1 /*
   2  * Copyright (c) 1994, 2013, 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.math.*;
  30 import java.util.Objects;
  31 import jdk.internal.HotSpotIntrinsicCandidate;
  32 
  33 
  34 /**
  35  * The {@code Long} class wraps a value of the primitive type {@code
  36  * long} in an object. An object of type {@code Long} contains a
  37  * single field whose type is {@code long}.
  38  *
  39  * <p> In addition, this class provides several methods for converting
  40  * a {@code long} to a {@code String} and a {@code String} to a {@code
  41  * long}, as well as other constants and methods useful when dealing
  42  * with a {@code long}.
  43  *
  44  * <p>Implementation note: The implementations of the "bit twiddling"
  45  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  46  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  47  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  48  * Delight</i>, (Addison Wesley, 2002).
  49  *
  50  * @author  Lee Boynton
  51  * @author  Arthur van Hoff
  52  * @author  Josh Bloch
  53  * @author  Joseph D. Darcy
  54  * @since   1.0
  55  */
  56 public final class Long extends Number implements Comparable<Long> {
  57     /**
  58      * A constant holding the minimum value a {@code long} can
  59      * have, -2<sup>63</sup>.
  60      */
  61     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  62 
  63     /**
  64      * A constant holding the maximum value a {@code long} can
  65      * have, 2<sup>63</sup>-1.
  66      */
  67     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  68 
  69     /**
  70      * The {@code Class} instance representing the primitive type
  71      * {@code long}.
  72      *
  73      * @since   1.1
  74      */
  75     @SuppressWarnings("unchecked")
  76     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  77 
  78     /**
  79      * Returns a string representation of the first argument in the
  80      * radix specified by the second argument.
  81      *
  82      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  83      * or larger than {@code Character.MAX_RADIX}, then the radix
  84      * {@code 10} is used instead.
  85      *
  86      * <p>If the first argument is negative, the first element of the
  87      * result is the ASCII minus sign {@code '-'}
  88      * ({@code '\u005Cu002d'}). If the first argument is not
  89      * negative, no sign character appears in the result.
  90      *
  91      * <p>The remaining characters of the result represent the magnitude
  92      * of the first argument. If the magnitude is zero, it is
  93      * represented by a single zero character {@code '0'}
  94      * ({@code '\u005Cu0030'}); otherwise, the first character of
  95      * the representation of the magnitude will not be the zero
  96      * character.  The following ASCII characters are used as digits:
  97      *
  98      * <blockquote>
  99      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 100      * </blockquote>
 101      *
 102      * These are {@code '\u005Cu0030'} through
 103      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 104      * {@code '\u005Cu007a'}. If {@code radix} is
 105      * <var>N</var>, then the first <var>N</var> of these characters
 106      * are used as radix-<var>N</var> digits in the order shown. Thus,
 107      * the digits for hexadecimal (radix 16) are
 108      * {@code 0123456789abcdef}. If uppercase letters are
 109      * desired, the {@link java.lang.String#toUpperCase()} method may
 110      * be called on the result:
 111      *
 112      * <blockquote>
 113      *  {@code Long.toString(n, 16).toUpperCase()}
 114      * </blockquote>
 115      *
 116      * @param   i       a {@code long} to be converted to a string.
 117      * @param   radix   the radix to use in the string representation.
 118      * @return  a string representation of the argument in the specified radix.
 119      * @see     java.lang.Character#MAX_RADIX
 120      * @see     java.lang.Character#MIN_RADIX
 121      */
 122     public static String toString(long i, int radix) {
 123         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 124             radix = 10;
 125         if (radix == 10)
 126             return toString(i);
 127         char[] buf = new char[65];
 128         int charPos = 64;
 129         boolean negative = (i < 0);
 130 
 131         if (!negative) {
 132             i = -i;
 133         }
 134 
 135         while (i <= -radix) {
 136             buf[charPos--] = Integer.digits[(int)(-(i % radix))];
 137             i = i / radix;
 138         }
 139         buf[charPos] = Integer.digits[(int)(-i)];
 140 
 141         if (negative) {
 142             buf[--charPos] = '-';
 143         }
 144 
 145         return new String(buf, charPos, (65 - charPos));
 146     }
 147 
 148     /**
 149      * Returns a string representation of the first argument as an
 150      * unsigned integer value in the radix specified by the second
 151      * argument.
 152      *
 153      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 154      * or larger than {@code Character.MAX_RADIX}, then the radix
 155      * {@code 10} is used instead.
 156      *
 157      * <p>Note that since the first argument is treated as an unsigned
 158      * value, no leading sign character is printed.
 159      *
 160      * <p>If the magnitude is zero, it is represented by a single zero
 161      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 162      * the first character of the representation of the magnitude will
 163      * not be the zero character.
 164      *
 165      * <p>The behavior of radixes and the characters used as digits
 166      * are the same as {@link #toString(long, int) toString}.
 167      *
 168      * @param   i       an integer to be converted to an unsigned string.
 169      * @param   radix   the radix to use in the string representation.
 170      * @return  an unsigned string representation of the argument in the specified radix.
 171      * @see     #toString(long, int)
 172      * @since 1.8
 173      */
 174     public static String toUnsignedString(long i, int radix) {
 175         if (i >= 0)
 176             return toString(i, radix);
 177         else {
 178             switch (radix) {
 179             case 2:
 180                 return toBinaryString(i);
 181 
 182             case 4:
 183                 return toUnsignedString0(i, 2);
 184 
 185             case 8:
 186                 return toOctalString(i);
 187 
 188             case 10:
 189                 /*
 190                  * We can get the effect of an unsigned division by 10
 191                  * on a long value by first shifting right, yielding a
 192                  * positive value, and then dividing by 5.  This
 193                  * allows the last digit and preceding digits to be
 194                  * isolated more quickly than by an initial conversion
 195                  * to BigInteger.
 196                  */
 197                 long quot = (i >>> 1) / 5;
 198                 long rem = i - quot * 10;
 199                 return toString(quot) + rem;
 200 
 201             case 16:
 202                 return toHexString(i);
 203 
 204             case 32:
 205                 return toUnsignedString0(i, 5);
 206 
 207             default:
 208                 return toUnsignedBigInteger(i).toString(radix);
 209             }
 210         }
 211     }
 212 
 213     /**
 214      * Return a BigInteger equal to the unsigned value of the
 215      * argument.
 216      */
 217     private static BigInteger toUnsignedBigInteger(long i) {
 218         if (i >= 0L)
 219             return BigInteger.valueOf(i);
 220         else {
 221             int upper = (int) (i >>> 32);
 222             int lower = (int) i;
 223 
 224             // return (upper << 32) + lower
 225             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 226                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 227         }
 228     }
 229 
 230     /**
 231      * Returns a string representation of the {@code long}
 232      * argument as an unsigned integer in base&nbsp;16.
 233      *
 234      * <p>The unsigned {@code long} value is the argument plus
 235      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 236      * equal to the argument.  This value is converted to a string of
 237      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 238      * leading {@code 0}s.
 239      *
 240      * <p>The value of the argument can be recovered from the returned
 241      * string {@code s} by calling {@link
 242      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 243      * 16)}.
 244      *
 245      * <p>If the unsigned magnitude is zero, it is represented by a
 246      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 247      * otherwise, the first character of the representation of the
 248      * unsigned magnitude will not be the zero character. The
 249      * following characters are used as hexadecimal digits:
 250      *
 251      * <blockquote>
 252      *  {@code 0123456789abcdef}
 253      * </blockquote>
 254      *
 255      * These are the characters {@code '\u005Cu0030'} through
 256      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 257      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 258      * the {@link java.lang.String#toUpperCase()} method may be called
 259      * on the result:
 260      *
 261      * <blockquote>
 262      *  {@code Long.toHexString(n).toUpperCase()}
 263      * </blockquote>
 264      *
 265      * @param   i   a {@code long} to be converted to a string.
 266      * @return  the string representation of the unsigned {@code long}
 267      *          value represented by the argument in hexadecimal
 268      *          (base&nbsp;16).
 269      * @see #parseUnsignedLong(String, int)
 270      * @see #toUnsignedString(long, int)
 271      * @since   1.0.2
 272      */
 273     public static String toHexString(long i) {
 274         return toUnsignedString0(i, 4);
 275     }
 276 
 277     /**
 278      * Returns a string representation of the {@code long}
 279      * argument as an unsigned integer in base&nbsp;8.
 280      *
 281      * <p>The unsigned {@code long} value is the argument plus
 282      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 283      * equal to the argument.  This value is converted to a string of
 284      * ASCII digits in octal (base&nbsp;8) with no extra leading
 285      * {@code 0}s.
 286      *
 287      * <p>The value of the argument can be recovered from the returned
 288      * string {@code s} by calling {@link
 289      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 290      * 8)}.
 291      *
 292      * <p>If the unsigned magnitude is zero, it is represented by a
 293      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 294      * otherwise, the first character of the representation of the
 295      * unsigned magnitude will not be the zero character. The
 296      * following characters are used as octal digits:
 297      *
 298      * <blockquote>
 299      *  {@code 01234567}
 300      * </blockquote>
 301      *
 302      * These are the characters {@code '\u005Cu0030'} through
 303      * {@code '\u005Cu0037'}.
 304      *
 305      * @param   i   a {@code long} to be converted to a string.
 306      * @return  the string representation of the unsigned {@code long}
 307      *          value represented by the argument in octal (base&nbsp;8).
 308      * @see #parseUnsignedLong(String, int)
 309      * @see #toUnsignedString(long, int)
 310      * @since   1.0.2
 311      */
 312     public static String toOctalString(long i) {
 313         return toUnsignedString0(i, 3);
 314     }
 315 
 316     /**
 317      * Returns a string representation of the {@code long}
 318      * argument as an unsigned integer in base&nbsp;2.
 319      *
 320      * <p>The unsigned {@code long} value is the argument plus
 321      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 322      * equal to the argument.  This value is converted to a string of
 323      * ASCII digits in binary (base&nbsp;2) with no extra leading
 324      * {@code 0}s.
 325      *
 326      * <p>The value of the argument can be recovered from the returned
 327      * string {@code s} by calling {@link
 328      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 329      * 2)}.
 330      *
 331      * <p>If the unsigned magnitude is zero, it is represented by a
 332      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 333      * otherwise, the first character of the representation of the
 334      * unsigned magnitude will not be the zero character. The
 335      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 336      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 337      *
 338      * @param   i   a {@code long} to be converted to a string.
 339      * @return  the string representation of the unsigned {@code long}
 340      *          value represented by the argument in binary (base&nbsp;2).
 341      * @see #parseUnsignedLong(String, int)
 342      * @see #toUnsignedString(long, int)
 343      * @since   1.0.2
 344      */
 345     public static String toBinaryString(long i) {
 346         return toUnsignedString0(i, 1);
 347     }
 348 
 349     /**
 350      * Format a long (treated as unsigned) into a String.
 351      * @param val the value to format
 352      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 353      */
 354     static String toUnsignedString0(long val, int shift) {
 355         // assert shift > 0 && shift <=5 : "Illegal shift value";
 356         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 357         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 358         char[] buf = new char[chars];
 359 
 360         formatUnsignedLong(val, shift, buf, 0, chars);
 361         return new String(buf, true);
 362     }
 363 
 364     /**
 365      * Format a long (treated as unsigned) into a character buffer. If
 366      * {@code len} exceeds the formatted ASCII representation of {@code val},
 367      * {@code buf} will be padded with leading zeroes.
 368      *
 369      * @param val the unsigned long to format
 370      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 371      * @param buf the character buffer to write to
 372      * @param offset the offset in the destination buffer to start at
 373      * @param len the number of characters to write
 374      */
 375      static void formatUnsignedLong(long val, int shift, char[] buf, int offset, int len) {
 376         // assert shift > 0 && shift <=5 : "Illegal shift value";
 377         // assert offset >= 0 && offset < buf.length : "illegal offset";
 378         // assert len > 0 && (offset + len) <= buf.length : "illegal length";
 379         int charPos = offset + len;
 380         int radix = 1 << shift;
 381         int mask = radix - 1;
 382         do {
 383             buf[--charPos] = Integer.digits[((int) val) & mask];
 384             val >>>= shift;
 385         } while (charPos > offset);
 386     }
 387 
 388     /**
 389      * Returns a {@code String} object representing the specified
 390      * {@code long}.  The argument is converted to signed decimal
 391      * representation and returned as a string, exactly as if the
 392      * argument and the radix 10 were given as arguments to the {@link
 393      * #toString(long, int)} method.
 394      *
 395      * @param   i   a {@code long} to be converted.
 396      * @return  a string representation of the argument in base&nbsp;10.
 397      */
 398     public static String toString(long i) {
 399         if (i == Long.MIN_VALUE)
 400             return "-9223372036854775808";
 401         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
 402         char[] buf = new char[size];
 403         getChars(i, size, buf);
 404         return new String(buf, true);
 405     }
 406 
 407     /**
 408      * Returns a string representation of the argument as an unsigned
 409      * decimal value.
 410      *
 411      * The argument is converted to unsigned decimal representation
 412      * and returned as a string exactly as if the argument and radix
 413      * 10 were given as arguments to the {@link #toUnsignedString(long,
 414      * int)} method.
 415      *
 416      * @param   i  an integer to be converted to an unsigned string.
 417      * @return  an unsigned string representation of the argument.
 418      * @see     #toUnsignedString(long, int)
 419      * @since 1.8
 420      */
 421     public static String toUnsignedString(long i) {
 422         return toUnsignedString(i, 10);
 423     }
 424 
 425     /**
 426      * Places characters representing the integer i into the
 427      * character array buf. The characters are placed into
 428      * the buffer backwards starting with the least significant
 429      * digit at the specified index (exclusive), and working
 430      * backwards from there.
 431      *
 432      * Will fail if i == Long.MIN_VALUE
 433      */
 434     static void getChars(long i, int index, char[] buf) {
 435         long q;
 436         int r;
 437         int charPos = index;
 438         char sign = 0;
 439 
 440         if (i < 0) {
 441             sign = '-';
 442             i = -i;
 443         }
 444 
 445         // Get 2 digits/iteration using longs until quotient fits into an int
 446         while (i > Integer.MAX_VALUE) {
 447             q = i / 100;
 448             // really: r = i - (q * 100);
 449             r = (int)(i - ((q << 6) + (q << 5) + (q << 2)));
 450             i = q;
 451             buf[--charPos] = Integer.DigitOnes[r];
 452             buf[--charPos] = Integer.DigitTens[r];
 453         }
 454 
 455         // Get 2 digits/iteration using ints
 456         int q2;
 457         int i2 = (int)i;
 458         while (i2 >= 65536) {
 459             q2 = i2 / 100;
 460             // really: r = i2 - (q * 100);
 461             r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
 462             i2 = q2;
 463             buf[--charPos] = Integer.DigitOnes[r];
 464             buf[--charPos] = Integer.DigitTens[r];
 465         }
 466 
 467         // Fall thru to fast mode for smaller numbers
 468         // assert(i2 <= 65536, i2);
 469         for (;;) {
 470             q2 = (i2 * 52429) >>> (16+3);
 471             r = i2 - ((q2 << 3) + (q2 << 1));  // r = i2-(q2*10) ...
 472             buf[--charPos] = Integer.digits[r];
 473             i2 = q2;
 474             if (i2 == 0) break;
 475         }
 476         if (sign != 0) {
 477             buf[--charPos] = sign;
 478         }
 479     }
 480 
 481     // Requires positive x
 482     static int stringSize(long x) {
 483         long p = 10;
 484         for (int i=1; i<19; i++) {
 485             if (x < p)
 486                 return i;
 487             p = 10*p;
 488         }
 489         return 19;
 490     }
 491 
 492     /**
 493      * Parses the string argument as a signed {@code long} in the
 494      * radix specified by the second argument. The characters in the
 495      * string must all be digits of the specified radix (as determined
 496      * by whether {@link java.lang.Character#digit(char, int)} returns
 497      * a nonnegative value), except that the first character may be an
 498      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 499      * indicate a negative value or an ASCII plus sign {@code '+'}
 500      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 501      * resulting {@code long} value is returned.
 502      *
 503      * <p>Note that neither the character {@code L}
 504      * ({@code '\u005Cu004C'}) nor {@code l}
 505      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 506      * of the string as a type indicator, as would be permitted in
 507      * Java programming language source code - except that either
 508      * {@code L} or {@code l} may appear as a digit for a
 509      * radix greater than or equal to 22.
 510      *
 511      * <p>An exception of type {@code NumberFormatException} is
 512      * thrown if any of the following situations occurs:
 513      * <ul>
 514      *
 515      * <li>The first argument is {@code null} or is a string of
 516      * length zero.
 517      *
 518      * <li>The {@code radix} is either smaller than {@link
 519      * java.lang.Character#MIN_RADIX} or larger than {@link
 520      * java.lang.Character#MAX_RADIX}.
 521      *
 522      * <li>Any character of the string is not a digit of the specified
 523      * radix, except that the first character may be a minus sign
 524      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 525      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 526      * longer than length 1.
 527      *
 528      * <li>The value represented by the string is not a value of type
 529      *      {@code long}.
 530      * </ul>
 531      *
 532      * <p>Examples:
 533      * <blockquote><pre>
 534      * parseLong("0", 10) returns 0L
 535      * parseLong("473", 10) returns 473L
 536      * parseLong("+42", 10) returns 42L
 537      * parseLong("-0", 10) returns 0L
 538      * parseLong("-FF", 16) returns -255L
 539      * parseLong("1100110", 2) returns 102L
 540      * parseLong("99", 8) throws a NumberFormatException
 541      * parseLong("Hazelnut", 10) throws a NumberFormatException
 542      * parseLong("Hazelnut", 36) returns 1356099454469L
 543      * </pre></blockquote>
 544      *
 545      * @param      s       the {@code String} containing the
 546      *                     {@code long} representation to be parsed.
 547      * @param      radix   the radix to be used while parsing {@code s}.
 548      * @return     the {@code long} represented by the string argument in
 549      *             the specified radix.
 550      * @throws     NumberFormatException  if the string does not contain a
 551      *             parsable {@code long}.
 552      */
 553     public static long parseLong(String s, int radix)
 554               throws NumberFormatException
 555     {
 556         if (s == null) {
 557             throw new NumberFormatException("null");
 558         }
 559 
 560         if (radix < Character.MIN_RADIX) {
 561             throw new NumberFormatException("radix " + radix +
 562                                             " less than Character.MIN_RADIX");
 563         }
 564         if (radix > Character.MAX_RADIX) {
 565             throw new NumberFormatException("radix " + radix +
 566                                             " greater than Character.MAX_RADIX");
 567         }
 568 
 569         boolean negative = false;
 570         int i = 0, len = s.length();
 571         long limit = -Long.MAX_VALUE;
 572 
 573         if (len > 0) {
 574             char firstChar = s.charAt(0);
 575             if (firstChar < '0') { // Possible leading "+" or "-"
 576                 if (firstChar == '-') {
 577                     negative = true;
 578                     limit = Long.MIN_VALUE;
 579                 } else if (firstChar != '+') {
 580                     throw NumberFormatException.forInputString(s);
 581                 }
 582 
 583                 if (len == 1) { // Cannot have lone "+" or "-"
 584                     throw NumberFormatException.forInputString(s);
 585                 }
 586                 i++;
 587             }
 588             long multmin = limit / radix;
 589             long result = 0;
 590             while (i < len) {
 591                 // Accumulating negatively avoids surprises near MAX_VALUE
 592                 int digit = Character.digit(s.charAt(i++),radix);
 593                 if (digit < 0 || result < multmin) {
 594                     throw NumberFormatException.forInputString(s);
 595                 }
 596                 result *= radix;
 597                 if (result < limit + digit) {
 598                     throw NumberFormatException.forInputString(s);
 599                 }
 600                 result -= digit;
 601             }
 602             return negative ? result : -result;
 603         } else {
 604             throw NumberFormatException.forInputString(s);
 605         }
 606     }
 607 
 608     /**
 609      * Parses the {@link CharSequence} argument as a signed {@code long} in
 610      * the specified {@code radix}, beginning at the specified
 611      * {@code beginIndex} and extending to {@code endIndex - 1}.
 612      *
 613      * <p>The method does not take steps to guard against the
 614      * {@code CharSequence} being mutated while parsing.
 615      *
 616      * @param      s   the {@code CharSequence} containing the {@code long}
 617      *                  representation to be parsed
 618      * @param      beginIndex   the beginning index, inclusive.
 619      * @param      endIndex     the ending index, exclusive.
 620      * @param      radix   the radix to be used while parsing {@code s}.
 621      * @return     the signed {@code long} represented by the subsequence in
 622      *             the specified radix.
 623      * @throws     NullPointerException  if {@code s} is null.
 624      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 625      *             negative, or if {@code beginIndex} is greater than
 626      *             {@code endIndex} or if {@code endIndex} is greater than
 627      *             {@code s.length()}.
 628      * @throws     NumberFormatException  if the {@code CharSequence} does not
 629      *             contain a parsable {@code int} in the specified
 630      *             {@code radix}, or if {@code radix} is either smaller than
 631      *             {@link java.lang.Character#MIN_RADIX} or larger than
 632      *             {@link java.lang.Character#MAX_RADIX}.
 633      * @since  1.9
 634      */
 635     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 636                 throws NumberFormatException {
 637         s = Objects.requireNonNull(s);
 638 
 639         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 640             throw new IndexOutOfBoundsException();
 641         }
 642         if (radix < Character.MIN_RADIX) {
 643             throw new NumberFormatException("radix " + radix +
 644                     " less than Character.MIN_RADIX");
 645         }
 646         if (radix > Character.MAX_RADIX) {
 647             throw new NumberFormatException("radix " + radix +
 648                     " greater than Character.MAX_RADIX");
 649         }
 650 
 651         boolean negative = false;
 652         int i = beginIndex;
 653         long limit = -Long.MAX_VALUE;
 654 
 655         if (i < endIndex) {
 656             char firstChar = s.charAt(i);
 657             if (firstChar < '0') { // Possible leading "+" or "-"
 658                 if (firstChar == '-') {
 659                     negative = true;
 660                     limit = Long.MIN_VALUE;
 661                 } else if (firstChar != '+') {
 662                     throw NumberFormatException.forCharSequence(s, beginIndex,
 663                             endIndex, i);
 664                 }
 665                 i++;
 666             }
 667             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 668                 throw NumberFormatException.forCharSequence(s, beginIndex,
 669                         endIndex, i);
 670             }
 671             long multmin = limit / radix;
 672             long result = 0;
 673             while (i < endIndex) {
 674                 // Accumulating negatively avoids surprises near MAX_VALUE
 675                 int digit = Character.digit(s.charAt(i), radix);
 676                 if (digit < 0 || result < multmin) {
 677                     throw NumberFormatException.forCharSequence(s, beginIndex,
 678                             endIndex, i);
 679                 }
 680                 result *= radix;
 681                 if (result < limit + digit) {
 682                     throw NumberFormatException.forCharSequence(s, beginIndex,
 683                             endIndex, i);
 684                 }
 685                 i++;
 686                 result -= digit;
 687             }
 688             return negative ? result : -result;
 689         } else {
 690             throw new NumberFormatException("");
 691         }
 692     }
 693 
 694     /**
 695      * Parses the string argument as a signed decimal {@code long}.
 696      * The characters in the string must all be decimal digits, except
 697      * that the first character may be an ASCII minus sign {@code '-'}
 698      * ({@code \u005Cu002D'}) to indicate a negative value or an
 699      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 700      * indicate a positive value. The resulting {@code long} value is
 701      * returned, exactly as if the argument and the radix {@code 10}
 702      * were given as arguments to the {@link
 703      * #parseLong(java.lang.String, int)} method.
 704      *
 705      * <p>Note that neither the character {@code L}
 706      * ({@code '\u005Cu004C'}) nor {@code l}
 707      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 708      * of the string as a type indicator, as would be permitted in
 709      * Java programming language source code.
 710      *
 711      * @param      s   a {@code String} containing the {@code long}
 712      *             representation to be parsed
 713      * @return     the {@code long} represented by the argument in
 714      *             decimal.
 715      * @throws     NumberFormatException  if the string does not contain a
 716      *             parsable {@code long}.
 717      */
 718     public static long parseLong(String s) throws NumberFormatException {
 719         return parseLong(s, 10);
 720     }
 721 
 722     /**
 723      * Parses the string argument as an unsigned {@code long} in the
 724      * radix specified by the second argument.  An unsigned integer
 725      * maps the values usually associated with negative numbers to
 726      * positive numbers larger than {@code MAX_VALUE}.
 727      *
 728      * The characters in the string must all be digits of the
 729      * specified radix (as determined by whether {@link
 730      * java.lang.Character#digit(char, int)} returns a nonnegative
 731      * value), except that the first character may be an ASCII plus
 732      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 733      * integer value is returned.
 734      *
 735      * <p>An exception of type {@code NumberFormatException} is
 736      * thrown if any of the following situations occurs:
 737      * <ul>
 738      * <li>The first argument is {@code null} or is a string of
 739      * length zero.
 740      *
 741      * <li>The radix is either smaller than
 742      * {@link java.lang.Character#MIN_RADIX} or
 743      * larger than {@link java.lang.Character#MAX_RADIX}.
 744      *
 745      * <li>Any character of the string is not a digit of the specified
 746      * radix, except that the first character may be a plus sign
 747      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 748      * string is longer than length 1.
 749      *
 750      * <li>The value represented by the string is larger than the
 751      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 752      *
 753      * </ul>
 754      *
 755      *
 756      * @param      s   the {@code String} containing the unsigned integer
 757      *                  representation to be parsed
 758      * @param      radix   the radix to be used while parsing {@code s}.
 759      * @return     the unsigned {@code long} represented by the string
 760      *             argument in the specified radix.
 761      * @throws     NumberFormatException if the {@code String}
 762      *             does not contain a parsable {@code long}.
 763      * @since 1.8
 764      */
 765     public static long parseUnsignedLong(String s, int radix)
 766                 throws NumberFormatException {
 767         if (s == null)  {
 768             throw new NumberFormatException("null");
 769         }
 770 
 771         int len = s.length();
 772         if (len > 0) {
 773             char firstChar = s.charAt(0);
 774             if (firstChar == '-') {
 775                 throw new
 776                     NumberFormatException(String.format("Illegal leading minus sign " +
 777                                                        "on unsigned string %s.", s));
 778             } else {
 779                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 780                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 781                     return parseLong(s, radix);
 782                 }
 783 
 784                 // No need for range checks on len due to testing above.
 785                 long first = parseLong(s, 0, len - 1, radix);
 786                 int second = Character.digit(s.charAt(len - 1), radix);
 787                 if (second < 0) {
 788                     throw new NumberFormatException("Bad digit at end of " + s);
 789                 }
 790                 long result = first * radix + second;
 791 
 792                 /*
 793                  * Test leftmost bits of multiprecision extension of first*radix
 794                  * for overflow. The number of bits needed is defined by
 795                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 796                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 797                  * overflow is tested by splitting guard in the ranges
 798                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 799                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 800                  * on a value which does not include a prime factor in the legal
 801                  * radix range.
 802                  */
 803                 int guard = radix * (int) (first >>> 57);
 804                 if (guard >= 128 ||
 805                     (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 806                     /*
 807                      * For purposes of exposition, the programmatic statements
 808                      * below should be taken to be multi-precision, i.e., not
 809                      * subject to overflow.
 810                      *
 811                      * A) Condition guard >= 128:
 812                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 813                      * hence always overflow.
 814                      *
 815                      * B) Condition guard < 92:
 816                      * Define left7 = first >>> 57.
 817                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 818                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 819                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 820                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 821                      * never overflow.
 822                      *
 823                      * C) Condition 92 <= guard < 128:
 824                      * first*radix + second >= radix*left7*2^57 + second
 825                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 826                      *
 827                      * D) Condition guard < 128:
 828                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 829                      * so
 830                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 831                      * thus
 832                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 833                      * whence
 834                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 835                      *
 836                      * E) Conditions C, D, and result >= 0:
 837                      * C and D combined imply the mathematical result
 838                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 839                      * bound is therefore negative as a signed long, but the
 840                      * upper bound is too small to overflow again after the
 841                      * signed long overflows to positive above 2^64 - 1. Hence
 842                      * result >= 0 implies overflow given C and D.
 843                      */
 844                     throw new NumberFormatException(String.format("String value %s exceeds " +
 845                                                                   "range of unsigned long.", s));
 846                 }
 847                 return result;
 848             }
 849         } else {
 850             throw NumberFormatException.forInputString(s);
 851         }
 852     }
 853 
 854     /**
 855      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 856      * the specified {@code radix}, beginning at the specified
 857      * {@code beginIndex} and extending to {@code endIndex - 1}.
 858      *
 859      * <p>The method does not take steps to guard against the
 860      * {@code CharSequence} being mutated while parsing.
 861      *
 862      * @param      s   the {@code CharSequence} containing the unsigned
 863      *                 {@code long} representation to be parsed
 864      * @param      beginIndex   the beginning index, inclusive.
 865      * @param      endIndex     the ending index, exclusive.
 866      * @param      radix   the radix to be used while parsing {@code s}.
 867      * @return     the unsigned {@code long} represented by the subsequence in
 868      *             the specified radix.
 869      * @throws     NullPointerException  if {@code s} is null.
 870      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 871      *             negative, or if {@code beginIndex} is greater than
 872      *             {@code endIndex} or if {@code endIndex} is greater than
 873      *             {@code s.length()}.
 874      * @throws     NumberFormatException  if the {@code CharSequence} does not
 875      *             contain a parsable unsigned {@code long} in the specified
 876      *             {@code radix}, or if {@code radix} is either smaller than
 877      *             {@link java.lang.Character#MIN_RADIX} or larger than
 878      *             {@link java.lang.Character#MAX_RADIX}.
 879      * @since  1.9
 880      */
 881     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
 882                 throws NumberFormatException {
 883         s = Objects.requireNonNull(s);
 884 
 885         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 886             throw new IndexOutOfBoundsException();
 887         }
 888         int start = beginIndex, len = endIndex - beginIndex;
 889 
 890         if (len > 0) {
 891             char firstChar = s.charAt(start);
 892             if (firstChar == '-') {
 893                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
 894                         "on unsigned string %s.", s.subSequence(start, start + len)));
 895             } else {
 896                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 897                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 898                     return parseLong(s, start, start + len, radix);
 899                 }
 900 
 901                 // No need for range checks on end due to testing above.
 902                 long first = parseLong(s, start, start + len - 1, radix);
 903                 int second = Character.digit(s.charAt(start + len - 1), radix);
 904                 if (second < 0) {
 905                     throw new NumberFormatException("Bad digit at end of " +
 906                             s.subSequence(start, start + len));
 907                 }
 908                 long result = first * radix + second;
 909 
 910                 /*
 911                  * Test leftmost bits of multiprecision extension of first*radix
 912                  * for overflow. The number of bits needed is defined by
 913                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 914                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 915                  * overflow is tested by splitting guard in the ranges
 916                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 917                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 918                  * on a value which does not include a prime factor in the legal
 919                  * radix range.
 920                  */
 921                 int guard = radix * (int) (first >>> 57);
 922                 if (guard >= 128 ||
 923                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 924                     /*
 925                      * For purposes of exposition, the programmatic statements
 926                      * below should be taken to be multi-precision, i.e., not
 927                      * subject to overflow.
 928                      *
 929                      * A) Condition guard >= 128:
 930                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 931                      * hence always overflow.
 932                      *
 933                      * B) Condition guard < 92:
 934                      * Define left7 = first >>> 57.
 935                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 936                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 937                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 938                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 939                      * never overflow.
 940                      *
 941                      * C) Condition 92 <= guard < 128:
 942                      * first*radix + second >= radix*left7*2^57 + second
 943                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 944                      *
 945                      * D) Condition guard < 128:
 946                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 947                      * so
 948                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 949                      * thus
 950                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 951                      * whence
 952                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 953                      *
 954                      * E) Conditions C, D, and result >= 0:
 955                      * C and D combined imply the mathematical result
 956                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 957                      * bound is therefore negative as a signed long, but the
 958                      * upper bound is too small to overflow again after the
 959                      * signed long overflows to positive above 2^64 - 1. Hence
 960                      * result >= 0 implies overflow given C and D.
 961                      */
 962                     throw new NumberFormatException(String.format("String value %s exceeds " +
 963                             "range of unsigned long.", s.subSequence(start, start + len)));
 964                 }
 965                 return result;
 966             }
 967         } else {
 968             throw NumberFormatException.forInputString("");
 969         }
 970     }
 971 
 972     /**
 973      * Parses the string argument as an unsigned decimal {@code long}. The
 974      * characters in the string must all be decimal digits, except
 975      * that the first character may be an ASCII plus sign {@code
 976      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
 977      * is returned, exactly as if the argument and the radix 10 were
 978      * given as arguments to the {@link
 979      * #parseUnsignedLong(java.lang.String, int)} method.
 980      *
 981      * @param s   a {@code String} containing the unsigned {@code long}
 982      *            representation to be parsed
 983      * @return    the unsigned {@code long} value represented by the decimal string argument
 984      * @throws    NumberFormatException  if the string does not contain a
 985      *            parsable unsigned integer.
 986      * @since 1.8
 987      */
 988     public static long parseUnsignedLong(String s) throws NumberFormatException {
 989         return parseUnsignedLong(s, 10);
 990     }
 991 
 992     /**
 993      * Returns a {@code Long} object holding the value
 994      * extracted from the specified {@code String} when parsed
 995      * with the radix given by the second argument.  The first
 996      * argument is interpreted as representing a signed
 997      * {@code long} in the radix specified by the second
 998      * argument, exactly as if the arguments were given to the {@link
 999      * #parseLong(java.lang.String, int)} method. The result is a
1000      * {@code Long} object that represents the {@code long}
1001      * value specified by the string.
1002      *
1003      * <p>In other words, this method returns a {@code Long} object equal
1004      * to the value of:
1005      *
1006      * <blockquote>
1007      *  {@code new Long(Long.parseLong(s, radix))}
1008      * </blockquote>
1009      *
1010      * @param      s       the string to be parsed
1011      * @param      radix   the radix to be used in interpreting {@code s}
1012      * @return     a {@code Long} object holding the value
1013      *             represented by the string argument in the specified
1014      *             radix.
1015      * @throws     NumberFormatException  If the {@code String} does not
1016      *             contain a parsable {@code long}.
1017      */
1018     public static Long valueOf(String s, int radix) throws NumberFormatException {
1019         return Long.valueOf(parseLong(s, radix));
1020     }
1021 
1022     /**
1023      * Returns a {@code Long} object holding the value
1024      * of the specified {@code String}. The argument is
1025      * interpreted as representing a signed decimal {@code long},
1026      * exactly as if the argument were given to the {@link
1027      * #parseLong(java.lang.String)} method. The result is a
1028      * {@code Long} object that represents the integer value
1029      * specified by the string.
1030      *
1031      * <p>In other words, this method returns a {@code Long} object
1032      * equal to the value of:
1033      *
1034      * <blockquote>
1035      *  {@code new Long(Long.parseLong(s))}
1036      * </blockquote>
1037      *
1038      * @param      s   the string to be parsed.
1039      * @return     a {@code Long} object holding the value
1040      *             represented by the string argument.
1041      * @throws     NumberFormatException  If the string cannot be parsed
1042      *             as a {@code long}.
1043      */
1044     public static Long valueOf(String s) throws NumberFormatException
1045     {
1046         return Long.valueOf(parseLong(s, 10));
1047     }
1048 
1049     private static class LongCache {
1050         private LongCache(){}
1051 
1052         static final Long cache[] = new Long[-(-128) + 127 + 1];
1053 
1054         static {
1055             for(int i = 0; i < cache.length; i++)
1056                 cache[i] = new Long(i - 128);
1057         }
1058     }
1059 
1060     /**
1061      * Returns a {@code Long} instance representing the specified
1062      * {@code long} value.
1063      * If a new {@code Long} instance is not required, this method
1064      * should generally be used in preference to the constructor
1065      * {@link #Long(long)}, as this method is likely to yield
1066      * significantly better space and time performance by caching
1067      * frequently requested values.
1068      *
1069      * Note that unlike the {@linkplain Integer#valueOf(int)
1070      * corresponding method} in the {@code Integer} class, this method
1071      * is <em>not</em> required to cache values within a particular
1072      * range.
1073      *
1074      * @param  l a long value.
1075      * @return a {@code Long} instance representing {@code l}.
1076      * @since  1.5
1077      */
1078     @HotSpotIntrinsicCandidate
1079     public static Long valueOf(long l) {
1080         final int offset = 128;
1081         if (l >= -128 && l <= 127) { // will cache
1082             return LongCache.cache[(int)l + offset];
1083         }
1084         return new Long(l);
1085     }
1086 
1087     /**
1088      * Decodes a {@code String} into a {@code Long}.
1089      * Accepts decimal, hexadecimal, and octal numbers given by the
1090      * following grammar:
1091      *
1092      * <blockquote>
1093      * <dl>
1094      * <dt><i>DecodableString:</i>
1095      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1096      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1097      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1098      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1099      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1100      *
1101      * <dt><i>Sign:</i>
1102      * <dd>{@code -}
1103      * <dd>{@code +}
1104      * </dl>
1105      * </blockquote>
1106      *
1107      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1108      * are as defined in section 3.10.1 of
1109      * <cite>The Java&trade; Language Specification</cite>,
1110      * except that underscores are not accepted between digits.
1111      *
1112      * <p>The sequence of characters following an optional
1113      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1114      * "{@code #}", or leading zero) is parsed as by the {@code
1115      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1116      * This sequence of characters must represent a positive value or
1117      * a {@link NumberFormatException} will be thrown.  The result is
1118      * negated if first character of the specified {@code String} is
1119      * the minus sign.  No whitespace characters are permitted in the
1120      * {@code String}.
1121      *
1122      * @param     nm the {@code String} to decode.
1123      * @return    a {@code Long} object holding the {@code long}
1124      *            value represented by {@code nm}
1125      * @throws    NumberFormatException  if the {@code String} does not
1126      *            contain a parsable {@code long}.
1127      * @see java.lang.Long#parseLong(String, int)
1128      * @since 1.2
1129      */
1130     public static Long decode(String nm) throws NumberFormatException {
1131         int radix = 10;
1132         int index = 0;
1133         boolean negative = false;
1134         Long result;
1135 
1136         if (nm.length() == 0)
1137             throw new NumberFormatException("Zero length string");
1138         char firstChar = nm.charAt(0);
1139         // Handle sign, if present
1140         if (firstChar == '-') {
1141             negative = true;
1142             index++;
1143         } else if (firstChar == '+')
1144             index++;
1145 
1146         // Handle radix specifier, if present
1147         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1148             index += 2;
1149             radix = 16;
1150         }
1151         else if (nm.startsWith("#", index)) {
1152             index ++;
1153             radix = 16;
1154         }
1155         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1156             index ++;
1157             radix = 8;
1158         }
1159 
1160         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1161             throw new NumberFormatException("Sign character in wrong position");
1162 
1163         try {
1164             result = Long.valueOf(nm.substring(index), radix);
1165             result = negative ? Long.valueOf(-result.longValue()) : result;
1166         } catch (NumberFormatException e) {
1167             // If number is Long.MIN_VALUE, we'll end up here. The next line
1168             // handles this case, and causes any genuine format error to be
1169             // rethrown.
1170             String constant = negative ? ("-" + nm.substring(index))
1171                                        : nm.substring(index);
1172             result = Long.valueOf(constant, radix);
1173         }
1174         return result;
1175     }
1176 
1177     /**
1178      * The value of the {@code Long}.
1179      *
1180      * @serial
1181      */
1182     private final long value;
1183 
1184     /**
1185      * Constructs a newly allocated {@code Long} object that
1186      * represents the specified {@code long} argument.
1187      *
1188      * @param   value   the value to be represented by the
1189      *          {@code Long} object.
1190      */
1191     public Long(long value) {
1192         this.value = value;
1193     }
1194 
1195     /**
1196      * Constructs a newly allocated {@code Long} object that
1197      * represents the {@code long} value indicated by the
1198      * {@code String} parameter. The string is converted to a
1199      * {@code long} value in exactly the manner used by the
1200      * {@code parseLong} method for radix 10.
1201      *
1202      * @param      s   the {@code String} to be converted to a
1203      *             {@code Long}.
1204      * @throws     NumberFormatException  if the {@code String} does not
1205      *             contain a parsable {@code long}.
1206      * @see        java.lang.Long#parseLong(java.lang.String, int)
1207      */
1208     public Long(String s) throws NumberFormatException {
1209         this.value = parseLong(s, 10);
1210     }
1211 
1212     /**
1213      * Returns the value of this {@code Long} as a {@code byte} after
1214      * a narrowing primitive conversion.
1215      * @jls 5.1.3 Narrowing Primitive Conversions
1216      */
1217     public byte byteValue() {
1218         return (byte)value;
1219     }
1220 
1221     /**
1222      * Returns the value of this {@code Long} as a {@code short} after
1223      * a narrowing primitive conversion.
1224      * @jls 5.1.3 Narrowing Primitive Conversions
1225      */
1226     public short shortValue() {
1227         return (short)value;
1228     }
1229 
1230     /**
1231      * Returns the value of this {@code Long} as an {@code int} after
1232      * a narrowing primitive conversion.
1233      * @jls 5.1.3 Narrowing Primitive Conversions
1234      */
1235     public int intValue() {
1236         return (int)value;
1237     }
1238 
1239     /**
1240      * Returns the value of this {@code Long} as a
1241      * {@code long} value.
1242      */
1243     @HotSpotIntrinsicCandidate
1244     public long longValue() {
1245         return value;
1246     }
1247 
1248     /**
1249      * Returns the value of this {@code Long} as a {@code float} after
1250      * a widening primitive conversion.
1251      * @jls 5.1.2 Widening Primitive Conversions
1252      */
1253     public float floatValue() {
1254         return (float)value;
1255     }
1256 
1257     /**
1258      * Returns the value of this {@code Long} as a {@code double}
1259      * after a widening primitive conversion.
1260      * @jls 5.1.2 Widening Primitive Conversions
1261      */
1262     public double doubleValue() {
1263         return (double)value;
1264     }
1265 
1266     /**
1267      * Returns a {@code String} object representing this
1268      * {@code Long}'s value.  The value is converted to signed
1269      * decimal representation and returned as a string, exactly as if
1270      * the {@code long} value were given as an argument to the
1271      * {@link java.lang.Long#toString(long)} method.
1272      *
1273      * @return  a string representation of the value of this object in
1274      *          base&nbsp;10.
1275      */
1276     public String toString() {
1277         return toString(value);
1278     }
1279 
1280     /**
1281      * Returns a hash code for this {@code Long}. The result is
1282      * the exclusive OR of the two halves of the primitive
1283      * {@code long} value held by this {@code Long}
1284      * object. That is, the hashcode is the value of the expression:
1285      *
1286      * <blockquote>
1287      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1288      * </blockquote>
1289      *
1290      * @return  a hash code value for this object.
1291      */
1292     @Override
1293     public int hashCode() {
1294         return Long.hashCode(value);
1295     }
1296 
1297     /**
1298      * Returns a hash code for a {@code long} value; compatible with
1299      * {@code Long.hashCode()}.
1300      *
1301      * @param value the value to hash
1302      * @return a hash code value for a {@code long} value.
1303      * @since 1.8
1304      */
1305     public static int hashCode(long value) {
1306         return (int)(value ^ (value >>> 32));
1307     }
1308 
1309     /**
1310      * Compares this object to the specified object.  The result is
1311      * {@code true} if and only if the argument is not
1312      * {@code null} and is a {@code Long} object that
1313      * contains the same {@code long} value as this object.
1314      *
1315      * @param   obj   the object to compare with.
1316      * @return  {@code true} if the objects are the same;
1317      *          {@code false} otherwise.
1318      */
1319     public boolean equals(Object obj) {
1320         if (obj instanceof Long) {
1321             return value == ((Long)obj).longValue();
1322         }
1323         return false;
1324     }
1325 
1326     /**
1327      * Determines the {@code long} value of the system property
1328      * with the specified name.
1329      *
1330      * <p>The first argument is treated as the name of a system
1331      * property.  System properties are accessible through the {@link
1332      * java.lang.System#getProperty(java.lang.String)} method. The
1333      * string value of this property is then interpreted as a {@code
1334      * long} value using the grammar supported by {@link Long#decode decode}
1335      * and a {@code Long} object representing this value is returned.
1336      *
1337      * <p>If there is no property with the specified name, if the
1338      * specified name is empty or {@code null}, or if the property
1339      * does not have the correct numeric format, then {@code null} is
1340      * returned.
1341      *
1342      * <p>In other words, this method returns a {@code Long} object
1343      * equal to the value of:
1344      *
1345      * <blockquote>
1346      *  {@code getLong(nm, null)}
1347      * </blockquote>
1348      *
1349      * @param   nm   property name.
1350      * @return  the {@code Long} value of the property.
1351      * @throws  SecurityException for the same reasons as
1352      *          {@link System#getProperty(String) System.getProperty}
1353      * @see     java.lang.System#getProperty(java.lang.String)
1354      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1355      */
1356     public static Long getLong(String nm) {
1357         return getLong(nm, null);
1358     }
1359 
1360     /**
1361      * Determines the {@code long} value of the system property
1362      * with the specified name.
1363      *
1364      * <p>The first argument is treated as the name of a system
1365      * property.  System properties are accessible through the {@link
1366      * java.lang.System#getProperty(java.lang.String)} method. The
1367      * string value of this property is then interpreted as a {@code
1368      * long} value using the grammar supported by {@link Long#decode decode}
1369      * and a {@code Long} object representing this value is returned.
1370      *
1371      * <p>The second argument is the default value. A {@code Long} object
1372      * that represents the value of the second argument is returned if there
1373      * is no property of the specified name, if the property does not have
1374      * the correct numeric format, or if the specified name is empty or null.
1375      *
1376      * <p>In other words, this method returns a {@code Long} object equal
1377      * to the value of:
1378      *
1379      * <blockquote>
1380      *  {@code getLong(nm, new Long(val))}
1381      * </blockquote>
1382      *
1383      * but in practice it may be implemented in a manner such as:
1384      *
1385      * <blockquote><pre>
1386      * Long result = getLong(nm, null);
1387      * return (result == null) ? new Long(val) : result;
1388      * </pre></blockquote>
1389      *
1390      * to avoid the unnecessary allocation of a {@code Long} object when
1391      * the default value is not needed.
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     java.lang.System#getProperty(java.lang.String)
1399      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1400      */
1401     public static Long getLong(String nm, long val) {
1402         Long result = Long.getLong(nm, null);
1403         return (result == null) ? Long.valueOf(val) : result;
1404     }
1405 
1406     /**
1407      * Returns the {@code long} value of the system property with
1408      * the specified name.  The first argument is treated as the name
1409      * of a system property.  System properties are accessible through
1410      * the {@link java.lang.System#getProperty(java.lang.String)}
1411      * method. The string value of this property is then interpreted
1412      * as a {@code long} value, as per the
1413      * {@link Long#decode decode} method, and a {@code Long} object
1414      * representing this value is returned; in summary:
1415      *
1416      * <ul>
1417      * <li>If the property value begins with the two ASCII characters
1418      * {@code 0x} or the ASCII character {@code #}, not followed by
1419      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1420      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1421      * with radix 16.
1422      * <li>If the property value begins with the ASCII character
1423      * {@code 0} followed by another character, it is parsed as
1424      * an octal integer exactly as by the method {@link
1425      * #valueOf(java.lang.String, int)} with radix 8.
1426      * <li>Otherwise the property value is parsed as a decimal
1427      * integer exactly as by the method
1428      * {@link #valueOf(java.lang.String, int)} with radix 10.
1429      * </ul>
1430      *
1431      * <p>Note that, in every case, neither {@code L}
1432      * ({@code '\u005Cu004C'}) nor {@code l}
1433      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1434      * of the property value as a type indicator, as would be
1435      * permitted in Java programming language source code.
1436      *
1437      * <p>The second argument is the default value. The default value is
1438      * returned if there is no property of the specified name, if the
1439      * property does not have the correct numeric format, or if the
1440      * specified name is empty or {@code null}.
1441      *
1442      * @param   nm   property name.
1443      * @param   val   default value.
1444      * @return  the {@code Long} value of the property.
1445      * @throws  SecurityException for the same reasons as
1446      *          {@link System#getProperty(String) System.getProperty}
1447      * @see     System#getProperty(java.lang.String)
1448      * @see     System#getProperty(java.lang.String, java.lang.String)
1449      */
1450     public static Long getLong(String nm, Long val) {
1451         String v = null;
1452         try {
1453             v = System.getProperty(nm);
1454         } catch (IllegalArgumentException | NullPointerException e) {
1455         }
1456         if (v != null) {
1457             try {
1458                 return Long.decode(v);
1459             } catch (NumberFormatException e) {
1460             }
1461         }
1462         return val;
1463     }
1464 
1465     /**
1466      * Compares two {@code Long} objects numerically.
1467      *
1468      * @param   anotherLong   the {@code Long} to be compared.
1469      * @return  the value {@code 0} if this {@code Long} is
1470      *          equal to the argument {@code Long}; a value less than
1471      *          {@code 0} if this {@code Long} is numerically less
1472      *          than the argument {@code Long}; and a value greater
1473      *          than {@code 0} if this {@code Long} is numerically
1474      *           greater than the argument {@code Long} (signed
1475      *           comparison).
1476      * @since   1.2
1477      */
1478     public int compareTo(Long anotherLong) {
1479         return compare(this.value, anotherLong.value);
1480     }
1481 
1482     /**
1483      * Compares two {@code long} values numerically.
1484      * The value returned is identical to what would be returned by:
1485      * <pre>
1486      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1487      * </pre>
1488      *
1489      * @param  x the first {@code long} to compare
1490      * @param  y the second {@code long} to compare
1491      * @return the value {@code 0} if {@code x == y};
1492      *         a value less than {@code 0} if {@code x < y}; and
1493      *         a value greater than {@code 0} if {@code x > y}
1494      * @since 1.7
1495      */
1496     public static int compare(long x, long y) {
1497         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1498     }
1499 
1500     /**
1501      * Compares two {@code long} values numerically treating the values
1502      * as unsigned.
1503      *
1504      * @param  x the first {@code long} to compare
1505      * @param  y the second {@code long} to compare
1506      * @return the value {@code 0} if {@code x == y}; a value less
1507      *         than {@code 0} if {@code x < y} as unsigned values; and
1508      *         a value greater than {@code 0} if {@code x > y} as
1509      *         unsigned values
1510      * @since 1.8
1511      */
1512     public static int compareUnsigned(long x, long y) {
1513         return compare(x + MIN_VALUE, y + MIN_VALUE);
1514     }
1515 
1516 
1517     /**
1518      * Returns the unsigned quotient of dividing the first argument by
1519      * the second where each argument and the result is interpreted as
1520      * an unsigned value.
1521      *
1522      * <p>Note that in two's complement arithmetic, the three other
1523      * basic arithmetic operations of add, subtract, and multiply are
1524      * bit-wise identical if the two operands are regarded as both
1525      * being signed or both being unsigned.  Therefore separate {@code
1526      * addUnsigned}, etc. methods are not provided.
1527      *
1528      * @param dividend the value to be divided
1529      * @param divisor the value doing the dividing
1530      * @return the unsigned quotient of the first argument divided by
1531      * the second argument
1532      * @see #remainderUnsigned
1533      * @since 1.8
1534      */
1535     public static long divideUnsigned(long dividend, long divisor) {
1536         if (divisor < 0L) { // signed comparison
1537             // Answer must be 0 or 1 depending on relative magnitude
1538             // of dividend and divisor.
1539             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1540         }
1541 
1542         if (dividend > 0) //  Both inputs non-negative
1543             return dividend/divisor;
1544         else {
1545             /*
1546              * For simple code, leveraging BigInteger.  Longer and faster
1547              * code written directly in terms of operations on longs is
1548              * possible; see "Hacker's Delight" for divide and remainder
1549              * algorithms.
1550              */
1551             return toUnsignedBigInteger(dividend).
1552                 divide(toUnsignedBigInteger(divisor)).longValue();
1553         }
1554     }
1555 
1556     /**
1557      * Returns the unsigned remainder from dividing the first argument
1558      * by the second where each argument and the result is interpreted
1559      * as an unsigned value.
1560      *
1561      * @param dividend the value to be divided
1562      * @param divisor the value doing the dividing
1563      * @return the unsigned remainder of the first argument divided by
1564      * the second argument
1565      * @see #divideUnsigned
1566      * @since 1.8
1567      */
1568     public static long remainderUnsigned(long dividend, long divisor) {
1569         if (dividend > 0 && divisor > 0) { // signed comparisons
1570             return dividend % divisor;
1571         } else {
1572             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1573                 return dividend;
1574             else
1575                 return toUnsignedBigInteger(dividend).
1576                     remainder(toUnsignedBigInteger(divisor)).longValue();
1577         }
1578     }
1579 
1580     // Bit Twiddling
1581 
1582     /**
1583      * The number of bits used to represent a {@code long} value in two's
1584      * complement binary form.
1585      *
1586      * @since 1.5
1587      */
1588     @Native public static final int SIZE = 64;
1589 
1590     /**
1591      * The number of bytes used to represent a {@code long} value in two's
1592      * complement binary form.
1593      *
1594      * @since 1.8
1595      */
1596     public static final int BYTES = SIZE / Byte.SIZE;
1597 
1598     /**
1599      * Returns a {@code long} value with at most a single one-bit, in the
1600      * position of the highest-order ("leftmost") one-bit in the specified
1601      * {@code long} value.  Returns zero if the specified value has no
1602      * one-bits in its two's complement binary representation, that is, if it
1603      * is equal to zero.
1604      *
1605      * @param i the value whose highest one bit is to be computed
1606      * @return a {@code long} value with a single one-bit, in the position
1607      *     of the highest-order one-bit in the specified value, or zero if
1608      *     the specified value is itself equal to zero.
1609      * @since 1.5
1610      */
1611     public static long highestOneBit(long i) {
1612         // HD, Figure 3-1
1613         i |= (i >>  1);
1614         i |= (i >>  2);
1615         i |= (i >>  4);
1616         i |= (i >>  8);
1617         i |= (i >> 16);
1618         i |= (i >> 32);
1619         return i - (i >>> 1);
1620     }
1621 
1622     /**
1623      * Returns a {@code long} value with at most a single one-bit, in the
1624      * position of the lowest-order ("rightmost") one-bit in the specified
1625      * {@code long} value.  Returns zero if the specified value has no
1626      * one-bits in its two's complement binary representation, that is, if it
1627      * is equal to zero.
1628      *
1629      * @param i the value whose lowest one bit is to be computed
1630      * @return a {@code long} value with a single one-bit, in the position
1631      *     of the lowest-order one-bit in the specified value, or zero if
1632      *     the specified value is itself equal to zero.
1633      * @since 1.5
1634      */
1635     public static long lowestOneBit(long i) {
1636         // HD, Section 2-1
1637         return i & -i;
1638     }
1639 
1640     /**
1641      * Returns the number of zero bits preceding the highest-order
1642      * ("leftmost") one-bit in the two's complement binary representation
1643      * of the specified {@code long} value.  Returns 64 if the
1644      * specified value has no one-bits in its two's complement representation,
1645      * in other words if it is equal to zero.
1646      *
1647      * <p>Note that this method is closely related to the logarithm base 2.
1648      * For all positive {@code long} values x:
1649      * <ul>
1650      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1651      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1652      * </ul>
1653      *
1654      * @param i the value whose number of leading zeros is to be computed
1655      * @return the number of zero bits preceding the highest-order
1656      *     ("leftmost") one-bit in the two's complement binary representation
1657      *     of the specified {@code long} value, or 64 if the value
1658      *     is equal to zero.
1659      * @since 1.5
1660      */
1661     @HotSpotIntrinsicCandidate
1662     public static int numberOfLeadingZeros(long i) {
1663         // HD, Figure 5-6
1664          if (i == 0)
1665             return 64;
1666         int n = 1;
1667         int x = (int)(i >>> 32);
1668         if (x == 0) { n += 32; x = (int)i; }
1669         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1670         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1671         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1672         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1673         n -= x >>> 31;
1674         return n;
1675     }
1676 
1677     /**
1678      * Returns the number of zero bits following the lowest-order ("rightmost")
1679      * one-bit in the two's complement binary representation of the specified
1680      * {@code long} value.  Returns 64 if the specified value has no
1681      * one-bits in its two's complement representation, in other words if it is
1682      * equal to zero.
1683      *
1684      * @param i the value whose number of trailing zeros is to be computed
1685      * @return the number of zero bits following the lowest-order ("rightmost")
1686      *     one-bit in the two's complement binary representation of the
1687      *     specified {@code long} value, or 64 if the value is equal
1688      *     to zero.
1689      * @since 1.5
1690      */
1691     @HotSpotIntrinsicCandidate
1692     public static int numberOfTrailingZeros(long i) {
1693         // HD, Figure 5-14
1694         int x, y;
1695         if (i == 0) return 64;
1696         int n = 63;
1697         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1698         y = x <<16; if (y != 0) { n = n -16; x = y; }
1699         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1700         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1701         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1702         return n - ((x << 1) >>> 31);
1703     }
1704 
1705     /**
1706      * Returns the number of one-bits in the two's complement binary
1707      * representation of the specified {@code long} value.  This function is
1708      * sometimes referred to as the <i>population count</i>.
1709      *
1710      * @param i the value whose bits are to be counted
1711      * @return the number of one-bits in the two's complement binary
1712      *     representation of the specified {@code long} value.
1713      * @since 1.5
1714      */
1715      @HotSpotIntrinsicCandidate
1716      public static int bitCount(long i) {
1717         // HD, Figure 5-2
1718         i = i - ((i >>> 1) & 0x5555555555555555L);
1719         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1720         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1721         i = i + (i >>> 8);
1722         i = i + (i >>> 16);
1723         i = i + (i >>> 32);
1724         return (int)i & 0x7f;
1725      }
1726 
1727     /**
1728      * Returns the value obtained by rotating the two's complement binary
1729      * representation of the specified {@code long} value left by the
1730      * specified number of bits.  (Bits shifted out of the left hand, or
1731      * high-order, side reenter on the right, or low-order.)
1732      *
1733      * <p>Note that left rotation with a negative distance is equivalent to
1734      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1735      * distance)}.  Note also that rotation by any multiple of 64 is a
1736      * no-op, so all but the last six bits of the rotation distance can be
1737      * ignored, even if the distance is negative: {@code rotateLeft(val,
1738      * distance) == rotateLeft(val, distance & 0x3F)}.
1739      *
1740      * @param i the value whose bits are to be rotated left
1741      * @param distance the number of bit positions to rotate left
1742      * @return the value obtained by rotating the two's complement binary
1743      *     representation of the specified {@code long} value left by the
1744      *     specified number of bits.
1745      * @since 1.5
1746      */
1747     public static long rotateLeft(long i, int distance) {
1748         return (i << distance) | (i >>> -distance);
1749     }
1750 
1751     /**
1752      * Returns the value obtained by rotating the two's complement binary
1753      * representation of the specified {@code long} value right by the
1754      * specified number of bits.  (Bits shifted out of the right hand, or
1755      * low-order, side reenter on the left, or high-order.)
1756      *
1757      * <p>Note that right rotation with a negative distance is equivalent to
1758      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1759      * distance)}.  Note also that rotation by any multiple of 64 is a
1760      * no-op, so all but the last six bits of the rotation distance can be
1761      * ignored, even if the distance is negative: {@code rotateRight(val,
1762      * distance) == rotateRight(val, distance & 0x3F)}.
1763      *
1764      * @param i the value whose bits are to be rotated right
1765      * @param distance the number of bit positions to rotate right
1766      * @return the value obtained by rotating the two's complement binary
1767      *     representation of the specified {@code long} value right by the
1768      *     specified number of bits.
1769      * @since 1.5
1770      */
1771     public static long rotateRight(long i, int distance) {
1772         return (i >>> distance) | (i << -distance);
1773     }
1774 
1775     /**
1776      * Returns the value obtained by reversing the order of the bits in the
1777      * two's complement binary representation of the specified {@code long}
1778      * value.
1779      *
1780      * @param i the value to be reversed
1781      * @return the value obtained by reversing order of the bits in the
1782      *     specified {@code long} value.
1783      * @since 1.5
1784      */
1785     public static long reverse(long i) {
1786         // HD, Figure 7-1
1787         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1788         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1789         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1790         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1791         i = (i << 48) | ((i & 0xffff0000L) << 16) |
1792             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1793         return i;
1794     }
1795 
1796     /**
1797      * Returns the signum function of the specified {@code long} value.  (The
1798      * return value is -1 if the specified value is negative; 0 if the
1799      * specified value is zero; and 1 if the specified value is positive.)
1800      *
1801      * @param i the value whose signum is to be computed
1802      * @return the signum function of the specified {@code long} value.
1803      * @since 1.5
1804      */
1805     public static int signum(long i) {
1806         // HD, Section 2-7
1807         return (int) ((i >> 63) | (-i >>> 63));
1808     }
1809 
1810     /**
1811      * Returns the value obtained by reversing the order of the bytes in the
1812      * two's complement representation of the specified {@code long} value.
1813      *
1814      * @param i the value whose bytes are to be reversed
1815      * @return the value obtained by reversing the bytes in the specified
1816      *     {@code long} value.
1817      * @since 1.5
1818      */
1819     @HotSpotIntrinsicCandidate
1820     public static long reverseBytes(long i) {
1821         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1822         return (i << 48) | ((i & 0xffff0000L) << 16) |
1823             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1824     }
1825 
1826     /**
1827      * Adds two {@code long} values together as per the + operator.
1828      *
1829      * @param a the first operand
1830      * @param b the second operand
1831      * @return the sum of {@code a} and {@code b}
1832      * @see java.util.function.BinaryOperator
1833      * @since 1.8
1834      */
1835     public static long sum(long a, long b) {
1836         return a + b;
1837     }
1838 
1839     /**
1840      * Returns the greater of two {@code long} values
1841      * as if by calling {@link Math#max(long, long) Math.max}.
1842      *
1843      * @param a the first operand
1844      * @param b the second operand
1845      * @return the greater of {@code a} and {@code b}
1846      * @see java.util.function.BinaryOperator
1847      * @since 1.8
1848      */
1849     public static long max(long a, long b) {
1850         return Math.max(a, b);
1851     }
1852 
1853     /**
1854      * Returns the smaller of two {@code long} values
1855      * as if by calling {@link Math#min(long, long) Math.min}.
1856      *
1857      * @param a the first operand
1858      * @param b the second operand
1859      * @return the smaller of {@code a} and {@code b}
1860      * @see java.util.function.BinaryOperator
1861      * @since 1.8
1862      */
1863     public static long min(long a, long b) {
1864         return Math.min(a, b);
1865     }
1866 
1867     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1868     @Native private static final long serialVersionUID = 4290774380558885855L;
1869 }