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 import static java.lang.String.COMPACT_STRINGS;
  34 import static java.lang.String.LATIN1;
  35 import static java.lang.String.UTF16;
  36 
  37 /**
  38  * The {@code Long} class wraps a value of the primitive type {@code
  39  * long} in an object. An object of type {@code Long} contains a
  40  * single field whose type is {@code long}.
  41  *
  42  * <p> In addition, this class provides several methods for converting
  43  * a {@code long} to a {@code String} and a {@code String} to a {@code
  44  * long}, as well as other constants and methods useful when dealing
  45  * with a {@code long}.
  46  *
  47  * <p>Implementation note: The implementations of the "bit twiddling"
  48  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  49  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  50  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  51  * Delight</i>, (Addison Wesley, 2002).
  52  *
  53  * @author  Lee Boynton
  54  * @author  Arthur van Hoff
  55  * @author  Josh Bloch
  56  * @author  Joseph D. Darcy
  57  * @since   1.0
  58  */
  59 public final class Long extends Number implements Comparable<Long> {
  60     /**
  61      * A constant holding the minimum value a {@code long} can
  62      * have, -2<sup>63</sup>.
  63      */
  64     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  65 
  66     /**
  67      * A constant holding the maximum value a {@code long} can
  68      * have, 2<sup>63</sup>-1.
  69      */
  70     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  71 
  72     /**
  73      * The {@code Class} instance representing the primitive type
  74      * {@code long}.
  75      *
  76      * @since   1.1
  77      */
  78     @SuppressWarnings("unchecked")
  79     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  80 
  81     /**
  82      * Returns a string representation of the first argument in the
  83      * radix specified by the second argument.
  84      *
  85      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  86      * or larger than {@code Character.MAX_RADIX}, then the radix
  87      * {@code 10} is used instead.
  88      *
  89      * <p>If the first argument is negative, the first element of the
  90      * result is the ASCII minus sign {@code '-'}
  91      * ({@code '\u005Cu002d'}). If the first argument is not
  92      * negative, no sign character appears in the result.
  93      *
  94      * <p>The remaining characters of the result represent the magnitude
  95      * of the first argument. If the magnitude is zero, it is
  96      * represented by a single zero character {@code '0'}
  97      * ({@code '\u005Cu0030'}); otherwise, the first character of
  98      * the representation of the magnitude will not be the zero
  99      * character.  The following ASCII characters are used as digits:
 100      *
 101      * <blockquote>
 102      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 103      * </blockquote>
 104      *
 105      * These are {@code '\u005Cu0030'} through
 106      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 107      * {@code '\u005Cu007a'}. If {@code radix} is
 108      * <var>N</var>, then the first <var>N</var> of these characters
 109      * are used as radix-<var>N</var> digits in the order shown. Thus,
 110      * the digits for hexadecimal (radix 16) are
 111      * {@code 0123456789abcdef}. If uppercase letters are
 112      * desired, the {@link java.lang.String#toUpperCase()} method may
 113      * be called on the result:
 114      *
 115      * <blockquote>
 116      *  {@code Long.toString(n, 16).toUpperCase()}
 117      * </blockquote>
 118      *
 119      * @param   i       a {@code long} to be converted to a string.
 120      * @param   radix   the radix to use in the string representation.
 121      * @return  a string representation of the argument in the specified radix.
 122      * @see     java.lang.Character#MAX_RADIX
 123      * @see     java.lang.Character#MIN_RADIX
 124      */
 125     public static String toString(long i, int radix) {
 126         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 127             radix = 10;
 128         if (radix == 10)
 129             return toString(i);
 130 
 131         if (COMPACT_STRINGS) {
 132             byte[] buf = new byte[65];
 133             int charPos = 64;
 134             boolean negative = (i < 0);
 135 
 136             if (!negative) {
 137                 i = -i;
 138             }
 139 
 140             while (i <= -radix) {
 141                 buf[charPos--] = (byte)Integer.digits[(int)(-(i % radix))];
 142                 i = i / radix;
 143             }
 144             buf[charPos] = (byte)Integer.digits[(int)(-i)];
 145 
 146             if (negative) {
 147                 buf[--charPos] = '-';
 148             }
 149             return StringLatin1.newString(buf, charPos, (65 - charPos));
 150         }
 151         return toStringUTF16(i, radix);
 152     }
 153 
 154     private static String toStringUTF16(long i, int radix) {
 155         byte[] buf = new byte[65 * 2];
 156         int charPos = 64;
 157         boolean negative = (i < 0);
 158         if (!negative) {
 159             i = -i;
 160         }
 161         while (i <= -radix) {
 162             StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 163             i = i / radix;
 164         }
 165         StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 166         if (negative) {
 167             StringUTF16.putChar(buf, --charPos, '-');
 168         }
 169         return StringUTF16.newString(buf, charPos, (65 - charPos));
 170     }
 171 
 172     /**
 173      * Returns a string representation of the first argument as an
 174      * unsigned integer value in the radix specified by the second
 175      * argument.
 176      *
 177      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 178      * or larger than {@code Character.MAX_RADIX}, then the radix
 179      * {@code 10} is used instead.
 180      *
 181      * <p>Note that since the first argument is treated as an unsigned
 182      * value, no leading sign character is printed.
 183      *
 184      * <p>If the magnitude is zero, it is represented by a single zero
 185      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 186      * the first character of the representation of the magnitude will
 187      * not be the zero character.
 188      *
 189      * <p>The behavior of radixes and the characters used as digits
 190      * are the same as {@link #toString(long, int) toString}.
 191      *
 192      * @param   i       an integer to be converted to an unsigned string.
 193      * @param   radix   the radix to use in the string representation.
 194      * @return  an unsigned string representation of the argument in the specified radix.
 195      * @see     #toString(long, int)
 196      * @since 1.8
 197      */
 198     public static String toUnsignedString(long i, int radix) {
 199         if (i >= 0)
 200             return toString(i, radix);
 201         else {
 202             switch (radix) {
 203             case 2:
 204                 return toBinaryString(i);
 205 
 206             case 4:
 207                 return toUnsignedString0(i, 2);
 208 
 209             case 8:
 210                 return toOctalString(i);
 211 
 212             case 10:
 213                 /*
 214                  * We can get the effect of an unsigned division by 10
 215                  * on a long value by first shifting right, yielding a
 216                  * positive value, and then dividing by 5.  This
 217                  * allows the last digit and preceding digits to be
 218                  * isolated more quickly than by an initial conversion
 219                  * to BigInteger.
 220                  */
 221                 long quot = (i >>> 1) / 5;
 222                 long rem = i - quot * 10;
 223                 return toString(quot) + rem;
 224 
 225             case 16:
 226                 return toHexString(i);
 227 
 228             case 32:
 229                 return toUnsignedString0(i, 5);
 230 
 231             default:
 232                 return toUnsignedBigInteger(i).toString(radix);
 233             }
 234         }
 235     }
 236 
 237     /**
 238      * Return a BigInteger equal to the unsigned value of the
 239      * argument.
 240      */
 241     private static BigInteger toUnsignedBigInteger(long i) {
 242         if (i >= 0L)
 243             return BigInteger.valueOf(i);
 244         else {
 245             int upper = (int) (i >>> 32);
 246             int lower = (int) i;
 247 
 248             // return (upper << 32) + lower
 249             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 250                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 251         }
 252     }
 253 
 254     /**
 255      * Returns a string representation of the {@code long}
 256      * argument as an unsigned integer in base&nbsp;16.
 257      *
 258      * <p>The unsigned {@code long} value is the argument plus
 259      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 260      * equal to the argument.  This value is converted to a string of
 261      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 262      * leading {@code 0}s.
 263      *
 264      * <p>The value of the argument can be recovered from the returned
 265      * string {@code s} by calling {@link
 266      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 267      * 16)}.
 268      *
 269      * <p>If the unsigned magnitude is zero, it is represented by a
 270      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 271      * otherwise, the first character of the representation of the
 272      * unsigned magnitude will not be the zero character. The
 273      * following characters are used as hexadecimal digits:
 274      *
 275      * <blockquote>
 276      *  {@code 0123456789abcdef}
 277      * </blockquote>
 278      *
 279      * These are the characters {@code '\u005Cu0030'} through
 280      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 281      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 282      * the {@link java.lang.String#toUpperCase()} method may be called
 283      * on the result:
 284      *
 285      * <blockquote>
 286      *  {@code Long.toHexString(n).toUpperCase()}
 287      * </blockquote>
 288      *
 289      * @param   i   a {@code long} to be converted to a string.
 290      * @return  the string representation of the unsigned {@code long}
 291      *          value represented by the argument in hexadecimal
 292      *          (base&nbsp;16).
 293      * @see #parseUnsignedLong(String, int)
 294      * @see #toUnsignedString(long, int)
 295      * @since   1.0.2
 296      */
 297     public static String toHexString(long i) {
 298         return toUnsignedString0(i, 4);
 299     }
 300 
 301     /**
 302      * Returns a string representation of the {@code long}
 303      * argument as an unsigned integer in base&nbsp;8.
 304      *
 305      * <p>The unsigned {@code long} value is the argument plus
 306      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 307      * equal to the argument.  This value is converted to a string of
 308      * ASCII digits in octal (base&nbsp;8) with no extra leading
 309      * {@code 0}s.
 310      *
 311      * <p>The value of the argument can be recovered from the returned
 312      * string {@code s} by calling {@link
 313      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 314      * 8)}.
 315      *
 316      * <p>If the unsigned magnitude is zero, it is represented by a
 317      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 318      * otherwise, the first character of the representation of the
 319      * unsigned magnitude will not be the zero character. The
 320      * following characters are used as octal digits:
 321      *
 322      * <blockquote>
 323      *  {@code 01234567}
 324      * </blockquote>
 325      *
 326      * These are the characters {@code '\u005Cu0030'} through
 327      * {@code '\u005Cu0037'}.
 328      *
 329      * @param   i   a {@code long} to be converted to a string.
 330      * @return  the string representation of the unsigned {@code long}
 331      *          value represented by the argument in octal (base&nbsp;8).
 332      * @see #parseUnsignedLong(String, int)
 333      * @see #toUnsignedString(long, int)
 334      * @since   1.0.2
 335      */
 336     public static String toOctalString(long i) {
 337         return toUnsignedString0(i, 3);
 338     }
 339 
 340     /**
 341      * Returns a string representation of the {@code long}
 342      * argument as an unsigned integer in base&nbsp;2.
 343      *
 344      * <p>The unsigned {@code long} value is the argument plus
 345      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 346      * equal to the argument.  This value is converted to a string of
 347      * ASCII digits in binary (base&nbsp;2) with no extra leading
 348      * {@code 0}s.
 349      *
 350      * <p>The value of the argument can be recovered from the returned
 351      * string {@code s} by calling {@link
 352      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 353      * 2)}.
 354      *
 355      * <p>If the unsigned magnitude is zero, it is represented by a
 356      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 357      * otherwise, the first character of the representation of the
 358      * unsigned magnitude will not be the zero character. The
 359      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 360      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 361      *
 362      * @param   i   a {@code long} to be converted to a string.
 363      * @return  the string representation of the unsigned {@code long}
 364      *          value represented by the argument in binary (base&nbsp;2).
 365      * @see #parseUnsignedLong(String, int)
 366      * @see #toUnsignedString(long, int)
 367      * @since   1.0.2
 368      */
 369     public static String toBinaryString(long i) {
 370         return toUnsignedString0(i, 1);
 371     }
 372 
 373     /**
 374      * Format a long (treated as unsigned) into a String.
 375      * @param val the value to format
 376      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 377      */
 378     static String toUnsignedString0(long val, int shift) {
 379         // assert shift > 0 && shift <=5 : "Illegal shift value";
 380         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 381         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 382         if (COMPACT_STRINGS) {
 383             byte[] buf = new byte[chars];
 384             formatUnsignedLong0(val, shift, buf, 0, chars);
 385             return new String(buf, LATIN1);
 386         } else {
 387             byte[] buf = new byte[chars * 2];
 388             formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
 389             return new String(buf, UTF16);
 390         }
 391     }
 392 
 393     /**
 394      * Format a long (treated as unsigned) into a character buffer. If
 395      * {@code len} exceeds the formatted ASCII representation of {@code val},
 396      * {@code buf} will be padded with leading zeroes.
 397      *
 398      * @param val the unsigned long to format
 399      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 400      * @param buf the character buffer to write to
 401      * @param offset the offset in the destination buffer to start at
 402      * @param len the number of characters to write
 403      */
 404      static void formatUnsignedLong(long val, int shift, char[] buf, int offset, int len) {
 405         // assert shift > 0 && shift <=5 : "Illegal shift value";
 406         // assert offset >= 0 && offset < buf.length : "illegal offset";
 407         // assert len > 0 && (offset + len) <= buf.length : "illegal length";
 408         int charPos = offset + len;
 409         int radix = 1 << shift;
 410         int mask = radix - 1;
 411         do {
 412             buf[--charPos] = Integer.digits[((int) val) & mask];
 413             val >>>= shift;
 414         } while (charPos > offset);
 415     }
 416 
 417     /** byte[]/LATIN1 version    */
 418     static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
 419         int charPos = offset + len;
 420         int radix = 1 << shift;
 421         int mask = radix - 1;
 422         do {
 423             buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
 424             val >>>= shift;
 425         } while (charPos > offset);
 426     }
 427 
 428     /** byte[]/UTF16 version    */
 429     static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
 430         int charPos = offset + len;
 431         int radix = 1 << shift;
 432         int mask = radix - 1;
 433         do {
 434             StringUTF16.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
 435             val >>>= shift;
 436         } while (charPos > offset);
 437     }
 438 
 439     /**
 440      * Returns a {@code String} object representing the specified
 441      * {@code long}.  The argument is converted to signed decimal
 442      * representation and returned as a string, exactly as if the
 443      * argument and the radix 10 were given as arguments to the {@link
 444      * #toString(long, int)} method.
 445      *
 446      * @param   i   a {@code long} to be converted.
 447      * @return  a string representation of the argument in base&nbsp;10.
 448      */
 449     public static String toString(long i) {
 450         int size = stringSize(i);
 451         if (COMPACT_STRINGS) {
 452             byte[] buf = new byte[size];
 453             getChars(i, size, buf);
 454             return new String(buf, LATIN1);
 455         } else {
 456             byte[] buf = new byte[size * 2];
 457             getCharsUTF16(i, size, buf);
 458             return new String(buf, UTF16);
 459         }
 460     }
 461 
 462     /**
 463      * Returns a string representation of the argument as an unsigned
 464      * decimal value.
 465      *
 466      * The argument is converted to unsigned decimal representation
 467      * and returned as a string exactly as if the argument and radix
 468      * 10 were given as arguments to the {@link #toUnsignedString(long,
 469      * int)} method.
 470      *
 471      * @param   i  an integer to be converted to an unsigned string.
 472      * @return  an unsigned string representation of the argument.
 473      * @see     #toUnsignedString(long, int)
 474      * @since 1.8
 475      */
 476     public static String toUnsignedString(long i) {
 477         return toUnsignedString(i, 10);
 478     }
 479 
 480     /**
 481      * Places characters representing the long i into the
 482      * character array buf. The characters are placed into
 483      * the buffer backwards starting with the least significant
 484      * digit at the specified index (exclusive), and working
 485      * backwards from there.
 486      *
 487      * @implNote This method converts positive inputs into negative
 488      * values, to cover the Long.MIN_VALUE case. Converting otherwise
 489      * (negative to positive) will expose -Long.MIN_VALUE that overflows
 490      * long.
 491      *
 492      * @param i     value to convert
 493      * @param index next index, after the least significant digit
 494      * @param buf   target buffer, Latin1-encoded
 495      * @return index of the most significant digit or minus sign, if present
 496      */
 497     static int getChars(long i, int index, byte[] buf) {
 498         long q;
 499         int r;
 500         int charPos = index;
 501 
 502         boolean negative = (i < 0);
 503         if (!negative) {
 504             i = -i;
 505         }
 506 
 507         // Get 2 digits/iteration using longs until quotient fits into an int
 508         while (i <= Integer.MIN_VALUE) {
 509             q = i / 100;
 510             r = (int)((q * 100) - i);
 511             i = q;
 512             buf[--charPos] = Integer.DigitOnes[r];
 513             buf[--charPos] = Integer.DigitTens[r];
 514         }
 515 
 516         // Get 2 digits/iteration using ints
 517         int q2;
 518         int i2 = (int)i;
 519         while (i2 <= -100) {
 520             q2 = i2 / 100;
 521             r  = (q2 * 100) - i2;
 522             i2 = q2;
 523             buf[--charPos] = Integer.DigitOnes[r];
 524             buf[--charPos] = Integer.DigitTens[r];
 525         }
 526 
 527         // We know there are at most two digits left at this point.
 528         q2 = i2 / 10;
 529         r  = (q2 * 10) - i2;
 530         buf[--charPos] = (byte)('0' + r);
 531 
 532         // Whatever left is the remaining digit.
 533         if (q2 < 0) {
 534             buf[--charPos] = (byte)('0' - q2);
 535         }
 536 
 537         if (negative) {
 538             buf[--charPos] = (byte)'-';
 539         }
 540         return charPos;
 541     }
 542 
 543     /**
 544      * This is a variant of {@link #getChars(long, int, byte[])}, but for
 545      * UTF-16 coder.
 546      *
 547      * @param i     value to convert
 548      * @param index next index, after the least significant digit
 549      * @param buf   target buffer, UTF16-coded.
 550      * @return index of the most significant digit or minus sign, if present
 551      */
 552     static int getCharsUTF16(long i, int index, byte[] buf) {
 553         long q;
 554         int r;
 555         int charPos = index;
 556 
 557         boolean negative = (i < 0);
 558         if (!negative) {
 559             i = -i;
 560         }
 561 
 562         // Get 2 digits/iteration using longs until quotient fits into an int
 563         while (i <= Integer.MIN_VALUE) {
 564             q = i / 100;
 565             r = (int)((q * 100) - i);
 566             i = q;
 567             StringUTF16.putChar(buf, --charPos, Integer.DigitOnes[r]);
 568             StringUTF16.putChar(buf, --charPos, Integer.DigitTens[r]);
 569         }
 570 
 571         // Get 2 digits/iteration using ints
 572         int q2;
 573         int i2 = (int)i;
 574         while (i2 <= -100) {
 575             q2 = i2 / 100;
 576             r  = (q2 * 100) - i2;
 577             i2 = q2;
 578             StringUTF16.putChar(buf, --charPos, Integer.DigitOnes[r]);
 579             StringUTF16.putChar(buf, --charPos, Integer.DigitTens[r]);
 580         }
 581 
 582         // We know there are at most two digits left at this point.
 583         q2 = i2 / 10;
 584         r  = (q2 * 10) - i2;
 585         StringUTF16.putChar(buf, --charPos, '0' + r);
 586 
 587         // Whatever left is the remaining digit.
 588         if (q2 < 0) {
 589             StringUTF16.putChar(buf, --charPos, '0' - q2);
 590         }
 591 
 592         if (negative) {
 593             StringUTF16.putChar(buf, --charPos, '-');
 594         }
 595         return charPos;
 596     }
 597 
 598     /**
 599      * Returns the string representation size for a given long value.
 600      *
 601      * @param x long value
 602      * @return string size
 603      *
 604      * @implNote There are other ways to compute this: e.g. binary search,
 605      * but values are biased heavily towards zero, and therefore linear search
 606      * wins. The iteration results are also routinely inlined in the generated
 607      * code after loop unrolling.
 608      */
 609     static int stringSize(long x) {
 610         int d = 1;
 611         if (x >= 0) {
 612             d = 0;
 613             x = -x;
 614         }
 615         long p = -10;
 616         for (int i = 1; i < 19; i++) {
 617             if (x > p)
 618                 return i + d;
 619             p = 10 * p;
 620         }
 621         return 19 + d;
 622     }
 623 
 624     /**
 625      * Parses the string argument as a signed {@code long} in the
 626      * radix specified by the second argument. The characters in the
 627      * string must all be digits of the specified radix (as determined
 628      * by whether {@link java.lang.Character#digit(char, int)} returns
 629      * a nonnegative value), except that the first character may be an
 630      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 631      * indicate a negative value or an ASCII plus sign {@code '+'}
 632      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 633      * resulting {@code long} value is returned.
 634      *
 635      * <p>Note that neither the character {@code L}
 636      * ({@code '\u005Cu004C'}) nor {@code l}
 637      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 638      * of the string as a type indicator, as would be permitted in
 639      * Java programming language source code - except that either
 640      * {@code L} or {@code l} may appear as a digit for a
 641      * radix greater than or equal to 22.
 642      *
 643      * <p>An exception of type {@code NumberFormatException} is
 644      * thrown if any of the following situations occurs:
 645      * <ul>
 646      *
 647      * <li>The first argument is {@code null} or is a string of
 648      * length zero.
 649      *
 650      * <li>The {@code radix} is either smaller than {@link
 651      * java.lang.Character#MIN_RADIX} or larger than {@link
 652      * java.lang.Character#MAX_RADIX}.
 653      *
 654      * <li>Any character of the string is not a digit of the specified
 655      * radix, except that the first character may be a minus sign
 656      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 657      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 658      * longer than length 1.
 659      *
 660      * <li>The value represented by the string is not a value of type
 661      *      {@code long}.
 662      * </ul>
 663      *
 664      * <p>Examples:
 665      * <blockquote><pre>
 666      * parseLong("0", 10) returns 0L
 667      * parseLong("473", 10) returns 473L
 668      * parseLong("+42", 10) returns 42L
 669      * parseLong("-0", 10) returns 0L
 670      * parseLong("-FF", 16) returns -255L
 671      * parseLong("1100110", 2) returns 102L
 672      * parseLong("99", 8) throws a NumberFormatException
 673      * parseLong("Hazelnut", 10) throws a NumberFormatException
 674      * parseLong("Hazelnut", 36) returns 1356099454469L
 675      * </pre></blockquote>
 676      *
 677      * @param      s       the {@code String} containing the
 678      *                     {@code long} representation to be parsed.
 679      * @param      radix   the radix to be used while parsing {@code s}.
 680      * @return     the {@code long} represented by the string argument in
 681      *             the specified radix.
 682      * @throws     NumberFormatException  if the string does not contain a
 683      *             parsable {@code long}.
 684      */
 685     public static long parseLong(String s, int radix)
 686               throws NumberFormatException
 687     {
 688         if (s == null) {
 689             throw new NumberFormatException("null");
 690         }
 691 
 692         if (radix < Character.MIN_RADIX) {
 693             throw new NumberFormatException("radix " + radix +
 694                                             " less than Character.MIN_RADIX");
 695         }
 696         if (radix > Character.MAX_RADIX) {
 697             throw new NumberFormatException("radix " + radix +
 698                                             " greater than Character.MAX_RADIX");
 699         }
 700 
 701         boolean negative = false;
 702         int i = 0, len = s.length();
 703         long limit = -Long.MAX_VALUE;
 704 
 705         if (len > 0) {
 706             char firstChar = s.charAt(0);
 707             if (firstChar < '0') { // Possible leading "+" or "-"
 708                 if (firstChar == '-') {
 709                     negative = true;
 710                     limit = Long.MIN_VALUE;
 711                 } else if (firstChar != '+') {
 712                     throw NumberFormatException.forInputString(s);
 713                 }
 714 
 715                 if (len == 1) { // Cannot have lone "+" or "-"
 716                     throw NumberFormatException.forInputString(s);
 717                 }
 718                 i++;
 719             }
 720             long multmin = limit / radix;
 721             long result = 0;
 722             while (i < len) {
 723                 // Accumulating negatively avoids surprises near MAX_VALUE
 724                 int digit = Character.digit(s.charAt(i++),radix);
 725                 if (digit < 0 || result < multmin) {
 726                     throw NumberFormatException.forInputString(s);
 727                 }
 728                 result *= radix;
 729                 if (result < limit + digit) {
 730                     throw NumberFormatException.forInputString(s);
 731                 }
 732                 result -= digit;
 733             }
 734             return negative ? result : -result;
 735         } else {
 736             throw NumberFormatException.forInputString(s);
 737         }
 738     }
 739 
 740     /**
 741      * Parses the {@link CharSequence} argument as a signed {@code long} in
 742      * the specified {@code radix}, beginning at the specified
 743      * {@code beginIndex} and extending to {@code endIndex - 1}.
 744      *
 745      * <p>The method does not take steps to guard against the
 746      * {@code CharSequence} being mutated while parsing.
 747      *
 748      * @param      s   the {@code CharSequence} containing the {@code long}
 749      *                  representation to be parsed
 750      * @param      beginIndex   the beginning index, inclusive.
 751      * @param      endIndex     the ending index, exclusive.
 752      * @param      radix   the radix to be used while parsing {@code s}.
 753      * @return     the signed {@code long} represented by the subsequence in
 754      *             the specified radix.
 755      * @throws     NullPointerException  if {@code s} is null.
 756      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 757      *             negative, or if {@code beginIndex} is greater than
 758      *             {@code endIndex} or if {@code endIndex} is greater than
 759      *             {@code s.length()}.
 760      * @throws     NumberFormatException  if the {@code CharSequence} does not
 761      *             contain a parsable {@code int} in the specified
 762      *             {@code radix}, or if {@code radix} is either smaller than
 763      *             {@link java.lang.Character#MIN_RADIX} or larger than
 764      *             {@link java.lang.Character#MAX_RADIX}.
 765      * @since  9
 766      */
 767     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 768                 throws NumberFormatException {
 769         s = Objects.requireNonNull(s);
 770 
 771         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 772             throw new IndexOutOfBoundsException();
 773         }
 774         if (radix < Character.MIN_RADIX) {
 775             throw new NumberFormatException("radix " + radix +
 776                     " less than Character.MIN_RADIX");
 777         }
 778         if (radix > Character.MAX_RADIX) {
 779             throw new NumberFormatException("radix " + radix +
 780                     " greater than Character.MAX_RADIX");
 781         }
 782 
 783         boolean negative = false;
 784         int i = beginIndex;
 785         long limit = -Long.MAX_VALUE;
 786 
 787         if (i < endIndex) {
 788             char firstChar = s.charAt(i);
 789             if (firstChar < '0') { // Possible leading "+" or "-"
 790                 if (firstChar == '-') {
 791                     negative = true;
 792                     limit = Long.MIN_VALUE;
 793                 } else if (firstChar != '+') {
 794                     throw NumberFormatException.forCharSequence(s, beginIndex,
 795                             endIndex, i);
 796                 }
 797                 i++;
 798             }
 799             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 800                 throw NumberFormatException.forCharSequence(s, beginIndex,
 801                         endIndex, i);
 802             }
 803             long multmin = limit / radix;
 804             long result = 0;
 805             while (i < endIndex) {
 806                 // Accumulating negatively avoids surprises near MAX_VALUE
 807                 int digit = Character.digit(s.charAt(i), radix);
 808                 if (digit < 0 || result < multmin) {
 809                     throw NumberFormatException.forCharSequence(s, beginIndex,
 810                             endIndex, i);
 811                 }
 812                 result *= radix;
 813                 if (result < limit + digit) {
 814                     throw NumberFormatException.forCharSequence(s, beginIndex,
 815                             endIndex, i);
 816                 }
 817                 i++;
 818                 result -= digit;
 819             }
 820             return negative ? result : -result;
 821         } else {
 822             throw new NumberFormatException("");
 823         }
 824     }
 825 
 826     /**
 827      * Parses the string argument as a signed decimal {@code long}.
 828      * The characters in the string must all be decimal digits, except
 829      * that the first character may be an ASCII minus sign {@code '-'}
 830      * ({@code \u005Cu002D'}) to indicate a negative value or an
 831      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 832      * indicate a positive value. The resulting {@code long} value is
 833      * returned, exactly as if the argument and the radix {@code 10}
 834      * were given as arguments to the {@link
 835      * #parseLong(java.lang.String, int)} method.
 836      *
 837      * <p>Note that neither the character {@code L}
 838      * ({@code '\u005Cu004C'}) nor {@code l}
 839      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 840      * of the string as a type indicator, as would be permitted in
 841      * Java programming language source code.
 842      *
 843      * @param      s   a {@code String} containing the {@code long}
 844      *             representation to be parsed
 845      * @return     the {@code long} represented by the argument in
 846      *             decimal.
 847      * @throws     NumberFormatException  if the string does not contain a
 848      *             parsable {@code long}.
 849      */
 850     public static long parseLong(String s) throws NumberFormatException {
 851         return parseLong(s, 10);
 852     }
 853 
 854     /**
 855      * Parses the string argument as an unsigned {@code long} in the
 856      * radix specified by the second argument.  An unsigned integer
 857      * maps the values usually associated with negative numbers to
 858      * positive numbers larger than {@code MAX_VALUE}.
 859      *
 860      * The characters in the string must all be digits of the
 861      * specified radix (as determined by whether {@link
 862      * java.lang.Character#digit(char, int)} returns a nonnegative
 863      * value), except that the first character may be an ASCII plus
 864      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 865      * integer value is returned.
 866      *
 867      * <p>An exception of type {@code NumberFormatException} is
 868      * thrown if any of the following situations occurs:
 869      * <ul>
 870      * <li>The first argument is {@code null} or is a string of
 871      * length zero.
 872      *
 873      * <li>The radix is either smaller than
 874      * {@link java.lang.Character#MIN_RADIX} or
 875      * larger than {@link java.lang.Character#MAX_RADIX}.
 876      *
 877      * <li>Any character of the string is not a digit of the specified
 878      * radix, except that the first character may be a plus sign
 879      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 880      * string is longer than length 1.
 881      *
 882      * <li>The value represented by the string is larger than the
 883      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 884      *
 885      * </ul>
 886      *
 887      *
 888      * @param      s   the {@code String} containing the unsigned integer
 889      *                  representation to be parsed
 890      * @param      radix   the radix to be used while parsing {@code s}.
 891      * @return     the unsigned {@code long} represented by the string
 892      *             argument in the specified radix.
 893      * @throws     NumberFormatException if the {@code String}
 894      *             does not contain a parsable {@code long}.
 895      * @since 1.8
 896      */
 897     public static long parseUnsignedLong(String s, int radix)
 898                 throws NumberFormatException {
 899         if (s == null)  {
 900             throw new NumberFormatException("null");
 901         }
 902 
 903         int len = s.length();
 904         if (len > 0) {
 905             char firstChar = s.charAt(0);
 906             if (firstChar == '-') {
 907                 throw new
 908                     NumberFormatException(String.format("Illegal leading minus sign " +
 909                                                        "on unsigned string %s.", s));
 910             } else {
 911                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 912                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 913                     return parseLong(s, radix);
 914                 }
 915 
 916                 // No need for range checks on len due to testing above.
 917                 long first = parseLong(s, 0, len - 1, radix);
 918                 int second = Character.digit(s.charAt(len - 1), radix);
 919                 if (second < 0) {
 920                     throw new NumberFormatException("Bad digit at end of " + s);
 921                 }
 922                 long result = first * radix + second;
 923 
 924                 /*
 925                  * Test leftmost bits of multiprecision extension of first*radix
 926                  * for overflow. The number of bits needed is defined by
 927                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 928                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 929                  * overflow is tested by splitting guard in the ranges
 930                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 931                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 932                  * on a value which does not include a prime factor in the legal
 933                  * radix range.
 934                  */
 935                 int guard = radix * (int) (first >>> 57);
 936                 if (guard >= 128 ||
 937                     (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 938                     /*
 939                      * For purposes of exposition, the programmatic statements
 940                      * below should be taken to be multi-precision, i.e., not
 941                      * subject to overflow.
 942                      *
 943                      * A) Condition guard >= 128:
 944                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 945                      * hence always overflow.
 946                      *
 947                      * B) Condition guard < 92:
 948                      * Define left7 = first >>> 57.
 949                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 950                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 951                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 952                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 953                      * never overflow.
 954                      *
 955                      * C) Condition 92 <= guard < 128:
 956                      * first*radix + second >= radix*left7*2^57 + second
 957                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 958                      *
 959                      * D) Condition guard < 128:
 960                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 961                      * so
 962                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 963                      * thus
 964                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 965                      * whence
 966                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 967                      *
 968                      * E) Conditions C, D, and result >= 0:
 969                      * C and D combined imply the mathematical result
 970                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 971                      * bound is therefore negative as a signed long, but the
 972                      * upper bound is too small to overflow again after the
 973                      * signed long overflows to positive above 2^64 - 1. Hence
 974                      * result >= 0 implies overflow given C and D.
 975                      */
 976                     throw new NumberFormatException(String.format("String value %s exceeds " +
 977                                                                   "range of unsigned long.", s));
 978                 }
 979                 return result;
 980             }
 981         } else {
 982             throw NumberFormatException.forInputString(s);
 983         }
 984     }
 985 
 986     /**
 987      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 988      * the specified {@code radix}, beginning at the specified
 989      * {@code beginIndex} and extending to {@code endIndex - 1}.
 990      *
 991      * <p>The method does not take steps to guard against the
 992      * {@code CharSequence} being mutated while parsing.
 993      *
 994      * @param      s   the {@code CharSequence} containing the unsigned
 995      *                 {@code long} representation to be parsed
 996      * @param      beginIndex   the beginning index, inclusive.
 997      * @param      endIndex     the ending index, exclusive.
 998      * @param      radix   the radix to be used while parsing {@code s}.
 999      * @return     the unsigned {@code long} represented by the subsequence in
1000      *             the specified radix.
1001      * @throws     NullPointerException  if {@code s} is null.
1002      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
1003      *             negative, or if {@code beginIndex} is greater than
1004      *             {@code endIndex} or if {@code endIndex} is greater than
1005      *             {@code s.length()}.
1006      * @throws     NumberFormatException  if the {@code CharSequence} does not
1007      *             contain a parsable unsigned {@code long} in the specified
1008      *             {@code radix}, or if {@code radix} is either smaller than
1009      *             {@link java.lang.Character#MIN_RADIX} or larger than
1010      *             {@link java.lang.Character#MAX_RADIX}.
1011      * @since  9
1012      */
1013     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
1014                 throws NumberFormatException {
1015         s = Objects.requireNonNull(s);
1016 
1017         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
1018             throw new IndexOutOfBoundsException();
1019         }
1020         int start = beginIndex, len = endIndex - beginIndex;
1021 
1022         if (len > 0) {
1023             char firstChar = s.charAt(start);
1024             if (firstChar == '-') {
1025                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
1026                         "on unsigned string %s.", s.subSequence(start, start + len)));
1027             } else {
1028                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
1029                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
1030                     return parseLong(s, start, start + len, radix);
1031                 }
1032 
1033                 // No need for range checks on end due to testing above.
1034                 long first = parseLong(s, start, start + len - 1, radix);
1035                 int second = Character.digit(s.charAt(start + len - 1), radix);
1036                 if (second < 0) {
1037                     throw new NumberFormatException("Bad digit at end of " +
1038                             s.subSequence(start, start + len));
1039                 }
1040                 long result = first * radix + second;
1041 
1042                 /*
1043                  * Test leftmost bits of multiprecision extension of first*radix
1044                  * for overflow. The number of bits needed is defined by
1045                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
1046                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
1047                  * overflow is tested by splitting guard in the ranges
1048                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
1049                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
1050                  * on a value which does not include a prime factor in the legal
1051                  * radix range.
1052                  */
1053                 int guard = radix * (int) (first >>> 57);
1054                 if (guard >= 128 ||
1055                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
1056                     /*
1057                      * For purposes of exposition, the programmatic statements
1058                      * below should be taken to be multi-precision, i.e., not
1059                      * subject to overflow.
1060                      *
1061                      * A) Condition guard >= 128:
1062                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
1063                      * hence always overflow.
1064                      *
1065                      * B) Condition guard < 92:
1066                      * Define left7 = first >>> 57.
1067                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
1068                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
1069                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
1070                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
1071                      * never overflow.
1072                      *
1073                      * C) Condition 92 <= guard < 128:
1074                      * first*radix + second >= radix*left7*2^57 + second
1075                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
1076                      *
1077                      * D) Condition guard < 128:
1078                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
1079                      * so
1080                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
1081                      * thus
1082                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
1083                      * whence
1084                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
1085                      *
1086                      * E) Conditions C, D, and result >= 0:
1087                      * C and D combined imply the mathematical result
1088                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
1089                      * bound is therefore negative as a signed long, but the
1090                      * upper bound is too small to overflow again after the
1091                      * signed long overflows to positive above 2^64 - 1. Hence
1092                      * result >= 0 implies overflow given C and D.
1093                      */
1094                     throw new NumberFormatException(String.format("String value %s exceeds " +
1095                             "range of unsigned long.", s.subSequence(start, start + len)));
1096                 }
1097                 return result;
1098             }
1099         } else {
1100             throw NumberFormatException.forInputString("");
1101         }
1102     }
1103 
1104     /**
1105      * Parses the string argument as an unsigned decimal {@code long}. The
1106      * characters in the string must all be decimal digits, except
1107      * that the first character may be an ASCII plus sign {@code
1108      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
1109      * is returned, exactly as if the argument and the radix 10 were
1110      * given as arguments to the {@link
1111      * #parseUnsignedLong(java.lang.String, int)} method.
1112      *
1113      * @param s   a {@code String} containing the unsigned {@code long}
1114      *            representation to be parsed
1115      * @return    the unsigned {@code long} value represented by the decimal string argument
1116      * @throws    NumberFormatException  if the string does not contain a
1117      *            parsable unsigned integer.
1118      * @since 1.8
1119      */
1120     public static long parseUnsignedLong(String s) throws NumberFormatException {
1121         return parseUnsignedLong(s, 10);
1122     }
1123 
1124     /**
1125      * Returns a {@code Long} object holding the value
1126      * extracted from the specified {@code String} when parsed
1127      * with the radix given by the second argument.  The first
1128      * argument is interpreted as representing a signed
1129      * {@code long} in the radix specified by the second
1130      * argument, exactly as if the arguments were given to the {@link
1131      * #parseLong(java.lang.String, int)} method. The result is a
1132      * {@code Long} object that represents the {@code long}
1133      * value specified by the string.
1134      *
1135      * <p>In other words, this method returns a {@code Long} object equal
1136      * to the value of:
1137      *
1138      * <blockquote>
1139      *  {@code new Long(Long.parseLong(s, radix))}
1140      * </blockquote>
1141      *
1142      * @param      s       the string to be parsed
1143      * @param      radix   the radix to be used in interpreting {@code s}
1144      * @return     a {@code Long} object holding the value
1145      *             represented by the string argument in the specified
1146      *             radix.
1147      * @throws     NumberFormatException  If the {@code String} does not
1148      *             contain a parsable {@code long}.
1149      */
1150     public static Long valueOf(String s, int radix) throws NumberFormatException {
1151         return Long.valueOf(parseLong(s, radix));
1152     }
1153 
1154     /**
1155      * Returns a {@code Long} object holding the value
1156      * of the specified {@code String}. The argument is
1157      * interpreted as representing a signed decimal {@code long},
1158      * exactly as if the argument were given to the {@link
1159      * #parseLong(java.lang.String)} method. The result is a
1160      * {@code Long} object that represents the integer value
1161      * specified by the string.
1162      *
1163      * <p>In other words, this method returns a {@code Long} object
1164      * equal to the value of:
1165      *
1166      * <blockquote>
1167      *  {@code new Long(Long.parseLong(s))}
1168      * </blockquote>
1169      *
1170      * @param      s   the string to be parsed.
1171      * @return     a {@code Long} object holding the value
1172      *             represented by the string argument.
1173      * @throws     NumberFormatException  If the string cannot be parsed
1174      *             as a {@code long}.
1175      */
1176     public static Long valueOf(String s) throws NumberFormatException
1177     {
1178         return Long.valueOf(parseLong(s, 10));
1179     }
1180 
1181     private static class LongCache {
1182         private LongCache(){}
1183 
1184         static final Long cache[] = new Long[-(-128) + 127 + 1];
1185 
1186         static {
1187             for(int i = 0; i < cache.length; i++)
1188                 cache[i] = new Long(i - 128);
1189         }
1190     }
1191 
1192     /**
1193      * Returns a {@code Long} instance representing the specified
1194      * {@code long} value.
1195      * If a new {@code Long} instance is not required, this method
1196      * should generally be used in preference to the constructor
1197      * {@link #Long(long)}, as this method is likely to yield
1198      * significantly better space and time performance by caching
1199      * frequently requested values.
1200      *
1201      * Note that unlike the {@linkplain Integer#valueOf(int)
1202      * corresponding method} in the {@code Integer} class, this method
1203      * is <em>not</em> required to cache values within a particular
1204      * range.
1205      *
1206      * @param  l a long value.
1207      * @return a {@code Long} instance representing {@code l}.
1208      * @since  1.5
1209      */
1210     @HotSpotIntrinsicCandidate
1211     public static Long valueOf(long l) {
1212         final int offset = 128;
1213         if (l >= -128 && l <= 127) { // will cache
1214             return LongCache.cache[(int)l + offset];
1215         }
1216         return new Long(l);
1217     }
1218 
1219     /**
1220      * Decodes a {@code String} into a {@code Long}.
1221      * Accepts decimal, hexadecimal, and octal numbers given by the
1222      * following grammar:
1223      *
1224      * <blockquote>
1225      * <dl>
1226      * <dt><i>DecodableString:</i>
1227      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1228      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1229      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1230      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1231      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1232      *
1233      * <dt><i>Sign:</i>
1234      * <dd>{@code -}
1235      * <dd>{@code +}
1236      * </dl>
1237      * </blockquote>
1238      *
1239      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1240      * are as defined in section 3.10.1 of
1241      * <cite>The Java&trade; Language Specification</cite>,
1242      * except that underscores are not accepted between digits.
1243      *
1244      * <p>The sequence of characters following an optional
1245      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1246      * "{@code #}", or leading zero) is parsed as by the {@code
1247      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1248      * This sequence of characters must represent a positive value or
1249      * a {@link NumberFormatException} will be thrown.  The result is
1250      * negated if first character of the specified {@code String} is
1251      * the minus sign.  No whitespace characters are permitted in the
1252      * {@code String}.
1253      *
1254      * @param     nm the {@code String} to decode.
1255      * @return    a {@code Long} object holding the {@code long}
1256      *            value represented by {@code nm}
1257      * @throws    NumberFormatException  if the {@code String} does not
1258      *            contain a parsable {@code long}.
1259      * @see java.lang.Long#parseLong(String, int)
1260      * @since 1.2
1261      */
1262     public static Long decode(String nm) throws NumberFormatException {
1263         int radix = 10;
1264         int index = 0;
1265         boolean negative = false;
1266         Long result;
1267 
1268         if (nm.length() == 0)
1269             throw new NumberFormatException("Zero length string");
1270         char firstChar = nm.charAt(0);
1271         // Handle sign, if present
1272         if (firstChar == '-') {
1273             negative = true;
1274             index++;
1275         } else if (firstChar == '+')
1276             index++;
1277 
1278         // Handle radix specifier, if present
1279         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1280             index += 2;
1281             radix = 16;
1282         }
1283         else if (nm.startsWith("#", index)) {
1284             index ++;
1285             radix = 16;
1286         }
1287         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1288             index ++;
1289             radix = 8;
1290         }
1291 
1292         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1293             throw new NumberFormatException("Sign character in wrong position");
1294 
1295         try {
1296             result = Long.valueOf(nm.substring(index), radix);
1297             result = negative ? Long.valueOf(-result.longValue()) : result;
1298         } catch (NumberFormatException e) {
1299             // If number is Long.MIN_VALUE, we'll end up here. The next line
1300             // handles this case, and causes any genuine format error to be
1301             // rethrown.
1302             String constant = negative ? ("-" + nm.substring(index))
1303                                        : nm.substring(index);
1304             result = Long.valueOf(constant, radix);
1305         }
1306         return result;
1307     }
1308 
1309     /**
1310      * The value of the {@code Long}.
1311      *
1312      * @serial
1313      */
1314     private final long value;
1315 
1316     /**
1317      * Constructs a newly allocated {@code Long} object that
1318      * represents the specified {@code long} argument.
1319      *
1320      * @param   value   the value to be represented by the
1321      *          {@code Long} object.
1322      */
1323     public Long(long value) {
1324         this.value = value;
1325     }
1326 
1327     /**
1328      * Constructs a newly allocated {@code Long} object that
1329      * represents the {@code long} value indicated by the
1330      * {@code String} parameter. The string is converted to a
1331      * {@code long} value in exactly the manner used by the
1332      * {@code parseLong} method for radix 10.
1333      *
1334      * @param      s   the {@code String} to be converted to a
1335      *             {@code Long}.
1336      * @throws     NumberFormatException  if the {@code String} does not
1337      *             contain a parsable {@code long}.
1338      * @see        java.lang.Long#parseLong(java.lang.String, int)
1339      */
1340     public Long(String s) throws NumberFormatException {
1341         this.value = parseLong(s, 10);
1342     }
1343 
1344     /**
1345      * Returns the value of this {@code Long} as a {@code byte} after
1346      * a narrowing primitive conversion.
1347      * @jls 5.1.3 Narrowing Primitive Conversions
1348      */
1349     public byte byteValue() {
1350         return (byte)value;
1351     }
1352 
1353     /**
1354      * Returns the value of this {@code Long} as a {@code short} after
1355      * a narrowing primitive conversion.
1356      * @jls 5.1.3 Narrowing Primitive Conversions
1357      */
1358     public short shortValue() {
1359         return (short)value;
1360     }
1361 
1362     /**
1363      * Returns the value of this {@code Long} as an {@code int} after
1364      * a narrowing primitive conversion.
1365      * @jls 5.1.3 Narrowing Primitive Conversions
1366      */
1367     public int intValue() {
1368         return (int)value;
1369     }
1370 
1371     /**
1372      * Returns the value of this {@code Long} as a
1373      * {@code long} value.
1374      */
1375     @HotSpotIntrinsicCandidate
1376     public long longValue() {
1377         return value;
1378     }
1379 
1380     /**
1381      * Returns the value of this {@code Long} as a {@code float} after
1382      * a widening primitive conversion.
1383      * @jls 5.1.2 Widening Primitive Conversions
1384      */
1385     public float floatValue() {
1386         return (float)value;
1387     }
1388 
1389     /**
1390      * Returns the value of this {@code Long} as a {@code double}
1391      * after a widening primitive conversion.
1392      * @jls 5.1.2 Widening Primitive Conversions
1393      */
1394     public double doubleValue() {
1395         return (double)value;
1396     }
1397 
1398     /**
1399      * Returns a {@code String} object representing this
1400      * {@code Long}'s value.  The value is converted to signed
1401      * decimal representation and returned as a string, exactly as if
1402      * the {@code long} value were given as an argument to the
1403      * {@link java.lang.Long#toString(long)} method.
1404      *
1405      * @return  a string representation of the value of this object in
1406      *          base&nbsp;10.
1407      */
1408     public String toString() {
1409         return toString(value);
1410     }
1411 
1412     /**
1413      * Returns a hash code for this {@code Long}. The result is
1414      * the exclusive OR of the two halves of the primitive
1415      * {@code long} value held by this {@code Long}
1416      * object. That is, the hashcode is the value of the expression:
1417      *
1418      * <blockquote>
1419      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1420      * </blockquote>
1421      *
1422      * @return  a hash code value for this object.
1423      */
1424     @Override
1425     public int hashCode() {
1426         return Long.hashCode(value);
1427     }
1428 
1429     /**
1430      * Returns a hash code for a {@code long} value; compatible with
1431      * {@code Long.hashCode()}.
1432      *
1433      * @param value the value to hash
1434      * @return a hash code value for a {@code long} value.
1435      * @since 1.8
1436      */
1437     public static int hashCode(long value) {
1438         return (int)(value ^ (value >>> 32));
1439     }
1440 
1441     /**
1442      * Compares this object to the specified object.  The result is
1443      * {@code true} if and only if the argument is not
1444      * {@code null} and is a {@code Long} object that
1445      * contains the same {@code long} value as this object.
1446      *
1447      * @param   obj   the object to compare with.
1448      * @return  {@code true} if the objects are the same;
1449      *          {@code false} otherwise.
1450      */
1451     public boolean equals(Object obj) {
1452         if (obj instanceof Long) {
1453             return value == ((Long)obj).longValue();
1454         }
1455         return false;
1456     }
1457 
1458     /**
1459      * Determines the {@code long} value of the system property
1460      * with the specified name.
1461      *
1462      * <p>The first argument is treated as the name of a system
1463      * property.  System properties are accessible through the {@link
1464      * java.lang.System#getProperty(java.lang.String)} method. The
1465      * string value of this property is then interpreted as a {@code
1466      * long} value using the grammar supported by {@link Long#decode decode}
1467      * and a {@code Long} object representing this value is returned.
1468      *
1469      * <p>If there is no property with the specified name, if the
1470      * specified name is empty or {@code null}, or if the property
1471      * does not have the correct numeric format, then {@code null} is
1472      * returned.
1473      *
1474      * <p>In other words, this method returns a {@code Long} object
1475      * equal to the value of:
1476      *
1477      * <blockquote>
1478      *  {@code getLong(nm, null)}
1479      * </blockquote>
1480      *
1481      * @param   nm   property name.
1482      * @return  the {@code Long} value of the property.
1483      * @throws  SecurityException for the same reasons as
1484      *          {@link System#getProperty(String) System.getProperty}
1485      * @see     java.lang.System#getProperty(java.lang.String)
1486      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1487      */
1488     public static Long getLong(String nm) {
1489         return getLong(nm, null);
1490     }
1491 
1492     /**
1493      * Determines the {@code long} value of the system property
1494      * with the specified name.
1495      *
1496      * <p>The first argument is treated as the name of a system
1497      * property.  System properties are accessible through the {@link
1498      * java.lang.System#getProperty(java.lang.String)} method. The
1499      * string value of this property is then interpreted as a {@code
1500      * long} value using the grammar supported by {@link Long#decode decode}
1501      * and a {@code Long} object representing this value is returned.
1502      *
1503      * <p>The second argument is the default value. A {@code Long} object
1504      * that represents the value of the second argument is returned if there
1505      * is no property of the specified name, if the property does not have
1506      * the correct numeric format, or if the specified name is empty or null.
1507      *
1508      * <p>In other words, this method returns a {@code Long} object equal
1509      * to the value of:
1510      *
1511      * <blockquote>
1512      *  {@code getLong(nm, new Long(val))}
1513      * </blockquote>
1514      *
1515      * but in practice it may be implemented in a manner such as:
1516      *
1517      * <blockquote><pre>
1518      * Long result = getLong(nm, null);
1519      * return (result == null) ? new Long(val) : result;
1520      * </pre></blockquote>
1521      *
1522      * to avoid the unnecessary allocation of a {@code Long} object when
1523      * the default value is not needed.
1524      *
1525      * @param   nm    property name.
1526      * @param   val   default value.
1527      * @return  the {@code Long} value of the property.
1528      * @throws  SecurityException for the same reasons as
1529      *          {@link System#getProperty(String) System.getProperty}
1530      * @see     java.lang.System#getProperty(java.lang.String)
1531      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1532      */
1533     public static Long getLong(String nm, long val) {
1534         Long result = Long.getLong(nm, null);
1535         return (result == null) ? Long.valueOf(val) : result;
1536     }
1537 
1538     /**
1539      * Returns the {@code long} value of the system property with
1540      * the specified name.  The first argument is treated as the name
1541      * of a system property.  System properties are accessible through
1542      * the {@link java.lang.System#getProperty(java.lang.String)}
1543      * method. The string value of this property is then interpreted
1544      * as a {@code long} value, as per the
1545      * {@link Long#decode decode} method, and a {@code Long} object
1546      * representing this value is returned; in summary:
1547      *
1548      * <ul>
1549      * <li>If the property value begins with the two ASCII characters
1550      * {@code 0x} or the ASCII character {@code #}, not followed by
1551      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1552      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1553      * with radix 16.
1554      * <li>If the property value begins with the ASCII character
1555      * {@code 0} followed by another character, it is parsed as
1556      * an octal integer exactly as by the method {@link
1557      * #valueOf(java.lang.String, int)} with radix 8.
1558      * <li>Otherwise the property value is parsed as a decimal
1559      * integer exactly as by the method
1560      * {@link #valueOf(java.lang.String, int)} with radix 10.
1561      * </ul>
1562      *
1563      * <p>Note that, in every case, neither {@code L}
1564      * ({@code '\u005Cu004C'}) nor {@code l}
1565      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1566      * of the property value as a type indicator, as would be
1567      * permitted in Java programming language source code.
1568      *
1569      * <p>The second argument is the default value. The default value is
1570      * returned if there is no property of the specified name, if the
1571      * property does not have the correct numeric format, or if the
1572      * specified name is empty or {@code null}.
1573      *
1574      * @param   nm   property name.
1575      * @param   val   default value.
1576      * @return  the {@code Long} value of the property.
1577      * @throws  SecurityException for the same reasons as
1578      *          {@link System#getProperty(String) System.getProperty}
1579      * @see     System#getProperty(java.lang.String)
1580      * @see     System#getProperty(java.lang.String, java.lang.String)
1581      */
1582     public static Long getLong(String nm, Long val) {
1583         String v = null;
1584         try {
1585             v = System.getProperty(nm);
1586         } catch (IllegalArgumentException | NullPointerException e) {
1587         }
1588         if (v != null) {
1589             try {
1590                 return Long.decode(v);
1591             } catch (NumberFormatException e) {
1592             }
1593         }
1594         return val;
1595     }
1596 
1597     /**
1598      * Compares two {@code Long} objects numerically.
1599      *
1600      * @param   anotherLong   the {@code Long} to be compared.
1601      * @return  the value {@code 0} if this {@code Long} is
1602      *          equal to the argument {@code Long}; a value less than
1603      *          {@code 0} if this {@code Long} is numerically less
1604      *          than the argument {@code Long}; and a value greater
1605      *          than {@code 0} if this {@code Long} is numerically
1606      *           greater than the argument {@code Long} (signed
1607      *           comparison).
1608      * @since   1.2
1609      */
1610     public int compareTo(Long anotherLong) {
1611         return compare(this.value, anotherLong.value);
1612     }
1613 
1614     /**
1615      * Compares two {@code long} values numerically.
1616      * The value returned is identical to what would be returned by:
1617      * <pre>
1618      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1619      * </pre>
1620      *
1621      * @param  x the first {@code long} to compare
1622      * @param  y the second {@code long} to compare
1623      * @return the value {@code 0} if {@code x == y};
1624      *         a value less than {@code 0} if {@code x < y}; and
1625      *         a value greater than {@code 0} if {@code x > y}
1626      * @since 1.7
1627      */
1628     public static int compare(long x, long y) {
1629         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1630     }
1631 
1632     /**
1633      * Compares two {@code long} values numerically treating the values
1634      * as unsigned.
1635      *
1636      * @param  x the first {@code long} to compare
1637      * @param  y the second {@code long} to compare
1638      * @return the value {@code 0} if {@code x == y}; a value less
1639      *         than {@code 0} if {@code x < y} as unsigned values; and
1640      *         a value greater than {@code 0} if {@code x > y} as
1641      *         unsigned values
1642      * @since 1.8
1643      */
1644     public static int compareUnsigned(long x, long y) {
1645         return compare(x + MIN_VALUE, y + MIN_VALUE);
1646     }
1647 
1648 
1649     /**
1650      * Returns the unsigned quotient of dividing the first argument by
1651      * the second where each argument and the result is interpreted as
1652      * an unsigned value.
1653      *
1654      * <p>Note that in two's complement arithmetic, the three other
1655      * basic arithmetic operations of add, subtract, and multiply are
1656      * bit-wise identical if the two operands are regarded as both
1657      * being signed or both being unsigned.  Therefore separate {@code
1658      * addUnsigned}, etc. methods are not provided.
1659      *
1660      * @param dividend the value to be divided
1661      * @param divisor the value doing the dividing
1662      * @return the unsigned quotient of the first argument divided by
1663      * the second argument
1664      * @see #remainderUnsigned
1665      * @since 1.8
1666      */
1667     public static long divideUnsigned(long dividend, long divisor) {
1668         if (divisor < 0L) { // signed comparison
1669             // Answer must be 0 or 1 depending on relative magnitude
1670             // of dividend and divisor.
1671             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1672         }
1673 
1674         if (dividend > 0) //  Both inputs non-negative
1675             return dividend/divisor;
1676         else {
1677             /*
1678              * For simple code, leveraging BigInteger.  Longer and faster
1679              * code written directly in terms of operations on longs is
1680              * possible; see "Hacker's Delight" for divide and remainder
1681              * algorithms.
1682              */
1683             return toUnsignedBigInteger(dividend).
1684                 divide(toUnsignedBigInteger(divisor)).longValue();
1685         }
1686     }
1687 
1688     /**
1689      * Returns the unsigned remainder from dividing the first argument
1690      * by the second where each argument and the result is interpreted
1691      * as an unsigned value.
1692      *
1693      * @param dividend the value to be divided
1694      * @param divisor the value doing the dividing
1695      * @return the unsigned remainder of the first argument divided by
1696      * the second argument
1697      * @see #divideUnsigned
1698      * @since 1.8
1699      */
1700     public static long remainderUnsigned(long dividend, long divisor) {
1701         if (dividend > 0 && divisor > 0) { // signed comparisons
1702             return dividend % divisor;
1703         } else {
1704             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1705                 return dividend;
1706             else
1707                 return toUnsignedBigInteger(dividend).
1708                     remainder(toUnsignedBigInteger(divisor)).longValue();
1709         }
1710     }
1711 
1712     // Bit Twiddling
1713 
1714     /**
1715      * The number of bits used to represent a {@code long} value in two's
1716      * complement binary form.
1717      *
1718      * @since 1.5
1719      */
1720     @Native public static final int SIZE = 64;
1721 
1722     /**
1723      * The number of bytes used to represent a {@code long} value in two's
1724      * complement binary form.
1725      *
1726      * @since 1.8
1727      */
1728     public static final int BYTES = SIZE / Byte.SIZE;
1729 
1730     /**
1731      * Returns a {@code long} value with at most a single one-bit, in the
1732      * position of the highest-order ("leftmost") one-bit in the specified
1733      * {@code long} value.  Returns zero if the specified value has no
1734      * one-bits in its two's complement binary representation, that is, if it
1735      * is equal to zero.
1736      *
1737      * @param i the value whose highest one bit is to be computed
1738      * @return a {@code long} value with a single one-bit, in the position
1739      *     of the highest-order one-bit in the specified value, or zero if
1740      *     the specified value is itself equal to zero.
1741      * @since 1.5
1742      */
1743     public static long highestOneBit(long i) {
1744         // HD, Figure 3-1
1745         i |= (i >>  1);
1746         i |= (i >>  2);
1747         i |= (i >>  4);
1748         i |= (i >>  8);
1749         i |= (i >> 16);
1750         i |= (i >> 32);
1751         return i - (i >>> 1);
1752     }
1753 
1754     /**
1755      * Returns a {@code long} value with at most a single one-bit, in the
1756      * position of the lowest-order ("rightmost") one-bit in the specified
1757      * {@code long} value.  Returns zero if the specified value has no
1758      * one-bits in its two's complement binary representation, that is, if it
1759      * is equal to zero.
1760      *
1761      * @param i the value whose lowest one bit is to be computed
1762      * @return a {@code long} value with a single one-bit, in the position
1763      *     of the lowest-order one-bit in the specified value, or zero if
1764      *     the specified value is itself equal to zero.
1765      * @since 1.5
1766      */
1767     public static long lowestOneBit(long i) {
1768         // HD, Section 2-1
1769         return i & -i;
1770     }
1771 
1772     /**
1773      * Returns the number of zero bits preceding the highest-order
1774      * ("leftmost") one-bit in the two's complement binary representation
1775      * of the specified {@code long} value.  Returns 64 if the
1776      * specified value has no one-bits in its two's complement representation,
1777      * in other words if it is equal to zero.
1778      *
1779      * <p>Note that this method is closely related to the logarithm base 2.
1780      * For all positive {@code long} values x:
1781      * <ul>
1782      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1783      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1784      * </ul>
1785      *
1786      * @param i the value whose number of leading zeros is to be computed
1787      * @return the number of zero bits preceding the highest-order
1788      *     ("leftmost") one-bit in the two's complement binary representation
1789      *     of the specified {@code long} value, or 64 if the value
1790      *     is equal to zero.
1791      * @since 1.5
1792      */
1793     @HotSpotIntrinsicCandidate
1794     public static int numberOfLeadingZeros(long i) {
1795         // HD, Figure 5-6
1796          if (i == 0)
1797             return 64;
1798         int n = 1;
1799         int x = (int)(i >>> 32);
1800         if (x == 0) { n += 32; x = (int)i; }
1801         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1802         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1803         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1804         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1805         n -= x >>> 31;
1806         return n;
1807     }
1808 
1809     /**
1810      * Returns the number of zero bits following the lowest-order ("rightmost")
1811      * one-bit in the two's complement binary representation of the specified
1812      * {@code long} value.  Returns 64 if the specified value has no
1813      * one-bits in its two's complement representation, in other words if it is
1814      * equal to zero.
1815      *
1816      * @param i the value whose number of trailing zeros is to be computed
1817      * @return the number of zero bits following the lowest-order ("rightmost")
1818      *     one-bit in the two's complement binary representation of the
1819      *     specified {@code long} value, or 64 if the value is equal
1820      *     to zero.
1821      * @since 1.5
1822      */
1823     @HotSpotIntrinsicCandidate
1824     public static int numberOfTrailingZeros(long i) {
1825         // HD, Figure 5-14
1826         int x, y;
1827         if (i == 0) return 64;
1828         int n = 63;
1829         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1830         y = x <<16; if (y != 0) { n = n -16; x = y; }
1831         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1832         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1833         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1834         return n - ((x << 1) >>> 31);
1835     }
1836 
1837     /**
1838      * Returns the number of one-bits in the two's complement binary
1839      * representation of the specified {@code long} value.  This function is
1840      * sometimes referred to as the <i>population count</i>.
1841      *
1842      * @param i the value whose bits are to be counted
1843      * @return the number of one-bits in the two's complement binary
1844      *     representation of the specified {@code long} value.
1845      * @since 1.5
1846      */
1847      @HotSpotIntrinsicCandidate
1848      public static int bitCount(long i) {
1849         // HD, Figure 5-2
1850         i = i - ((i >>> 1) & 0x5555555555555555L);
1851         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1852         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1853         i = i + (i >>> 8);
1854         i = i + (i >>> 16);
1855         i = i + (i >>> 32);
1856         return (int)i & 0x7f;
1857      }
1858 
1859     /**
1860      * Returns the value obtained by rotating the two's complement binary
1861      * representation of the specified {@code long} value left by the
1862      * specified number of bits.  (Bits shifted out of the left hand, or
1863      * high-order, side reenter on the right, or low-order.)
1864      *
1865      * <p>Note that left rotation with a negative distance is equivalent to
1866      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1867      * distance)}.  Note also that rotation by any multiple of 64 is a
1868      * no-op, so all but the last six bits of the rotation distance can be
1869      * ignored, even if the distance is negative: {@code rotateLeft(val,
1870      * distance) == rotateLeft(val, distance & 0x3F)}.
1871      *
1872      * @param i the value whose bits are to be rotated left
1873      * @param distance the number of bit positions to rotate left
1874      * @return the value obtained by rotating the two's complement binary
1875      *     representation of the specified {@code long} value left by the
1876      *     specified number of bits.
1877      * @since 1.5
1878      */
1879     public static long rotateLeft(long i, int distance) {
1880         return (i << distance) | (i >>> -distance);
1881     }
1882 
1883     /**
1884      * Returns the value obtained by rotating the two's complement binary
1885      * representation of the specified {@code long} value right by the
1886      * specified number of bits.  (Bits shifted out of the right hand, or
1887      * low-order, side reenter on the left, or high-order.)
1888      *
1889      * <p>Note that right rotation with a negative distance is equivalent to
1890      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1891      * distance)}.  Note also that rotation by any multiple of 64 is a
1892      * no-op, so all but the last six bits of the rotation distance can be
1893      * ignored, even if the distance is negative: {@code rotateRight(val,
1894      * distance) == rotateRight(val, distance & 0x3F)}.
1895      *
1896      * @param i the value whose bits are to be rotated right
1897      * @param distance the number of bit positions to rotate right
1898      * @return the value obtained by rotating the two's complement binary
1899      *     representation of the specified {@code long} value right by the
1900      *     specified number of bits.
1901      * @since 1.5
1902      */
1903     public static long rotateRight(long i, int distance) {
1904         return (i >>> distance) | (i << -distance);
1905     }
1906 
1907     /**
1908      * Returns the value obtained by reversing the order of the bits in the
1909      * two's complement binary representation of the specified {@code long}
1910      * value.
1911      *
1912      * @param i the value to be reversed
1913      * @return the value obtained by reversing order of the bits in the
1914      *     specified {@code long} value.
1915      * @since 1.5
1916      */
1917     public static long reverse(long i) {
1918         // HD, Figure 7-1
1919         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1920         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1921         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1922         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1923         i = (i << 48) | ((i & 0xffff0000L) << 16) |
1924             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1925         return i;
1926     }
1927 
1928     /**
1929      * Returns the signum function of the specified {@code long} value.  (The
1930      * return value is -1 if the specified value is negative; 0 if the
1931      * specified value is zero; and 1 if the specified value is positive.)
1932      *
1933      * @param i the value whose signum is to be computed
1934      * @return the signum function of the specified {@code long} value.
1935      * @since 1.5
1936      */
1937     public static int signum(long i) {
1938         // HD, Section 2-7
1939         return (int) ((i >> 63) | (-i >>> 63));
1940     }
1941 
1942     /**
1943      * Returns the value obtained by reversing the order of the bytes in the
1944      * two's complement representation of the specified {@code long} value.
1945      *
1946      * @param i the value whose bytes are to be reversed
1947      * @return the value obtained by reversing the bytes in the specified
1948      *     {@code long} value.
1949      * @since 1.5
1950      */
1951     @HotSpotIntrinsicCandidate
1952     public static long reverseBytes(long i) {
1953         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1954         return (i << 48) | ((i & 0xffff0000L) << 16) |
1955             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1956     }
1957 
1958     /**
1959      * Adds two {@code long} values together as per the + operator.
1960      *
1961      * @param a the first operand
1962      * @param b the second operand
1963      * @return the sum of {@code a} and {@code b}
1964      * @see java.util.function.BinaryOperator
1965      * @since 1.8
1966      */
1967     public static long sum(long a, long b) {
1968         return a + b;
1969     }
1970 
1971     /**
1972      * Returns the greater of two {@code long} values
1973      * as if by calling {@link Math#max(long, long) Math.max}.
1974      *
1975      * @param a the first operand
1976      * @param b the second operand
1977      * @return the greater of {@code a} and {@code b}
1978      * @see java.util.function.BinaryOperator
1979      * @since 1.8
1980      */
1981     public static long max(long a, long b) {
1982         return Math.max(a, b);
1983     }
1984 
1985     /**
1986      * Returns the smaller of two {@code long} values
1987      * as if by calling {@link Math#min(long, long) Math.min}.
1988      *
1989      * @param a the first operand
1990      * @param b the second operand
1991      * @return the smaller of {@code a} and {@code b}
1992      * @see java.util.function.BinaryOperator
1993      * @since 1.8
1994      */
1995     public static long min(long a, long b) {
1996         return Math.min(a, b);
1997     }
1998 
1999     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2000     @Native private static final long serialVersionUID = 4290774380558885855L;
2001 }