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