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