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