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.vm.annotation.ForceInline;
  38 import jdk.internal.vm.annotation.IntrinsicCandidate;
  39 import jdk.internal.vm.annotation.Stable;
  40 
  41 import static java.lang.Character.digit;
  42 import static java.lang.String.COMPACT_STRINGS;
  43 import static java.lang.String.LATIN1;
  44 import static java.lang.String.UTF16;
  45 
  46 /**
  47  * The {@code Long} class wraps a value of the primitive type {@code
  48  * long} in an object. An object of type {@code Long} contains a
  49  * single field whose type is {@code long}.
  50  *
  51  * <p> In addition, this class provides several methods for converting
  52  * a {@code long} to a {@code String} and a {@code String} to a {@code
  53  * long}, as well as other constants and methods useful when dealing
  54  * with a {@code long}.
  55  *
  56  * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
  57  * class; programmers should treat instances that are
  58  * {@linkplain #equals(Object) equal} as interchangeable and should not
  59  * use instances for synchronization, or unpredictable behavior may
  60  * occur. For example, in a future release, synchronization may fail.
  61  *
  62  * <p>Implementation note: The implementations of the "bit twiddling"
  63  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  64  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  65  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  66  * Delight</i>, (Addison Wesley, 2002).
  67  *
  68  * @author  Lee Boynton
  69  * @author  Arthur van Hoff
  70  * @author  Josh Bloch
  71  * @author  Joseph D. Darcy
  72  * @since   1.0
  73  */
  74 @jdk.internal.ValueBased
  75 public final class Long extends Number
  76         implements Comparable<Long>, Constable, ConstantDesc {
  77     /**
  78      * A constant holding the minimum value a {@code long} can
  79      * have, -2<sup>63</sup>.
  80      */
  81     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  82 
  83     /**
  84      * A constant holding the maximum value a {@code long} can
  85      * have, 2<sup>63</sup>-1.
  86      */
  87     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  88 
  89     /**
  90      * The {@code Class} instance representing the primitive type
  91      * {@code long}.
  92      *
  93      * @since   1.1
  94      */
  95     @SuppressWarnings("unchecked")
  96     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  97 
  98     /**
  99      * Returns a string representation of the first argument in the
 100      * radix specified by the second argument.
 101      *
 102      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 103      * or larger than {@code Character.MAX_RADIX}, then the radix
 104      * {@code 10} is used instead.
 105      *
 106      * <p>If the first argument is negative, the first element of the
 107      * result is the ASCII minus sign {@code '-'}
 108      * ({@code '\u005Cu002d'}). If the first argument is not
 109      * negative, no sign character appears in the result.
 110      *
 111      * <p>The remaining characters of the result represent the magnitude
 112      * of the first argument. If the magnitude is zero, it is
 113      * represented by a single zero character {@code '0'}
 114      * ({@code '\u005Cu0030'}); otherwise, the first character of
 115      * the representation of the magnitude will not be the zero
 116      * character.  The following ASCII characters are used as digits:
 117      *
 118      * <blockquote>
 119      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 120      * </blockquote>
 121      *
 122      * These are {@code '\u005Cu0030'} through
 123      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 124      * {@code '\u005Cu007a'}. If {@code radix} is
 125      * <var>N</var>, then the first <var>N</var> of these characters
 126      * are used as radix-<var>N</var> digits in the order shown. Thus,
 127      * the digits for hexadecimal (radix 16) are
 128      * {@code 0123456789abcdef}. If uppercase letters are
 129      * desired, the {@link java.lang.String#toUpperCase()} method may
 130      * be called on the result:
 131      *
 132      * <blockquote>
 133      *  {@code Long.toString(n, 16).toUpperCase()}
 134      * </blockquote>
 135      *
 136      * @param   i       a {@code long} to be converted to a string.
 137      * @param   radix   the radix to use in the string representation.
 138      * @return  a string representation of the argument in the specified radix.
 139      * @see     java.lang.Character#MAX_RADIX
 140      * @see     java.lang.Character#MIN_RADIX
 141      */
 142     public static String toString(long i, int radix) {
 143         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 144             radix = 10;
 145         if (radix == 10)
 146             return toString(i);
 147 
 148         if (COMPACT_STRINGS) {
 149             byte[] buf = new byte[65];
 150             int charPos = 64;
 151             boolean negative = (i < 0);
 152 
 153             if (!negative) {
 154                 i = -i;
 155             }
 156 
 157             while (i <= -radix) {
 158                 buf[charPos--] = (byte)Integer.digits[(int)(-(i % radix))];
 159                 i = i / radix;
 160             }
 161             buf[charPos] = (byte)Integer.digits[(int)(-i)];
 162 
 163             if (negative) {
 164                 buf[--charPos] = '-';
 165             }
 166             return StringLatin1.newString(buf, charPos, (65 - charPos));
 167         }
 168         return toStringUTF16(i, radix);
 169     }
 170 
 171     private static String toStringUTF16(long i, int radix) {
 172         byte[] buf = new byte[65 * 2];
 173         int charPos = 64;
 174         boolean negative = (i < 0);
 175         if (!negative) {
 176             i = -i;
 177         }
 178         while (i <= -radix) {
 179             StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 180             i = i / radix;
 181         }
 182         StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 183         if (negative) {
 184             StringUTF16.putChar(buf, --charPos, '-');
 185         }
 186         return StringUTF16.newString(buf, charPos, (65 - charPos));
 187     }
 188 
 189     /**
 190      * Returns a string representation of the first argument as an
 191      * unsigned integer value in the radix specified by the second
 192      * argument.
 193      *
 194      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 195      * or larger than {@code Character.MAX_RADIX}, then the radix
 196      * {@code 10} is used instead.
 197      *
 198      * <p>Note that since the first argument is treated as an unsigned
 199      * value, no leading sign character is printed.
 200      *
 201      * <p>If the magnitude is zero, it is represented by a single zero
 202      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 203      * the first character of the representation of the magnitude will
 204      * not be the zero character.
 205      *
 206      * <p>The behavior of radixes and the characters used as digits
 207      * are the same as {@link #toString(long, int) toString}.
 208      *
 209      * @param   i       an integer to be converted to an unsigned string.
 210      * @param   radix   the radix to use in the string representation.
 211      * @return  an unsigned string representation of the argument in the specified radix.
 212      * @see     #toString(long, int)
 213      * @since 1.8
 214      */
 215     public static String toUnsignedString(long i, int radix) {
 216         if (i >= 0)
 217             return toString(i, radix);
 218         else {
 219             return switch (radix) {
 220                 case 2  -> toBinaryString(i);
 221                 case 4  -> toUnsignedString0(i, 2);
 222                 case 8  -> toOctalString(i);
 223                 case 10 -> {
 224                     /*
 225                      * We can get the effect of an unsigned division by 10
 226                      * on a long value by first shifting right, yielding a
 227                      * positive value, and then dividing by 5.  This
 228                      * allows the last digit and preceding digits to be
 229                      * isolated more quickly than by an initial conversion
 230                      * to BigInteger.
 231                      */
 232                     long quot = (i >>> 1) / 5;
 233                     long rem = i - quot * 10;
 234                     yield toString(quot) + rem;
 235                 }
 236                 case 16 -> toHexString(i);
 237                 case 32 -> toUnsignedString0(i, 5);
 238                 default -> toUnsignedBigInteger(i).toString(radix);
 239             };
 240         }
 241     }
 242 
 243     /**
 244      * Return a BigInteger equal to the unsigned value of the
 245      * argument.
 246      */
 247     private static BigInteger toUnsignedBigInteger(long i) {
 248         if (i >= 0L)
 249             return BigInteger.valueOf(i);
 250         else {
 251             int upper = (int) (i >>> 32);
 252             int lower = (int) i;
 253 
 254             // return (upper << 32) + lower
 255             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 256                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 257         }
 258     }
 259 
 260     /**
 261      * Returns a string representation of the {@code long}
 262      * argument as an unsigned integer in base&nbsp;16.
 263      *
 264      * <p>The unsigned {@code long} value is the argument plus
 265      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 266      * equal to the argument.  This value is converted to a string of
 267      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 268      * leading {@code 0}s.
 269      *
 270      * <p>The value of the argument can be recovered from the returned
 271      * string {@code s} by calling {@link
 272      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 273      * 16)}.
 274      *
 275      * <p>If the unsigned magnitude is zero, it is represented by a
 276      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 277      * otherwise, the first character of the representation of the
 278      * unsigned magnitude will not be the zero character. The
 279      * following characters are used as hexadecimal digits:
 280      *
 281      * <blockquote>
 282      *  {@code 0123456789abcdef}
 283      * </blockquote>
 284      *
 285      * These are the characters {@code '\u005Cu0030'} through
 286      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 287      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 288      * the {@link java.lang.String#toUpperCase()} method may be called
 289      * on the result:
 290      *
 291      * <blockquote>
 292      *  {@code Long.toHexString(n).toUpperCase()}
 293      * </blockquote>
 294      *
 295      * @apiNote
 296      * The {@link java.util.HexFormat} class provides formatting and parsing
 297      * of byte arrays and primitives to return a string or adding to an {@link Appendable}.
 298      * {@code HexFormat} formats and parses uppercase or lowercase hexadecimal characters,
 299      * with leading zeros and for byte arrays includes for each byte
 300      * a delimiter, prefix, and suffix.
 301      *
 302      * @param   i   a {@code long} to be converted to a string.
 303      * @return  the string representation of the unsigned {@code long}
 304      *          value represented by the argument in hexadecimal
 305      *          (base&nbsp;16).
 306      * @see java.util.HexFormat
 307      * @see #parseUnsignedLong(String, int)
 308      * @see #toUnsignedString(long, int)
 309      * @since   1.0.2
 310      */
 311     public static String toHexString(long i) {
 312         return toUnsignedString0(i, 4);
 313     }
 314 
 315     /**
 316      * Returns a string representation of the {@code long}
 317      * argument as an unsigned integer in base&nbsp;8.
 318      *
 319      * <p>The unsigned {@code long} value is the argument plus
 320      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 321      * equal to the argument.  This value is converted to a string of
 322      * ASCII digits in octal (base&nbsp;8) with no extra leading
 323      * {@code 0}s.
 324      *
 325      * <p>The value of the argument can be recovered from the returned
 326      * string {@code s} by calling {@link
 327      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 328      * 8)}.
 329      *
 330      * <p>If the unsigned magnitude is zero, it is represented by a
 331      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 332      * otherwise, the first character of the representation of the
 333      * unsigned magnitude will not be the zero character. The
 334      * following characters are used as octal digits:
 335      *
 336      * <blockquote>
 337      *  {@code 01234567}
 338      * </blockquote>
 339      *
 340      * These are the characters {@code '\u005Cu0030'} through
 341      * {@code '\u005Cu0037'}.
 342      *
 343      * @param   i   a {@code long} to be converted to a string.
 344      * @return  the string representation of the unsigned {@code long}
 345      *          value represented by the argument in octal (base&nbsp;8).
 346      * @see #parseUnsignedLong(String, int)
 347      * @see #toUnsignedString(long, int)
 348      * @since   1.0.2
 349      */
 350     public static String toOctalString(long i) {
 351         return toUnsignedString0(i, 3);
 352     }
 353 
 354     /**
 355      * Returns a string representation of the {@code long}
 356      * argument as an unsigned integer in base&nbsp;2.
 357      *
 358      * <p>The unsigned {@code long} value is the argument plus
 359      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 360      * equal to the argument.  This value is converted to a string of
 361      * ASCII digits in binary (base&nbsp;2) with no extra leading
 362      * {@code 0}s.
 363      *
 364      * <p>The value of the argument can be recovered from the returned
 365      * string {@code s} by calling {@link
 366      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 367      * 2)}.
 368      *
 369      * <p>If the unsigned magnitude is zero, it is represented by a
 370      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 371      * otherwise, the first character of the representation of the
 372      * unsigned magnitude will not be the zero character. The
 373      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 374      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 375      *
 376      * @param   i   a {@code long} to be converted to a string.
 377      * @return  the string representation of the unsigned {@code long}
 378      *          value represented by the argument in binary (base&nbsp;2).
 379      * @see #parseUnsignedLong(String, int)
 380      * @see #toUnsignedString(long, int)
 381      * @since   1.0.2
 382      */
 383     public static String toBinaryString(long i) {
 384         return toUnsignedString0(i, 1);
 385     }
 386 
 387     /**
 388      * Format a long (treated as unsigned) into a String.
 389      * @param val the value to format
 390      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 391      */
 392     static String toUnsignedString0(long val, int shift) {
 393         // assert shift > 0 && shift <=5 : "Illegal shift value";
 394         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 395         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 396         if (COMPACT_STRINGS) {
 397             byte[] buf = new byte[chars];
 398             formatUnsignedLong0(val, shift, buf, 0, chars);
 399             return new String(buf, LATIN1);
 400         } else {
 401             byte[] buf = new byte[chars * 2];
 402             formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
 403             return new String(buf, UTF16);
 404         }
 405     }
 406 
 407     /**
 408      * Format a long (treated as unsigned) into a byte buffer (LATIN1 version). If
 409      * {@code len} exceeds the formatted ASCII representation of {@code val},
 410      * {@code buf} will be padded with leading zeroes.
 411      *
 412      * @param val the unsigned long to format
 413      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 414      * @param buf the byte buffer to write to
 415      * @param offset the offset in the destination buffer to start at
 416      * @param len the number of characters to write
 417      */
 418     private static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
 419         int charPos = offset + len;
 420         int radix = 1 << shift;
 421         int mask = radix - 1;
 422         do {
 423             buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
 424             val >>>= shift;
 425         } while (charPos > offset);
 426     }
 427 
 428     /**
 429      * Format a long (treated as unsigned) into a byte buffer (UTF16 version). If
 430      * {@code len} exceeds the formatted ASCII representation of {@code val},
 431      * {@code buf} will be padded with leading zeroes.
 432      *
 433      * @param val the unsigned long to format
 434      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 435      * @param buf the byte buffer to write to
 436      * @param offset the offset in the destination buffer to start at
 437      * @param len the number of characters to write
 438      */
 439     private static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
 440         int charPos = offset + len;
 441         int radix = 1 << shift;
 442         int mask = radix - 1;
 443         do {
 444             StringUTF16.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
 445             val >>>= shift;
 446         } while (charPos > offset);
 447     }
 448 
 449     /**
 450      * Returns a {@code String} object representing the specified
 451      * {@code long}.  The argument is converted to signed decimal
 452      * representation and returned as a string, exactly as if the
 453      * argument and the radix 10 were given as arguments to the {@link
 454      * #toString(long, int)} method.
 455      *
 456      * @param   i   a {@code long} to be converted.
 457      * @return  a string representation of the argument in base&nbsp;10.
 458      */
 459     public static String toString(long i) {
 460         int size = stringSize(i);
 461         if (COMPACT_STRINGS) {
 462             byte[] buf = new byte[size];
 463             StringLatin1.getChars(i, size, buf);
 464             return new String(buf, LATIN1);
 465         } else {
 466             byte[] buf = new byte[size * 2];
 467             StringUTF16.getChars(i, size, buf);
 468             return new String(buf, UTF16);
 469         }
 470     }
 471 
 472     /**
 473      * Returns a string representation of the argument as an unsigned
 474      * decimal value.
 475      *
 476      * The argument is converted to unsigned decimal representation
 477      * and returned as a string exactly as if the argument and radix
 478      * 10 were given as arguments to the {@link #toUnsignedString(long,
 479      * int)} method.
 480      *
 481      * @param   i  an integer to be converted to an unsigned string.
 482      * @return  an unsigned string representation of the argument.
 483      * @see     #toUnsignedString(long, int)
 484      * @since 1.8
 485      */
 486     public static String toUnsignedString(long i) {
 487         return toUnsignedString(i, 10);
 488     }
 489 
 490     /**
 491      * Returns the string representation size for a given long value.
 492      *
 493      * @param x long value
 494      * @return string size
 495      *
 496      * @implNote There are other ways to compute this: e.g. binary search,
 497      * but values are biased heavily towards zero, and therefore linear search
 498      * wins. The iteration results are also routinely inlined in the generated
 499      * code after loop unrolling.
 500      */
 501     static int stringSize(long x) {
 502         int d = 1;
 503         if (x >= 0) {
 504             d = 0;
 505             x = -x;
 506         }
 507         long p = -10;
 508         for (int i = 1; i < 19; i++) {
 509             if (x > p)
 510                 return i + d;
 511             p = 10 * p;
 512         }
 513         return 19 + d;
 514     }
 515 
 516     /**
 517      * Parses the string argument as a signed {@code long} in the
 518      * radix specified by the second argument. The characters in the
 519      * string must all be digits of the specified radix (as determined
 520      * by whether {@link java.lang.Character#digit(char, int)} returns
 521      * a nonnegative value), except that the first character may be an
 522      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 523      * indicate a negative value or an ASCII plus sign {@code '+'}
 524      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 525      * resulting {@code long} value is returned.
 526      *
 527      * <p>Note that neither the character {@code L}
 528      * ({@code '\u005Cu004C'}) nor {@code l}
 529      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 530      * of the string as a type indicator, as would be permitted in
 531      * Java programming language source code - except that either
 532      * {@code L} or {@code l} may appear as a digit for a
 533      * radix greater than or equal to 22.
 534      *
 535      * <p>An exception of type {@code NumberFormatException} is
 536      * thrown if any of the following situations occurs:
 537      * <ul>
 538      *
 539      * <li>The first argument is {@code null} or is a string of
 540      * length zero.
 541      *
 542      * <li>The {@code radix} is either smaller than {@link
 543      * java.lang.Character#MIN_RADIX} or larger than {@link
 544      * java.lang.Character#MAX_RADIX}.
 545      *
 546      * <li>Any character of the string is not a digit of the specified
 547      * radix, except that the first character may be a minus sign
 548      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 549      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 550      * longer than length 1.
 551      *
 552      * <li>The value represented by the string is not a value of type
 553      *      {@code long}.
 554      * </ul>
 555      *
 556      * <p>Examples:
 557      * <blockquote><pre>
 558      * parseLong("0", 10) returns 0L
 559      * parseLong("473", 10) returns 473L
 560      * parseLong("+42", 10) returns 42L
 561      * parseLong("-0", 10) returns 0L
 562      * parseLong("-FF", 16) returns -255L
 563      * parseLong("1100110", 2) returns 102L
 564      * parseLong("99", 8) throws a NumberFormatException
 565      * parseLong("Hazelnut", 10) throws a NumberFormatException
 566      * parseLong("Hazelnut", 36) returns 1356099454469L
 567      * </pre></blockquote>
 568      *
 569      * @param      s       the {@code String} containing the
 570      *                     {@code long} representation to be parsed.
 571      * @param      radix   the radix to be used while parsing {@code s}.
 572      * @return     the {@code long} represented by the string argument in
 573      *             the specified radix.
 574      * @throws     NumberFormatException  if the string does not contain a
 575      *             parsable {@code long}.
 576      */
 577     public static long parseLong(String s, int radix)
 578                 throws NumberFormatException {
 579         if (s == null) {
 580             throw new NumberFormatException("Cannot parse null string");
 581         }
 582 
 583         if (radix < Character.MIN_RADIX) {
 584             throw new NumberFormatException(String.format(
 585                 "radix %s less than Character.MIN_RADIX", radix));
 586         }
 587 
 588         if (radix > Character.MAX_RADIX) {
 589             throw new NumberFormatException(String.format(
 590                 "radix %s greater than Character.MAX_RADIX", radix));
 591         }
 592 
 593         int len = s.length();
 594         if (len == 0) {
 595             throw NumberFormatException.forInputString("", radix);
 596         }
 597         int digit = ~0xFF;
 598         int i = 0;
 599         char firstChar = s.charAt(i++);
 600         if (firstChar != '-' && firstChar != '+') {
 601             digit = digit(firstChar, radix);
 602         }
 603         if (digit >= 0 || digit == ~0xFF && len > 1) {
 604             long limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 605             long multmin = limit / radix;
 606             long result = -(digit & 0xFF);
 607             boolean inRange = true;
 608             /* Accumulating negatively avoids surprises near MAX_VALUE */
 609             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 610                     && (inRange = result > multmin
 611                         || result == multmin && digit <= (int) (radix * multmin - limit))) {
 612                 result = radix * result - digit;
 613             }
 614             if (inRange && i == len && digit >= 0) {
 615                 return firstChar != '-' ? -result : result;
 616             }
 617         }
 618         throw NumberFormatException.forInputString(s, radix);
 619     }
 620 
 621     /**
 622      * Parses the {@link CharSequence} argument as a signed {@code long} in
 623      * the specified {@code radix}, beginning at the specified
 624      * {@code beginIndex} and extending to {@code endIndex - 1}.
 625      *
 626      * <p>The method does not take steps to guard against the
 627      * {@code CharSequence} being mutated while parsing.
 628      *
 629      * @param      s   the {@code CharSequence} containing the {@code long}
 630      *                  representation to be parsed
 631      * @param      beginIndex   the beginning index, inclusive.
 632      * @param      endIndex     the ending index, exclusive.
 633      * @param      radix   the radix to be used while parsing {@code s}.
 634      * @return     the signed {@code long} represented by the subsequence in
 635      *             the specified radix.
 636      * @throws     NullPointerException  if {@code s} is null.
 637      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 638      *             negative, or if {@code beginIndex} is greater than
 639      *             {@code endIndex} or if {@code endIndex} is greater than
 640      *             {@code s.length()}.
 641      * @throws     NumberFormatException  if the {@code CharSequence} does not
 642      *             contain a parsable {@code long} in the specified
 643      *             {@code radix}, or if {@code radix} is either smaller than
 644      *             {@link java.lang.Character#MIN_RADIX} or larger than
 645      *             {@link java.lang.Character#MAX_RADIX}.
 646      * @since  9
 647      */
 648     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 649                 throws NumberFormatException {
 650         Objects.requireNonNull(s);
 651         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 652 
 653         if (radix < Character.MIN_RADIX) {
 654             throw new NumberFormatException(String.format(
 655                 "radix %s less than Character.MIN_RADIX", radix));
 656         }
 657 
 658         if (radix > Character.MAX_RADIX) {
 659             throw new NumberFormatException(String.format(
 660                 "radix %s greater than Character.MAX_RADIX", radix));
 661         }
 662 
 663         /*
 664          * While s can be concurrently modified, it is ensured that each
 665          * of its characters is read at most once, from lower to higher indices.
 666          * This is obtained by reading them using the pattern s.charAt(i++),
 667          * and by not updating i anywhere else.
 668          */
 669         if (beginIndex == endIndex) {
 670             throw NumberFormatException.forInputString("", radix);
 671         }
 672         int digit = ~0xFF;  // ~0xFF means firstChar char is sign
 673         int i = beginIndex;
 674         char firstChar = s.charAt(i++);
 675         if (firstChar != '-' && firstChar != '+') {
 676             digit = digit(firstChar, radix);
 677         }
 678         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 679             long limit = firstChar != '-' ? MIN_VALUE + 1 : MIN_VALUE;
 680             long multmin = limit / radix;
 681             long result = -(digit & 0xFF);
 682             boolean inRange = true;
 683             /* Accumulating negatively avoids surprises near MAX_VALUE */
 684             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 685                     && (inRange = result > multmin
 686                         || result == multmin && digit <= (int) (radix * multmin - limit))) {
 687                 result = radix * result - digit;
 688             }
 689             if (inRange && i == endIndex && digit >= 0) {
 690                 return firstChar != '-' ? -result : result;
 691             }
 692         }
 693         throw NumberFormatException.forCharSequence(s, beginIndex,
 694             endIndex, i - (digit < -1 ? 0 : 1));
 695     }
 696 
 697     /**
 698      * Parses the string argument as a signed decimal {@code long}.
 699      * The characters in the string must all be decimal digits, except
 700      * that the first character may be an ASCII minus sign {@code '-'}
 701      * ({@code \u005Cu002D'}) to indicate a negative value or an
 702      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 703      * indicate a positive value. The resulting {@code long} value is
 704      * returned, exactly as if the argument and the radix {@code 10}
 705      * were given as arguments to the {@link
 706      * #parseLong(java.lang.String, int)} method.
 707      *
 708      * <p>Note that neither the character {@code L}
 709      * ({@code '\u005Cu004C'}) nor {@code l}
 710      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 711      * of the string as a type indicator, as would be permitted in
 712      * Java programming language source code.
 713      *
 714      * @param      s   a {@code String} containing the {@code long}
 715      *             representation to be parsed
 716      * @return     the {@code long} represented by the argument in
 717      *             decimal.
 718      * @throws     NumberFormatException  if the string does not contain a
 719      *             parsable {@code long}.
 720      */
 721     public static long parseLong(String s) throws NumberFormatException {
 722         return parseLong(s, 10);
 723     }
 724 
 725     /**
 726      * Parses the string argument as an unsigned {@code long} in the
 727      * radix specified by the second argument.  An unsigned integer
 728      * maps the values usually associated with negative numbers to
 729      * positive numbers larger than {@code MAX_VALUE}.
 730      *
 731      * The characters in the string must all be digits of the
 732      * specified radix (as determined by whether {@link
 733      * java.lang.Character#digit(char, int)} returns a nonnegative
 734      * value), except that the first character may be an ASCII plus
 735      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 736      * integer value is returned.
 737      *
 738      * <p>An exception of type {@code NumberFormatException} is
 739      * thrown if any of the following situations occurs:
 740      * <ul>
 741      * <li>The first argument is {@code null} or is a string of
 742      * length zero.
 743      *
 744      * <li>The radix is either smaller than
 745      * {@link java.lang.Character#MIN_RADIX} or
 746      * larger than {@link java.lang.Character#MAX_RADIX}.
 747      *
 748      * <li>Any character of the string is not a digit of the specified
 749      * radix, except that the first character may be a plus sign
 750      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 751      * string is longer than length 1.
 752      *
 753      * <li>The value represented by the string is larger than the
 754      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 755      *
 756      * </ul>
 757      *
 758      *
 759      * @param      s   the {@code String} containing the unsigned integer
 760      *                  representation to be parsed
 761      * @param      radix   the radix to be used while parsing {@code s}.
 762      * @return     the unsigned {@code long} represented by the string
 763      *             argument in the specified radix.
 764      * @throws     NumberFormatException if the {@code String}
 765      *             does not contain a parsable {@code long}.
 766      * @since 1.8
 767      */
 768     public static long parseUnsignedLong(String s, int radix)
 769                 throws NumberFormatException {
 770         if (s == null)  {
 771             throw new NumberFormatException("Cannot parse null string");
 772         }
 773 
 774         if (radix < Character.MIN_RADIX) {
 775             throw new NumberFormatException(String.format(
 776                 "radix %s less than Character.MIN_RADIX", radix));
 777         }
 778 
 779         if (radix > Character.MAX_RADIX) {
 780             throw new NumberFormatException(String.format(
 781                 "radix %s greater than Character.MAX_RADIX", radix));
 782         }
 783 
 784         int len = s.length();
 785         if (len == 0) {
 786             throw NumberFormatException.forInputString(s, radix);
 787         }
 788         int i = 0;
 789         char firstChar = s.charAt(i++);
 790         if (firstChar == '-') {
 791             throw new NumberFormatException(String.format(
 792                 "Illegal leading minus sign on unsigned string %s.", s));
 793         }
 794         int digit = ~0xFF;
 795         if (firstChar != '+') {
 796             digit = digit(firstChar, radix);
 797         }
 798         if (digit >= 0 || digit == ~0xFF && len > 1) {
 799             long multmax = divideUnsigned(-1L, radix);  // -1L is max unsigned long
 800             long result = digit & 0xFF;
 801             boolean inRange = true;
 802             while (i < len && (digit = digit(s.charAt(i++), radix)) >= 0
 803                     && (inRange = compareUnsigned(result, multmax) < 0
 804                         || result == multmax && digit < (int) (-radix * multmax))) {
 805                 result = radix * result + digit;
 806             }
 807             if (inRange && i == len && digit >= 0) {
 808                 return result;
 809             }
 810         }
 811         if (digit < 0) {
 812             throw NumberFormatException.forInputString(s, radix);
 813         }
 814         throw new NumberFormatException(String.format(
 815             "String value %s exceeds range of unsigned long.", s));
 816     }
 817 
 818     /**
 819      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 820      * the specified {@code radix}, beginning at the specified
 821      * {@code beginIndex} and extending to {@code endIndex - 1}.
 822      *
 823      * <p>The method does not take steps to guard against the
 824      * {@code CharSequence} being mutated while parsing.
 825      *
 826      * @param      s   the {@code CharSequence} containing the unsigned
 827      *                 {@code long} representation to be parsed
 828      * @param      beginIndex   the beginning index, inclusive.
 829      * @param      endIndex     the ending index, exclusive.
 830      * @param      radix   the radix to be used while parsing {@code s}.
 831      * @return     the unsigned {@code long} represented by the subsequence in
 832      *             the specified radix.
 833      * @throws     NullPointerException  if {@code s} is null.
 834      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 835      *             negative, or if {@code beginIndex} is greater than
 836      *             {@code endIndex} or if {@code endIndex} is greater than
 837      *             {@code s.length()}.
 838      * @throws     NumberFormatException  if the {@code CharSequence} does not
 839      *             contain a parsable unsigned {@code long} in the specified
 840      *             {@code radix}, or if {@code radix} is either smaller than
 841      *             {@link java.lang.Character#MIN_RADIX} or larger than
 842      *             {@link java.lang.Character#MAX_RADIX}.
 843      * @since  9
 844      */
 845     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
 846                 throws NumberFormatException {
 847         Objects.requireNonNull(s);
 848         Objects.checkFromToIndex(beginIndex, endIndex, s.length());
 849 
 850         if (radix < Character.MIN_RADIX) {
 851             throw new NumberFormatException(String.format(
 852                 "radix %s less than Character.MIN_RADIX", radix));
 853         }
 854 
 855         if (radix > Character.MAX_RADIX) {
 856             throw new NumberFormatException(String.format(
 857                 "radix %s greater than Character.MAX_RADIX", radix));
 858         }
 859 
 860         /*
 861          * While s can be concurrently modified, it is ensured that each
 862          * of its characters is read at most once, from lower to higher indices.
 863          * This is obtained by reading them using the pattern s.charAt(i++),
 864          * and by not updating i anywhere else.
 865          */
 866         if (beginIndex == endIndex) {
 867             throw NumberFormatException.forInputString("", radix);
 868         }
 869         int i = beginIndex;
 870         char firstChar = s.charAt(i++);
 871         if (firstChar == '-') {
 872             throw new NumberFormatException(
 873                 "Illegal leading minus sign on unsigned string " + s + ".");
 874         }
 875         int digit = ~0xFF;
 876         if (firstChar != '+') {
 877             digit = digit(firstChar, radix);
 878         }
 879         if (digit >= 0 || digit == ~0xFF && endIndex - beginIndex > 1) {
 880             long multmax = divideUnsigned(-1L, radix);  // -1L is max unsigned long
 881             long result = digit & 0xFF;
 882             boolean inRange = true;
 883             while (i < endIndex && (digit = digit(s.charAt(i++), radix)) >= 0
 884                     && (inRange = compareUnsigned(result, multmax) < 0
 885                         || result == multmax && digit < (int) (-radix * multmax))) {
 886                 result = radix * result + digit;
 887             }
 888             if (inRange && i == endIndex && digit >= 0) {
 889                 return result;
 890             }
 891         }
 892         if (digit < 0) {
 893             throw NumberFormatException.forCharSequence(s, beginIndex,
 894                 endIndex, i - (digit < -1 ? 0 : 1));
 895         }
 896         throw new NumberFormatException(String.format(
 897             "String value %s exceeds range of unsigned long.", s));
 898     }
 899 
 900     /**
 901      * Parses the string argument as an unsigned decimal {@code long}. The
 902      * characters in the string must all be decimal digits, except
 903      * that the first character may be an ASCII plus sign {@code
 904      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 905      * is returned, exactly as if the argument and the radix 10 were
 906      * given as arguments to the {@link
 907      * #parseUnsignedLong(java.lang.String, int)} method.
 908      *
 909      * @param s   a {@code String} containing the unsigned {@code long}
 910      *            representation to be parsed
 911      * @return    the unsigned {@code long} value represented by the decimal string argument
 912      * @throws    NumberFormatException  if the string does not contain a
 913      *            parsable unsigned integer.
 914      * @since 1.8
 915      */
 916     public static long parseUnsignedLong(String s) throws NumberFormatException {
 917         return parseUnsignedLong(s, 10);
 918     }
 919 
 920     /**
 921      * Returns a {@code Long} object holding the value
 922      * extracted from the specified {@code String} when parsed
 923      * with the radix given by the second argument.  The first
 924      * argument is interpreted as representing a signed
 925      * {@code long} in the radix specified by the second
 926      * argument, exactly as if the arguments were given to the {@link
 927      * #parseLong(java.lang.String, int)} method. The result is a
 928      * {@code Long} object that represents the {@code long}
 929      * value specified by the string.
 930      *
 931      * <p>In other words, this method returns a {@code Long} object equal
 932      * to the value of:
 933      *
 934      * <blockquote>
 935      *  {@code Long.valueOf(Long.parseLong(s, radix))}
 936      * </blockquote>
 937      *
 938      * @param      s       the string to be parsed
 939      * @param      radix   the radix to be used in interpreting {@code s}
 940      * @return     a {@code Long} object holding the value
 941      *             represented by the string argument in the specified
 942      *             radix.
 943      * @throws     NumberFormatException  If the {@code String} does not
 944      *             contain a parsable {@code long}.
 945      */
 946     public static Long valueOf(String s, int radix) throws NumberFormatException {
 947         return Long.valueOf(parseLong(s, radix));
 948     }
 949 
 950     /**
 951      * Returns a {@code Long} object holding the value
 952      * of the specified {@code String}. The argument is
 953      * interpreted as representing a signed decimal {@code long},
 954      * exactly as if the argument were given to the {@link
 955      * #parseLong(java.lang.String)} method. The result is a
 956      * {@code Long} object that represents the integer value
 957      * specified by the string.
 958      *
 959      * <p>In other words, this method returns a {@code Long} object
 960      * equal to the value of:
 961      *
 962      * <blockquote>
 963      *  {@code Long.valueOf(Long.parseLong(s))}
 964      * </blockquote>
 965      *
 966      * @param      s   the string to be parsed.
 967      * @return     a {@code Long} object holding the value
 968      *             represented by the string argument.
 969      * @throws     NumberFormatException  If the string cannot be parsed
 970      *             as a {@code long}.
 971      */
 972     public static Long valueOf(String s) throws NumberFormatException
 973     {
 974         return Long.valueOf(parseLong(s, 10));
 975     }
 976 
 977     private static final class LongCache {
 978         private LongCache() {}
 979 
 980         @Stable
 981         static final Long[] cache;
 982         static Long[] archivedCache;
 983 
 984         static {
 985             int size = -(-128) + 127 + 1;
 986 
 987             // Load and use the archived cache if it exists
 988             CDS.initializeFromArchive(LongCache.class);
 989             if (archivedCache == null || archivedCache.length != size) {
 990                 Long[] c = new Long[size];
 991                 long value = -128;
 992                 for(int i = 0; i < size; i++) {
 993                     c[i] = new Long(value++);
 994                 }
 995                 archivedCache = c;
 996             }
 997             cache = archivedCache;
 998         }
 999     }
1000 
1001     /**
1002      * Returns a {@code Long} instance representing the specified
1003      * {@code long} value.
1004      * If a new {@code Long} instance is not required, this method
1005      * should generally be used in preference to the constructor
1006      * {@link #Long(long)}, as this method is likely to yield
1007      * significantly better space and time performance by caching
1008      * frequently requested values.
1009      *
1010      * This method will always cache values in the range -128 to 127,
1011      * inclusive, and may cache other values outside of this range.
1012      *
1013      * @param  l a long value.
1014      * @return a {@code Long} instance representing {@code l}.
1015      * @since  1.5
1016      */
1017     @IntrinsicCandidate
1018     public static Long valueOf(long l) {
1019         final int offset = 128;
1020         if (l >= -128 && l <= 127) { // will cache
1021             return LongCache.cache[(int)l + offset];
1022         }
1023         return new Long(l);
1024     }
1025 
1026     /**
1027      * Decodes a {@code String} into a {@code Long}.
1028      * Accepts decimal, hexadecimal, and octal numbers given by the
1029      * following grammar:
1030      *
1031      * <blockquote>
1032      * <dl>
1033      * <dt><i>DecodableString:</i>
1034      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1035      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1036      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1037      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1038      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1039      *
1040      * <dt><i>Sign:</i>
1041      * <dd>{@code -}
1042      * <dd>{@code +}
1043      * </dl>
1044      * </blockquote>
1045      *
1046      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1047      * are as defined in section {@jls 3.10.1} of
1048      * <cite>The Java Language Specification</cite>,
1049      * except that underscores are not accepted between digits.
1050      *
1051      * <p>The sequence of characters following an optional
1052      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1053      * "{@code #}", or leading zero) is parsed as by the {@code
1054      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1055      * This sequence of characters must represent a positive value or
1056      * a {@link NumberFormatException} will be thrown.  The result is
1057      * negated if first character of the specified {@code String} is
1058      * the minus sign.  No whitespace characters are permitted in the
1059      * {@code String}.
1060      *
1061      * @param     nm the {@code String} to decode.
1062      * @return    a {@code Long} object holding the {@code long}
1063      *            value represented by {@code nm}
1064      * @throws    NumberFormatException  if the {@code String} does not
1065      *            contain a parsable {@code long}.
1066      * @see java.lang.Long#parseLong(String, int)
1067      * @since 1.2
1068      */
1069     public static Long decode(String nm) throws NumberFormatException {
1070         int radix = 10;
1071         int index = 0;
1072         boolean negative = false;
1073         long result;
1074 
1075         if (nm.isEmpty())
1076             throw new NumberFormatException("Zero length string");
1077         char firstChar = nm.charAt(0);
1078         // Handle sign, if present
1079         if (firstChar == '-') {
1080             negative = true;
1081             index++;
1082         } else if (firstChar == '+')
1083             index++;
1084 
1085         // Handle radix specifier, if present
1086         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1087             index += 2;
1088             radix = 16;
1089         }
1090         else if (nm.startsWith("#", index)) {
1091             index ++;
1092             radix = 16;
1093         }
1094         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1095             index ++;
1096             radix = 8;
1097         }
1098 
1099         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1100             throw new NumberFormatException("Sign character in wrong position");
1101 
1102         try {
1103             result = parseLong(nm, index, nm.length(), radix);
1104             result = negative ? -result : result;
1105         } catch (NumberFormatException e) {
1106             // If number is Long.MIN_VALUE, we'll end up here. The next line
1107             // handles this case, and causes any genuine format error to be
1108             // rethrown.
1109             String constant = negative ? ("-" + nm.substring(index))
1110                                        : nm.substring(index);
1111             result = parseLong(constant, radix);
1112         }
1113         return result;
1114     }
1115 
1116     /**
1117      * The value of the {@code Long}.
1118      *
1119      * @serial
1120      */
1121     private final long value;
1122 
1123     /**
1124      * Constructs a newly allocated {@code Long} object that
1125      * represents the specified {@code long} argument.
1126      *
1127      * @param   value   the value to be represented by the
1128      *          {@code Long} object.
1129      *
1130      * @deprecated
1131      * It is rarely appropriate to use this constructor. The static factory
1132      * {@link #valueOf(long)} is generally a better choice, as it is
1133      * likely to yield significantly better space and time performance.
1134      */
1135     @Deprecated(since="9", forRemoval = true)
1136     public Long(long value) {
1137         this.value = value;
1138     }
1139 
1140     /**
1141      * Constructs a newly allocated {@code Long} object that
1142      * represents the {@code long} value indicated by the
1143      * {@code String} parameter. The string is converted to a
1144      * {@code long} value in exactly the manner used by the
1145      * {@code parseLong} method for radix 10.
1146      *
1147      * @param      s   the {@code String} to be converted to a
1148      *             {@code Long}.
1149      * @throws     NumberFormatException  if the {@code String} does not
1150      *             contain a parsable {@code long}.
1151      *
1152      * @deprecated
1153      * It is rarely appropriate to use this constructor.
1154      * Use {@link #parseLong(String)} to convert a string to a
1155      * {@code long} primitive, or use {@link #valueOf(String)}
1156      * to convert a string to a {@code Long} object.
1157      */
1158     @Deprecated(since="9", forRemoval = true)
1159     public Long(String s) throws NumberFormatException {
1160         this.value = parseLong(s, 10);
1161     }
1162 
1163     /**
1164      * Returns the value of this {@code Long} as a {@code byte} after
1165      * a narrowing primitive conversion.
1166      * @jls 5.1.3 Narrowing Primitive Conversion
1167      */
1168     public byte byteValue() {
1169         return (byte)value;
1170     }
1171 
1172     /**
1173      * Returns the value of this {@code Long} as a {@code short} after
1174      * a narrowing primitive conversion.
1175      * @jls 5.1.3 Narrowing Primitive Conversion
1176      */
1177     public short shortValue() {
1178         return (short)value;
1179     }
1180 
1181     /**
1182      * Returns the value of this {@code Long} as an {@code int} after
1183      * a narrowing primitive conversion.
1184      * @jls 5.1.3 Narrowing Primitive Conversion
1185      */
1186     public int intValue() {
1187         return (int)value;
1188     }
1189 
1190     /**
1191      * Returns the value of this {@code Long} as a
1192      * {@code long} value.
1193      */
1194     @IntrinsicCandidate
1195     public long longValue() {
1196         return value;
1197     }
1198 
1199     /**
1200      * Returns the value of this {@code Long} as a {@code float} after
1201      * a widening primitive conversion.
1202      * @jls 5.1.2 Widening Primitive Conversion
1203      */
1204     public float floatValue() {
1205         return (float)value;
1206     }
1207 
1208     /**
1209      * Returns the value of this {@code Long} as a {@code double}
1210      * after a widening primitive conversion.
1211      * @jls 5.1.2 Widening Primitive Conversion
1212      */
1213     public double doubleValue() {
1214         return (double)value;
1215     }
1216 
1217     /**
1218      * Returns a {@code String} object representing this
1219      * {@code Long}'s value.  The value is converted to signed
1220      * decimal representation and returned as a string, exactly as if
1221      * the {@code long} value were given as an argument to the
1222      * {@link java.lang.Long#toString(long)} method.
1223      *
1224      * @return  a string representation of the value of this object in
1225      *          base&nbsp;10.
1226      */
1227     public String toString() {
1228         return toString(value);
1229     }
1230 
1231     /**
1232      * Returns a hash code for this {@code Long}. The result is
1233      * the exclusive OR of the two halves of the primitive
1234      * {@code long} value held by this {@code Long}
1235      * object. That is, the hashcode is the value of the expression:
1236      *
1237      * <blockquote>
1238      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1239      * </blockquote>
1240      *
1241      * @return  a hash code value for this object.
1242      */
1243     @Override
1244     public int hashCode() {
1245         return Long.hashCode(value);
1246     }
1247 
1248     /**
1249      * Returns a hash code for a {@code long} value; compatible with
1250      * {@code Long.hashCode()}.
1251      *
1252      * @param value the value to hash
1253      * @return a hash code value for a {@code long} value.
1254      * @since 1.8
1255      */
1256     public static int hashCode(long value) {
1257         return (int)(value ^ (value >>> 32));
1258     }
1259 
1260     /**
1261      * Compares this object to the specified object.  The result is
1262      * {@code true} if and only if the argument is not
1263      * {@code null} and is a {@code Long} object that
1264      * contains the same {@code long} value as this object.
1265      *
1266      * @param   obj   the object to compare with.
1267      * @return  {@code true} if the objects are the same;
1268      *          {@code false} otherwise.
1269      */
1270     public boolean equals(Object obj) {
1271         if (obj instanceof Long) {
1272             return value == ((Long)obj).longValue();
1273         }
1274         return false;
1275     }
1276 
1277     /**
1278      * Determines the {@code long} value of the system property
1279      * with the specified name.
1280      *
1281      * <p>The first argument is treated as the name of a system
1282      * property.  System properties are accessible through the {@link
1283      * java.lang.System#getProperty(java.lang.String)} method. The
1284      * string value of this property is then interpreted as a {@code
1285      * long} value using the grammar supported by {@link Long#decode decode}
1286      * and a {@code Long} object representing this value is returned.
1287      *
1288      * <p>If there is no property with the specified name, if the
1289      * specified name is empty or {@code null}, or if the property
1290      * does not have the correct numeric format, then {@code null} is
1291      * returned.
1292      *
1293      * <p>In other words, this method returns a {@code Long} object
1294      * equal to the value of:
1295      *
1296      * <blockquote>
1297      *  {@code getLong(nm, null)}
1298      * </blockquote>
1299      *
1300      * @param   nm   property name.
1301      * @return  the {@code Long} value of the property.
1302      * @throws  SecurityException for the same reasons as
1303      *          {@link System#getProperty(String) System.getProperty}
1304      * @see     java.lang.System#getProperty(java.lang.String)
1305      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1306      */
1307     public static Long getLong(String nm) {
1308         return getLong(nm, null);
1309     }
1310 
1311     /**
1312      * Determines the {@code long} value of the system property
1313      * with the specified name.
1314      *
1315      * <p>The first argument is treated as the name of a system
1316      * property.  System properties are accessible through the {@link
1317      * java.lang.System#getProperty(java.lang.String)} method. The
1318      * string value of this property is then interpreted as a {@code
1319      * long} value using the grammar supported by {@link Long#decode decode}
1320      * and a {@code Long} object representing this value is returned.
1321      *
1322      * <p>The second argument is the default value. A {@code Long} object
1323      * that represents the value of the second argument is returned if there
1324      * is no property of the specified name, if the property does not have
1325      * the correct numeric format, or if the specified name is empty or null.
1326      *
1327      * <p>In other words, this method returns a {@code Long} object equal
1328      * to the value of:
1329      *
1330      * <blockquote>
1331      *  {@code getLong(nm, Long.valueOf(val))}
1332      * </blockquote>
1333      *
1334      * but in practice it may be implemented in a manner such as:
1335      *
1336      * <blockquote><pre>
1337      * Long result = getLong(nm, null);
1338      * return (result == null) ? Long.valueOf(val) : result;
1339      * </pre></blockquote>
1340      *
1341      * to avoid the unnecessary allocation of a {@code Long} object when
1342      * the default value is not needed.
1343      *
1344      * @param   nm    property name.
1345      * @param   val   default value.
1346      * @return  the {@code Long} value of the property.
1347      * @throws  SecurityException for the same reasons as
1348      *          {@link System#getProperty(String) System.getProperty}
1349      * @see     java.lang.System#getProperty(java.lang.String)
1350      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1351      */
1352     public static Long getLong(String nm, long val) {
1353         Long result = Long.getLong(nm, null);
1354         return (result == null) ? Long.valueOf(val) : result;
1355     }
1356 
1357     /**
1358      * Returns the {@code long} value of the system property with
1359      * the specified name.  The first argument is treated as the name
1360      * of a system property.  System properties are accessible through
1361      * the {@link java.lang.System#getProperty(java.lang.String)}
1362      * method. The string value of this property is then interpreted
1363      * as a {@code long} value, as per the
1364      * {@link Long#decode decode} method, and a {@code Long} object
1365      * representing this value is returned; in summary:
1366      *
1367      * <ul>
1368      * <li>If the property value begins with the two ASCII characters
1369      * {@code 0x} or the ASCII character {@code #}, not followed by
1370      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1371      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1372      * with radix 16.
1373      * <li>If the property value begins with the ASCII character
1374      * {@code 0} followed by another character, it is parsed as
1375      * an octal integer exactly as by the method {@link
1376      * #valueOf(java.lang.String, int)} with radix 8.
1377      * <li>Otherwise the property value is parsed as a decimal
1378      * integer exactly as by the method
1379      * {@link #valueOf(java.lang.String, int)} with radix 10.
1380      * </ul>
1381      *
1382      * <p>Note that, in every case, neither {@code L}
1383      * ({@code '\u005Cu004C'}) nor {@code l}
1384      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1385      * of the property value as a type indicator, as would be
1386      * permitted in Java programming language source code.
1387      *
1388      * <p>The second argument is the default value. The default value is
1389      * returned if there is no property of the specified name, if the
1390      * property does not have the correct numeric format, or if the
1391      * specified name is empty or {@code null}.
1392      *
1393      * @param   nm   property name.
1394      * @param   val   default value.
1395      * @return  the {@code Long} value of the property.
1396      * @throws  SecurityException for the same reasons as
1397      *          {@link System#getProperty(String) System.getProperty}
1398      * @see     System#getProperty(java.lang.String)
1399      * @see     System#getProperty(java.lang.String, java.lang.String)
1400      */
1401     public static Long getLong(String nm, Long val) {
1402         String v = null;
1403         try {
1404             v = System.getProperty(nm);
1405         } catch (IllegalArgumentException | NullPointerException e) {
1406         }
1407         if (v != null) {
1408             try {
1409                 return Long.decode(v);
1410             } catch (NumberFormatException e) {
1411             }
1412         }
1413         return val;
1414     }
1415 
1416     /**
1417      * Compares two {@code Long} objects numerically.
1418      *
1419      * @param   anotherLong   the {@code Long} to be compared.
1420      * @return  the value {@code 0} if this {@code Long} is
1421      *          equal to the argument {@code Long}; a value less than
1422      *          {@code 0} if this {@code Long} is numerically less
1423      *          than the argument {@code Long}; and a value greater
1424      *          than {@code 0} if this {@code Long} is numerically
1425      *           greater than the argument {@code Long} (signed
1426      *           comparison).
1427      * @since   1.2
1428      */
1429     public int compareTo(Long anotherLong) {
1430         return compare(this.value, anotherLong.value);
1431     }
1432 
1433     /**
1434      * Compares two {@code long} values numerically.
1435      * The value returned is identical to what would be returned by:
1436      * <pre>
1437      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1438      * </pre>
1439      *
1440      * @param  x the first {@code long} to compare
1441      * @param  y the second {@code long} to compare
1442      * @return the value {@code 0} if {@code x == y};
1443      *         a value less than {@code 0} if {@code x < y}; and
1444      *         a value greater than {@code 0} if {@code x > y}
1445      * @since 1.7
1446      */
1447     public static int compare(long x, long y) {
1448         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1449     }
1450 
1451     /**
1452      * Compares two {@code long} values numerically treating the values
1453      * as unsigned.
1454      *
1455      * @param  x the first {@code long} to compare
1456      * @param  y the second {@code long} to compare
1457      * @return the value {@code 0} if {@code x == y}; a value less
1458      *         than {@code 0} if {@code x < y} as unsigned values; and
1459      *         a value greater than {@code 0} if {@code x > y} as
1460      *         unsigned values
1461      * @since 1.8
1462      */
1463     @IntrinsicCandidate
1464     public static int compareUnsigned(long x, long y) {
1465         return compare(x + MIN_VALUE, y + MIN_VALUE);
1466     }
1467 
1468 
1469     /**
1470      * Returns the unsigned quotient of dividing the first argument by
1471      * the second where each argument and the result is interpreted as
1472      * an unsigned value.
1473      *
1474      * <p>Note that in two's complement arithmetic, the three other
1475      * basic arithmetic operations of add, subtract, and multiply are
1476      * bit-wise identical if the two operands are regarded as both
1477      * being signed or both being unsigned.  Therefore separate {@code
1478      * addUnsigned}, etc. methods are not provided.
1479      *
1480      * @param dividend the value to be divided
1481      * @param divisor the value doing the dividing
1482      * @return the unsigned quotient of the first argument divided by
1483      * the second argument
1484      * @see #remainderUnsigned
1485      * @since 1.8
1486      */
1487     @IntrinsicCandidate
1488     public static long divideUnsigned(long dividend, long divisor) {
1489         /* See Hacker's Delight (2nd ed), section 9.3 */
1490         if (divisor >= 0) {
1491             final long q = (dividend >>> 1) / divisor << 1;
1492             final long r = dividend - q * divisor;
1493             return q + ((r | ~(r - divisor)) >>> (Long.SIZE - 1));
1494         }
1495         return (dividend & ~(dividend - divisor)) >>> (Long.SIZE - 1);
1496     }
1497 
1498     /**
1499      * Returns the unsigned remainder from dividing the first argument
1500      * by the second where each argument and the result is interpreted
1501      * as an unsigned value.
1502      *
1503      * @param dividend the value to be divided
1504      * @param divisor the value doing the dividing
1505      * @return the unsigned remainder of the first argument divided by
1506      * the second argument
1507      * @see #divideUnsigned
1508      * @since 1.8
1509      */
1510     @IntrinsicCandidate
1511     public static long remainderUnsigned(long dividend, long divisor) {
1512         /* See Hacker's Delight (2nd ed), section 9.3 */
1513         if (divisor >= 0) {
1514             final long q = (dividend >>> 1) / divisor << 1;
1515             final long r = dividend - q * divisor;
1516             /*
1517              * Here, 0 <= r < 2 * divisor
1518              * (1) When 0 <= r < divisor, the remainder is simply r.
1519              * (2) Otherwise the remainder is r - divisor.
1520              *
1521              * In case (1), r - divisor < 0. Applying ~ produces a long with
1522              * sign bit 0, so >> produces 0. The returned value is thus r.
1523              *
1524              * In case (2), a similar reasoning shows that >> produces -1,
1525              * so the returned value is r - divisor.
1526              */
1527             return r - ((~(r - divisor) >> (Long.SIZE - 1)) & divisor);
1528         }
1529         /*
1530          * (1) When dividend >= 0, the remainder is dividend.
1531          * (2) Otherwise
1532          *      (2.1) When dividend < divisor, the remainder is dividend.
1533          *      (2.2) Otherwise the remainder is dividend - divisor
1534          *
1535          * A reasoning similar to the above shows that the returned value
1536          * is as expected.
1537          */
1538         return dividend - (((dividend & ~(dividend - divisor)) >> (Long.SIZE - 1)) & divisor);
1539     }
1540 
1541     // Bit Twiddling
1542 
1543     /**
1544      * The number of bits used to represent a {@code long} value in two's
1545      * complement binary form.
1546      *
1547      * @since 1.5
1548      */
1549     @Native public static final int SIZE = 64;
1550 
1551     /**
1552      * The number of bytes used to represent a {@code long} value in two's
1553      * complement binary form.
1554      *
1555      * @since 1.8
1556      */
1557     public static final int BYTES = SIZE / Byte.SIZE;
1558 
1559     /**
1560      * Returns a {@code long} value with at most a single one-bit, in the
1561      * position of the highest-order ("leftmost") one-bit in the specified
1562      * {@code long} value.  Returns zero if the specified value has no
1563      * one-bits in its two's complement binary representation, that is, if it
1564      * is equal to zero.
1565      *
1566      * @param i the value whose highest one bit is to be computed
1567      * @return a {@code long} value with a single one-bit, in the position
1568      *     of the highest-order one-bit in the specified value, or zero if
1569      *     the specified value is itself equal to zero.
1570      * @since 1.5
1571      */
1572     public static long highestOneBit(long i) {
1573         return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
1574     }
1575 
1576     /**
1577      * Returns a {@code long} value with at most a single one-bit, in the
1578      * position of the lowest-order ("rightmost") one-bit in the specified
1579      * {@code long} value.  Returns zero if the specified value has no
1580      * one-bits in its two's complement binary representation, that is, if it
1581      * is equal to zero.
1582      *
1583      * @param i the value whose lowest one bit is to be computed
1584      * @return a {@code long} value with a single one-bit, in the position
1585      *     of the lowest-order one-bit in the specified value, or zero if
1586      *     the specified value is itself equal to zero.
1587      * @since 1.5
1588      */
1589     public static long lowestOneBit(long i) {
1590         // HD, Section 2-1
1591         return i & -i;
1592     }
1593 
1594     /**
1595      * Returns the number of zero bits preceding the highest-order
1596      * ("leftmost") one-bit in the two's complement binary representation
1597      * of the specified {@code long} value.  Returns 64 if the
1598      * specified value has no one-bits in its two's complement representation,
1599      * in other words if it is equal to zero.
1600      *
1601      * <p>Note that this method is closely related to the logarithm base 2.
1602      * For all positive {@code long} values x:
1603      * <ul>
1604      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1605      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1606      * </ul>
1607      *
1608      * @param i the value whose number of leading zeros is to be computed
1609      * @return the number of zero bits preceding the highest-order
1610      *     ("leftmost") one-bit in the two's complement binary representation
1611      *     of the specified {@code long} value, or 64 if the value
1612      *     is equal to zero.
1613      * @since 1.5
1614      */
1615     @IntrinsicCandidate
1616     public static int numberOfLeadingZeros(long i) {
1617         int x = (int)(i >>> 32);
1618         return x == 0 ? 32 + Integer.numberOfLeadingZeros((int)i)
1619                 : Integer.numberOfLeadingZeros(x);
1620     }
1621 
1622     /**
1623      * Returns the number of zero bits following the lowest-order ("rightmost")
1624      * one-bit in the two's complement binary representation of the specified
1625      * {@code long} value.  Returns 64 if the specified value has no
1626      * one-bits in its two's complement representation, in other words if it is
1627      * equal to zero.
1628      *
1629      * @param i the value whose number of trailing zeros is to be computed
1630      * @return the number of zero bits following the lowest-order ("rightmost")
1631      *     one-bit in the two's complement binary representation of the
1632      *     specified {@code long} value, or 64 if the value is equal
1633      *     to zero.
1634      * @since 1.5
1635      */
1636     @IntrinsicCandidate
1637     public static int numberOfTrailingZeros(long i) {
1638         int x = (int)i;
1639         return x == 0 ? 32 + Integer.numberOfTrailingZeros((int)(i >>> 32))
1640                 : Integer.numberOfTrailingZeros(x);
1641     }
1642 
1643     /**
1644      * Returns the number of one-bits in the two's complement binary
1645      * representation of the specified {@code long} value.  This function is
1646      * sometimes referred to as the <i>population count</i>.
1647      *
1648      * @param i the value whose bits are to be counted
1649      * @return the number of one-bits in the two's complement binary
1650      *     representation of the specified {@code long} value.
1651      * @since 1.5
1652      */
1653      @IntrinsicCandidate
1654      public static int bitCount(long i) {
1655         // HD, Figure 5-2
1656         i = i - ((i >>> 1) & 0x5555555555555555L);
1657         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1658         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1659         i = i + (i >>> 8);
1660         i = i + (i >>> 16);
1661         i = i + (i >>> 32);
1662         return (int)i & 0x7f;
1663      }
1664 
1665     /**
1666      * Returns the value obtained by rotating the two's complement binary
1667      * representation of the specified {@code long} value left by the
1668      * specified number of bits.  (Bits shifted out of the left hand, or
1669      * high-order, side reenter on the right, or low-order.)
1670      *
1671      * <p>Note that left rotation with a negative distance is equivalent to
1672      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1673      * distance)}.  Note also that rotation by any multiple of 64 is a
1674      * no-op, so all but the last six bits of the rotation distance can be
1675      * ignored, even if the distance is negative: {@code rotateLeft(val,
1676      * distance) == rotateLeft(val, distance & 0x3F)}.
1677      *
1678      * @param i the value whose bits are to be rotated left
1679      * @param distance the number of bit positions to rotate left
1680      * @return the value obtained by rotating the two's complement binary
1681      *     representation of the specified {@code long} value left by the
1682      *     specified number of bits.
1683      * @since 1.5
1684      */
1685     public static long rotateLeft(long i, int distance) {
1686         return (i << distance) | (i >>> -distance);
1687     }
1688 
1689     /**
1690      * Returns the value obtained by rotating the two's complement binary
1691      * representation of the specified {@code long} value right by the
1692      * specified number of bits.  (Bits shifted out of the right hand, or
1693      * low-order, side reenter on the left, or high-order.)
1694      *
1695      * <p>Note that right rotation with a negative distance is equivalent to
1696      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1697      * distance)}.  Note also that rotation by any multiple of 64 is a
1698      * no-op, so all but the last six bits of the rotation distance can be
1699      * ignored, even if the distance is negative: {@code rotateRight(val,
1700      * distance) == rotateRight(val, distance & 0x3F)}.
1701      *
1702      * @param i the value whose bits are to be rotated right
1703      * @param distance the number of bit positions to rotate right
1704      * @return the value obtained by rotating the two's complement binary
1705      *     representation of the specified {@code long} value right by the
1706      *     specified number of bits.
1707      * @since 1.5
1708      */
1709     public static long rotateRight(long i, int distance) {
1710         return (i >>> distance) | (i << -distance);
1711     }
1712 
1713     /**
1714      * Returns the value obtained by reversing the order of the bits in the
1715      * two's complement binary representation of the specified {@code long}
1716      * value.
1717      *
1718      * @param i the value to be reversed
1719      * @return the value obtained by reversing order of the bits in the
1720      *     specified {@code long} value.
1721      * @since 1.5
1722      */
1723     @IntrinsicCandidate
1724     public static long reverse(long i) {
1725         // HD, Figure 7-1
1726         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1727         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1728         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1729 
1730         return reverseBytes(i);
1731     }
1732 
1733     /**
1734      * Returns the value obtained by compressing the bits of the
1735      * specified {@code long} value, {@code i}, in accordance with
1736      * the specified bit mask.
1737      * <p>
1738      * For each one-bit value {@code mb} of the mask, from least
1739      * significant to most significant, the bit value of {@code i} at
1740      * the same bit location as {@code mb} is assigned to the compressed
1741      * value contiguously starting from the least significant bit location.
1742      * All the upper remaining bits of the compressed value are set
1743      * to zero.
1744      *
1745      * @apiNote
1746      * Consider the simple case of compressing the digits of a hexadecimal
1747      * value:
1748      * {@snippet lang="java" :
1749      * // Compressing drink to food
1750      * compress(0xCAFEBABEL, 0xFF00FFF0L) == 0xCABABL
1751      * }
1752      * Starting from the least significant hexadecimal digit at position 0
1753      * from the right, the mask {@code 0xFF00FFF0} selects hexadecimal digits
1754      * at positions 1, 2, 3, 6 and 7 of {@code 0xCAFEBABE}. The selected digits
1755      * occur in the resulting compressed value contiguously from digit position
1756      * 0 in the same order.
1757      * <p>
1758      * The following identities all return {@code true} and are helpful to
1759      * understand the behaviour of {@code compress}:
1760      * {@snippet lang="java" :
1761      * // Returns 1 if the bit at position n is one
1762      * compress(x, 1L << n) == (x >> n & 1)
1763      *
1764      * // Logical shift right
1765      * compress(x, -1L << n) == x >>> n
1766      *
1767      * // Any bits not covered by the mask are ignored
1768      * compress(x, m) == compress(x & m, m)
1769      *
1770      * // Compressing a value by itself
1771      * compress(m, m) == (m == -1 || m == 0) ? m : (1L << bitCount(m)) - 1
1772      *
1773      * // Expanding then compressing with the same mask
1774      * compress(expand(x, m), m) == x & compress(m, m)
1775      * }
1776      * <p>
1777      * The Sheep And Goats (SAG) operation (see Hacker's Delight, section 7.7)
1778      * can be implemented as follows:
1779      * {@snippet lang="java" :
1780      * long compressLeft(long i, long mask) {
1781      *     // This implementation follows the description in Hacker's Delight which
1782      *     // is informative. A more optimal implementation is:
1783      *     //   Long.compress(i, mask) << -Long.bitCount(mask)
1784      *     return Long.reverse(
1785      *         Long.compress(Long.reverse(i), Long.reverse(mask)));
1786      * }
1787      *
1788      * long sag(long i, long mask) {
1789      *     return compressLeft(i, mask) | Long.compress(i, ~mask);
1790      * }
1791      *
1792      * // Separate the sheep from the goats
1793      * sag(0x00000000_CAFEBABEL, 0xFFFFFFFF_FF00FFF0L) == 0x00000000_CABABFEEL
1794      * }
1795      *
1796      * @param i the value whose bits are to be compressed
1797      * @param mask the bit mask
1798      * @return the compressed value
1799      * @see #expand
1800      * @since 19
1801      */
1802     @IntrinsicCandidate
1803     public static long compress(long i, long mask) {
1804         // See Hacker's Delight (2nd ed) section 7.4 Compress, or Generalized Extract
1805 
1806         i = i & mask; // Clear irrelevant bits
1807         long maskCount = ~mask << 1; // Count 0's to right
1808 
1809         for (int j = 0; j < 6; j++) {
1810             // Parallel prefix
1811             // Mask prefix identifies bits of the mask that have an odd number of 0's to the right
1812             long maskPrefix = parallelSuffix(maskCount);
1813             // Bits to move
1814             long maskMove = maskPrefix & mask;
1815             // Compress mask
1816             mask = (mask ^ maskMove) | (maskMove >>> (1 << j));
1817             // Bits of i to be moved
1818             long t = i & maskMove;
1819             // Compress i
1820             i = (i ^ t) | (t >>> (1 << j));
1821             // Adjust the mask count by identifying bits that have 0 to the right
1822             maskCount = maskCount & ~maskPrefix;
1823         }
1824         return i;
1825     }
1826 
1827     /**
1828      * Returns the value obtained by expanding the bits of the
1829      * specified {@code long} value, {@code i}, in accordance with
1830      * the specified bit mask.
1831      * <p>
1832      * For each one-bit value {@code mb} of the mask, from least
1833      * significant to most significant, the next contiguous bit value
1834      * of {@code i} starting at the least significant bit is assigned
1835      * to the expanded value at the same bit location as {@code mb}.
1836      * All other remaining bits of the expanded value are set to zero.
1837      *
1838      * @apiNote
1839      * Consider the simple case of expanding the digits of a hexadecimal
1840      * value:
1841      * {@snippet lang="java" :
1842      * expand(0x0000CABABL, 0xFF00FFF0L) == 0xCA00BAB0L
1843      * }
1844      * Starting from the least significant hexadecimal digit at position 0
1845      * from the right, the mask {@code 0xFF00FFF0} selects the first five
1846      * hexadecimal digits of {@code 0x0000CABAB}. The selected digits occur
1847      * in the resulting expanded value in order at positions 1, 2, 3, 6, and 7.
1848      * <p>
1849      * The following identities all return {@code true} and are helpful to
1850      * understand the behaviour of {@code expand}:
1851      * {@snippet lang="java" :
1852      * // Logically shift right the bit at position 0
1853      * expand(x, 1L << n) == (x & 1) << n
1854      *
1855      * // Logically shift right
1856      * expand(x, -1L << n) == x << n
1857      *
1858      * // Expanding all bits returns the mask
1859      * expand(-1L, m) == m
1860      *
1861      * // Any bits not covered by the mask are ignored
1862      * expand(x, m) == expand(x, m) & m
1863      *
1864      * // Compressing then expanding with the same mask
1865      * expand(compress(x, m), m) == x & m
1866      * }
1867      * <p>
1868      * The select operation for determining the position of the one-bit with
1869      * index {@code n} in a {@code long} value can be implemented as follows:
1870      * {@snippet lang="java" :
1871      * long select(long i, long n) {
1872      *     // the one-bit in i (the mask) with index n
1873      *     long nthBit = Long.expand(1L << n, i);
1874      *     // the bit position of the one-bit with index n
1875      *     return Long.numberOfTrailingZeros(nthBit);
1876      * }
1877      *
1878      * // The one-bit with index 0 is at bit position 1
1879      * select(0b10101010_10101010, 0) == 1
1880      * // The one-bit with index 3 is at bit position 7
1881      * select(0b10101010_10101010, 3) == 7
1882      * }
1883      *
1884      * @param i the value whose bits are to be expanded
1885      * @param mask the bit mask
1886      * @return the expanded value
1887      * @see #compress
1888      * @since 19
1889      */
1890     @IntrinsicCandidate
1891     public static long expand(long i, long mask) {
1892         // Save original mask
1893         long originalMask = mask;
1894         // Count 0's to right
1895         long maskCount = ~mask << 1;
1896         long maskPrefix = parallelSuffix(maskCount);
1897         // Bits to move
1898         long maskMove1 = maskPrefix & mask;
1899         // Compress mask
1900         mask = (mask ^ maskMove1) | (maskMove1 >>> (1 << 0));
1901         maskCount = maskCount & ~maskPrefix;
1902 
1903         maskPrefix = parallelSuffix(maskCount);
1904         // Bits to move
1905         long maskMove2 = maskPrefix & mask;
1906         // Compress mask
1907         mask = (mask ^ maskMove2) | (maskMove2 >>> (1 << 1));
1908         maskCount = maskCount & ~maskPrefix;
1909 
1910         maskPrefix = parallelSuffix(maskCount);
1911         // Bits to move
1912         long maskMove3 = maskPrefix & mask;
1913         // Compress mask
1914         mask = (mask ^ maskMove3) | (maskMove3 >>> (1 << 2));
1915         maskCount = maskCount & ~maskPrefix;
1916 
1917         maskPrefix = parallelSuffix(maskCount);
1918         // Bits to move
1919         long maskMove4 = maskPrefix & mask;
1920         // Compress mask
1921         mask = (mask ^ maskMove4) | (maskMove4 >>> (1 << 3));
1922         maskCount = maskCount & ~maskPrefix;
1923 
1924         maskPrefix = parallelSuffix(maskCount);
1925         // Bits to move
1926         long maskMove5 = maskPrefix & mask;
1927         // Compress mask
1928         mask = (mask ^ maskMove5) | (maskMove5 >>> (1 << 4));
1929         maskCount = maskCount & ~maskPrefix;
1930 
1931         maskPrefix = parallelSuffix(maskCount);
1932         // Bits to move
1933         long maskMove6 = maskPrefix & mask;
1934 
1935         long t = i << (1 << 5);
1936         i = (i & ~maskMove6) | (t & maskMove6);
1937         t = i << (1 << 4);
1938         i = (i & ~maskMove5) | (t & maskMove5);
1939         t = i << (1 << 3);
1940         i = (i & ~maskMove4) | (t & maskMove4);
1941         t = i << (1 << 2);
1942         i = (i & ~maskMove3) | (t & maskMove3);
1943         t = i << (1 << 1);
1944         i = (i & ~maskMove2) | (t & maskMove2);
1945         t = i << (1 << 0);
1946         i = (i & ~maskMove1) | (t & maskMove1);
1947 
1948         // Clear irrelevant bits
1949         return i & originalMask;
1950     }
1951 
1952     @ForceInline
1953     private static long parallelSuffix(long maskCount) {
1954         long maskPrefix = maskCount ^ (maskCount << 1);
1955         maskPrefix = maskPrefix ^ (maskPrefix << 2);
1956         maskPrefix = maskPrefix ^ (maskPrefix << 4);
1957         maskPrefix = maskPrefix ^ (maskPrefix << 8);
1958         maskPrefix = maskPrefix ^ (maskPrefix << 16);
1959         maskPrefix = maskPrefix ^ (maskPrefix << 32);
1960         return maskPrefix;
1961     }
1962 
1963     /**
1964      * Returns the signum function of the specified {@code long} value.  (The
1965      * return value is -1 if the specified value is negative; 0 if the
1966      * specified value is zero; and 1 if the specified value is positive.)
1967      *
1968      * @param i the value whose signum is to be computed
1969      * @return the signum function of the specified {@code long} value.
1970      * @since 1.5
1971      */
1972     public static int signum(long i) {
1973         // HD, Section 2-7
1974         return (int) ((i >> 63) | (-i >>> 63));
1975     }
1976 
1977     /**
1978      * Returns the value obtained by reversing the order of the bytes in the
1979      * two's complement representation of the specified {@code long} value.
1980      *
1981      * @param i the value whose bytes are to be reversed
1982      * @return the value obtained by reversing the bytes in the specified
1983      *     {@code long} value.
1984      * @since 1.5
1985      */
1986     @IntrinsicCandidate
1987     public static long reverseBytes(long i) {
1988         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1989         return (i << 48) | ((i & 0xffff0000L) << 16) |
1990             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1991     }
1992 
1993     /**
1994      * Adds two {@code long} values together as per the + operator.
1995      *
1996      * @param a the first operand
1997      * @param b the second operand
1998      * @return the sum of {@code a} and {@code b}
1999      * @see java.util.function.BinaryOperator
2000      * @since 1.8
2001      */
2002     public static long sum(long a, long b) {
2003         return a + b;
2004     }
2005 
2006     /**
2007      * Returns the greater of two {@code long} values
2008      * as if by calling {@link Math#max(long, long) Math.max}.
2009      *
2010      * @param a the first operand
2011      * @param b the second operand
2012      * @return the greater of {@code a} and {@code b}
2013      * @see java.util.function.BinaryOperator
2014      * @since 1.8
2015      */
2016     public static long max(long a, long b) {
2017         return Math.max(a, b);
2018     }
2019 
2020     /**
2021      * Returns the smaller of two {@code long} values
2022      * as if by calling {@link Math#min(long, long) Math.min}.
2023      *
2024      * @param a the first operand
2025      * @param b the second operand
2026      * @return the smaller of {@code a} and {@code b}
2027      * @see java.util.function.BinaryOperator
2028      * @since 1.8
2029      */
2030     public static long min(long a, long b) {
2031         return Math.min(a, b);
2032     }
2033 
2034     /**
2035      * Returns an {@link Optional} containing the nominal descriptor for this
2036      * instance, which is the instance itself.
2037      *
2038      * @return an {@link Optional} describing the {@linkplain Long} instance
2039      * @since 12
2040      */
2041     @Override
2042     public Optional<Long> describeConstable() {
2043         return Optional.of(this);
2044     }
2045 
2046     /**
2047      * Resolves this instance as a {@link ConstantDesc}, the result of which is
2048      * the instance itself.
2049      *
2050      * @param lookup ignored
2051      * @return the {@linkplain Long} instance
2052      * @since 12
2053      */
2054     @Override
2055     public Long resolveConstantDesc(MethodHandles.Lookup lookup) {
2056         return this;
2057     }
2058 
2059     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2060     @java.io.Serial
2061     @Native private static final long serialVersionUID = 4290774380558885855L;
2062 }