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 
  32 
  33 /**
  34  * The {@code Long} class wraps a value of the primitive type {@code
  35  * long} in an object. An object of type {@code Long} contains a
  36  * single field whose type is {@code long}.
  37  *
  38  * <p> In addition, this class provides several methods for converting
  39  * a {@code long} to a {@code String} and a {@code String} to a {@code
  40  * long}, as well as other constants and methods useful when dealing
  41  * with a {@code long}.
  42  *
  43  * <p>Implementation note: The implementations of the "bit twiddling"
  44  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  45  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  46  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  47  * Delight</i>, (Addison Wesley, 2002).
  48  *
  49  * @author  Lee Boynton
  50  * @author  Arthur van Hoff
  51  * @author  Josh Bloch
  52  * @author  Joseph D. Darcy
  53  * @since   JDK1.0
  54  */
  55 public final class Long extends Number implements Comparable<Long> {
  56     /**
  57      * A constant holding the minimum value a {@code long} can
  58      * have, -2<sup>63</sup>.
  59      */
  60     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  61 
  62     /**
  63      * A constant holding the maximum value a {@code long} can
  64      * have, 2<sup>63</sup>-1.
  65      */
  66     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  67 
  68     /**
  69      * The {@code Class} instance representing the primitive type
  70      * {@code long}.
  71      *
  72      * @since   JDK1.1
  73      */
  74     @SuppressWarnings("unchecked")
  75     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  76 
  77     /**
  78      * Returns a string representation of the first argument in the
  79      * radix specified by the second argument.
  80      *
  81      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  82      * or larger than {@code Character.MAX_RADIX}, then the radix
  83      * {@code 10} is used instead.
  84      *
  85      * <p>If the first argument is negative, the first element of the
  86      * result is the ASCII minus sign {@code '-'}
  87      * ({@code '\u005Cu002d'}). If the first argument is not
  88      * negative, no sign character appears in the result.
  89      *
  90      * <p>The remaining characters of the result represent the magnitude
  91      * of the first argument. If the magnitude is zero, it is
  92      * represented by a single zero character {@code '0'}
  93      * ({@code '\u005Cu0030'}); otherwise, the first character of
  94      * the representation of the magnitude will not be the zero
  95      * character.  The following ASCII characters are used as digits:
  96      *
  97      * <blockquote>
  98      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
  99      * </blockquote>
 100      *
 101      * These are {@code '\u005Cu0030'} through
 102      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 103      * {@code '\u005Cu007a'}. If {@code radix} is
 104      * <var>N</var>, then the first <var>N</var> of these characters
 105      * are used as radix-<var>N</var> digits in the order shown. Thus,
 106      * the digits for hexadecimal (radix 16) are
 107      * {@code 0123456789abcdef}. If uppercase letters are
 108      * desired, the {@link java.lang.String#toUpperCase()} method may
 109      * be called on the result:
 110      *
 111      * <blockquote>
 112      *  {@code Long.toString(n, 16).toUpperCase()}
 113      * </blockquote>
 114      *
 115      * @param   i       a {@code long} to be converted to a string.
 116      * @param   radix   the radix to use in the string representation.
 117      * @return  a string representation of the argument in the specified radix.
 118      * @see     java.lang.Character#MAX_RADIX
 119      * @see     java.lang.Character#MIN_RADIX
 120      */
 121     public static String toString(long i, int radix) {
 122         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 123             radix = 10;
 124         if (radix == 10)
 125             return toString(i);
 126         char[] buf = new char[65];
 127         int charPos = 64;
 128         boolean negative = (i < 0);
 129 
 130         if (!negative) {
 131             i = -i;
 132         }
 133 
 134         while (i <= -radix) {
 135             buf[charPos--] = Integer.digits[(int)(-(i % radix))];
 136             i = i / radix;
 137         }
 138         buf[charPos] = Integer.digits[(int)(-i)];
 139 
 140         if (negative) {
 141             buf[--charPos] = '-';
 142         }
 143 
 144         return new String(buf, charPos, (65 - charPos));
 145     }
 146 
 147     /**
 148      * Returns a string representation of the first argument as an
 149      * unsigned integer value in the radix specified by the second
 150      * argument.
 151      *
 152      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 153      * or larger than {@code Character.MAX_RADIX}, then the radix
 154      * {@code 10} is used instead.
 155      *
 156      * <p>Note that since the first argument is treated as an unsigned
 157      * value, no leading sign character is printed.
 158      *
 159      * <p>If the magnitude is zero, it is represented by a single zero
 160      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 161      * the first character of the representation of the magnitude will
 162      * not be the zero character.
 163      *
 164      * <p>The behavior of radixes and the characters used as digits
 165      * are the same as {@link #toString(long, int) toString}.
 166      *
 167      * @param   i       an integer to be converted to an unsigned string.
 168      * @param   radix   the radix to use in the string representation.
 169      * @return  an unsigned string representation of the argument in the specified radix.
 170      * @see     #toString(long, int)
 171      * @since 1.8
 172      */
 173     public static String toUnsignedString(long i, int radix) {
 174         if (i >= 0)
 175             return toString(i, radix);
 176         else {
 177             switch (radix) {
 178             case 2:
 179                 return toBinaryString(i);
 180 
 181             case 4:
 182                 return toUnsignedString0(i, 2);
 183 
 184             case 8:
 185                 return toOctalString(i);
 186 
 187             case 10:
 188                 /*
 189                  * We can get the effect of an unsigned division by 10
 190                  * on a long value by first shifting right, yielding a
 191                  * positive value, and then dividing by 5.  This
 192                  * allows the last digit and preceding digits to be
 193                  * isolated more quickly than by an initial conversion
 194                  * to BigInteger.
 195                  */
 196                 long quot = (i >>> 1) / 5;
 197                 long rem = i - quot * 10;
 198                 return toString(quot) + rem;
 199 
 200             case 16:
 201                 return toHexString(i);
 202 
 203             case 32:
 204                 return toUnsignedString0(i, 5);
 205 
 206             default:
 207                 return toUnsignedBigInteger(i).toString(radix);
 208             }
 209         }
 210     }
 211 
 212     /**
 213      * Return a BigInteger equal to the unsigned value of the
 214      * argument.
 215      */
 216     private static BigInteger toUnsignedBigInteger(long i) {
 217         if (i >= 0L)
 218             return BigInteger.valueOf(i);
 219         else {
 220             int upper = (int) (i >>> 32);
 221             int lower = (int) i;
 222 
 223             // return (upper << 32) + lower
 224             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 225                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 226         }
 227     }
 228 
 229     /**
 230      * Returns a string representation of the {@code long}
 231      * argument as an unsigned integer in base&nbsp;16.
 232      *
 233      * <p>The unsigned {@code long} value is the argument plus
 234      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 235      * equal to the argument.  This value is converted to a string of
 236      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 237      * leading {@code 0}s.
 238      *
 239      * <p>The value of the argument can be recovered from the returned
 240      * string {@code s} by calling {@link
 241      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 242      * 16)}.
 243      *
 244      * <p>If the unsigned magnitude is zero, it is represented by a
 245      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 246      * otherwise, the first character of the representation of the
 247      * unsigned magnitude will not be the zero character. The
 248      * following characters are used as hexadecimal digits:
 249      *
 250      * <blockquote>
 251      *  {@code 0123456789abcdef}
 252      * </blockquote>
 253      *
 254      * These are the characters {@code '\u005Cu0030'} through
 255      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 256      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 257      * the {@link java.lang.String#toUpperCase()} method may be called
 258      * on the result:
 259      *
 260      * <blockquote>
 261      *  {@code Long.toHexString(n).toUpperCase()}
 262      * </blockquote>
 263      *
 264      * @param   i   a {@code long} to be converted to a string.
 265      * @return  the string representation of the unsigned {@code long}
 266      *          value represented by the argument in hexadecimal
 267      *          (base&nbsp;16).
 268      * @see #parseUnsignedLong(String, int)
 269      * @see #toUnsignedString(long, int)
 270      * @since   JDK 1.0.2
 271      */
 272     public static String toHexString(long i) {
 273         return toUnsignedString0(i, 4);
 274     }
 275 
 276     /**
 277      * Returns a string representation of the {@code long}
 278      * argument as an unsigned integer in base&nbsp;8.
 279      *
 280      * <p>The unsigned {@code long} value is the argument plus
 281      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 282      * equal to the argument.  This value is converted to a string of
 283      * ASCII digits in octal (base&nbsp;8) with no extra leading
 284      * {@code 0}s.
 285      *
 286      * <p>The value of the argument can be recovered from the returned
 287      * string {@code s} by calling {@link
 288      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 289      * 8)}.
 290      *
 291      * <p>If the unsigned magnitude is zero, it is represented by a
 292      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 293      * otherwise, the first character of the representation of the
 294      * unsigned magnitude will not be the zero character. The
 295      * following characters are used as octal digits:
 296      *
 297      * <blockquote>
 298      *  {@code 01234567}
 299      * </blockquote>
 300      *
 301      * These are the characters {@code '\u005Cu0030'} through
 302      * {@code '\u005Cu0037'}.
 303      *
 304      * @param   i   a {@code long} to be converted to a string.
 305      * @return  the string representation of the unsigned {@code long}
 306      *          value represented by the argument in octal (base&nbsp;8).
 307      * @see #parseUnsignedLong(String, int)
 308      * @see #toUnsignedString(long, int)
 309      * @since   JDK 1.0.2
 310      */
 311     public static String toOctalString(long i) {
 312         return toUnsignedString0(i, 3);
 313     }
 314 
 315     /**
 316      * Returns a string representation of the {@code long}
 317      * argument as an unsigned integer in base&nbsp;2.
 318      *
 319      * <p>The unsigned {@code long} value is the argument plus
 320      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 321      * equal to the argument.  This value is converted to a string of
 322      * ASCII digits in binary (base&nbsp;2) with no extra leading
 323      * {@code 0}s.
 324      *
 325      * <p>The value of the argument can be recovered from the returned
 326      * string {@code s} by calling {@link
 327      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 328      * 2)}.
 329      *
 330      * <p>If the unsigned magnitude is zero, it is represented by a
 331      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 332      * otherwise, the first character of the representation of the
 333      * unsigned magnitude will not be the zero character. The
 334      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 335      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 336      *
 337      * @param   i   a {@code long} to be converted to a string.
 338      * @return  the string representation of the unsigned {@code long}
 339      *          value represented by the argument in binary (base&nbsp;2).
 340      * @see #parseUnsignedLong(String, int)
 341      * @see #toUnsignedString(long, int)
 342      * @since   JDK 1.0.2
 343      */
 344     public static String toBinaryString(long i) {
 345         return toUnsignedString0(i, 1);
 346     }
 347 
 348     /**
 349      * Format a long (treated as unsigned) into a String.
 350      * @param val the value to format
 351      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 352      */
 353     static String toUnsignedString0(long val, int shift) {
 354         // assert shift > 0 && shift <=5 : "Illegal shift value";
 355         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 356         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 357         char[] buf = new char[chars];
 358 
 359         formatUnsignedLong(val, shift, buf, 0, chars);
 360         return new String(buf, true);
 361     }
 362 
 363     /**
 364      * Format a long (treated as unsigned) into a character buffer. If
 365      * {@code len} exceeds the formatted ASCII representation of {@code val},
 366      * {@code buf} will be padded with leading zeroes.
 367      *
 368      * @param val the unsigned long to format
 369      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 370      * @param buf the character buffer to write to
 371      * @param offset the offset in the destination buffer to start at
 372      * @param len the number of characters to write
 373      */
 374      static void formatUnsignedLong(long val, int shift, char[] buf, int offset, int len) {
 375         // assert shift > 0 && shift <=5 : "Illegal shift value";
 376         // assert offset >= 0 && offset < buf.length : "illegal offset";
 377         // assert len > 0 && (offset + len) <= buf.length : "illegal length";
 378         int charPos = offset + len;
 379         int radix = 1 << shift;
 380         int mask = radix - 1;
 381         do {
 382             buf[--charPos] = Integer.digits[((int) val) & mask];
 383             val >>>= shift;
 384         } while (charPos > offset);
 385     }
 386 
 387     /**
 388      * Returns a {@code String} object representing the specified
 389      * {@code long}.  The argument is converted to signed decimal
 390      * representation and returned as a string, exactly as if the
 391      * argument and the radix 10 were given as arguments to the {@link
 392      * #toString(long, int)} method.
 393      *
 394      * @param   i   a {@code long} to be converted.
 395      * @return  a string representation of the argument in base&nbsp;10.
 396      */
 397     public static String toString(long i) {
 398         if (i == Long.MIN_VALUE)
 399             return "-9223372036854775808";
 400         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
 401         char[] buf = new char[size];
 402         getChars(i, size, buf);
 403         return new String(buf, true);
 404     }
 405 
 406     /**
 407      * Returns a string representation of the argument as an unsigned
 408      * decimal value.
 409      *
 410      * The argument is converted to unsigned decimal representation
 411      * and returned as a string exactly as if the argument and radix
 412      * 10 were given as arguments to the {@link #toUnsignedString(long,
 413      * int)} method.
 414      *
 415      * @param   i  an integer to be converted to an unsigned string.
 416      * @return  an unsigned string representation of the argument.
 417      * @see     #toUnsignedString(long, int)
 418      * @since 1.8
 419      */
 420     public static String toUnsignedString(long i) {
 421         return toUnsignedString(i, 10);
 422     }
 423 
 424     /**
 425      * Places characters representing the integer i into the
 426      * character array buf. The characters are placed into
 427      * the buffer backwards starting with the least significant
 428      * digit at the specified index (exclusive), and working
 429      * backwards from there.
 430      *
 431      * Will fail if i == Long.MIN_VALUE
 432      */
 433     static void getChars(long i, int index, char[] buf) {
 434         long q;
 435         int r;
 436         int charPos = index;
 437         char sign = 0;
 438 
 439         if (i < 0) {
 440             sign = '-';
 441             i = -i;
 442         }
 443 
 444         // Get 2 digits/iteration using longs until quotient fits into an int
 445         while (i > Integer.MAX_VALUE) {
 446             q = i / 100;
 447             // really: r = i - (q * 100);
 448             r = (int)(i - ((q << 6) + (q << 5) + (q << 2)));
 449             i = q;
 450             buf[--charPos] = Integer.DigitOnes[r];
 451             buf[--charPos] = Integer.DigitTens[r];
 452         }
 453 
 454         // Get 2 digits/iteration using ints
 455         int q2;
 456         int i2 = (int)i;
 457         while (i2 >= 65536) {
 458             q2 = i2 / 100;
 459             // really: r = i2 - (q * 100);
 460             r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
 461             i2 = q2;
 462             buf[--charPos] = Integer.DigitOnes[r];
 463             buf[--charPos] = Integer.DigitTens[r];
 464         }
 465 
 466         // Fall thru to fast mode for smaller numbers
 467         // assert(i2 <= 65536, i2);
 468         for (;;) {
 469             q2 = (i2 * 52429) >>> (16+3);
 470             r = i2 - ((q2 << 3) + (q2 << 1));  // r = i2-(q2*10) ...
 471             buf[--charPos] = Integer.digits[r];
 472             i2 = q2;
 473             if (i2 == 0) break;
 474         }
 475         if (sign != 0) {
 476             buf[--charPos] = sign;
 477         }
 478     }
 479 
 480     // Requires positive x
 481     static int stringSize(long x) {
 482         long p = 10;
 483         for (int i=1; i<19; i++) {
 484             if (x < p)
 485                 return i;
 486             p = 10*p;
 487         }
 488         return 19;
 489     }
 490 
 491     /**
 492      * Parses the string argument as a signed {@code long} in the
 493      * radix specified by the second argument. The characters in the
 494      * string must all be digits of the specified radix (as determined
 495      * by whether {@link java.lang.Character#digit(char, int)} returns
 496      * a nonnegative value), except that the first character may be an
 497      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 498      * indicate a negative value or an ASCII plus sign {@code '+'}
 499      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 500      * resulting {@code long} value is returned.
 501      *
 502      * <p>Note that neither the character {@code L}
 503      * ({@code '\u005Cu004C'}) nor {@code l}
 504      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 505      * of the string as a type indicator, as would be permitted in
 506      * Java programming language source code - except that either
 507      * {@code L} or {@code l} may appear as a digit for a
 508      * radix greater than or equal to 22.
 509      *
 510      * <p>An exception of type {@code NumberFormatException} is
 511      * thrown if any of the following situations occurs:
 512      * <ul>
 513      *
 514      * <li>The first argument is {@code null} or is a string of
 515      * length zero.
 516      *
 517      * <li>The {@code radix} is either smaller than {@link
 518      * java.lang.Character#MIN_RADIX} or larger than {@link
 519      * java.lang.Character#MAX_RADIX}.
 520      *
 521      * <li>Any character of the string is not a digit of the specified
 522      * radix, except that the first character may be a minus sign
 523      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 524      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 525      * longer than length 1.
 526      *
 527      * <li>The value represented by the string is not a value of type
 528      *      {@code long}.
 529      * </ul>
 530      *
 531      * <p>Examples:
 532      * <blockquote><pre>
 533      * parseLong("0", 10) returns 0L
 534      * parseLong("473", 10) returns 473L
 535      * parseLong("+42", 10) returns 42L
 536      * parseLong("-0", 10) returns 0L
 537      * parseLong("-FF", 16) returns -255L
 538      * parseLong("1100110", 2) returns 102L
 539      * parseLong("99", 8) throws a NumberFormatException
 540      * parseLong("Hazelnut", 10) throws a NumberFormatException
 541      * parseLong("Hazelnut", 36) returns 1356099454469L
 542      * </pre></blockquote>
 543      *
 544      * @param      s       the {@code String} containing the
 545      *                     {@code long} representation to be parsed.
 546      * @param      radix   the radix to be used while parsing {@code s}.
 547      * @return     the {@code long} represented by the string argument in
 548      *             the specified radix.
 549      * @throws     NumberFormatException  if the string does not contain a
 550      *             parsable {@code long}.
 551      */
 552     public static long parseLong(String s, int radix)
 553               throws NumberFormatException
 554     {
 555         if (s == null) {
 556             throw new NumberFormatException("null");
 557         }
 558 
 559         if (radix < Character.MIN_RADIX) {
 560             throw new NumberFormatException("radix " + radix +
 561                                             " less than Character.MIN_RADIX");
 562         }
 563         if (radix > Character.MAX_RADIX) {
 564             throw new NumberFormatException("radix " + radix +
 565                                             " greater than Character.MAX_RADIX");
 566         }
 567 
 568         boolean negative = false;
 569         int i = 0, len = s.length();
 570         long limit = -Long.MAX_VALUE;
 571 
 572         if (len > 0) {
 573             char firstChar = s.charAt(0);
 574             if (firstChar < '0') { // Possible leading "+" or "-"
 575                 if (firstChar == '-') {
 576                     negative = true;
 577                     limit = Long.MIN_VALUE;
 578                 } else if (firstChar != '+') {
 579                     throw NumberFormatException.forInputString(s);
 580                 }
 581 
 582                 if (len == 1) { // Cannot have lone "+" or "-"
 583                     throw NumberFormatException.forInputString(s);
 584                 }
 585                 i++;
 586             }
 587             long multmin = limit / radix;
 588             long result = 0;
 589             while (i < len) {
 590                 // Accumulating negatively avoids surprises near MAX_VALUE
 591                 int digit = Character.digit(s.charAt(i++),radix);
 592                 if (digit < 0 || result < multmin) {
 593                     throw NumberFormatException.forInputString(s);
 594                 }
 595                 result *= radix;
 596                 if (result < limit + digit) {
 597                     throw NumberFormatException.forInputString(s);
 598                 }
 599                 result -= digit;
 600             }
 601             return negative ? result : -result;
 602         } else {
 603             throw NumberFormatException.forInputString(s);
 604         }
 605     }
 606 
 607     /**
 608      * Parses the {@link CharSequence} argument as a signed {@code long} in
 609      * the specified {@code radix}, beginning at the specified {@code beginIndex}
 610      * and extending to the end of the sequence.
 611      *
 612      * <p>The method does not take steps to guard against the
 613      * {@code CharSequence} being mutated while parsing.
 614      *
 615      * @param      s   the {@code CharSequence} containing the {@code long}
 616      *                  representation to be parsed
 617      * @param      radix   the radix to be used while parsing {@code s}.
 618      * @param      beginIndex   the beginning index, inclusive.
 619      * @return     the signed {@code long} represented by the subsequence in
 620      *             the specified radix.
 621      * @throws     NullPointerException  if {@code s} is null.
 622      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 623      *             negative, or if {@code beginIndex} is greater than
 624      *             {@code s.length()}.
 625      * @throws     NumberFormatException  if the {@code CharSequence} does not
 626      *             contain a parsable {@code long} in the specified
 627      *             {@code radix}, or if {@code radix} is either smaller than
 628      *             {@link java.lang.Character#MIN_RADIX} or larger than
 629      *             {@link java.lang.Character#MAX_RADIX}.
 630      * @since  1.9
 631      */
 632     static long parseLong(CharSequence s, int radix, int beginIndex)
 633             throws NumberFormatException {
 634         // forces a null check of s
 635         return parseLong(s, radix, beginIndex, s.length());
 636     }
 637 
 638     /**
 639      * Parses the {@link CharSequence} argument as a signed {@code long} in
 640      * the specified {@code radix}, beginning at the specified
 641      * {@code beginIndex} and extending to {@code endIndex - 1}.
 642      *
 643      * <p>The method does not take steps to guard against the
 644      * {@code CharSequence} being mutated while parsing.
 645      *
 646      * @param      s   the {@code CharSequence} containing the {@code long}
 647      *                  representation to be parsed
 648      * @param      radix   the radix to be used while parsing {@code s}.
 649      * @param      beginIndex   the beginning index, inclusive.
 650      * @param      endIndex     the ending index, exclusive.
 651      * @return     the signed {@code long} represented by the subsequence in
 652      *             the specified radix.
 653      * @throws     NullPointerException  if {@code s} is null.
 654      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 655      *             negative, or if {@code beginIndex} is greater than
 656      *             {@code endIndex} or if {@code endIndex} is greater than
 657      *             {@code s.length()}.
 658      * @throws     NumberFormatException  if the {@code CharSequence} does not
 659      *             contain a parsable {@code int} in the specified
 660      *             {@code radix}, or if {@code radix} is either smaller than
 661      *             {@link java.lang.Character#MIN_RADIX} or larger than
 662      *             {@link java.lang.Character#MAX_RADIX}.
 663      * @since  1.9
 664      */
 665     static long parseLong(CharSequence s, int radix, int beginIndex, int endIndex)
 666                 throws NumberFormatException {
 667         s = Objects.requireNonNull(s);
 668 
 669         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 670             throw new IndexOutOfBoundsException();
 671         }
 672         if (radix < Character.MIN_RADIX) {
 673             throw new NumberFormatException("radix " + radix +
 674                     " less than Character.MIN_RADIX");
 675         }
 676         if (radix > Character.MAX_RADIX) {
 677             throw new NumberFormatException("radix " + radix +
 678                     " greater than Character.MAX_RADIX");
 679         }
 680 
 681         boolean negative = false;
 682         int i = beginIndex;
 683         long limit = -Long.MAX_VALUE;
 684 
 685         if (i < endIndex) {
 686             char firstChar = s.charAt(i);
 687             if (firstChar < '0') { // Possible leading "+" or "-"
 688                 if (firstChar == '-') {
 689                     negative = true;
 690                     limit = Long.MIN_VALUE;
 691                 } else if (firstChar != '+') {
 692                     throw NumberFormatException.forCharSequence(s, beginIndex,
 693                             endIndex, i);
 694                 }
 695                 i++;
 696             }
 697             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 698                 throw NumberFormatException.forCharSequence(s, beginIndex,
 699                         endIndex, i);
 700             }
 701             long multmin = limit / radix;
 702             long result = 0;
 703             while (i < endIndex) {
 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.forCharSequence(s, beginIndex,
 708                             endIndex, i);
 709                 }
 710                 result *= radix;
 711                 if (result < limit + digit) {
 712                     throw NumberFormatException.forCharSequence(s, beginIndex,
 713                             endIndex, i);
 714                 }
 715                 result -= digit;
 716             }
 717             return negative ? result : -result;
 718         } else {
 719             throw new NumberFormatException("");
 720         }
 721     }
 722 
 723     /**
 724      * Parses the string argument as a signed decimal {@code long}.
 725      * The characters in the string must all be decimal digits, except
 726      * that the first character may be an ASCII minus sign {@code '-'}
 727      * ({@code \u005Cu002D'}) to indicate a negative value or an
 728      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 729      * indicate a positive value. The resulting {@code long} value is
 730      * returned, exactly as if the argument and the radix {@code 10}
 731      * were given as arguments to the {@link
 732      * #parseLong(java.lang.String, int)} method.
 733      *
 734      * <p>Note that neither the character {@code L}
 735      * ({@code '\u005Cu004C'}) nor {@code l}
 736      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 737      * of the string as a type indicator, as would be permitted in
 738      * Java programming language source code.
 739      *
 740      * @param      s   a {@code String} containing the {@code long}
 741      *             representation to be parsed
 742      * @return     the {@code long} represented by the argument in
 743      *             decimal.
 744      * @throws     NumberFormatException  if the string does not contain a
 745      *             parsable {@code long}.
 746      */
 747     public static long parseLong(String s) throws NumberFormatException {
 748         return parseLong(s, 10);
 749     }
 750 
 751     /**
 752      * Parses the string argument as an unsigned {@code long} in the
 753      * radix specified by the second argument.  An unsigned integer
 754      * maps the values usually associated with negative numbers to
 755      * positive numbers larger than {@code MAX_VALUE}.
 756      *
 757      * The characters in the string must all be digits of the
 758      * specified radix (as determined by whether {@link
 759      * java.lang.Character#digit(char, int)} returns a nonnegative
 760      * value), except that the first character may be an ASCII plus
 761      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 762      * integer value is returned.
 763      *
 764      * <p>An exception of type {@code NumberFormatException} is
 765      * thrown if any of the following situations occurs:
 766      * <ul>
 767      * <li>The first argument is {@code null} or is a string of
 768      * length zero.
 769      *
 770      * <li>The radix is either smaller than
 771      * {@link java.lang.Character#MIN_RADIX} or
 772      * larger than {@link java.lang.Character#MAX_RADIX}.
 773      *
 774      * <li>Any character of the string is not a digit of the specified
 775      * radix, except that the first character may be a plus sign
 776      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 777      * string is longer than length 1.
 778      *
 779      * <li>The value represented by the string is larger than the
 780      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 781      *
 782      * </ul>
 783      *
 784      *
 785      * @param      s   the {@code String} containing the unsigned integer
 786      *                  representation to be parsed
 787      * @param      radix   the radix to be used while parsing {@code s}.
 788      * @return     the unsigned {@code long} represented by the string
 789      *             argument in the specified radix.
 790      * @throws     NumberFormatException if the {@code String}
 791      *             does not contain a parsable {@code long}.
 792      * @since 1.8
 793      */
 794     public static long parseUnsignedLong(String s, int radix)
 795                 throws NumberFormatException {
 796         if (s == null)  {
 797             throw new NumberFormatException("null");
 798         }
 799 
 800         int len = s.length();
 801         if (len > 0) {
 802             char firstChar = s.charAt(0);
 803             if (firstChar == '-') {
 804                 throw new
 805                     NumberFormatException(String.format("Illegal leading minus sign " +
 806                                                        "on unsigned string %s.", s));
 807             } else {
 808                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 809                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 810                     return parseLong(s, radix);
 811                 }
 812 
 813                 // No need for range checks on len due to testing above.
 814                 long first = parseLong(s, radix, 0, len - 1);
 815                 int second = Character.digit(s.charAt(len - 1), radix);
 816                 if (second < 0) {
 817                     throw new NumberFormatException("Bad digit at end of " + s);
 818                 }
 819                 long result = first * radix + second;
 820                 if (compareUnsigned(result, first) < 0) {
 821                     /*
 822                      * The maximum unsigned value, (2^64)-1, takes at
 823                      * most one more digit to represent than the
 824                      * maximum signed value, (2^63)-1.  Therefore,
 825                      * parsing (len - 1) digits will be appropriately
 826                      * in-range of the signed parsing.  In other
 827                      * words, if parsing (len -1) digits overflows
 828                      * signed parsing, parsing len digits will
 829                      * certainly overflow unsigned parsing.
 830                      *
 831                      * The compareUnsigned check above catches
 832                      * situations where an unsigned overflow occurs
 833                      * incorporating the contribution of the final
 834                      * digit.
 835                      */
 836                     throw new NumberFormatException(String.format("String value %s exceeds " +
 837                                                                   "range of unsigned long.", s));
 838                 }
 839                 return result;
 840             }
 841         } else {
 842             throw NumberFormatException.forInputString(s);
 843         }
 844     }
 845 
 846     /**
 847      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 848      * the specified {@code radix}, beginning at the specified
 849      * {@code beginIndex} and extending to the end of the sequence.
 850      *
 851      * <p>The method does not take steps to guard against the
 852      * {@code CharSequence} being mutated while parsing.
 853      *
 854      * @param      s   the {@code CharSequence} containing the unsigned
 855      *                 {@code long} representation to be parsed
 856      * @param      radix   the radix to be used while parsing {@code s}.
 857      * @param      beginIndex   the beginning index, inclusive.
 858      * @return     the unsigned {@code long} represented by the subsequence in
 859      *             the specified radix.
 860      * @throws     NullPointerException  if {@code s} is null.
 861      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 862      *             negative, or if {@code beginIndex} is greater than
 863      *             {@code s.length()}.
 864      * @throws     NumberFormatException  if the {@code CharSequence} does not
 865      *             contain a parsable unsigned {@code long} in the specified
 866      *             {@code radix}, or if {@code radix} is either smaller than
 867      *             {@link java.lang.Character#MIN_RADIX} or larger than
 868      *             {@link java.lang.Character#MAX_RADIX}.
 869      * @since  1.9
 870      */
 871     static long parseUnsignedLong(CharSequence s, int radix, int beginIndex)
 872                 throws NumberFormatException {
 873         // forces a null check of s
 874         return parseUnsignedLong(s, radix, beginIndex, s.length());
 875     }
 876 
 877     /**
 878      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 879      * the specified {@code radix}, beginning at the specified
 880      * {@code beginIndex} and extending to {@code endIndex - 1}.
 881      *
 882      * <p>The method does not take steps to guard against the
 883      * {@code CharSequence} being mutated while parsing.
 884      *
 885      * @param      s   the {@code CharSequence} containing the unsigned
 886      *                 {@code long} representation to be parsed
 887      * @param      radix   the radix to be used while parsing {@code s}.
 888      * @param      beginIndex   the beginning index, inclusive.
 889      * @param      endIndex     the ending index, exclusive.
 890      * @return     the unsigned {@code long} represented by the subsequence in
 891      *             the specified radix.
 892      * @throws     NullPointerException  if {@code s} is null.
 893      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 894      *             negative, or if {@code beginIndex} is greater than
 895      *             {@code endIndex} or if {@code endIndex} is greater than
 896      *             {@code s.length()}.
 897      * @throws     NumberFormatException  if the {@code CharSequence} does not
 898      *             contain a parsable unsigned {@code long} in the specified
 899      *             {@code radix}, or if {@code radix} is either smaller than
 900      *             {@link java.lang.Character#MIN_RADIX} or larger than
 901      *             {@link java.lang.Character#MAX_RADIX}.
 902      * @since  1.9
 903      */
 904     static long parseUnsignedLong(CharSequence s, int radix, int beginIndex, int endIndex)
 905                 throws NumberFormatException {
 906         s = Objects.requireNonNull(s);
 907 
 908         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 909             throw new IndexOutOfBoundsException();
 910         }
 911         int start = beginIndex, len = endIndex - beginIndex;
 912 
 913         if (len > 0) {
 914             char firstChar = s.charAt(start);
 915             if (firstChar == '-') {
 916                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
 917                         "on unsigned string %s.", s.subSequence(start, start + len)));
 918             } else {
 919                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 920                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 921                     return parseLong(s, radix, start, start + len);
 922                 }
 923 
 924                 // No need for range checks on end due to testing above.
 925                 long first = parseLong(s, radix, start, start + len - 1);
 926                 int second = Character.digit(s.charAt(start + len - 1), radix);
 927                 if (second < 0) {
 928                     throw new NumberFormatException("Bad digit at end of " +
 929                             s.subSequence(start, start + len));
 930                 }
 931                 long result = first * radix + second;
 932 
 933                 /*
 934                  * Test leftmost bits of multiprecision extension of first*radix
 935                  * for overflow. The number of bits needed is defined by
 936                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 937                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 938                  * overflow is tested by splitting guard in the ranges
 939                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 940                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 941                  * on a value which does not include a prime factor in the legal
 942                  * radix range.
 943                  */
 944                 int guard = radix * (int) (first >>> 57);
 945                 if (guard >= 128 ||
 946                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 947                     /*
 948                      * For purposes of exposition, the programmatic statements
 949                      * below should be taken to be multi-precision, i.e., not
 950                      * subject to overflow.
 951                      *
 952                      * A) Condition guard >= 128:
 953                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 954                      * hence always overflow.
 955                      *
 956                      * B) Condition guard < 92:
 957                      * Define left7 = first >>> 57.
 958                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 959                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 960                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 961                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 962                      * never overflow.
 963                      *
 964                      * C) Condition 92 <= guard < 128:
 965                      * first*radix + second >= radix*left7*2^57 + second
 966                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 967                      *
 968                      * D) Condition guard < 128:
 969                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 970                      * so
 971                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 972                      * thus
 973                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 974                      * whence
 975                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 976                      *
 977                      * E) Conditions C, D, and result >= 0:
 978                      * C and D combined imply the mathematical result
 979                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 980                      * bound is therefore negative as a signed long, but the
 981                      * upper bound is too small to overflow again after the
 982                      * signed long overflows to positive above 2^64 - 1. Hence
 983                      * result >= 0 implies overflow given C and D.
 984                      */
 985                     throw new NumberFormatException(String.format("String value %s exceeds " +
 986                             "range of unsigned long.", s.subSequence(start, start + len)));
 987                 }
 988                 return result;
 989             }
 990         } else {
 991             throw NumberFormatException.forInputString("");
 992         }
 993     }
 994 
 995     /**
 996      * Parses the string argument as an unsigned decimal {@code long}. The
 997      * characters in the string must all be decimal digits, except
 998      * that the first character may be an an ASCII plus sign {@code
 999      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
1000      * is returned, exactly as if the argument and the radix 10 were
1001      * given as arguments to the {@link
1002      * #parseUnsignedLong(java.lang.String, int)} method.
1003      *
1004      * @param s   a {@code String} containing the unsigned {@code long}
1005      *            representation to be parsed
1006      * @return    the unsigned {@code long} value represented by the decimal string argument
1007      * @throws    NumberFormatException  if the string does not contain a
1008      *            parsable unsigned integer.
1009      * @since 1.8
1010      */
1011     public static long parseUnsignedLong(String s) throws NumberFormatException {
1012         return parseUnsignedLong(s, 10);
1013     }
1014 
1015     /**
1016      * Returns a {@code Long} object holding the value
1017      * extracted from the specified {@code String} when parsed
1018      * with the radix given by the second argument.  The first
1019      * argument is interpreted as representing a signed
1020      * {@code long} in the radix specified by the second
1021      * argument, exactly as if the arguments were given to the {@link
1022      * #parseLong(java.lang.String, int)} method. The result is a
1023      * {@code Long} object that represents the {@code long}
1024      * value specified by the string.
1025      *
1026      * <p>In other words, this method returns a {@code Long} object equal
1027      * to the value of:
1028      *
1029      * <blockquote>
1030      *  {@code new Long(Long.parseLong(s, radix))}
1031      * </blockquote>
1032      *
1033      * @param      s       the string to be parsed
1034      * @param      radix   the radix to be used in interpreting {@code s}
1035      * @return     a {@code Long} object holding the value
1036      *             represented by the string argument in the specified
1037      *             radix.
1038      * @throws     NumberFormatException  If the {@code String} does not
1039      *             contain a parsable {@code long}.
1040      */
1041     public static Long valueOf(String s, int radix) throws NumberFormatException {
1042         return Long.valueOf(parseLong(s, radix));
1043     }
1044 
1045     /**
1046      * Returns a {@code Long} object holding the value
1047      * of the specified {@code String}. The argument is
1048      * interpreted as representing a signed decimal {@code long},
1049      * exactly as if the argument were given to the {@link
1050      * #parseLong(java.lang.String)} method. The result is a
1051      * {@code Long} object that represents the integer value
1052      * specified by the string.
1053      *
1054      * <p>In other words, this method returns a {@code Long} object
1055      * equal to the value of:
1056      *
1057      * <blockquote>
1058      *  {@code new Long(Long.parseLong(s))}
1059      * </blockquote>
1060      *
1061      * @param      s   the string to be parsed.
1062      * @return     a {@code Long} object holding the value
1063      *             represented by the string argument.
1064      * @throws     NumberFormatException  If the string cannot be parsed
1065      *             as a {@code long}.
1066      */
1067     public static Long valueOf(String s) throws NumberFormatException
1068     {
1069         return Long.valueOf(parseLong(s, 10));
1070     }
1071 
1072     private static class LongCache {
1073         private LongCache(){}
1074 
1075         static final Long cache[] = new Long[-(-128) + 127 + 1];
1076 
1077         static {
1078             for(int i = 0; i < cache.length; i++)
1079                 cache[i] = new Long(i - 128);
1080         }
1081     }
1082 
1083     /**
1084      * Returns a {@code Long} instance representing the specified
1085      * {@code long} value.
1086      * If a new {@code Long} instance is not required, this method
1087      * should generally be used in preference to the constructor
1088      * {@link #Long(long)}, as this method is likely to yield
1089      * significantly better space and time performance by caching
1090      * frequently requested values.
1091      *
1092      * Note that unlike the {@linkplain Integer#valueOf(int)
1093      * corresponding method} in the {@code Integer} class, this method
1094      * is <em>not</em> required to cache values within a particular
1095      * range.
1096      *
1097      * @param  l a long value.
1098      * @return a {@code Long} instance representing {@code l}.
1099      * @since  1.5
1100      */
1101     public static Long valueOf(long l) {
1102         final int offset = 128;
1103         if (l >= -128 && l <= 127) { // will cache
1104             return LongCache.cache[(int)l + offset];
1105         }
1106         return new Long(l);
1107     }
1108 
1109     /**
1110      * Decodes a {@code String} into a {@code Long}.
1111      * Accepts decimal, hexadecimal, and octal numbers given by the
1112      * following grammar:
1113      *
1114      * <blockquote>
1115      * <dl>
1116      * <dt><i>DecodableString:</i>
1117      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1118      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1119      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1120      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1121      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1122      *
1123      * <dt><i>Sign:</i>
1124      * <dd>{@code -}
1125      * <dd>{@code +}
1126      * </dl>
1127      * </blockquote>
1128      *
1129      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1130      * are as defined in section 3.10.1 of
1131      * <cite>The Java&trade; Language Specification</cite>,
1132      * except that underscores are not accepted between digits.
1133      *
1134      * <p>The sequence of characters following an optional
1135      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1136      * "{@code #}", or leading zero) is parsed as by the {@code
1137      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1138      * This sequence of characters must represent a positive value or
1139      * a {@link NumberFormatException} will be thrown.  The result is
1140      * negated if first character of the specified {@code String} is
1141      * the minus sign.  No whitespace characters are permitted in the
1142      * {@code String}.
1143      *
1144      * @param     nm the {@code String} to decode.
1145      * @return    a {@code Long} object holding the {@code long}
1146      *            value represented by {@code nm}
1147      * @throws    NumberFormatException  if the {@code String} does not
1148      *            contain a parsable {@code long}.
1149      * @see java.lang.Long#parseLong(String, int)
1150      * @since 1.2
1151      */
1152     public static Long decode(String nm) throws NumberFormatException {
1153         int radix = 10;
1154         int index = 0;
1155         boolean negative = false;
1156         Long result;
1157 
1158         if (nm.length() == 0)
1159             throw new NumberFormatException("Zero length string");
1160         char firstChar = nm.charAt(0);
1161         // Handle sign, if present
1162         if (firstChar == '-') {
1163             negative = true;
1164             index++;
1165         } else if (firstChar == '+')
1166             index++;
1167 
1168         // Handle radix specifier, if present
1169         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1170             index += 2;
1171             radix = 16;
1172         }
1173         else if (nm.startsWith("#", index)) {
1174             index ++;
1175             radix = 16;
1176         }
1177         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1178             index ++;
1179             radix = 8;
1180         }
1181 
1182         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1183             throw new NumberFormatException("Sign character in wrong position");
1184 
1185         try {
1186             result = Long.valueOf(nm.substring(index), radix);
1187             result = negative ? Long.valueOf(-result.longValue()) : result;
1188         } catch (NumberFormatException e) {
1189             // If number is Long.MIN_VALUE, we'll end up here. The next line
1190             // handles this case, and causes any genuine format error to be
1191             // rethrown.
1192             String constant = negative ? ("-" + nm.substring(index))
1193                                        : nm.substring(index);
1194             result = Long.valueOf(constant, radix);
1195         }
1196         return result;
1197     }
1198 
1199     /**
1200      * The value of the {@code Long}.
1201      *
1202      * @serial
1203      */
1204     private final long value;
1205 
1206     /**
1207      * Constructs a newly allocated {@code Long} object that
1208      * represents the specified {@code long} argument.
1209      *
1210      * @param   value   the value to be represented by the
1211      *          {@code Long} object.
1212      */
1213     public Long(long value) {
1214         this.value = value;
1215     }
1216 
1217     /**
1218      * Constructs a newly allocated {@code Long} object that
1219      * represents the {@code long} value indicated by the
1220      * {@code String} parameter. The string is converted to a
1221      * {@code long} value in exactly the manner used by the
1222      * {@code parseLong} method for radix 10.
1223      *
1224      * @param      s   the {@code String} to be converted to a
1225      *             {@code Long}.
1226      * @throws     NumberFormatException  if the {@code String} does not
1227      *             contain a parsable {@code long}.
1228      * @see        java.lang.Long#parseLong(java.lang.String, int)
1229      */
1230     public Long(String s) throws NumberFormatException {
1231         this.value = parseLong(s, 10);
1232     }
1233 
1234     /**
1235      * Returns the value of this {@code Long} as a {@code byte} after
1236      * a narrowing primitive conversion.
1237      * @jls 5.1.3 Narrowing Primitive Conversions
1238      */
1239     public byte byteValue() {
1240         return (byte)value;
1241     }
1242 
1243     /**
1244      * Returns the value of this {@code Long} as a {@code short} after
1245      * a narrowing primitive conversion.
1246      * @jls 5.1.3 Narrowing Primitive Conversions
1247      */
1248     public short shortValue() {
1249         return (short)value;
1250     }
1251 
1252     /**
1253      * Returns the value of this {@code Long} as an {@code int} after
1254      * a narrowing primitive conversion.
1255      * @jls 5.1.3 Narrowing Primitive Conversions
1256      */
1257     public int intValue() {
1258         return (int)value;
1259     }
1260 
1261     /**
1262      * Returns the value of this {@code Long} as a
1263      * {@code long} value.
1264      */
1265     public long longValue() {
1266         return value;
1267     }
1268 
1269     /**
1270      * Returns the value of this {@code Long} as a {@code float} after
1271      * a widening primitive conversion.
1272      * @jls 5.1.2 Widening Primitive Conversions
1273      */
1274     public float floatValue() {
1275         return (float)value;
1276     }
1277 
1278     /**
1279      * Returns the value of this {@code Long} as a {@code double}
1280      * after a widening primitive conversion.
1281      * @jls 5.1.2 Widening Primitive Conversions
1282      */
1283     public double doubleValue() {
1284         return (double)value;
1285     }
1286 
1287     /**
1288      * Returns a {@code String} object representing this
1289      * {@code Long}'s value.  The value is converted to signed
1290      * decimal representation and returned as a string, exactly as if
1291      * the {@code long} value were given as an argument to the
1292      * {@link java.lang.Long#toString(long)} method.
1293      *
1294      * @return  a string representation of the value of this object in
1295      *          base&nbsp;10.
1296      */
1297     public String toString() {
1298         return toString(value);
1299     }
1300 
1301     /**
1302      * Returns a hash code for this {@code Long}. The result is
1303      * the exclusive OR of the two halves of the primitive
1304      * {@code long} value held by this {@code Long}
1305      * object. That is, the hashcode is the value of the expression:
1306      *
1307      * <blockquote>
1308      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1309      * </blockquote>
1310      *
1311      * @return  a hash code value for this object.
1312      */
1313     @Override
1314     public int hashCode() {
1315         return Long.hashCode(value);
1316     }
1317 
1318     /**
1319      * Returns a hash code for a {@code long} value; compatible with
1320      * {@code Long.hashCode()}.
1321      *
1322      * @param value the value to hash
1323      * @return a hash code value for a {@code long} value.
1324      * @since 1.8
1325      */
1326     public static int hashCode(long value) {
1327         return (int)(value ^ (value >>> 32));
1328     }
1329 
1330     /**
1331      * Compares this object to the specified object.  The result is
1332      * {@code true} if and only if the argument is not
1333      * {@code null} and is a {@code Long} object that
1334      * contains the same {@code long} value as this object.
1335      *
1336      * @param   obj   the object to compare with.
1337      * @return  {@code true} if the objects are the same;
1338      *          {@code false} otherwise.
1339      */
1340     public boolean equals(Object obj) {
1341         if (obj instanceof Long) {
1342             return value == ((Long)obj).longValue();
1343         }
1344         return false;
1345     }
1346 
1347     /**
1348      * Determines the {@code long} value of the system property
1349      * with the specified name.
1350      *
1351      * <p>The first argument is treated as the name of a system
1352      * property.  System properties are accessible through the {@link
1353      * java.lang.System#getProperty(java.lang.String)} method. The
1354      * string value of this property is then interpreted as a {@code
1355      * long} value using the grammar supported by {@link Long#decode decode}
1356      * and a {@code Long} object representing this value is returned.
1357      *
1358      * <p>If there is no property with the specified name, if the
1359      * specified name is empty or {@code null}, or if the property
1360      * does not have the correct numeric format, then {@code null} is
1361      * returned.
1362      *
1363      * <p>In other words, this method returns a {@code Long} object
1364      * equal to the value of:
1365      *
1366      * <blockquote>
1367      *  {@code getLong(nm, null)}
1368      * </blockquote>
1369      *
1370      * @param   nm   property name.
1371      * @return  the {@code Long} value of the property.
1372      * @throws  SecurityException for the same reasons as
1373      *          {@link System#getProperty(String) System.getProperty}
1374      * @see     java.lang.System#getProperty(java.lang.String)
1375      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1376      */
1377     public static Long getLong(String nm) {
1378         return getLong(nm, null);
1379     }
1380 
1381     /**
1382      * Determines the {@code long} value of the system property
1383      * with the specified name.
1384      *
1385      * <p>The first argument is treated as the name of a system
1386      * property.  System properties are accessible through the {@link
1387      * java.lang.System#getProperty(java.lang.String)} method. The
1388      * string value of this property is then interpreted as a {@code
1389      * long} value using the grammar supported by {@link Long#decode decode}
1390      * and a {@code Long} object representing this value is returned.
1391      *
1392      * <p>The second argument is the default value. A {@code Long} object
1393      * that represents the value of the second argument is returned if there
1394      * is no property of the specified name, if the property does not have
1395      * the correct numeric format, or if the specified name is empty or null.
1396      *
1397      * <p>In other words, this method returns a {@code Long} object equal
1398      * to the value of:
1399      *
1400      * <blockquote>
1401      *  {@code getLong(nm, new Long(val))}
1402      * </blockquote>
1403      *
1404      * but in practice it may be implemented in a manner such as:
1405      *
1406      * <blockquote><pre>
1407      * Long result = getLong(nm, null);
1408      * return (result == null) ? new Long(val) : result;
1409      * </pre></blockquote>
1410      *
1411      * to avoid the unnecessary allocation of a {@code Long} object when
1412      * the default value is not needed.
1413      *
1414      * @param   nm    property name.
1415      * @param   val   default value.
1416      * @return  the {@code Long} value of the property.
1417      * @throws  SecurityException for the same reasons as
1418      *          {@link System#getProperty(String) System.getProperty}
1419      * @see     java.lang.System#getProperty(java.lang.String)
1420      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1421      */
1422     public static Long getLong(String nm, long val) {
1423         Long result = Long.getLong(nm, null);
1424         return (result == null) ? Long.valueOf(val) : result;
1425     }
1426 
1427     /**
1428      * Returns the {@code long} value of the system property with
1429      * the specified name.  The first argument is treated as the name
1430      * of a system property.  System properties are accessible through
1431      * the {@link java.lang.System#getProperty(java.lang.String)}
1432      * method. The string value of this property is then interpreted
1433      * as a {@code long} value, as per the
1434      * {@link Long#decode decode} method, and a {@code Long} object
1435      * representing this value is returned; in summary:
1436      *
1437      * <ul>
1438      * <li>If the property value begins with the two ASCII characters
1439      * {@code 0x} or the ASCII character {@code #}, not followed by
1440      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1441      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1442      * with radix 16.
1443      * <li>If the property value begins with the ASCII character
1444      * {@code 0} followed by another character, it is parsed as
1445      * an octal integer exactly as by the method {@link
1446      * #valueOf(java.lang.String, int)} with radix 8.
1447      * <li>Otherwise the property value is parsed as a decimal
1448      * integer exactly as by the method
1449      * {@link #valueOf(java.lang.String, int)} with radix 10.
1450      * </ul>
1451      *
1452      * <p>Note that, in every case, neither {@code L}
1453      * ({@code '\u005Cu004C'}) nor {@code l}
1454      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1455      * of the property value as a type indicator, as would be
1456      * permitted in Java programming language source code.
1457      *
1458      * <p>The second argument is the default value. The default value is
1459      * returned if there is no property of the specified name, if the
1460      * property does not have the correct numeric format, or if the
1461      * specified name is empty or {@code null}.
1462      *
1463      * @param   nm   property name.
1464      * @param   val   default value.
1465      * @return  the {@code Long} value of the property.
1466      * @throws  SecurityException for the same reasons as
1467      *          {@link System#getProperty(String) System.getProperty}
1468      * @see     System#getProperty(java.lang.String)
1469      * @see     System#getProperty(java.lang.String, java.lang.String)
1470      */
1471     public static Long getLong(String nm, Long val) {
1472         String v = null;
1473         try {
1474             v = System.getProperty(nm);
1475         } catch (IllegalArgumentException | NullPointerException e) {
1476         }
1477         if (v != null) {
1478             try {
1479                 return Long.decode(v);
1480             } catch (NumberFormatException e) {
1481             }
1482         }
1483         return val;
1484     }
1485 
1486     /**
1487      * Compares two {@code Long} objects numerically.
1488      *
1489      * @param   anotherLong   the {@code Long} to be compared.
1490      * @return  the value {@code 0} if this {@code Long} is
1491      *          equal to the argument {@code Long}; a value less than
1492      *          {@code 0} if this {@code Long} is numerically less
1493      *          than the argument {@code Long}; and a value greater
1494      *          than {@code 0} if this {@code Long} is numerically
1495      *           greater than the argument {@code Long} (signed
1496      *           comparison).
1497      * @since   1.2
1498      */
1499     public int compareTo(Long anotherLong) {
1500         return compare(this.value, anotherLong.value);
1501     }
1502 
1503     /**
1504      * Compares two {@code long} values numerically.
1505      * The value returned is identical to what would be returned by:
1506      * <pre>
1507      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1508      * </pre>
1509      *
1510      * @param  x the first {@code long} to compare
1511      * @param  y the second {@code long} to compare
1512      * @return the value {@code 0} if {@code x == y};
1513      *         a value less than {@code 0} if {@code x < y}; and
1514      *         a value greater than {@code 0} if {@code x > y}
1515      * @since 1.7
1516      */
1517     public static int compare(long x, long y) {
1518         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1519     }
1520 
1521     /**
1522      * Compares two {@code long} values numerically treating the values
1523      * as unsigned.
1524      *
1525      * @param  x the first {@code long} to compare
1526      * @param  y the second {@code long} to compare
1527      * @return the value {@code 0} if {@code x == y}; a value less
1528      *         than {@code 0} if {@code x < y} as unsigned values; and
1529      *         a value greater than {@code 0} if {@code x > y} as
1530      *         unsigned values
1531      * @since 1.8
1532      */
1533     public static int compareUnsigned(long x, long y) {
1534         return compare(x + MIN_VALUE, y + MIN_VALUE);
1535     }
1536 
1537 
1538     /**
1539      * Returns the unsigned quotient of dividing the first argument by
1540      * the second where each argument and the result is interpreted as
1541      * an unsigned value.
1542      *
1543      * <p>Note that in two's complement arithmetic, the three other
1544      * basic arithmetic operations of add, subtract, and multiply are
1545      * bit-wise identical if the two operands are regarded as both
1546      * being signed or both being unsigned.  Therefore separate {@code
1547      * addUnsigned}, etc. methods are not provided.
1548      *
1549      * @param dividend the value to be divided
1550      * @param divisor the value doing the dividing
1551      * @return the unsigned quotient of the first argument divided by
1552      * the second argument
1553      * @see #remainderUnsigned
1554      * @since 1.8
1555      */
1556     public static long divideUnsigned(long dividend, long divisor) {
1557         if (divisor < 0L) { // signed comparison
1558             // Answer must be 0 or 1 depending on relative magnitude
1559             // of dividend and divisor.
1560             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1561         }
1562 
1563         if (dividend > 0) //  Both inputs non-negative
1564             return dividend/divisor;
1565         else {
1566             /*
1567              * For simple code, leveraging BigInteger.  Longer and faster
1568              * code written directly in terms of operations on longs is
1569              * possible; see "Hacker's Delight" for divide and remainder
1570              * algorithms.
1571              */
1572             return toUnsignedBigInteger(dividend).
1573                 divide(toUnsignedBigInteger(divisor)).longValue();
1574         }
1575     }
1576 
1577     /**
1578      * Returns the unsigned remainder from dividing the first argument
1579      * by the second where each argument and the result is interpreted
1580      * as an unsigned value.
1581      *
1582      * @param dividend the value to be divided
1583      * @param divisor the value doing the dividing
1584      * @return the unsigned remainder of the first argument divided by
1585      * the second argument
1586      * @see #divideUnsigned
1587      * @since 1.8
1588      */
1589     public static long remainderUnsigned(long dividend, long divisor) {
1590         if (dividend > 0 && divisor > 0) { // signed comparisons
1591             return dividend % divisor;
1592         } else {
1593             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1594                 return dividend;
1595             else
1596                 return toUnsignedBigInteger(dividend).
1597                     remainder(toUnsignedBigInteger(divisor)).longValue();
1598         }
1599     }
1600 
1601     // Bit Twiddling
1602 
1603     /**
1604      * The number of bits used to represent a {@code long} value in two's
1605      * complement binary form.
1606      *
1607      * @since 1.5
1608      */
1609     @Native public static final int SIZE = 64;
1610 
1611     /**
1612      * The number of bytes used to represent a {@code long} value in two's
1613      * complement binary form.
1614      *
1615      * @since 1.8
1616      */
1617     public static final int BYTES = SIZE / Byte.SIZE;
1618 
1619     /**
1620      * Returns a {@code long} value with at most a single one-bit, in the
1621      * position of the highest-order ("leftmost") one-bit in the specified
1622      * {@code long} value.  Returns zero if the specified value has no
1623      * one-bits in its two's complement binary representation, that is, if it
1624      * is equal to zero.
1625      *
1626      * @param i the value whose highest one bit is to be computed
1627      * @return a {@code long} value with a single one-bit, in the position
1628      *     of the highest-order one-bit in the specified value, or zero if
1629      *     the specified value is itself equal to zero.
1630      * @since 1.5
1631      */
1632     public static long highestOneBit(long i) {
1633         // HD, Figure 3-1
1634         i |= (i >>  1);
1635         i |= (i >>  2);
1636         i |= (i >>  4);
1637         i |= (i >>  8);
1638         i |= (i >> 16);
1639         i |= (i >> 32);
1640         return i - (i >>> 1);
1641     }
1642 
1643     /**
1644      * Returns a {@code long} value with at most a single one-bit, in the
1645      * position of the lowest-order ("rightmost") one-bit in the specified
1646      * {@code long} value.  Returns zero if the specified value has no
1647      * one-bits in its two's complement binary representation, that is, if it
1648      * is equal to zero.
1649      *
1650      * @param i the value whose lowest one bit is to be computed
1651      * @return a {@code long} value with a single one-bit, in the position
1652      *     of the lowest-order one-bit in the specified value, or zero if
1653      *     the specified value is itself equal to zero.
1654      * @since 1.5
1655      */
1656     public static long lowestOneBit(long i) {
1657         // HD, Section 2-1
1658         return i & -i;
1659     }
1660 
1661     /**
1662      * Returns the number of zero bits preceding the highest-order
1663      * ("leftmost") one-bit in the two's complement binary representation
1664      * of the specified {@code long} value.  Returns 64 if the
1665      * specified value has no one-bits in its two's complement representation,
1666      * in other words if it is equal to zero.
1667      *
1668      * <p>Note that this method is closely related to the logarithm base 2.
1669      * For all positive {@code long} values x:
1670      * <ul>
1671      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1672      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1673      * </ul>
1674      *
1675      * @param i the value whose number of leading zeros is to be computed
1676      * @return the number of zero bits preceding the highest-order
1677      *     ("leftmost") one-bit in the two's complement binary representation
1678      *     of the specified {@code long} value, or 64 if the value
1679      *     is equal to zero.
1680      * @since 1.5
1681      */
1682     public static int numberOfLeadingZeros(long i) {
1683         // HD, Figure 5-6
1684          if (i == 0)
1685             return 64;
1686         int n = 1;
1687         int x = (int)(i >>> 32);
1688         if (x == 0) { n += 32; x = (int)i; }
1689         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1690         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1691         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1692         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1693         n -= x >>> 31;
1694         return n;
1695     }
1696 
1697     /**
1698      * Returns the number of zero bits following the lowest-order ("rightmost")
1699      * one-bit in the two's complement binary representation of the specified
1700      * {@code long} value.  Returns 64 if the specified value has no
1701      * one-bits in its two's complement representation, in other words if it is
1702      * equal to zero.
1703      *
1704      * @param i the value whose number of trailing zeros is to be computed
1705      * @return the number of zero bits following the lowest-order ("rightmost")
1706      *     one-bit in the two's complement binary representation of the
1707      *     specified {@code long} value, or 64 if the value is equal
1708      *     to zero.
1709      * @since 1.5
1710      */
1711     public static int numberOfTrailingZeros(long i) {
1712         // HD, Figure 5-14
1713         int x, y;
1714         if (i == 0) return 64;
1715         int n = 63;
1716         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1717         y = x <<16; if (y != 0) { n = n -16; x = y; }
1718         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1719         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1720         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1721         return n - ((x << 1) >>> 31);
1722     }
1723 
1724     /**
1725      * Returns the number of one-bits in the two's complement binary
1726      * representation of the specified {@code long} value.  This function is
1727      * sometimes referred to as the <i>population count</i>.
1728      *
1729      * @param i the value whose bits are to be counted
1730      * @return the number of one-bits in the two's complement binary
1731      *     representation of the specified {@code long} value.
1732      * @since 1.5
1733      */
1734      public static int bitCount(long i) {
1735         // HD, Figure 5-14
1736         i = i - ((i >>> 1) & 0x5555555555555555L);
1737         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1738         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1739         i = i + (i >>> 8);
1740         i = i + (i >>> 16);
1741         i = i + (i >>> 32);
1742         return (int)i & 0x7f;
1743      }
1744 
1745     /**
1746      * Returns the value obtained by rotating the two's complement binary
1747      * representation of the specified {@code long} value left by the
1748      * specified number of bits.  (Bits shifted out of the left hand, or
1749      * high-order, side reenter on the right, or low-order.)
1750      *
1751      * <p>Note that left rotation with a negative distance is equivalent to
1752      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1753      * distance)}.  Note also that rotation by any multiple of 64 is a
1754      * no-op, so all but the last six bits of the rotation distance can be
1755      * ignored, even if the distance is negative: {@code rotateLeft(val,
1756      * distance) == rotateLeft(val, distance & 0x3F)}.
1757      *
1758      * @param i the value whose bits are to be rotated left
1759      * @param distance the number of bit positions to rotate left
1760      * @return the value obtained by rotating the two's complement binary
1761      *     representation of the specified {@code long} value left by the
1762      *     specified number of bits.
1763      * @since 1.5
1764      */
1765     public static long rotateLeft(long i, int distance) {
1766         return (i << distance) | (i >>> -distance);
1767     }
1768 
1769     /**
1770      * Returns the value obtained by rotating the two's complement binary
1771      * representation of the specified {@code long} value right by the
1772      * specified number of bits.  (Bits shifted out of the right hand, or
1773      * low-order, side reenter on the left, or high-order.)
1774      *
1775      * <p>Note that right rotation with a negative distance is equivalent to
1776      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1777      * distance)}.  Note also that rotation by any multiple of 64 is a
1778      * no-op, so all but the last six bits of the rotation distance can be
1779      * ignored, even if the distance is negative: {@code rotateRight(val,
1780      * distance) == rotateRight(val, distance & 0x3F)}.
1781      *
1782      * @param i the value whose bits are to be rotated right
1783      * @param distance the number of bit positions to rotate right
1784      * @return the value obtained by rotating the two's complement binary
1785      *     representation of the specified {@code long} value right by the
1786      *     specified number of bits.
1787      * @since 1.5
1788      */
1789     public static long rotateRight(long i, int distance) {
1790         return (i >>> distance) | (i << -distance);
1791     }
1792 
1793     /**
1794      * Returns the value obtained by reversing the order of the bits in the
1795      * two's complement binary representation of the specified {@code long}
1796      * value.
1797      *
1798      * @param i the value to be reversed
1799      * @return the value obtained by reversing order of the bits in the
1800      *     specified {@code long} value.
1801      * @since 1.5
1802      */
1803     public static long reverse(long i) {
1804         // HD, Figure 7-1
1805         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1806         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1807         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1808         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1809         i = (i << 48) | ((i & 0xffff0000L) << 16) |
1810             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1811         return i;
1812     }
1813 
1814     /**
1815      * Returns the signum function of the specified {@code long} value.  (The
1816      * return value is -1 if the specified value is negative; 0 if the
1817      * specified value is zero; and 1 if the specified value is positive.)
1818      *
1819      * @param i the value whose signum is to be computed
1820      * @return the signum function of the specified {@code long} value.
1821      * @since 1.5
1822      */
1823     public static int signum(long i) {
1824         // HD, Section 2-7
1825         return (int) ((i >> 63) | (-i >>> 63));
1826     }
1827 
1828     /**
1829      * Returns the value obtained by reversing the order of the bytes in the
1830      * two's complement representation of the specified {@code long} value.
1831      *
1832      * @param i the value whose bytes are to be reversed
1833      * @return the value obtained by reversing the bytes in the specified
1834      *     {@code long} value.
1835      * @since 1.5
1836      */
1837     public static long reverseBytes(long i) {
1838         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1839         return (i << 48) | ((i & 0xffff0000L) << 16) |
1840             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1841     }
1842 
1843     /**
1844      * Adds two {@code long} values together as per the + operator.
1845      *
1846      * @param a the first operand
1847      * @param b the second operand
1848      * @return the sum of {@code a} and {@code b}
1849      * @see java.util.function.BinaryOperator
1850      * @since 1.8
1851      */
1852     public static long sum(long a, long b) {
1853         return a + b;
1854     }
1855 
1856     /**
1857      * Returns the greater of two {@code long} values
1858      * as if by calling {@link Math#max(long, long) Math.max}.
1859      *
1860      * @param a the first operand
1861      * @param b the second operand
1862      * @return the greater of {@code a} and {@code b}
1863      * @see java.util.function.BinaryOperator
1864      * @since 1.8
1865      */
1866     public static long max(long a, long b) {
1867         return Math.max(a, b);
1868     }
1869 
1870     /**
1871      * Returns the smaller of two {@code long} values
1872      * as if by calling {@link Math#min(long, long) Math.min}.
1873      *
1874      * @param a the first operand
1875      * @param b the second operand
1876      * @return the smaller of {@code a} and {@code b}
1877      * @see java.util.function.BinaryOperator
1878      * @since 1.8
1879      */
1880     public static long min(long a, long b) {
1881         return Math.min(a, b);
1882     }
1883 
1884     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1885     @Native private static final long serialVersionUID = 4290774380558885855L;
1886 }