1 /*
   2  * Copyright (c) 1994, 2019, 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.HotSpotIntrinsicCandidate;
  37 import jdk.internal.misc.VM;
  38 
  39 import static java.lang.String.COMPACT_STRINGS;
  40 import static java.lang.String.LATIN1;
  41 import static java.lang.String.UTF16;
  42 
  43 /**
  44  * The {@code Long} class wraps a value of the primitive type {@code
  45  * long} in an object. An object of type {@code Long} contains a
  46  * single field whose type is {@code long}.
  47  *
  48  * <p> In addition, this class provides several methods for converting
  49  * a {@code long} to a {@code String} and a {@code String} to a {@code
  50  * long}, as well as other constants and methods useful when dealing
  51  * with a {@code long}.
  52  *
  53  * <p>Implementation note: The implementations of the "bit twiddling"
  54  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  55  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  56  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  57  * Delight</i>, (Addison Wesley, 2002).
  58  *
  59  * @author  Lee Boynton
  60  * @author  Arthur van Hoff
  61  * @author  Josh Bloch
  62  * @author  Joseph D. Darcy
  63  * @since   1.0
  64  */
  65 public final class Long extends Number
  66         implements Comparable<Long>, Constable, ConstantDesc {
  67     /**
  68      * A constant holding the minimum value a {@code long} can
  69      * have, -2<sup>63</sup>.
  70      */
  71     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  72 
  73     /**
  74      * A constant holding the maximum value a {@code long} can
  75      * have, 2<sup>63</sup>-1.
  76      */
  77     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  78 
  79     /**
  80      * The {@code Class} instance representing the primitive type
  81      * {@code long}.
  82      *
  83      * @since   1.1
  84      */
  85     @SuppressWarnings("unchecked")
  86     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  87 
  88     /**
  89      * Returns a string representation of the first argument in the
  90      * radix specified by the second argument.
  91      *
  92      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  93      * or larger than {@code Character.MAX_RADIX}, then the radix
  94      * {@code 10} is used instead.
  95      *
  96      * <p>If the first argument is negative, the first element of the
  97      * result is the ASCII minus sign {@code '-'}
  98      * ({@code '\u005Cu002d'}). If the first argument is not
  99      * negative, no sign character appears in the result.
 100      *
 101      * <p>The remaining characters of the result represent the magnitude
 102      * of the first argument. If the magnitude is zero, it is
 103      * represented by a single zero character {@code '0'}
 104      * ({@code '\u005Cu0030'}); otherwise, the first character of
 105      * the representation of the magnitude will not be the zero
 106      * character.  The following ASCII characters are used as digits:
 107      *
 108      * <blockquote>
 109      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 110      * </blockquote>
 111      *
 112      * These are {@code '\u005Cu0030'} through
 113      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 114      * {@code '\u005Cu007a'}. If {@code radix} is
 115      * <var>N</var>, then the first <var>N</var> of these characters
 116      * are used as radix-<var>N</var> digits in the order shown. Thus,
 117      * the digits for hexadecimal (radix 16) are
 118      * {@code 0123456789abcdef}. If uppercase letters are
 119      * desired, the {@link java.lang.String#toUpperCase()} method may
 120      * be called on the result:
 121      *
 122      * <blockquote>
 123      *  {@code Long.toString(n, 16).toUpperCase()}
 124      * </blockquote>
 125      *
 126      * @param   i       a {@code long} to be converted to a string.
 127      * @param   radix   the radix to use in the string representation.
 128      * @return  a string representation of the argument in the specified radix.
 129      * @see     java.lang.Character#MAX_RADIX
 130      * @see     java.lang.Character#MIN_RADIX
 131      */
 132     public static String toString(long i, int radix) {
 133         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 134             radix = 10;
 135         if (radix == 10)
 136             return toString(i);
 137 
 138         if (COMPACT_STRINGS) {
 139             byte[] buf = new byte[65];
 140             int charPos = 64;
 141             boolean negative = (i < 0);
 142 
 143             if (!negative) {
 144                 i = -i;
 145             }
 146 
 147             while (i <= -radix) {
 148                 buf[charPos--] = (byte)Integer.digits[(int)(-(i % radix))];
 149                 i = i / radix;
 150             }
 151             buf[charPos] = (byte)Integer.digits[(int)(-i)];
 152 
 153             if (negative) {
 154                 buf[--charPos] = '-';
 155             }
 156             return StringLatin1.newString(buf, charPos, (65 - charPos));
 157         }
 158         return toStringUTF16(i, radix);
 159     }
 160 
 161     private static String toStringUTF16(long i, int radix) {
 162         byte[] buf = new byte[65 * 2];
 163         int charPos = 64;
 164         boolean negative = (i < 0);
 165         if (!negative) {
 166             i = -i;
 167         }
 168         while (i <= -radix) {
 169             StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 170             i = i / radix;
 171         }
 172         StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 173         if (negative) {
 174             StringUTF16.putChar(buf, --charPos, '-');
 175         }
 176         return StringUTF16.newString(buf, charPos, (65 - charPos));
 177     }
 178 
 179     /**
 180      * Returns a string representation of the first argument as an
 181      * unsigned integer value in the radix specified by the second
 182      * argument.
 183      *
 184      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 185      * or larger than {@code Character.MAX_RADIX}, then the radix
 186      * {@code 10} is used instead.
 187      *
 188      * <p>Note that since the first argument is treated as an unsigned
 189      * value, no leading sign character is printed.
 190      *
 191      * <p>If the magnitude is zero, it is represented by a single zero
 192      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 193      * the first character of the representation of the magnitude will
 194      * not be the zero character.
 195      *
 196      * <p>The behavior of radixes and the characters used as digits
 197      * are the same as {@link #toString(long, int) toString}.
 198      *
 199      * @param   i       an integer to be converted to an unsigned string.
 200      * @param   radix   the radix to use in the string representation.
 201      * @return  an unsigned string representation of the argument in the specified radix.
 202      * @see     #toString(long, int)
 203      * @since 1.8
 204      */
 205     public static String toUnsignedString(long i, int radix) {
 206         if (i >= 0)
 207             return toString(i, radix);
 208         else {
 209             switch (radix) {
 210             case 2:
 211                 return toBinaryString(i);
 212 
 213             case 4:
 214                 return toUnsignedString0(i, 2);
 215 
 216             case 8:
 217                 return toOctalString(i);
 218 
 219             case 10:
 220                 /*
 221                  * We can get the effect of an unsigned division by 10
 222                  * on a long value by first shifting right, yielding a
 223                  * positive value, and then dividing by 5.  This
 224                  * allows the last digit and preceding digits to be
 225                  * isolated more quickly than by an initial conversion
 226                  * to BigInteger.
 227                  */
 228                 long quot = (i >>> 1) / 5;
 229                 long rem = i - quot * 10;
 230                 return toString(quot) + rem;
 231 
 232             case 16:
 233                 return toHexString(i);
 234 
 235             case 32:
 236                 return toUnsignedString0(i, 5);
 237 
 238             default:
 239                 return 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      * @param   i   a {@code long} to be converted to a string.
 297      * @return  the string representation of the unsigned {@code long}
 298      *          value represented by the argument in hexadecimal
 299      *          (base&nbsp;16).
 300      * @see #parseUnsignedLong(String, int)
 301      * @see #toUnsignedString(long, int)
 302      * @since   1.0.2
 303      */
 304     public static String toHexString(long i) {
 305         return toUnsignedString0(i, 4);
 306     }
 307 
 308     /**
 309      * Returns a string representation of the {@code long}
 310      * argument as an unsigned integer in base&nbsp;8.
 311      *
 312      * <p>The unsigned {@code long} value is the argument plus
 313      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 314      * equal to the argument.  This value is converted to a string of
 315      * ASCII digits in octal (base&nbsp;8) with no extra leading
 316      * {@code 0}s.
 317      *
 318      * <p>The value of the argument can be recovered from the returned
 319      * string {@code s} by calling {@link
 320      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 321      * 8)}.
 322      *
 323      * <p>If the unsigned magnitude is zero, it is represented by a
 324      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 325      * otherwise, the first character of the representation of the
 326      * unsigned magnitude will not be the zero character. The
 327      * following characters are used as octal digits:
 328      *
 329      * <blockquote>
 330      *  {@code 01234567}
 331      * </blockquote>
 332      *
 333      * These are the characters {@code '\u005Cu0030'} through
 334      * {@code '\u005Cu0037'}.
 335      *
 336      * @param   i   a {@code long} to be converted to a string.
 337      * @return  the string representation of the unsigned {@code long}
 338      *          value represented by the argument in octal (base&nbsp;8).
 339      * @see #parseUnsignedLong(String, int)
 340      * @see #toUnsignedString(long, int)
 341      * @since   1.0.2
 342      */
 343     public static String toOctalString(long i) {
 344         return toUnsignedString0(i, 3);
 345     }
 346 
 347     /**
 348      * Returns a string representation of the {@code long}
 349      * argument as an unsigned integer in base&nbsp;2.
 350      *
 351      * <p>The unsigned {@code long} value is the argument plus
 352      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 353      * equal to the argument.  This value is converted to a string of
 354      * ASCII digits in binary (base&nbsp;2) with no extra leading
 355      * {@code 0}s.
 356      *
 357      * <p>The value of the argument can be recovered from the returned
 358      * string {@code s} by calling {@link
 359      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 360      * 2)}.
 361      *
 362      * <p>If the unsigned magnitude is zero, it is represented by a
 363      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 364      * otherwise, the first character of the representation of the
 365      * unsigned magnitude will not be the zero character. The
 366      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 367      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 368      *
 369      * @param   i   a {@code long} to be converted to a string.
 370      * @return  the string representation of the unsigned {@code long}
 371      *          value represented by the argument in binary (base&nbsp;2).
 372      * @see #parseUnsignedLong(String, int)
 373      * @see #toUnsignedString(long, int)
 374      * @since   1.0.2
 375      */
 376     public static String toBinaryString(long i) {
 377         return toUnsignedString0(i, 1);
 378     }
 379 
 380     /**
 381      * Format a long (treated as unsigned) into a String.
 382      * @param val the value to format
 383      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 384      */
 385     static String toUnsignedString0(long val, int shift) {
 386         // assert shift > 0 && shift <=5 : "Illegal shift value";
 387         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 388         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 389         if (COMPACT_STRINGS) {
 390             byte[] buf = new byte[chars];
 391             formatUnsignedLong0(val, shift, buf, 0, chars);
 392             return new String(buf, LATIN1);
 393         } else {
 394             byte[] buf = new byte[chars * 2];
 395             formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
 396             return new String(buf, UTF16);
 397         }
 398     }
 399 
 400     /**
 401      * Format a long (treated as unsigned) into a byte buffer (LATIN1 version). If
 402      * {@code len} exceeds the formatted ASCII representation of {@code val},
 403      * {@code buf} will be padded with leading zeroes.
 404      *
 405      * @param val the unsigned long to format
 406      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 407      * @param buf the byte buffer to write to
 408      * @param offset the offset in the destination buffer to start at
 409      * @param len the number of characters to write
 410      */
 411     private static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
 412         int charPos = offset + len;
 413         int radix = 1 << shift;
 414         int mask = radix - 1;
 415         do {
 416             buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
 417             val >>>= shift;
 418         } while (charPos > offset);
 419     }
 420 
 421     /**
 422      * Format a long (treated as unsigned) into a byte buffer (UTF16 version). If
 423      * {@code len} exceeds the formatted ASCII representation of {@code val},
 424      * {@code buf} will be padded with leading zeroes.
 425      *
 426      * @param val the unsigned long to format
 427      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 428      * @param buf the byte buffer to write to
 429      * @param offset the offset in the destination buffer to start at
 430      * @param len the number of characters to write
 431      */
 432     private static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
 433         int charPos = offset + len;
 434         int radix = 1 << shift;
 435         int mask = radix - 1;
 436         do {
 437             StringUTF16.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
 438             val >>>= shift;
 439         } while (charPos > offset);
 440     }
 441 
 442     static String fastUUID(long lsb, long msb) {
 443         if (COMPACT_STRINGS) {
 444             byte[] buf = new byte[36];
 445             formatUnsignedLong0(lsb,        4, buf, 24, 12);
 446             formatUnsignedLong0(lsb >>> 48, 4, buf, 19, 4);
 447             formatUnsignedLong0(msb,        4, buf, 14, 4);
 448             formatUnsignedLong0(msb >>> 16, 4, buf, 9,  4);
 449             formatUnsignedLong0(msb >>> 32, 4, buf, 0,  8);
 450 
 451             buf[23] = '-';
 452             buf[18] = '-';
 453             buf[13] = '-';
 454             buf[8]  = '-';
 455 
 456             return new String(buf, LATIN1);
 457         } else {
 458             byte[] buf = new byte[72];
 459 
 460             formatUnsignedLong0UTF16(lsb,        4, buf, 24, 12);
 461             formatUnsignedLong0UTF16(lsb >>> 48, 4, buf, 19, 4);
 462             formatUnsignedLong0UTF16(msb,        4, buf, 14, 4);
 463             formatUnsignedLong0UTF16(msb >>> 16, 4, buf, 9,  4);
 464             formatUnsignedLong0UTF16(msb >>> 32, 4, buf, 0,  8);
 465 
 466             StringUTF16.putChar(buf, 23, '-');
 467             StringUTF16.putChar(buf, 18, '-');
 468             StringUTF16.putChar(buf, 13, '-');
 469             StringUTF16.putChar(buf,  8, '-');
 470 
 471             return new String(buf, UTF16);
 472         }
 473     }
 474 
 475     /**
 476      * Returns a {@code String} object representing the specified
 477      * {@code long}.  The argument is converted to signed decimal
 478      * representation and returned as a string, exactly as if the
 479      * argument and the radix 10 were given as arguments to the {@link
 480      * #toString(long, int)} method.
 481      *
 482      * @param   i   a {@code long} to be converted.
 483      * @return  a string representation of the argument in base&nbsp;10.
 484      */
 485     public static String toString(long i) {
 486         int size = stringSize(i);
 487         if (COMPACT_STRINGS) {
 488             byte[] buf = new byte[size];
 489             getChars(i, size, buf);
 490             return new String(buf, LATIN1);
 491         } else {
 492             byte[] buf = new byte[size * 2];
 493             StringUTF16.getChars(i, size, buf);
 494             return new String(buf, UTF16);
 495         }
 496     }
 497 
 498     /**
 499      * Returns a string representation of the argument as an unsigned
 500      * decimal value.
 501      *
 502      * The argument is converted to unsigned decimal representation
 503      * and returned as a string exactly as if the argument and radix
 504      * 10 were given as arguments to the {@link #toUnsignedString(long,
 505      * int)} method.
 506      *
 507      * @param   i  an integer to be converted to an unsigned string.
 508      * @return  an unsigned string representation of the argument.
 509      * @see     #toUnsignedString(long, int)
 510      * @since 1.8
 511      */
 512     public static String toUnsignedString(long i) {
 513         return toUnsignedString(i, 10);
 514     }
 515 
 516     /**
 517      * Places characters representing the long i into the
 518      * character array buf. The characters are placed into
 519      * the buffer backwards starting with the least significant
 520      * digit at the specified index (exclusive), and working
 521      * backwards from there.
 522      *
 523      * @implNote This method converts positive inputs into negative
 524      * values, to cover the Long.MIN_VALUE case. Converting otherwise
 525      * (negative to positive) will expose -Long.MIN_VALUE that overflows
 526      * long.
 527      *
 528      * @param i     value to convert
 529      * @param index next index, after the least significant digit
 530      * @param buf   target buffer, Latin1-encoded
 531      * @return index of the most significant digit or minus sign, if present
 532      */
 533     static int getChars(long i, int index, byte[] buf) {
 534         long q;
 535         int r;
 536         int charPos = index;
 537 
 538         boolean negative = (i < 0);
 539         if (!negative) {
 540             i = -i;
 541         }
 542 
 543         // Get 2 digits/iteration using longs until quotient fits into an int
 544         while (i <= Integer.MIN_VALUE) {
 545             q = i / 100;
 546             r = (int)((q * 100) - i);
 547             i = q;
 548             buf[--charPos] = Integer.DigitOnes[r];
 549             buf[--charPos] = Integer.DigitTens[r];
 550         }
 551 
 552         // Get 2 digits/iteration using ints
 553         int q2;
 554         int i2 = (int)i;
 555         while (i2 <= -100) {
 556             q2 = i2 / 100;
 557             r  = (q2 * 100) - i2;
 558             i2 = q2;
 559             buf[--charPos] = Integer.DigitOnes[r];
 560             buf[--charPos] = Integer.DigitTens[r];
 561         }
 562 
 563         // We know there are at most two digits left at this point.
 564         q2 = i2 / 10;
 565         r  = (q2 * 10) - i2;
 566         buf[--charPos] = (byte)('0' + r);
 567 
 568         // Whatever left is the remaining digit.
 569         if (q2 < 0) {
 570             buf[--charPos] = (byte)('0' - q2);
 571         }
 572 
 573         if (negative) {
 574             buf[--charPos] = (byte)'-';
 575         }
 576         return charPos;
 577     }
 578 
 579     /**
 580      * Returns the string representation size for a given long value.
 581      *
 582      * @param x long value
 583      * @return string size
 584      *
 585      * @implNote There are other ways to compute this: e.g. binary search,
 586      * but values are biased heavily towards zero, and therefore linear search
 587      * wins. The iteration results are also routinely inlined in the generated
 588      * code after loop unrolling.
 589      */
 590     static int stringSize(long x) {
 591         int d = 1;
 592         if (x >= 0) {
 593             d = 0;
 594             x = -x;
 595         }
 596         long p = -10;
 597         for (int i = 1; i < 19; i++) {
 598             if (x > p)
 599                 return i + d;
 600             p = 10 * p;
 601         }
 602         return 19 + d;
 603     }
 604 
 605     /**
 606      * Parses the string argument as a signed {@code long} in the
 607      * radix specified by the second argument. The characters in the
 608      * string must all be digits of the specified radix (as determined
 609      * by whether {@link java.lang.Character#digit(char, int)} returns
 610      * a nonnegative value), except that the first character may be an
 611      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 612      * indicate a negative value or an ASCII plus sign {@code '+'}
 613      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 614      * resulting {@code long} value is returned.
 615      *
 616      * <p>Note that neither the character {@code L}
 617      * ({@code '\u005Cu004C'}) nor {@code l}
 618      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 619      * of the string as a type indicator, as would be permitted in
 620      * Java programming language source code - except that either
 621      * {@code L} or {@code l} may appear as a digit for a
 622      * radix greater than or equal to 22.
 623      *
 624      * <p>An exception of type {@code NumberFormatException} is
 625      * thrown if any of the following situations occurs:
 626      * <ul>
 627      *
 628      * <li>The first argument is {@code null} or is a string of
 629      * length zero.
 630      *
 631      * <li>The {@code radix} is either smaller than {@link
 632      * java.lang.Character#MIN_RADIX} or larger than {@link
 633      * java.lang.Character#MAX_RADIX}.
 634      *
 635      * <li>Any character of the string is not a digit of the specified
 636      * radix, except that the first character may be a minus sign
 637      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 638      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 639      * longer than length 1.
 640      *
 641      * <li>The value represented by the string is not a value of type
 642      *      {@code long}.
 643      * </ul>
 644      *
 645      * <p>Examples:
 646      * <blockquote><pre>
 647      * parseLong("0", 10) returns 0L
 648      * parseLong("473", 10) returns 473L
 649      * parseLong("+42", 10) returns 42L
 650      * parseLong("-0", 10) returns 0L
 651      * parseLong("-FF", 16) returns -255L
 652      * parseLong("1100110", 2) returns 102L
 653      * parseLong("99", 8) throws a NumberFormatException
 654      * parseLong("Hazelnut", 10) throws a NumberFormatException
 655      * parseLong("Hazelnut", 36) returns 1356099454469L
 656      * </pre></blockquote>
 657      *
 658      * @param      s       the {@code String} containing the
 659      *                     {@code long} representation to be parsed.
 660      * @param      radix   the radix to be used while parsing {@code s}.
 661      * @return     the {@code long} represented by the string argument in
 662      *             the specified radix.
 663      * @throws     NumberFormatException  if the string does not contain a
 664      *             parsable {@code long}.
 665      */
 666     public static long parseLong(String s, int radix)
 667               throws NumberFormatException
 668     {
 669         if (s == null) {
 670             throw new NumberFormatException("null");
 671         }
 672 
 673         if (radix < Character.MIN_RADIX) {
 674             throw new NumberFormatException("radix " + radix +
 675                                             " less than Character.MIN_RADIX");
 676         }
 677         if (radix > Character.MAX_RADIX) {
 678             throw new NumberFormatException("radix " + radix +
 679                                             " greater than Character.MAX_RADIX");
 680         }
 681 
 682         boolean negative = false;
 683         int i = 0, len = s.length();
 684         long limit = -Long.MAX_VALUE;
 685 
 686         if (len > 0) {
 687             char firstChar = s.charAt(0);
 688             if (firstChar < '0') { // Possible leading "+" or "-"
 689                 if (firstChar == '-') {
 690                     negative = true;
 691                     limit = Long.MIN_VALUE;
 692                 } else if (firstChar != '+') {
 693                     throw NumberFormatException.forInputString(s, radix);
 694                 }
 695 
 696                 if (len == 1) { // Cannot have lone "+" or "-"
 697                     throw NumberFormatException.forInputString(s, radix);
 698                 }
 699                 i++;
 700             }
 701             long multmin = limit / radix;
 702             long result = 0;
 703             while (i < len) {
 704                 // Accumulating negatively avoids surprises near MAX_VALUE
 705                 int digit = Character.digit(s.charAt(i++),radix);
 706                 if (digit < 0 || result < multmin) {
 707                     throw NumberFormatException.forInputString(s, radix);
 708                 }
 709                 result *= radix;
 710                 if (result < limit + digit) {
 711                     throw NumberFormatException.forInputString(s, radix);
 712                 }
 713                 result -= digit;
 714             }
 715             return negative ? result : -result;
 716         } else {
 717             throw NumberFormatException.forInputString(s, radix);
 718         }
 719     }
 720 
 721     /**
 722      * Parses the {@link CharSequence} argument as a signed {@code long} in
 723      * the specified {@code radix}, beginning at the specified
 724      * {@code beginIndex} and extending to {@code endIndex - 1}.
 725      *
 726      * <p>The method does not take steps to guard against the
 727      * {@code CharSequence} being mutated while parsing.
 728      *
 729      * @param      s   the {@code CharSequence} containing the {@code long}
 730      *                  representation to be parsed
 731      * @param      beginIndex   the beginning index, inclusive.
 732      * @param      endIndex     the ending index, exclusive.
 733      * @param      radix   the radix to be used while parsing {@code s}.
 734      * @return     the signed {@code long} represented by the subsequence in
 735      *             the specified radix.
 736      * @throws     NullPointerException  if {@code s} is null.
 737      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 738      *             negative, or if {@code beginIndex} is greater than
 739      *             {@code endIndex} or if {@code endIndex} is greater than
 740      *             {@code s.length()}.
 741      * @throws     NumberFormatException  if the {@code CharSequence} does not
 742      *             contain a parsable {@code long} in the specified
 743      *             {@code radix}, or if {@code radix} is either smaller than
 744      *             {@link java.lang.Character#MIN_RADIX} or larger than
 745      *             {@link java.lang.Character#MAX_RADIX}.
 746      * @since  9
 747      */
 748     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 749                 throws NumberFormatException {
 750         Objects.requireNonNull(s);
 751 
 752         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 753             throw new IndexOutOfBoundsException();
 754         }
 755         if (radix < Character.MIN_RADIX) {
 756             throw new NumberFormatException("radix " + radix +
 757                     " less than Character.MIN_RADIX");
 758         }
 759         if (radix > Character.MAX_RADIX) {
 760             throw new NumberFormatException("radix " + radix +
 761                     " greater than Character.MAX_RADIX");
 762         }
 763 
 764         boolean negative = false;
 765         int i = beginIndex;
 766         long limit = -Long.MAX_VALUE;
 767 
 768         if (i < endIndex) {
 769             char firstChar = s.charAt(i);
 770             if (firstChar < '0') { // Possible leading "+" or "-"
 771                 if (firstChar == '-') {
 772                     negative = true;
 773                     limit = Long.MIN_VALUE;
 774                 } else if (firstChar != '+') {
 775                     throw NumberFormatException.forCharSequence(s, beginIndex,
 776                             endIndex, i);
 777                 }
 778                 i++;
 779             }
 780             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 781                 throw NumberFormatException.forCharSequence(s, beginIndex,
 782                         endIndex, i);
 783             }
 784             long multmin = limit / radix;
 785             long result = 0;
 786             while (i < endIndex) {
 787                 // Accumulating negatively avoids surprises near MAX_VALUE
 788                 int digit = Character.digit(s.charAt(i), radix);
 789                 if (digit < 0 || result < multmin) {
 790                     throw NumberFormatException.forCharSequence(s, beginIndex,
 791                             endIndex, i);
 792                 }
 793                 result *= radix;
 794                 if (result < limit + digit) {
 795                     throw NumberFormatException.forCharSequence(s, beginIndex,
 796                             endIndex, i);
 797                 }
 798                 i++;
 799                 result -= digit;
 800             }
 801             return negative ? result : -result;
 802         } else {
 803             throw new NumberFormatException("");
 804         }
 805     }
 806 
 807     /**
 808      * Parses the string argument as a signed decimal {@code long}.
 809      * The characters in the string must all be decimal digits, except
 810      * that the first character may be an ASCII minus sign {@code '-'}
 811      * ({@code \u005Cu002D'}) to indicate a negative value or an
 812      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 813      * indicate a positive value. The resulting {@code long} value is
 814      * returned, exactly as if the argument and the radix {@code 10}
 815      * were given as arguments to the {@link
 816      * #parseLong(java.lang.String, int)} method.
 817      *
 818      * <p>Note that neither the character {@code L}
 819      * ({@code '\u005Cu004C'}) nor {@code l}
 820      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 821      * of the string as a type indicator, as would be permitted in
 822      * Java programming language source code.
 823      *
 824      * @param      s   a {@code String} containing the {@code long}
 825      *             representation to be parsed
 826      * @return     the {@code long} represented by the argument in
 827      *             decimal.
 828      * @throws     NumberFormatException  if the string does not contain a
 829      *             parsable {@code long}.
 830      */
 831     public static long parseLong(String s) throws NumberFormatException {
 832         return parseLong(s, 10);
 833     }
 834 
 835     /**
 836      * Parses the string argument as an unsigned {@code long} in the
 837      * radix specified by the second argument.  An unsigned integer
 838      * maps the values usually associated with negative numbers to
 839      * positive numbers larger than {@code MAX_VALUE}.
 840      *
 841      * The characters in the string must all be digits of the
 842      * specified radix (as determined by whether {@link
 843      * java.lang.Character#digit(char, int)} returns a nonnegative
 844      * value), except that the first character may be an ASCII plus
 845      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 846      * integer value is returned.
 847      *
 848      * <p>An exception of type {@code NumberFormatException} is
 849      * thrown if any of the following situations occurs:
 850      * <ul>
 851      * <li>The first argument is {@code null} or is a string of
 852      * length zero.
 853      *
 854      * <li>The radix is either smaller than
 855      * {@link java.lang.Character#MIN_RADIX} or
 856      * larger than {@link java.lang.Character#MAX_RADIX}.
 857      *
 858      * <li>Any character of the string is not a digit of the specified
 859      * radix, except that the first character may be a plus sign
 860      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 861      * string is longer than length 1.
 862      *
 863      * <li>The value represented by the string is larger than the
 864      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 865      *
 866      * </ul>
 867      *
 868      *
 869      * @param      s   the {@code String} containing the unsigned integer
 870      *                  representation to be parsed
 871      * @param      radix   the radix to be used while parsing {@code s}.
 872      * @return     the unsigned {@code long} represented by the string
 873      *             argument in the specified radix.
 874      * @throws     NumberFormatException if the {@code String}
 875      *             does not contain a parsable {@code long}.
 876      * @since 1.8
 877      */
 878     public static long parseUnsignedLong(String s, int radix)
 879                 throws NumberFormatException {
 880         if (s == null)  {
 881             throw new NumberFormatException("null");
 882         }
 883 
 884         int len = s.length();
 885         if (len > 0) {
 886             char firstChar = s.charAt(0);
 887             if (firstChar == '-') {
 888                 throw new
 889                     NumberFormatException(String.format("Illegal leading minus sign " +
 890                                                        "on unsigned string %s.", s));
 891             } else {
 892                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 893                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 894                     return parseLong(s, radix);
 895                 }
 896 
 897                 // No need for range checks on len due to testing above.
 898                 long first = parseLong(s, 0, len - 1, radix);
 899                 int second = Character.digit(s.charAt(len - 1), radix);
 900                 if (second < 0) {
 901                     throw new NumberFormatException("Bad digit at end of " + s);
 902                 }
 903                 long result = first * radix + second;
 904 
 905                 /*
 906                  * Test leftmost bits of multiprecision extension of first*radix
 907                  * for overflow. The number of bits needed is defined by
 908                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 909                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 910                  * overflow is tested by splitting guard in the ranges
 911                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 912                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 913                  * on a value which does not include a prime factor in the legal
 914                  * radix range.
 915                  */
 916                 int guard = radix * (int) (first >>> 57);
 917                 if (guard >= 128 ||
 918                     (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 919                     /*
 920                      * For purposes of exposition, the programmatic statements
 921                      * below should be taken to be multi-precision, i.e., not
 922                      * subject to overflow.
 923                      *
 924                      * A) Condition guard >= 128:
 925                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 926                      * hence always overflow.
 927                      *
 928                      * B) Condition guard < 92:
 929                      * Define left7 = first >>> 57.
 930                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 931                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 932                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 933                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 934                      * never overflow.
 935                      *
 936                      * C) Condition 92 <= guard < 128:
 937                      * first*radix + second >= radix*left7*2^57 + second
 938                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 939                      *
 940                      * D) Condition guard < 128:
 941                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 942                      * so
 943                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 944                      * thus
 945                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 946                      * whence
 947                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 948                      *
 949                      * E) Conditions C, D, and result >= 0:
 950                      * C and D combined imply the mathematical result
 951                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 952                      * bound is therefore negative as a signed long, but the
 953                      * upper bound is too small to overflow again after the
 954                      * signed long overflows to positive above 2^64 - 1. Hence
 955                      * result >= 0 implies overflow given C and D.
 956                      */
 957                     throw new NumberFormatException(String.format("String value %s exceeds " +
 958                                                                   "range of unsigned long.", s));
 959                 }
 960                 return result;
 961             }
 962         } else {
 963             throw NumberFormatException.forInputString(s, radix);
 964         }
 965     }
 966 
 967     /**
 968      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 969      * the specified {@code radix}, beginning at the specified
 970      * {@code beginIndex} and extending to {@code endIndex - 1}.
 971      *
 972      * <p>The method does not take steps to guard against the
 973      * {@code CharSequence} being mutated while parsing.
 974      *
 975      * @param      s   the {@code CharSequence} containing the unsigned
 976      *                 {@code long} representation to be parsed
 977      * @param      beginIndex   the beginning index, inclusive.
 978      * @param      endIndex     the ending index, exclusive.
 979      * @param      radix   the radix to be used while parsing {@code s}.
 980      * @return     the unsigned {@code long} represented by the subsequence in
 981      *             the specified radix.
 982      * @throws     NullPointerException  if {@code s} is null.
 983      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 984      *             negative, or if {@code beginIndex} is greater than
 985      *             {@code endIndex} or if {@code endIndex} is greater than
 986      *             {@code s.length()}.
 987      * @throws     NumberFormatException  if the {@code CharSequence} does not
 988      *             contain a parsable unsigned {@code long} in the specified
 989      *             {@code radix}, or if {@code radix} is either smaller than
 990      *             {@link java.lang.Character#MIN_RADIX} or larger than
 991      *             {@link java.lang.Character#MAX_RADIX}.
 992      * @since  9
 993      */
 994     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
 995                 throws NumberFormatException {
 996         Objects.requireNonNull(s);
 997 
 998         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 999             throw new IndexOutOfBoundsException();
1000         }
1001         int start = beginIndex, len = endIndex - beginIndex;
1002 
1003         if (len > 0) {
1004             char firstChar = s.charAt(start);
1005             if (firstChar == '-') {
1006                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
1007                         "on unsigned string %s.", s.subSequence(start, start + len)));
1008             } else {
1009                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
1010                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
1011                     return parseLong(s, start, start + len, radix);
1012                 }
1013 
1014                 // No need for range checks on end due to testing above.
1015                 long first = parseLong(s, start, start + len - 1, radix);
1016                 int second = Character.digit(s.charAt(start + len - 1), radix);
1017                 if (second < 0) {
1018                     throw new NumberFormatException("Bad digit at end of " +
1019                             s.subSequence(start, start + len));
1020                 }
1021                 long result = first * radix + second;
1022 
1023                 /*
1024                  * Test leftmost bits of multiprecision extension of first*radix
1025                  * for overflow. The number of bits needed is defined by
1026                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
1027                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
1028                  * overflow is tested by splitting guard in the ranges
1029                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
1030                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
1031                  * on a value which does not include a prime factor in the legal
1032                  * radix range.
1033                  */
1034                 int guard = radix * (int) (first >>> 57);
1035                 if (guard >= 128 ||
1036                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
1037                     /*
1038                      * For purposes of exposition, the programmatic statements
1039                      * below should be taken to be multi-precision, i.e., not
1040                      * subject to overflow.
1041                      *
1042                      * A) Condition guard >= 128:
1043                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
1044                      * hence always overflow.
1045                      *
1046                      * B) Condition guard < 92:
1047                      * Define left7 = first >>> 57.
1048                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
1049                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
1050                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
1051                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
1052                      * never overflow.
1053                      *
1054                      * C) Condition 92 <= guard < 128:
1055                      * first*radix + second >= radix*left7*2^57 + second
1056                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
1057                      *
1058                      * D) Condition guard < 128:
1059                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
1060                      * so
1061                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
1062                      * thus
1063                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
1064                      * whence
1065                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
1066                      *
1067                      * E) Conditions C, D, and result >= 0:
1068                      * C and D combined imply the mathematical result
1069                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
1070                      * bound is therefore negative as a signed long, but the
1071                      * upper bound is too small to overflow again after the
1072                      * signed long overflows to positive above 2^64 - 1. Hence
1073                      * result >= 0 implies overflow given C and D.
1074                      */
1075                     throw new NumberFormatException(String.format("String value %s exceeds " +
1076                             "range of unsigned long.", s.subSequence(start, start + len)));
1077                 }
1078                 return result;
1079             }
1080         } else {
1081             throw NumberFormatException.forInputString("", radix);
1082         }
1083     }
1084 
1085     /**
1086      * Parses the string argument as an unsigned decimal {@code long}. The
1087      * characters in the string must all be decimal digits, except
1088      * that the first character may be an ASCII plus sign {@code
1089      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
1090      * is returned, exactly as if the argument and the radix 10 were
1091      * given as arguments to the {@link
1092      * #parseUnsignedLong(java.lang.String, int)} method.
1093      *
1094      * @param s   a {@code String} containing the unsigned {@code long}
1095      *            representation to be parsed
1096      * @return    the unsigned {@code long} value represented by the decimal string argument
1097      * @throws    NumberFormatException  if the string does not contain a
1098      *            parsable unsigned integer.
1099      * @since 1.8
1100      */
1101     public static long parseUnsignedLong(String s) throws NumberFormatException {
1102         return parseUnsignedLong(s, 10);
1103     }
1104 
1105     /**
1106      * Returns a {@code Long} object holding the value
1107      * extracted from the specified {@code String} when parsed
1108      * with the radix given by the second argument.  The first
1109      * argument is interpreted as representing a signed
1110      * {@code long} in the radix specified by the second
1111      * argument, exactly as if the arguments were given to the {@link
1112      * #parseLong(java.lang.String, int)} method. The result is a
1113      * {@code Long} object that represents the {@code long}
1114      * value specified by the string.
1115      *
1116      * <p>In other words, this method returns a {@code Long} object equal
1117      * to the value of:
1118      *
1119      * <blockquote>
1120      *  {@code new Long(Long.parseLong(s, radix))}
1121      * </blockquote>
1122      *
1123      * @param      s       the string to be parsed
1124      * @param      radix   the radix to be used in interpreting {@code s}
1125      * @return     a {@code Long} object holding the value
1126      *             represented by the string argument in the specified
1127      *             radix.
1128      * @throws     NumberFormatException  If the {@code String} does not
1129      *             contain a parsable {@code long}.
1130      */
1131     public static Long valueOf(String s, int radix) throws NumberFormatException {
1132         return Long.valueOf(parseLong(s, radix));
1133     }
1134 
1135     /**
1136      * Returns a {@code Long} object holding the value
1137      * of the specified {@code String}. The argument is
1138      * interpreted as representing a signed decimal {@code long},
1139      * exactly as if the argument were given to the {@link
1140      * #parseLong(java.lang.String)} method. The result is a
1141      * {@code Long} object that represents the integer value
1142      * specified by the string.
1143      *
1144      * <p>In other words, this method returns a {@code Long} object
1145      * equal to the value of:
1146      *
1147      * <blockquote>
1148      *  {@code new Long(Long.parseLong(s))}
1149      * </blockquote>
1150      *
1151      * @param      s   the string to be parsed.
1152      * @return     a {@code Long} object holding the value
1153      *             represented by the string argument.
1154      * @throws     NumberFormatException  If the string cannot be parsed
1155      *             as a {@code long}.
1156      */
1157     public static Long valueOf(String s) throws NumberFormatException
1158     {
1159         return Long.valueOf(parseLong(s, 10));
1160     }
1161 
1162     private static class LongCache {
1163         private LongCache() {}
1164 
1165         static final Long[] cache;
1166         static Long[] archivedCache;
1167 
1168         static {
1169             int size = -(-128) + 127 + 1;
1170 
1171             // Load and use the archived cache if it exists
1172             VM.initializeFromArchive(LongCache.class);
1173             if (archivedCache == null || archivedCache.length != size) {
1174                 Long[] c = new Long[size];
1175                 long value = -128;
1176                 for(int i = 0; i < size; i++) {
1177                     c[i] = new Long(value++);
1178                 }
1179                 archivedCache = c;
1180             }
1181             cache = archivedCache;
1182         }
1183     }
1184 
1185     /**
1186      * Returns a {@code Long} instance representing the specified
1187      * {@code long} value.
1188      * If a new {@code Long} instance is not required, this method
1189      * should generally be used in preference to the constructor
1190      * {@link #Long(long)}, as this method is likely to yield
1191      * significantly better space and time performance by caching
1192      * frequently requested values.
1193      *
1194      * This method will always cache values in the range -128 to 127,
1195      * inclusive, and may cache other values outside of this range.
1196      *
1197      * @param  l a long value.
1198      * @return a {@code Long} instance representing {@code l}.
1199      * @since  1.5
1200      */
1201     @HotSpotIntrinsicCandidate
1202     public static Long valueOf(long l) {
1203         final int offset = 128;
1204         if (l >= -128 && l <= 127) { // will cache
1205             return LongCache.cache[(int)l + offset];
1206         }
1207         return new Long(l);
1208     }
1209 
1210     /**
1211      * Decodes a {@code String} into a {@code Long}.
1212      * Accepts decimal, hexadecimal, and octal numbers given by the
1213      * following grammar:
1214      *
1215      * <blockquote>
1216      * <dl>
1217      * <dt><i>DecodableString:</i>
1218      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1219      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1220      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1221      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1222      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1223      *
1224      * <dt><i>Sign:</i>
1225      * <dd>{@code -}
1226      * <dd>{@code +}
1227      * </dl>
1228      * </blockquote>
1229      *
1230      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1231      * are as defined in section 3.10.1 of
1232      * <cite>The Java&trade; Language Specification</cite>,
1233      * except that underscores are not accepted between digits.
1234      *
1235      * <p>The sequence of characters following an optional
1236      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1237      * "{@code #}", or leading zero) is parsed as by the {@code
1238      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1239      * This sequence of characters must represent a positive value or
1240      * a {@link NumberFormatException} will be thrown.  The result is
1241      * negated if first character of the specified {@code String} is
1242      * the minus sign.  No whitespace characters are permitted in the
1243      * {@code String}.
1244      *
1245      * @param     nm the {@code String} to decode.
1246      * @return    a {@code Long} object holding the {@code long}
1247      *            value represented by {@code nm}
1248      * @throws    NumberFormatException  if the {@code String} does not
1249      *            contain a parsable {@code long}.
1250      * @see java.lang.Long#parseLong(String, int)
1251      * @since 1.2
1252      */
1253     public static Long decode(String nm) throws NumberFormatException {
1254         int radix = 10;
1255         int index = 0;
1256         boolean negative = false;
1257         Long result;
1258 
1259         if (nm.isEmpty())
1260             throw new NumberFormatException("Zero length string");
1261         char firstChar = nm.charAt(0);
1262         // Handle sign, if present
1263         if (firstChar == '-') {
1264             negative = true;
1265             index++;
1266         } else if (firstChar == '+')
1267             index++;
1268 
1269         // Handle radix specifier, if present
1270         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1271             index += 2;
1272             radix = 16;
1273         }
1274         else if (nm.startsWith("#", index)) {
1275             index ++;
1276             radix = 16;
1277         }
1278         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1279             index ++;
1280             radix = 8;
1281         }
1282 
1283         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1284             throw new NumberFormatException("Sign character in wrong position");
1285 
1286         try {
1287             result = Long.valueOf(nm.substring(index), radix);
1288             result = negative ? Long.valueOf(-result.longValue()) : result;
1289         } catch (NumberFormatException e) {
1290             // If number is Long.MIN_VALUE, we'll end up here. The next line
1291             // handles this case, and causes any genuine format error to be
1292             // rethrown.
1293             String constant = negative ? ("-" + nm.substring(index))
1294                                        : nm.substring(index);
1295             result = Long.valueOf(constant, radix);
1296         }
1297         return result;
1298     }
1299 
1300     /**
1301      * The value of the {@code Long}.
1302      *
1303      * @serial
1304      */
1305     private final long value;
1306 
1307     /**
1308      * Constructs a newly allocated {@code Long} object that
1309      * represents the specified {@code long} argument.
1310      *
1311      * @param   value   the value to be represented by the
1312      *          {@code Long} object.
1313      *
1314      * @deprecated
1315      * It is rarely appropriate to use this constructor. The static factory
1316      * {@link #valueOf(long)} is generally a better choice, as it is
1317      * likely to yield significantly better space and time performance.
1318      */
1319     @Deprecated(since="9")
1320     public Long(long value) {
1321         this.value = value;
1322     }
1323 
1324     /**
1325      * Constructs a newly allocated {@code Long} object that
1326      * represents the {@code long} value indicated by the
1327      * {@code String} parameter. The string is converted to a
1328      * {@code long} value in exactly the manner used by the
1329      * {@code parseLong} method for radix 10.
1330      *
1331      * @param      s   the {@code String} to be converted to a
1332      *             {@code Long}.
1333      * @throws     NumberFormatException  if the {@code String} does not
1334      *             contain a parsable {@code long}.
1335      *
1336      * @deprecated
1337      * It is rarely appropriate to use this constructor.
1338      * Use {@link #parseLong(String)} to convert a string to a
1339      * {@code long} primitive, or use {@link #valueOf(String)}
1340      * to convert a string to a {@code Long} object.
1341      */
1342     @Deprecated(since="9")
1343     public Long(String s) throws NumberFormatException {
1344         this.value = parseLong(s, 10);
1345     }
1346 
1347     /**
1348      * Returns the value of this {@code Long} as a {@code byte} after
1349      * a narrowing primitive conversion.
1350      * @jls 5.1.3 Narrowing Primitive Conversion
1351      */
1352     public byte byteValue() {
1353         return (byte)value;
1354     }
1355 
1356     /**
1357      * Returns the value of this {@code Long} as a {@code short} after
1358      * a narrowing primitive conversion.
1359      * @jls 5.1.3 Narrowing Primitive Conversion
1360      */
1361     public short shortValue() {
1362         return (short)value;
1363     }
1364 
1365     /**
1366      * Returns the value of this {@code Long} as an {@code int} after
1367      * a narrowing primitive conversion.
1368      * @jls 5.1.3 Narrowing Primitive Conversion
1369      */
1370     public int intValue() {
1371         return (int)value;
1372     }
1373 
1374     /**
1375      * Returns the value of this {@code Long} as a
1376      * {@code long} value.
1377      */
1378     @HotSpotIntrinsicCandidate
1379     public long longValue() {
1380         return value;
1381     }
1382 
1383     /**
1384      * Returns the value of this {@code Long} as a {@code float} after
1385      * a widening primitive conversion.
1386      * @jls 5.1.2 Widening Primitive Conversion
1387      */
1388     public float floatValue() {
1389         return (float)value;
1390     }
1391 
1392     /**
1393      * Returns the value of this {@code Long} as a {@code double}
1394      * after a widening primitive conversion.
1395      * @jls 5.1.2 Widening Primitive Conversion
1396      */
1397     public double doubleValue() {
1398         return (double)value;
1399     }
1400 
1401     /**
1402      * Returns a {@code String} object representing this
1403      * {@code Long}'s value.  The value is converted to signed
1404      * decimal representation and returned as a string, exactly as if
1405      * the {@code long} value were given as an argument to the
1406      * {@link java.lang.Long#toString(long)} method.
1407      *
1408      * @return  a string representation of the value of this object in
1409      *          base&nbsp;10.
1410      */
1411     public String toString() {
1412         return toString(value);
1413     }
1414 
1415     /**
1416      * Returns a hash code for this {@code Long}. The result is
1417      * the exclusive OR of the two halves of the primitive
1418      * {@code long} value held by this {@code Long}
1419      * object. That is, the hashcode is the value of the expression:
1420      *
1421      * <blockquote>
1422      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1423      * </blockquote>
1424      *
1425      * @return  a hash code value for this object.
1426      */
1427     @Override
1428     public int hashCode() {
1429         return Long.hashCode(value);
1430     }
1431 
1432     /**
1433      * Returns a hash code for a {@code long} value; compatible with
1434      * {@code Long.hashCode()}.
1435      *
1436      * @param value the value to hash
1437      * @return a hash code value for a {@code long} value.
1438      * @since 1.8
1439      */
1440     public static int hashCode(long value) {
1441         return (int)(value ^ (value >>> 32));
1442     }
1443 
1444     /**
1445      * Compares this object to the specified object.  The result is
1446      * {@code true} if and only if the argument is not
1447      * {@code null} and is a {@code Long} object that
1448      * contains the same {@code long} value as this object.
1449      *
1450      * @param   obj   the object to compare with.
1451      * @return  {@code true} if the objects are the same;
1452      *          {@code false} otherwise.
1453      */
1454     public boolean equals(Object obj) {
1455         if (obj instanceof Long) {
1456             return value == ((Long)obj).longValue();
1457         }
1458         return false;
1459     }
1460 
1461     /**
1462      * Determines the {@code long} value of the system property
1463      * with the specified name.
1464      *
1465      * <p>The first argument is treated as the name of a system
1466      * property.  System properties are accessible through the {@link
1467      * java.lang.System#getProperty(java.lang.String)} method. The
1468      * string value of this property is then interpreted as a {@code
1469      * long} value using the grammar supported by {@link Long#decode decode}
1470      * and a {@code Long} object representing this value is returned.
1471      *
1472      * <p>If there is no property with the specified name, if the
1473      * specified name is empty or {@code null}, or if the property
1474      * does not have the correct numeric format, then {@code null} is
1475      * returned.
1476      *
1477      * <p>In other words, this method returns a {@code Long} object
1478      * equal to the value of:
1479      *
1480      * <blockquote>
1481      *  {@code getLong(nm, null)}
1482      * </blockquote>
1483      *
1484      * @param   nm   property name.
1485      * @return  the {@code Long} value of the property.
1486      * @throws  SecurityException for the same reasons as
1487      *          {@link System#getProperty(String) System.getProperty}
1488      * @see     java.lang.System#getProperty(java.lang.String)
1489      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1490      */
1491     public static Long getLong(String nm) {
1492         return getLong(nm, null);
1493     }
1494 
1495     /**
1496      * Determines the {@code long} value of the system property
1497      * with the specified name.
1498      *
1499      * <p>The first argument is treated as the name of a system
1500      * property.  System properties are accessible through the {@link
1501      * java.lang.System#getProperty(java.lang.String)} method. The
1502      * string value of this property is then interpreted as a {@code
1503      * long} value using the grammar supported by {@link Long#decode decode}
1504      * and a {@code Long} object representing this value is returned.
1505      *
1506      * <p>The second argument is the default value. A {@code Long} object
1507      * that represents the value of the second argument is returned if there
1508      * is no property of the specified name, if the property does not have
1509      * the correct numeric format, or if the specified name is empty or null.
1510      *
1511      * <p>In other words, this method returns a {@code Long} object equal
1512      * to the value of:
1513      *
1514      * <blockquote>
1515      *  {@code getLong(nm, new Long(val))}
1516      * </blockquote>
1517      *
1518      * but in practice it may be implemented in a manner such as:
1519      *
1520      * <blockquote><pre>
1521      * Long result = getLong(nm, null);
1522      * return (result == null) ? new Long(val) : result;
1523      * </pre></blockquote>
1524      *
1525      * to avoid the unnecessary allocation of a {@code Long} object when
1526      * the default value is not needed.
1527      *
1528      * @param   nm    property name.
1529      * @param   val   default value.
1530      * @return  the {@code Long} value of the property.
1531      * @throws  SecurityException for the same reasons as
1532      *          {@link System#getProperty(String) System.getProperty}
1533      * @see     java.lang.System#getProperty(java.lang.String)
1534      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1535      */
1536     public static Long getLong(String nm, long val) {
1537         Long result = Long.getLong(nm, null);
1538         return (result == null) ? Long.valueOf(val) : result;
1539     }
1540 
1541     /**
1542      * Returns the {@code long} value of the system property with
1543      * the specified name.  The first argument is treated as the name
1544      * of a system property.  System properties are accessible through
1545      * the {@link java.lang.System#getProperty(java.lang.String)}
1546      * method. The string value of this property is then interpreted
1547      * as a {@code long} value, as per the
1548      * {@link Long#decode decode} method, and a {@code Long} object
1549      * representing this value is returned; in summary:
1550      *
1551      * <ul>
1552      * <li>If the property value begins with the two ASCII characters
1553      * {@code 0x} or the ASCII character {@code #}, not followed by
1554      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1555      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1556      * with radix 16.
1557      * <li>If the property value begins with the ASCII character
1558      * {@code 0} followed by another character, it is parsed as
1559      * an octal integer exactly as by the method {@link
1560      * #valueOf(java.lang.String, int)} with radix 8.
1561      * <li>Otherwise the property value is parsed as a decimal
1562      * integer exactly as by the method
1563      * {@link #valueOf(java.lang.String, int)} with radix 10.
1564      * </ul>
1565      *
1566      * <p>Note that, in every case, neither {@code L}
1567      * ({@code '\u005Cu004C'}) nor {@code l}
1568      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1569      * of the property value as a type indicator, as would be
1570      * permitted in Java programming language source code.
1571      *
1572      * <p>The second argument is the default value. The default value is
1573      * returned if there is no property of the specified name, if the
1574      * property does not have the correct numeric format, or if the
1575      * specified name is empty or {@code null}.
1576      *
1577      * @param   nm   property name.
1578      * @param   val   default value.
1579      * @return  the {@code Long} value of the property.
1580      * @throws  SecurityException for the same reasons as
1581      *          {@link System#getProperty(String) System.getProperty}
1582      * @see     System#getProperty(java.lang.String)
1583      * @see     System#getProperty(java.lang.String, java.lang.String)
1584      */
1585     public static Long getLong(String nm, Long val) {
1586         String v = null;
1587         try {
1588             v = System.getProperty(nm);
1589         } catch (IllegalArgumentException | NullPointerException e) {
1590         }
1591         if (v != null) {
1592             try {
1593                 return Long.decode(v);
1594             } catch (NumberFormatException e) {
1595             }
1596         }
1597         return val;
1598     }
1599 
1600     /**
1601      * Compares two {@code Long} objects numerically.
1602      *
1603      * @param   anotherLong   the {@code Long} to be compared.
1604      * @return  the value {@code 0} if this {@code Long} is
1605      *          equal to the argument {@code Long}; a value less than
1606      *          {@code 0} if this {@code Long} is numerically less
1607      *          than the argument {@code Long}; and a value greater
1608      *          than {@code 0} if this {@code Long} is numerically
1609      *           greater than the argument {@code Long} (signed
1610      *           comparison).
1611      * @since   1.2
1612      */
1613     public int compareTo(Long anotherLong) {
1614         return compare(this.value, anotherLong.value);
1615     }
1616 
1617     /**
1618      * Compares two {@code long} values numerically.
1619      * The value returned is identical to what would be returned by:
1620      * <pre>
1621      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1622      * </pre>
1623      *
1624      * @param  x the first {@code long} to compare
1625      * @param  y the second {@code long} to compare
1626      * @return the value {@code 0} if {@code x == y};
1627      *         a value less than {@code 0} if {@code x < y}; and
1628      *         a value greater than {@code 0} if {@code x > y}
1629      * @since 1.7
1630      */
1631     public static int compare(long x, long y) {
1632         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1633     }
1634 
1635     /**
1636      * Compares two {@code long} values numerically treating the values
1637      * as unsigned.
1638      *
1639      * @param  x the first {@code long} to compare
1640      * @param  y the second {@code long} to compare
1641      * @return the value {@code 0} if {@code x == y}; a value less
1642      *         than {@code 0} if {@code x < y} as unsigned values; and
1643      *         a value greater than {@code 0} if {@code x > y} as
1644      *         unsigned values
1645      * @since 1.8
1646      */
1647     public static int compareUnsigned(long x, long y) {
1648         return compare(x + MIN_VALUE, y + MIN_VALUE);
1649     }
1650 
1651 
1652     /**
1653      * Returns the unsigned quotient of dividing the first argument by
1654      * the second where each argument and the result is interpreted as
1655      * an unsigned value.
1656      *
1657      * <p>Note that in two's complement arithmetic, the three other
1658      * basic arithmetic operations of add, subtract, and multiply are
1659      * bit-wise identical if the two operands are regarded as both
1660      * being signed or both being unsigned.  Therefore separate {@code
1661      * addUnsigned}, etc. methods are not provided.
1662      *
1663      * @param dividend the value to be divided
1664      * @param divisor the value doing the dividing
1665      * @return the unsigned quotient of the first argument divided by
1666      * the second argument
1667      * @see #remainderUnsigned
1668      * @since 1.8
1669      */
1670     public static long divideUnsigned(long dividend, long divisor) {
1671         if (divisor < 0L) { // signed comparison
1672             // Answer must be 0 or 1 depending on relative magnitude
1673             // of dividend and divisor.
1674             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1675         }
1676 
1677         if (dividend > 0) //  Both inputs non-negative
1678             return dividend/divisor;
1679         else {
1680             /*
1681              * For simple code, leveraging BigInteger.  Longer and faster
1682              * code written directly in terms of operations on longs is
1683              * possible; see "Hacker's Delight" for divide and remainder
1684              * algorithms.
1685              */
1686             return toUnsignedBigInteger(dividend).
1687                 divide(toUnsignedBigInteger(divisor)).longValue();
1688         }
1689     }
1690 
1691     /**
1692      * Returns the unsigned remainder from dividing the first argument
1693      * by the second where each argument and the result is interpreted
1694      * as an unsigned value.
1695      *
1696      * @param dividend the value to be divided
1697      * @param divisor the value doing the dividing
1698      * @return the unsigned remainder of the first argument divided by
1699      * the second argument
1700      * @see #divideUnsigned
1701      * @since 1.8
1702      */
1703     public static long remainderUnsigned(long dividend, long divisor) {
1704         if (dividend > 0 && divisor > 0) { // signed comparisons
1705             return dividend % divisor;
1706         } else {
1707             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1708                 return dividend;
1709             else
1710                 return toUnsignedBigInteger(dividend).
1711                     remainder(toUnsignedBigInteger(divisor)).longValue();
1712         }
1713     }
1714 
1715     // Bit Twiddling
1716 
1717     /**
1718      * The number of bits used to represent a {@code long} value in two's
1719      * complement binary form.
1720      *
1721      * @since 1.5
1722      */
1723     @Native public static final int SIZE = 64;
1724 
1725     /**
1726      * The number of bytes used to represent a {@code long} value in two's
1727      * complement binary form.
1728      *
1729      * @since 1.8
1730      */
1731     public static final int BYTES = SIZE / Byte.SIZE;
1732 
1733     /**
1734      * Returns a {@code long} value with at most a single one-bit, in the
1735      * position of the highest-order ("leftmost") one-bit in the specified
1736      * {@code long} value.  Returns zero if the specified value has no
1737      * one-bits in its two's complement binary representation, that is, if it
1738      * is equal to zero.
1739      *
1740      * @param i the value whose highest one bit is to be computed
1741      * @return a {@code long} value with a single one-bit, in the position
1742      *     of the highest-order one-bit in the specified value, or zero if
1743      *     the specified value is itself equal to zero.
1744      * @since 1.5
1745      */
1746     public static long highestOneBit(long i) {
1747         return i & (MIN_VALUE >>> numberOfLeadingZeros(i));
1748     }
1749 
1750     /**
1751      * Returns a {@code long} value with at most a single one-bit, in the
1752      * position of the lowest-order ("rightmost") one-bit in the specified
1753      * {@code long} value.  Returns zero if the specified value has no
1754      * one-bits in its two's complement binary representation, that is, if it
1755      * is equal to zero.
1756      *
1757      * @param i the value whose lowest one bit is to be computed
1758      * @return a {@code long} value with a single one-bit, in the position
1759      *     of the lowest-order one-bit in the specified value, or zero if
1760      *     the specified value is itself equal to zero.
1761      * @since 1.5
1762      */
1763     public static long lowestOneBit(long i) {
1764         // HD, Section 2-1
1765         return i & -i;
1766     }
1767 
1768     /**
1769      * Returns the number of zero bits preceding the highest-order
1770      * ("leftmost") one-bit in the two's complement binary representation
1771      * of the specified {@code long} value.  Returns 64 if the
1772      * specified value has no one-bits in its two's complement representation,
1773      * in other words if it is equal to zero.
1774      *
1775      * <p>Note that this method is closely related to the logarithm base 2.
1776      * For all positive {@code long} values x:
1777      * <ul>
1778      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1779      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1780      * </ul>
1781      *
1782      * @param i the value whose number of leading zeros is to be computed
1783      * @return the number of zero bits preceding the highest-order
1784      *     ("leftmost") one-bit in the two's complement binary representation
1785      *     of the specified {@code long} value, or 64 if the value
1786      *     is equal to zero.
1787      * @since 1.5
1788      */
1789     @HotSpotIntrinsicCandidate
1790     public static int numberOfLeadingZeros(long i) {
1791         int x = (int)(i >>> 32);
1792         return x == 0 ? 32 + Integer.numberOfLeadingZeros((int)i)
1793                 : Integer.numberOfLeadingZeros(x);
1794     }
1795 
1796     /**
1797      * Returns the number of zero bits following the lowest-order ("rightmost")
1798      * one-bit in the two's complement binary representation of the specified
1799      * {@code long} value.  Returns 64 if the specified value has no
1800      * one-bits in its two's complement representation, in other words if it is
1801      * equal to zero.
1802      *
1803      * @param i the value whose number of trailing zeros is to be computed
1804      * @return the number of zero bits following the lowest-order ("rightmost")
1805      *     one-bit in the two's complement binary representation of the
1806      *     specified {@code long} value, or 64 if the value is equal
1807      *     to zero.
1808      * @since 1.5
1809      */
1810     @HotSpotIntrinsicCandidate
1811     public static int numberOfTrailingZeros(long i) {
1812         int x = (int)i;
1813         return x == 0 ? 32 + Integer.numberOfTrailingZeros((int)(i >>> 32))
1814                 : Integer.numberOfTrailingZeros(x);
1815     }
1816 
1817     /**
1818      * Returns the number of one-bits in the two's complement binary
1819      * representation of the specified {@code long} value.  This function is
1820      * sometimes referred to as the <i>population count</i>.
1821      *
1822      * @param i the value whose bits are to be counted
1823      * @return the number of one-bits in the two's complement binary
1824      *     representation of the specified {@code long} value.
1825      * @since 1.5
1826      */
1827      @HotSpotIntrinsicCandidate
1828      public static int bitCount(long i) {
1829         // HD, Figure 5-2
1830         i = i - ((i >>> 1) & 0x5555555555555555L);
1831         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1832         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1833         i = i + (i >>> 8);
1834         i = i + (i >>> 16);
1835         i = i + (i >>> 32);
1836         return (int)i & 0x7f;
1837      }
1838 
1839     /**
1840      * Returns the value obtained by rotating the two's complement binary
1841      * representation of the specified {@code long} value left by the
1842      * specified number of bits.  (Bits shifted out of the left hand, or
1843      * high-order, side reenter on the right, or low-order.)
1844      *
1845      * <p>Note that left rotation with a negative distance is equivalent to
1846      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1847      * distance)}.  Note also that rotation by any multiple of 64 is a
1848      * no-op, so all but the last six bits of the rotation distance can be
1849      * ignored, even if the distance is negative: {@code rotateLeft(val,
1850      * distance) == rotateLeft(val, distance & 0x3F)}.
1851      *
1852      * @param i the value whose bits are to be rotated left
1853      * @param distance the number of bit positions to rotate left
1854      * @return the value obtained by rotating the two's complement binary
1855      *     representation of the specified {@code long} value left by the
1856      *     specified number of bits.
1857      * @since 1.5
1858      */
1859     public static long rotateLeft(long i, int distance) {
1860         return (i << distance) | (i >>> -distance);
1861     }
1862 
1863     /**
1864      * Returns the value obtained by rotating the two's complement binary
1865      * representation of the specified {@code long} value right by the
1866      * specified number of bits.  (Bits shifted out of the right hand, or
1867      * low-order, side reenter on the left, or high-order.)
1868      *
1869      * <p>Note that right rotation with a negative distance is equivalent to
1870      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1871      * distance)}.  Note also that rotation by any multiple of 64 is a
1872      * no-op, so all but the last six bits of the rotation distance can be
1873      * ignored, even if the distance is negative: {@code rotateRight(val,
1874      * distance) == rotateRight(val, distance & 0x3F)}.
1875      *
1876      * @param i the value whose bits are to be rotated right
1877      * @param distance the number of bit positions to rotate right
1878      * @return the value obtained by rotating the two's complement binary
1879      *     representation of the specified {@code long} value right by the
1880      *     specified number of bits.
1881      * @since 1.5
1882      */
1883     public static long rotateRight(long i, int distance) {
1884         return (i >>> distance) | (i << -distance);
1885     }
1886 
1887     /**
1888      * Returns the value obtained by reversing the order of the bits in the
1889      * two's complement binary representation of the specified {@code long}
1890      * value.
1891      *
1892      * @param i the value to be reversed
1893      * @return the value obtained by reversing order of the bits in the
1894      *     specified {@code long} value.
1895      * @since 1.5
1896      */
1897     public static long reverse(long i) {
1898         // HD, Figure 7-1
1899         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1900         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1901         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1902 
1903         return reverseBytes(i);
1904     }
1905 
1906     /**
1907      * Returns the signum function of the specified {@code long} value.  (The
1908      * return value is -1 if the specified value is negative; 0 if the
1909      * specified value is zero; and 1 if the specified value is positive.)
1910      *
1911      * @param i the value whose signum is to be computed
1912      * @return the signum function of the specified {@code long} value.
1913      * @since 1.5
1914      */
1915     public static int signum(long i) {
1916         // HD, Section 2-7
1917         return (int) ((i >> 63) | (-i >>> 63));
1918     }
1919 
1920     /**
1921      * Returns the value obtained by reversing the order of the bytes in the
1922      * two's complement representation of the specified {@code long} value.
1923      *
1924      * @param i the value whose bytes are to be reversed
1925      * @return the value obtained by reversing the bytes in the specified
1926      *     {@code long} value.
1927      * @since 1.5
1928      */
1929     @HotSpotIntrinsicCandidate
1930     public static long reverseBytes(long i) {
1931         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1932         return (i << 48) | ((i & 0xffff0000L) << 16) |
1933             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1934     }
1935 
1936     /**
1937      * Adds two {@code long} values together as per the + operator.
1938      *
1939      * @param a the first operand
1940      * @param b the second operand
1941      * @return the sum of {@code a} and {@code b}
1942      * @see java.util.function.BinaryOperator
1943      * @since 1.8
1944      */
1945     public static long sum(long a, long b) {
1946         return a + b;
1947     }
1948 
1949     /**
1950      * Returns the greater of two {@code long} values
1951      * as if by calling {@link Math#max(long, long) Math.max}.
1952      *
1953      * @param a the first operand
1954      * @param b the second operand
1955      * @return the greater of {@code a} and {@code b}
1956      * @see java.util.function.BinaryOperator
1957      * @since 1.8
1958      */
1959     public static long max(long a, long b) {
1960         return Math.max(a, b);
1961     }
1962 
1963     /**
1964      * Returns the smaller of two {@code long} values
1965      * as if by calling {@link Math#min(long, long) Math.min}.
1966      *
1967      * @param a the first operand
1968      * @param b the second operand
1969      * @return the smaller of {@code a} and {@code b}
1970      * @see java.util.function.BinaryOperator
1971      * @since 1.8
1972      */
1973     public static long min(long a, long b) {
1974         return Math.min(a, b);
1975     }
1976 
1977     /**
1978      * Returns an {@link Optional} containing the nominal descriptor for this
1979      * instance, which is the instance itself.
1980      *
1981      * @return an {@link Optional} describing the {@linkplain Long} instance
1982      * @since 12
1983      */
1984     @Override
1985     public Optional<Long> describeConstable() {
1986         return Optional.of(this);
1987     }
1988 
1989     /**
1990      * Resolves this instance as a {@link ConstantDesc}, the result of which is
1991      * the instance itself.
1992      *
1993      * @param lookup ignored
1994      * @return the {@linkplain Long} instance
1995      * @since 12
1996      */
1997     @Override
1998     public Long resolveConstantDesc(MethodHandles.Lookup lookup) {
1999         return this;
2000     }
2001 
2002     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2003     @java.io.Serial
2004     @Native private static final long serialVersionUID = 4290774380558885855L;
2005 }