }
1692 
1693     /**
1694      * Returns the value obtained by reversing the order of the bits in the
1695      * two's complement binary representation of the specified {@code long}
1696      * value.
1697      *
1698      * @param i the value to be reversed
1699      * @return the value obtained by reversing order of the bits in the
1700      *     specified {@code long} value.
1701      * @since 1.5
1702      */
1703     @IntrinsicCandidate
1704     public static long reverse(long i) {
1705         // HD, Figure 7-1
1706         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1707         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1708         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1709 
1710         return reverseBytes(i);
1711     }
1712 
1713     /**
1714      * Returns the value obtained by compressing the bits of the
1715      * specified {@code long} value, {@code i}, in accordance with
1716      * the specified bit mask.
1717      * <p>
1718      * For each one-bit value {@code mb} of the mask, from least
1719      * significant to most significant, the bit value of {@code i} at
1720      * the same bit location as {@code mb} is assigned to the compressed
1721      * value contiguously starting from the least significant bit location.
1722      * All the upper remaining bits of the compressed value are set
1723      * to zero.
1724      *
1725      * @apiNote
1726      * Consider the simple case of compressing the digits of a hexadecimal
1727      * value:
1728      * {@snippet lang="java" :
1729      * // Compressing drink to food
1730      * compress(0xCAFEBABEL, 0xFF00FFF0L) == 0xCABABL
1731      * }
1732      * Starting from the least significant hexadecimal digit at position 0
1733      * from the right, the mask {@code 0xFF00FFF0} selects hexadecimal digits
1734      * at positions 1, 2, 3, 6 and 7 of {@code 0xCAFEBABE}. The selected digits
1735      * occur in the resulting compressed value contiguously from digit position
1736      * 0 in the same order.
1737      * <p>
1738      * The following identities all return {@code true} and are helpful to
1739      * understand the behaviour of {@code compress}:
1740      * {@snippet lang="java" :
1741      * // Returns 1 if the bit at position n is one
1742      * compress(x, 1L << n) == (x >> n & 1)
1743      *
1744      * // Logical shift right
1745      * compress(x, -1L << n) == x >>> n
1746      *
1747      * // Any bits not covered by the mask are ignored
1748      * compress(x, m) == compress(x & m, m)
1749      *
1750      * // Compressing a value by itself
1751      * compress(m, m) == (m == -1 || m == 0) ? m : (1L << bitCount(m)) - 1
1752      *
1753      * // Expanding then compressing with the same mask
1754      * compress(expand(x, m), m) == x & compress(m, m)
1755      * }
1756      * <p>
1757      * The Sheep And Goats (SAG) operation (see Hacker's Delight, Second Edition, section 7.7)
1758      * can be implemented as follows:
1759      * {@snippet lang="java" :
1760      * long compressLeft(long i, long mask) {
1761      *     // This implementation follows the description in Hacker's Delight which
1762      *     // is informative. A more optimal implementation is:
1763      *     //   Long.compress(i, mask) << -Long.bitCount(mask)
1764      *     return Long.reverse(
1765      *         Long.compress(Long.reverse(i), Long.reverse(mask)));
1766      * }
1767      *
1768      * long sag(long i, long mask) {
1769      *     return compressLeft(i, mask) | Long.compress(i, ~mask);
1770      * }
1771      *
1772      * // Separate the sheep from the goats
1773      * sag(0x00000000_CAFEBABEL, 0xFFFFFFFF_FF00FFF0L) == 0x00000000_CABABFEEL
1774      * }
1775      *
1776      * @param i the value whose bits are to be compressed
1777      * @param mask the bit mask
1778      * @return the compressed value
1779      * @see #expand
1780      * @since 19
1781      */
1782     @IntrinsicCandidate
1783     public static long compress(long i, long mask) {
1784         // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract
1785 
1786         i = i & mask; // Clear irrelevant bits
1787         long maskCount = ~mask << 1; // Count 0's to right
1788 
1789         for (int j = 0; j < 6; j++) {
1790             // Parallel prefix
1791             // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
1792             long maskPrefix = parallelSuffix(maskCount);
1793             // Bits to move
1794             long maskMove = maskPrefix & mask;
1795             // Compress mask
1796             mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
1797             // Bits of i to be moved
1798             long t = i & maskMove;
1799             // Compress i
1800             i = (i ^ t) | (t >>> (1 << j));
1801             // Adjust the mask count by identifying bits that have 0 to the right
1802             maskCount = maskCount & ~maskPrefix;
1803         }
1804         return i;
1805     }
1806 
1807     /**
1808      * Returns the value obtained by expanding the bits of the
1809      * specified {@code long} value, {@code i}, in accordance with
1810      * the specified bit mask.
1811      * <p>
1812      * For each one-bit value {@code mb} of the mask, from least
1813      * significant to most significant, the next contiguous bit value
1814      * of {@code i} starting at the least significant bit is assigned
1815      * to the expanded value at the same bit location as {@code mb}.
1816      * All other remaining bits of the expanded value are set to zero.
1817      *
1818      * @apiNote
1819      * Consider the simple case of expanding the digits of a hexadecimal
1820      * value:
1821      * {@snippet lang="java" :
1822      * expand(0x0000CABABL, 0xFF00FFF0L) == 0xCA00BAB0L
1823      * }
1824      * Starting from the least significant hexadecimal digit at position 0
1825      * from the right, the mask {@code 0xFF00FFF0} selects the first five
1826      * hexadecimal digits of {@code 0x0000CABAB}. The selected digits occur
1827      * in the resulting expanded value in order at positions 1, 2, 3, 6, and 7.
1828      * <p>
1829      * The following identities all return {@code true} and are helpful to
1830      * understand the behaviour of {@code expand}:
1831      * {@snippet lang="java" :
1832      * // Logically shift right the bit at position 0
1833      * expand(x, 1L << n) == (x & 1) << n
1834      *
1835      * // Logically shift right
1836      * expand(x, -1L << n) == x << n
1837      *
1838      * // Expanding all bits returns the mask
1839      * expand(-1L, m) == m
1840      *
1841      * // Any bits not covered by the mask are ignored
1842      * expand(x, m) == expand(x, m) & m
1843      *
1844      * // Compressing then expanding with the same mask
1845      * expand(compress(x, m), m) == x & m
1846      * }
1847      * <p>
1848      * The select operation for determining the position of the one-bit with
1849      * index {@code n} in a {@code long} value can be implemented as follows:
1850      * {@snippet lang="java" :
1851      * long select(long i, long n) {
1852      *     // the one-bit in i (the mask) with index n
1853      *     long nthBit = Long.expand(1L << n, i);
1854      *     // the bit position of the one-bit with index n
1855      *     return Long.numberOfTrailingZeros(nthBit);
1856      * }
1857      *
1858      * // The one-bit with index 0 is at bit position 1
1859      * select(0b10101010_10101010, 0) == 1
1860      * // The one-bit with index 3 is at bit position 7
1861      * select(0b10101010_10101010, 3) == 7
1862      * }
1863      *
1864      * @param i the value whose bits are to be expanded
1865      * @param mask the bit mask
1866      * @return the expanded value
1867      * @see #compress
1868      * @since 19
1869      */
1870     @IntrinsicCandidate
1871     public static long expand(long i, long mask) {
1872         // Save original mask
1873         long originalMask = mask;
1874         // Count 0's to right
1875         long maskCount = ~mask << 1;
1876         long maskPrefix = parallelSuffix(maskCount);
1877         // Bits to move
1878         long maskMove1 = maskPrefix & mask;
1879         // Compress mask
1880         mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
1881         maskCount = maskCount & ~maskPrefix;
1882 
1883         maskPrefix = parallelSuffix(maskCount);
1884         // Bits to move
1885         long maskMove2 = maskPrefix & mask;
1886         // Compress mask
1887         mask = (mask ^ maskMove2) | (maskMove2 >>> (1 << 1));
1888         maskCount = maskCount & ~maskPrefix;
1889 
1890         maskPrefix = parallelSuffix(maskCount);
1891         // Bits to move
1892         long maskMove3 = maskPrefix & mask;
1893         // Compress mask
1894         mask = (mask ^ maskMove3) | (maskMove3 >>> (1 << 2));
1895         maskCount = maskCount & ~maskPrefix;
1896 
1897         maskPrefix = parallelSuffix(maskCount);
1898         // Bits to move
1899         long maskMove4 = maskPrefix & mask;
1900         // Compress mask
1901         mask = (mask ^ maskMove4) | (maskMove4 >>> (1 << 3));
1902         maskCount = maskCount & ~maskPrefix;
1903 
1904         maskPrefix = parallelSuffix(maskCount);
1905         // Bits to move
1906         long maskMove5 = maskPrefix & mask;
1907         // Compress mask
1908         mask = (mask ^ maskMove5) | (maskMove5 >>> (1 << 4));
1909         maskCount = maskCount & ~maskPrefix;
1910 
1911         maskPrefix = parallelSuffix(maskCount);
1912         // Bits to move
1913         long maskMove6 = maskPrefix & mask;
1914 
1915         long t = i << (1 << 5);
1916         i = (i & ~maskMove6) | (t & maskMove6);
1917         t = i << (1 << 4);
1918         i = (i & ~maskMove5) | (t & maskMove5);
1919         t = i << (1 << 3);
1920         i = (i & ~maskMove4) | (t & maskMove4);
1921         t = i << (1 << 2);
1922         i = (i & ~maskMove3) | (t & maskMove3);
1923         t = i << (1 << 1);
1924         i = (i & ~maskMove2) | (t & maskMove2);
1925         t = i << (1 << 0);
1926         i = (i & ~maskMove1) | (t & maskMove1);
1927 
1928         // Clear irrelevant bits
1929         return i & originalMask;
1930     }
1931 
1932     @ForceInline
1933     private static long parallelSuffix(long maskCount) {
1934         long maskPrefix = maskCount ^ (maskCount << 1);
1935         maskPrefix = maskPrefix ^ (maskPrefix << 2);
1936         maskPrefix = maskPrefix ^ (maskPrefix << 4);
1937         maskPrefix = maskPrefix ^ (maskPrefix << 8);
1938         maskPrefix = maskPrefix ^ (maskPrefix << 16);
1939         maskPrefix = maskPrefix ^ (maskPrefix << 32);
1940         return maskPrefix;
1941     }
1942 
1943     /**
1944      * Returns the signum function of the specified {@code long} value.  (The
1945      * return value is -1 if the specified value is negative; 0 if the
1946      * specified value is zero; and 1 if the specified value is positive.)
1947      *
1948      * @param i the value whose signum is to be computed
1949      * @return the signum function of the specified {@code long} value.
1950      * @since 1.5
1951      */
1952     public static int signum(long i) {
1953         // HD, Section 2-7
1954         return (int) ((i >> 63) | (-i >>> 63));
1955     }
1956 
1957     /**
1958      * Returns the value obtained by reversing the order of the bytes in the
1959      * two's complement representation of the specified {@code long} value.
1960      *
1961      * @param i the value whose bytes are to be reversed
1962      * @return the value obtained by reversing the bytes in the specified
1963      *     {@code long} value.
1964      * @since 1.5
1965      */
1966     @IntrinsicCandidate
1967     public static long reverseBytes(long i) {
1968         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1969         return (i << 48) | ((i & 0xffff0000L) << 16) |
1970             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1971     }
1972 
1973     /**
1974      * Adds two {@code long} values together as per the + operator.
1975      *
1976      * @param a the first operand
1977      * @param b the second operand
1978      * @return the sum of {@code a} and {@code b}
1979      * @see java.util.function.BinaryOperator
1980      * @since 1.8
1981      */
1982     public static long sum(long a, long b) {
1983         return a + b;
1984     }
1985 
1986     /**
1987      * Returns the greater of two {@code long} values
1988      * as if by calling {@link Math#max(long, long) Math.max}.
1989      *
1990      * @param a the first operand
1991      * @param b the second operand
1992      * @return the greater of {@code a} and {@code b}
1993      * @see java.util.function.BinaryOperator
1994      * @since 1.8
1995      */
1996     public static long max(long a, long b) {
1997         return Math.max(a, b);
1998     }
1999 
2000     /**
2001      * Returns the smaller of two {@code long} values
2002      * as if by calling {@link Math#min(long, long) Math.min}.
2003      *
2004      * @param a the first operand
2005      * @param b the second operand
2006      * @return the smaller of {@code a} and {@code b}
2007      * @see java.util.function.BinaryOperator
2008      * @since 1.8
2009      */
2010     public static long min(long a, long b) {
2011         return Math.min(a, b);
2012     }
2013 
2014     /**
2015      * Returns an {@link Optional} containing the nominal descriptor for this
2016      * instance, which is the instance itself.
2017      *
2018      * @return an {@link Optional} describing the {@linkplain Long} instance
2019      * @since 12
2020      */
2021     @Override
2022     public Optional<Long> describeConstable() {
2023         return Optional.of(this);
2024     }
2025 
2026     /**
2027      * Resolves this instance as a {@link ConstantDesc}, the result of which is
2028      * the instance itself.
2029      *
2030      * @param lookup ignored
2031      * @return the {@linkplain Long} instance
2032      * @since 12
2033      */
2034     @Override
2035     public Long resolveConstantDesc(MethodHandles.Lookup lookup) {
2036         return this;
2037     }
2038 
2039     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2040     @java.io.Serial
2041     @Native private static final long serialVersionUID = 4290774380558885855L;
2042 }