1 /*
   2  * Copyright (c) 1994, 2017, 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.Trusted.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 163             i = i / radix;
 164         }
 165         StringUTF16.Trusted.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 166         if (negative) {
 167             StringUTF16.Trusted.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 
 405     /** byte[]/LATIN1 version    */
 406     static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
 407         int charPos = offset + len;
 408         int radix = 1 << shift;
 409         int mask = radix - 1;
 410         do {
 411             buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
 412             val >>>= shift;
 413         } while (charPos > offset);
 414     }
 415 
 416     /** byte[]/UTF16 version    */
 417     private static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
 418         int charPos = offset + len;
 419         int radix = 1 << shift;
 420         int mask = radix - 1;
 421         do {
 422             StringUTF16.Trusted.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
 423             val >>>= shift;
 424         } while (charPos > offset);
 425     }
 426 
 427     static String fastUUID(long lsb, long msb) {
 428         if (COMPACT_STRINGS) {
 429             byte[] buf = new byte[36];
 430             formatUnsignedLong0(lsb,        4, buf, 24, 12);
 431             formatUnsignedLong0(lsb >>> 48, 4, buf, 19, 4);
 432             formatUnsignedLong0(msb,        4, buf, 14, 4);
 433             formatUnsignedLong0(msb >>> 16, 4, buf, 9,  4);
 434             formatUnsignedLong0(msb >>> 32, 4, buf, 0,  8);
 435 
 436             buf[23] = '-';
 437             buf[18] = '-';
 438             buf[13] = '-';
 439             buf[8]  = '-';
 440 
 441             return new String(buf, LATIN1);
 442         } else {
 443             byte[] buf = new byte[72];
 444 
 445             formatUnsignedLong0UTF16(lsb,        4, buf, 24, 12);
 446             formatUnsignedLong0UTF16(lsb >>> 48, 4, buf, 19, 4);
 447             formatUnsignedLong0UTF16(msb,        4, buf, 14, 4);
 448             formatUnsignedLong0UTF16(msb >>> 16, 4, buf, 9,  4);
 449             formatUnsignedLong0UTF16(msb >>> 32, 4, buf, 0,  8);
 450 
 451             StringUTF16.Trusted.putChar(buf, 23, '-');
 452             StringUTF16.Trusted.putChar(buf, 18, '-');
 453             StringUTF16.Trusted.putChar(buf, 13, '-');
 454             StringUTF16.Trusted.putChar(buf,  8, '-');
 455 
 456             return new String(buf, UTF16);
 457         }
 458     }
 459 
 460     /**
 461      * Returns a {@code String} object representing the specified
 462      * {@code long}.  The argument is converted to signed decimal
 463      * representation and returned as a string, exactly as if the
 464      * argument and the radix 10 were given as arguments to the {@link
 465      * #toString(long, int)} method.
 466      *
 467      * @param   i   a {@code long} to be converted.
 468      * @return  a string representation of the argument in base&nbsp;10.
 469      */
 470     public static String toString(long i) {
 471         int size = stringSize(i);
 472         if (COMPACT_STRINGS) {
 473             byte[] buf = new byte[size];
 474             getChars(i, size, buf);
 475             return new String(buf, LATIN1);
 476         } else {
 477             byte[] buf = new byte[size * 2];
 478             StringUTF16.Trusted.getChars(i, size, buf);
 479             return new String(buf, UTF16);
 480         }
 481     }
 482 
 483     /**
 484      * Returns a string representation of the argument as an unsigned
 485      * decimal value.
 486      *
 487      * The argument is converted to unsigned decimal representation
 488      * and returned as a string exactly as if the argument and radix
 489      * 10 were given as arguments to the {@link #toUnsignedString(long,
 490      * int)} method.
 491      *
 492      * @param   i  an integer to be converted to an unsigned string.
 493      * @return  an unsigned string representation of the argument.
 494      * @see     #toUnsignedString(long, int)
 495      * @since 1.8
 496      */
 497     public static String toUnsignedString(long i) {
 498         return toUnsignedString(i, 10);
 499     }
 500 
 501     /**
 502      * Places characters representing the long i into the
 503      * character array buf. The characters are placed into
 504      * the buffer backwards starting with the least significant
 505      * digit at the specified index (exclusive), and working
 506      * backwards from there.
 507      *
 508      * @implNote This method converts positive inputs into negative
 509      * values, to cover the Long.MIN_VALUE case. Converting otherwise
 510      * (negative to positive) will expose -Long.MIN_VALUE that overflows
 511      * long.
 512      *
 513      * @param i     value to convert
 514      * @param index next index, after the least significant digit
 515      * @param buf   target buffer, Latin1-encoded
 516      * @return index of the most significant digit or minus sign, if present
 517      */
 518     static int getChars(long i, int index, byte[] buf) {
 519         long q;
 520         int r;
 521         int charPos = index;
 522 
 523         boolean negative = (i < 0);
 524         if (!negative) {
 525             i = -i;
 526         }
 527 
 528         // Get 2 digits/iteration using longs until quotient fits into an int
 529         while (i <= Integer.MIN_VALUE) {
 530             q = i / 100;
 531             r = (int)((q * 100) - i);
 532             i = q;
 533             buf[--charPos] = Integer.DigitOnes[r];
 534             buf[--charPos] = Integer.DigitTens[r];
 535         }
 536 
 537         // Get 2 digits/iteration using ints
 538         int q2;
 539         int i2 = (int)i;
 540         while (i2 <= -100) {
 541             q2 = i2 / 100;
 542             r  = (q2 * 100) - i2;
 543             i2 = q2;
 544             buf[--charPos] = Integer.DigitOnes[r];
 545             buf[--charPos] = Integer.DigitTens[r];
 546         }
 547 
 548         // We know there are at most two digits left at this point.
 549         q2 = i2 / 10;
 550         r  = (q2 * 10) - i2;
 551         buf[--charPos] = (byte)('0' + r);
 552 
 553         // Whatever left is the remaining digit.
 554         if (q2 < 0) {
 555             buf[--charPos] = (byte)('0' - q2);
 556         }
 557 
 558         if (negative) {
 559             buf[--charPos] = (byte)'-';
 560         }
 561         return charPos;
 562     }
 563 
 564     /**
 565      * Returns the string representation size for a given long value.
 566      *
 567      * @param x long value
 568      * @return string size
 569      *
 570      * @implNote There are other ways to compute this: e.g. binary search,
 571      * but values are biased heavily towards zero, and therefore linear search
 572      * wins. The iteration results are also routinely inlined in the generated
 573      * code after loop unrolling.
 574      */
 575     static int stringSize(long x) {
 576         int d = 1;
 577         if (x >= 0) {
 578             d = 0;
 579             x = -x;
 580         }
 581         long p = -10;
 582         for (int i = 1; i < 19; i++) {
 583             if (x > p)
 584                 return i + d;
 585             p = 10 * p;
 586         }
 587         return 19 + d;
 588     }
 589 
 590     /**
 591      * Parses the string argument as a signed {@code long} in the
 592      * radix specified by the second argument. The characters in the
 593      * string must all be digits of the specified radix (as determined
 594      * by whether {@link java.lang.Character#digit(char, int)} returns
 595      * a nonnegative value), except that the first character may be an
 596      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 597      * indicate a negative value or an ASCII plus sign {@code '+'}
 598      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 599      * resulting {@code long} value is returned.
 600      *
 601      * <p>Note that neither the character {@code L}
 602      * ({@code '\u005Cu004C'}) nor {@code l}
 603      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 604      * of the string as a type indicator, as would be permitted in
 605      * Java programming language source code - except that either
 606      * {@code L} or {@code l} may appear as a digit for a
 607      * radix greater than or equal to 22.
 608      *
 609      * <p>An exception of type {@code NumberFormatException} is
 610      * thrown if any of the following situations occurs:
 611      * <ul>
 612      *
 613      * <li>The first argument is {@code null} or is a string of
 614      * length zero.
 615      *
 616      * <li>The {@code radix} is either smaller than {@link
 617      * java.lang.Character#MIN_RADIX} or larger than {@link
 618      * java.lang.Character#MAX_RADIX}.
 619      *
 620      * <li>Any character of the string is not a digit of the specified
 621      * radix, except that the first character may be a minus sign
 622      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 623      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 624      * longer than length 1.
 625      *
 626      * <li>The value represented by the string is not a value of type
 627      *      {@code long}.
 628      * </ul>
 629      *
 630      * <p>Examples:
 631      * <blockquote><pre>
 632      * parseLong("0", 10) returns 0L
 633      * parseLong("473", 10) returns 473L
 634      * parseLong("+42", 10) returns 42L
 635      * parseLong("-0", 10) returns 0L
 636      * parseLong("-FF", 16) returns -255L
 637      * parseLong("1100110", 2) returns 102L
 638      * parseLong("99", 8) throws a NumberFormatException
 639      * parseLong("Hazelnut", 10) throws a NumberFormatException
 640      * parseLong("Hazelnut", 36) returns 1356099454469L
 641      * </pre></blockquote>
 642      *
 643      * @param      s       the {@code String} containing the
 644      *                     {@code long} representation to be parsed.
 645      * @param      radix   the radix to be used while parsing {@code s}.
 646      * @return     the {@code long} represented by the string argument in
 647      *             the specified radix.
 648      * @throws     NumberFormatException  if the string does not contain a
 649      *             parsable {@code long}.
 650      */
 651     public static long parseLong(String s, int radix)
 652               throws NumberFormatException
 653     {
 654         if (s == null) {
 655             throw new NumberFormatException("null");
 656         }
 657 
 658         if (radix < Character.MIN_RADIX) {
 659             throw new NumberFormatException("radix " + radix +
 660                                             " less than Character.MIN_RADIX");
 661         }
 662         if (radix > Character.MAX_RADIX) {
 663             throw new NumberFormatException("radix " + radix +
 664                                             " greater than Character.MAX_RADIX");
 665         }
 666 
 667         boolean negative = false;
 668         int i = 0, len = s.length();
 669         long limit = -Long.MAX_VALUE;
 670 
 671         if (len > 0) {
 672             char firstChar = s.charAt(0);
 673             if (firstChar < '0') { // Possible leading "+" or "-"
 674                 if (firstChar == '-') {
 675                     negative = true;
 676                     limit = Long.MIN_VALUE;
 677                 } else if (firstChar != '+') {
 678                     throw NumberFormatException.forInputString(s);
 679                 }
 680 
 681                 if (len == 1) { // Cannot have lone "+" or "-"
 682                     throw NumberFormatException.forInputString(s);
 683                 }
 684                 i++;
 685             }
 686             long multmin = limit / radix;
 687             long result = 0;
 688             while (i < len) {
 689                 // Accumulating negatively avoids surprises near MAX_VALUE
 690                 int digit = Character.digit(s.charAt(i++),radix);
 691                 if (digit < 0 || result < multmin) {
 692                     throw NumberFormatException.forInputString(s);
 693                 }
 694                 result *= radix;
 695                 if (result < limit + digit) {
 696                     throw NumberFormatException.forInputString(s);
 697                 }
 698                 result -= digit;
 699             }
 700             return negative ? result : -result;
 701         } else {
 702             throw NumberFormatException.forInputString(s);
 703         }
 704     }
 705 
 706     /**
 707      * Parses the {@link CharSequence} argument as a signed {@code long} in
 708      * the specified {@code radix}, beginning at the specified
 709      * {@code beginIndex} and extending to {@code endIndex - 1}.
 710      *
 711      * <p>The method does not take steps to guard against the
 712      * {@code CharSequence} being mutated while parsing.
 713      *
 714      * @param      s   the {@code CharSequence} containing the {@code long}
 715      *                  representation to be parsed
 716      * @param      beginIndex   the beginning index, inclusive.
 717      * @param      endIndex     the ending index, exclusive.
 718      * @param      radix   the radix to be used while parsing {@code s}.
 719      * @return     the signed {@code long} represented by the subsequence in
 720      *             the specified radix.
 721      * @throws     NullPointerException  if {@code s} is null.
 722      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 723      *             negative, or if {@code beginIndex} is greater than
 724      *             {@code endIndex} or if {@code endIndex} is greater than
 725      *             {@code s.length()}.
 726      * @throws     NumberFormatException  if the {@code CharSequence} does not
 727      *             contain a parsable {@code int} in the specified
 728      *             {@code radix}, or if {@code radix} is either smaller than
 729      *             {@link java.lang.Character#MIN_RADIX} or larger than
 730      *             {@link java.lang.Character#MAX_RADIX}.
 731      * @since  9
 732      */
 733     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 734                 throws NumberFormatException {
 735         s = Objects.requireNonNull(s);
 736 
 737         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 738             throw new IndexOutOfBoundsException();
 739         }
 740         if (radix < Character.MIN_RADIX) {
 741             throw new NumberFormatException("radix " + radix +
 742                     " less than Character.MIN_RADIX");
 743         }
 744         if (radix > Character.MAX_RADIX) {
 745             throw new NumberFormatException("radix " + radix +
 746                     " greater than Character.MAX_RADIX");
 747         }
 748 
 749         boolean negative = false;
 750         int i = beginIndex;
 751         long limit = -Long.MAX_VALUE;
 752 
 753         if (i < endIndex) {
 754             char firstChar = s.charAt(i);
 755             if (firstChar < '0') { // Possible leading "+" or "-"
 756                 if (firstChar == '-') {
 757                     negative = true;
 758                     limit = Long.MIN_VALUE;
 759                 } else if (firstChar != '+') {
 760                     throw NumberFormatException.forCharSequence(s, beginIndex,
 761                             endIndex, i);
 762                 }
 763                 i++;
 764             }
 765             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 766                 throw NumberFormatException.forCharSequence(s, beginIndex,
 767                         endIndex, i);
 768             }
 769             long multmin = limit / radix;
 770             long result = 0;
 771             while (i < endIndex) {
 772                 // Accumulating negatively avoids surprises near MAX_VALUE
 773                 int digit = Character.digit(s.charAt(i), radix);
 774                 if (digit < 0 || result < multmin) {
 775                     throw NumberFormatException.forCharSequence(s, beginIndex,
 776                             endIndex, i);
 777                 }
 778                 result *= radix;
 779                 if (result < limit + digit) {
 780                     throw NumberFormatException.forCharSequence(s, beginIndex,
 781                             endIndex, i);
 782                 }
 783                 i++;
 784                 result -= digit;
 785             }
 786             return negative ? result : -result;
 787         } else {
 788             throw new NumberFormatException("");
 789         }
 790     }
 791 
 792     /**
 793      * Parses the string argument as a signed decimal {@code long}.
 794      * The characters in the string must all be decimal digits, except
 795      * that the first character may be an ASCII minus sign {@code '-'}
 796      * ({@code \u005Cu002D'}) to indicate a negative value or an
 797      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 798      * indicate a positive value. The resulting {@code long} value is
 799      * returned, exactly as if the argument and the radix {@code 10}
 800      * were given as arguments to the {@link
 801      * #parseLong(java.lang.String, int)} method.
 802      *
 803      * <p>Note that neither the character {@code L}
 804      * ({@code '\u005Cu004C'}) nor {@code l}
 805      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 806      * of the string as a type indicator, as would be permitted in
 807      * Java programming language source code.
 808      *
 809      * @param      s   a {@code String} containing the {@code long}
 810      *             representation to be parsed
 811      * @return     the {@code long} represented by the argument in
 812      *             decimal.
 813      * @throws     NumberFormatException  if the string does not contain a
 814      *             parsable {@code long}.
 815      */
 816     public static long parseLong(String s) throws NumberFormatException {
 817         return parseLong(s, 10);
 818     }
 819 
 820     /**
 821      * Parses the string argument as an unsigned {@code long} in the
 822      * radix specified by the second argument.  An unsigned integer
 823      * maps the values usually associated with negative numbers to
 824      * positive numbers larger than {@code MAX_VALUE}.
 825      *
 826      * The characters in the string must all be digits of the
 827      * specified radix (as determined by whether {@link
 828      * java.lang.Character#digit(char, int)} returns a nonnegative
 829      * value), except that the first character may be an ASCII plus
 830      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 831      * integer value is returned.
 832      *
 833      * <p>An exception of type {@code NumberFormatException} is
 834      * thrown if any of the following situations occurs:
 835      * <ul>
 836      * <li>The first argument is {@code null} or is a string of
 837      * length zero.
 838      *
 839      * <li>The radix is either smaller than
 840      * {@link java.lang.Character#MIN_RADIX} or
 841      * larger than {@link java.lang.Character#MAX_RADIX}.
 842      *
 843      * <li>Any character of the string is not a digit of the specified
 844      * radix, except that the first character may be a plus sign
 845      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 846      * string is longer than length 1.
 847      *
 848      * <li>The value represented by the string is larger than the
 849      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 850      *
 851      * </ul>
 852      *
 853      *
 854      * @param      s   the {@code String} containing the unsigned integer
 855      *                  representation to be parsed
 856      * @param      radix   the radix to be used while parsing {@code s}.
 857      * @return     the unsigned {@code long} represented by the string
 858      *             argument in the specified radix.
 859      * @throws     NumberFormatException if the {@code String}
 860      *             does not contain a parsable {@code long}.
 861      * @since 1.8
 862      */
 863     public static long parseUnsignedLong(String s, int radix)
 864                 throws NumberFormatException {
 865         if (s == null)  {
 866             throw new NumberFormatException("null");
 867         }
 868 
 869         int len = s.length();
 870         if (len > 0) {
 871             char firstChar = s.charAt(0);
 872             if (firstChar == '-') {
 873                 throw new
 874                     NumberFormatException(String.format("Illegal leading minus sign " +
 875                                                        "on unsigned string %s.", s));
 876             } else {
 877                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 878                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 879                     return parseLong(s, radix);
 880                 }
 881 
 882                 // No need for range checks on len due to testing above.
 883                 long first = parseLong(s, 0, len - 1, radix);
 884                 int second = Character.digit(s.charAt(len - 1), radix);
 885                 if (second < 0) {
 886                     throw new NumberFormatException("Bad digit at end of " + s);
 887                 }
 888                 long result = first * radix + second;
 889 
 890                 /*
 891                  * Test leftmost bits of multiprecision extension of first*radix
 892                  * for overflow. The number of bits needed is defined by
 893                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 894                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 895                  * overflow is tested by splitting guard in the ranges
 896                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 897                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 898                  * on a value which does not include a prime factor in the legal
 899                  * radix range.
 900                  */
 901                 int guard = radix * (int) (first >>> 57);
 902                 if (guard >= 128 ||
 903                     (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 904                     /*
 905                      * For purposes of exposition, the programmatic statements
 906                      * below should be taken to be multi-precision, i.e., not
 907                      * subject to overflow.
 908                      *
 909                      * A) Condition guard >= 128:
 910                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 911                      * hence always overflow.
 912                      *
 913                      * B) Condition guard < 92:
 914                      * Define left7 = first >>> 57.
 915                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 916                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 917                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 918                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 919                      * never overflow.
 920                      *
 921                      * C) Condition 92 <= guard < 128:
 922                      * first*radix + second >= radix*left7*2^57 + second
 923                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 924                      *
 925                      * D) Condition guard < 128:
 926                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 927                      * so
 928                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 929                      * thus
 930                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 931                      * whence
 932                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 933                      *
 934                      * E) Conditions C, D, and result >= 0:
 935                      * C and D combined imply the mathematical result
 936                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 937                      * bound is therefore negative as a signed long, but the
 938                      * upper bound is too small to overflow again after the
 939                      * signed long overflows to positive above 2^64 - 1. Hence
 940                      * result >= 0 implies overflow given C and D.
 941                      */
 942                     throw new NumberFormatException(String.format("String value %s exceeds " +
 943                                                                   "range of unsigned long.", s));
 944                 }
 945                 return result;
 946             }
 947         } else {
 948             throw NumberFormatException.forInputString(s);
 949         }
 950     }
 951 
 952     /**
 953      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
 954      * the specified {@code radix}, beginning at the specified
 955      * {@code beginIndex} and extending to {@code endIndex - 1}.
 956      *
 957      * <p>The method does not take steps to guard against the
 958      * {@code CharSequence} being mutated while parsing.
 959      *
 960      * @param      s   the {@code CharSequence} containing the unsigned
 961      *                 {@code long} representation to be parsed
 962      * @param      beginIndex   the beginning index, inclusive.
 963      * @param      endIndex     the ending index, exclusive.
 964      * @param      radix   the radix to be used while parsing {@code s}.
 965      * @return     the unsigned {@code long} represented by the subsequence in
 966      *             the specified radix.
 967      * @throws     NullPointerException  if {@code s} is null.
 968      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 969      *             negative, or if {@code beginIndex} is greater than
 970      *             {@code endIndex} or if {@code endIndex} is greater than
 971      *             {@code s.length()}.
 972      * @throws     NumberFormatException  if the {@code CharSequence} does not
 973      *             contain a parsable unsigned {@code long} in the specified
 974      *             {@code radix}, or if {@code radix} is either smaller than
 975      *             {@link java.lang.Character#MIN_RADIX} or larger than
 976      *             {@link java.lang.Character#MAX_RADIX}.
 977      * @since  9
 978      */
 979     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
 980                 throws NumberFormatException {
 981         s = Objects.requireNonNull(s);
 982 
 983         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 984             throw new IndexOutOfBoundsException();
 985         }
 986         int start = beginIndex, len = endIndex - beginIndex;
 987 
 988         if (len > 0) {
 989             char firstChar = s.charAt(start);
 990             if (firstChar == '-') {
 991                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
 992                         "on unsigned string %s.", s.subSequence(start, start + len)));
 993             } else {
 994                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 995                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 996                     return parseLong(s, start, start + len, radix);
 997                 }
 998 
 999                 // No need for range checks on end due to testing above.
1000                 long first = parseLong(s, start, start + len - 1, radix);
1001                 int second = Character.digit(s.charAt(start + len - 1), radix);
1002                 if (second < 0) {
1003                     throw new NumberFormatException("Bad digit at end of " +
1004                             s.subSequence(start, start + len));
1005                 }
1006                 long result = first * radix + second;
1007 
1008                 /*
1009                  * Test leftmost bits of multiprecision extension of first*radix
1010                  * for overflow. The number of bits needed is defined by
1011                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
1012                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
1013                  * overflow is tested by splitting guard in the ranges
1014                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
1015                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
1016                  * on a value which does not include a prime factor in the legal
1017                  * radix range.
1018                  */
1019                 int guard = radix * (int) (first >>> 57);
1020                 if (guard >= 128 ||
1021                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
1022                     /*
1023                      * For purposes of exposition, the programmatic statements
1024                      * below should be taken to be multi-precision, i.e., not
1025                      * subject to overflow.
1026                      *
1027                      * A) Condition guard >= 128:
1028                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
1029                      * hence always overflow.
1030                      *
1031                      * B) Condition guard < 92:
1032                      * Define left7 = first >>> 57.
1033                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
1034                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
1035                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
1036                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
1037                      * never overflow.
1038                      *
1039                      * C) Condition 92 <= guard < 128:
1040                      * first*radix + second >= radix*left7*2^57 + second
1041                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
1042                      *
1043                      * D) Condition guard < 128:
1044                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
1045                      * so
1046                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
1047                      * thus
1048                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
1049                      * whence
1050                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
1051                      *
1052                      * E) Conditions C, D, and result >= 0:
1053                      * C and D combined imply the mathematical result
1054                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
1055                      * bound is therefore negative as a signed long, but the
1056                      * upper bound is too small to overflow again after the
1057                      * signed long overflows to positive above 2^64 - 1. Hence
1058                      * result >= 0 implies overflow given C and D.
1059                      */
1060                     throw new NumberFormatException(String.format("String value %s exceeds " +
1061                             "range of unsigned long.", s.subSequence(start, start + len)));
1062                 }
1063                 return result;
1064             }
1065         } else {
1066             throw NumberFormatException.forInputString("");
1067         }
1068     }
1069 
1070     /**
1071      * Parses the string argument as an unsigned decimal {@code long}. The
1072      * characters in the string must all be decimal digits, except
1073      * that the first character may be an ASCII plus sign {@code
1074      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
1075      * is returned, exactly as if the argument and the radix 10 were
1076      * given as arguments to the {@link
1077      * #parseUnsignedLong(java.lang.String, int)} method.
1078      *
1079      * @param s   a {@code String} containing the unsigned {@code long}
1080      *            representation to be parsed
1081      * @return    the unsigned {@code long} value represented by the decimal string argument
1082      * @throws    NumberFormatException  if the string does not contain a
1083      *            parsable unsigned integer.
1084      * @since 1.8
1085      */
1086     public static long parseUnsignedLong(String s) throws NumberFormatException {
1087         return parseUnsignedLong(s, 10);
1088     }
1089 
1090     /**
1091      * Returns a {@code Long} object holding the value
1092      * extracted from the specified {@code String} when parsed
1093      * with the radix given by the second argument.  The first
1094      * argument is interpreted as representing a signed
1095      * {@code long} in the radix specified by the second
1096      * argument, exactly as if the arguments were given to the {@link
1097      * #parseLong(java.lang.String, int)} method. The result is a
1098      * {@code Long} object that represents the {@code long}
1099      * value specified by the string.
1100      *
1101      * <p>In other words, this method returns a {@code Long} object equal
1102      * to the value of:
1103      *
1104      * <blockquote>
1105      *  {@code new Long(Long.parseLong(s, radix))}
1106      * </blockquote>
1107      *
1108      * @param      s       the string to be parsed
1109      * @param      radix   the radix to be used in interpreting {@code s}
1110      * @return     a {@code Long} object holding the value
1111      *             represented by the string argument in the specified
1112      *             radix.
1113      * @throws     NumberFormatException  If the {@code String} does not
1114      *             contain a parsable {@code long}.
1115      */
1116     public static Long valueOf(String s, int radix) throws NumberFormatException {
1117         return Long.valueOf(parseLong(s, radix));
1118     }
1119 
1120     /**
1121      * Returns a {@code Long} object holding the value
1122      * of the specified {@code String}. The argument is
1123      * interpreted as representing a signed decimal {@code long},
1124      * exactly as if the argument were given to the {@link
1125      * #parseLong(java.lang.String)} method. The result is a
1126      * {@code Long} object that represents the integer value
1127      * specified by the string.
1128      *
1129      * <p>In other words, this method returns a {@code Long} object
1130      * equal to the value of:
1131      *
1132      * <blockquote>
1133      *  {@code new Long(Long.parseLong(s))}
1134      * </blockquote>
1135      *
1136      * @param      s   the string to be parsed.
1137      * @return     a {@code Long} object holding the value
1138      *             represented by the string argument.
1139      * @throws     NumberFormatException  If the string cannot be parsed
1140      *             as a {@code long}.
1141      */
1142     public static Long valueOf(String s) throws NumberFormatException
1143     {
1144         return Long.valueOf(parseLong(s, 10));
1145     }
1146 
1147     private static class LongCache {
1148         private LongCache(){}
1149 
1150         static final Long cache[] = new Long[-(-128) + 127 + 1];
1151 
1152         static {
1153             for(int i = 0; i < cache.length; i++)
1154                 cache[i] = new Long(i - 128);
1155         }
1156     }
1157 
1158     /**
1159      * Returns a {@code Long} instance representing the specified
1160      * {@code long} value.
1161      * If a new {@code Long} instance is not required, this method
1162      * should generally be used in preference to the constructor
1163      * {@link #Long(long)}, as this method is likely to yield
1164      * significantly better space and time performance by caching
1165      * frequently requested values.
1166      *
1167      * Note that unlike the {@linkplain Integer#valueOf(int)
1168      * corresponding method} in the {@code Integer} class, this method
1169      * is <em>not</em> required to cache values within a particular
1170      * range.
1171      *
1172      * @param  l a long value.
1173      * @return a {@code Long} instance representing {@code l}.
1174      * @since  1.5
1175      */
1176     @HotSpotIntrinsicCandidate
1177     public static Long valueOf(long l) {
1178         final int offset = 128;
1179         if (l >= -128 && l <= 127) { // will cache
1180             return LongCache.cache[(int)l + offset];
1181         }
1182         return new Long(l);
1183     }
1184 
1185     /**
1186      * Decodes a {@code String} into a {@code Long}.
1187      * Accepts decimal, hexadecimal, and octal numbers given by the
1188      * following grammar:
1189      *
1190      * <blockquote>
1191      * <dl>
1192      * <dt><i>DecodableString:</i>
1193      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1194      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1195      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1196      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1197      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1198      *
1199      * <dt><i>Sign:</i>
1200      * <dd>{@code -}
1201      * <dd>{@code +}
1202      * </dl>
1203      * </blockquote>
1204      *
1205      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1206      * are as defined in section 3.10.1 of
1207      * <cite>The Java&trade; Language Specification</cite>,
1208      * except that underscores are not accepted between digits.
1209      *
1210      * <p>The sequence of characters following an optional
1211      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1212      * "{@code #}", or leading zero) is parsed as by the {@code
1213      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1214      * This sequence of characters must represent a positive value or
1215      * a {@link NumberFormatException} will be thrown.  The result is
1216      * negated if first character of the specified {@code String} is
1217      * the minus sign.  No whitespace characters are permitted in the
1218      * {@code String}.
1219      *
1220      * @param     nm the {@code String} to decode.
1221      * @return    a {@code Long} object holding the {@code long}
1222      *            value represented by {@code nm}
1223      * @throws    NumberFormatException  if the {@code String} does not
1224      *            contain a parsable {@code long}.
1225      * @see java.lang.Long#parseLong(String, int)
1226      * @since 1.2
1227      */
1228     public static Long decode(String nm) throws NumberFormatException {
1229         int radix = 10;
1230         int index = 0;
1231         boolean negative = false;
1232         Long result;
1233 
1234         if (nm.length() == 0)
1235             throw new NumberFormatException("Zero length string");
1236         char firstChar = nm.charAt(0);
1237         // Handle sign, if present
1238         if (firstChar == '-') {
1239             negative = true;
1240             index++;
1241         } else if (firstChar == '+')
1242             index++;
1243 
1244         // Handle radix specifier, if present
1245         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1246             index += 2;
1247             radix = 16;
1248         }
1249         else if (nm.startsWith("#", index)) {
1250             index ++;
1251             radix = 16;
1252         }
1253         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1254             index ++;
1255             radix = 8;
1256         }
1257 
1258         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1259             throw new NumberFormatException("Sign character in wrong position");
1260 
1261         try {
1262             result = Long.valueOf(nm.substring(index), radix);
1263             result = negative ? Long.valueOf(-result.longValue()) : result;
1264         } catch (NumberFormatException e) {
1265             // If number is Long.MIN_VALUE, we'll end up here. The next line
1266             // handles this case, and causes any genuine format error to be
1267             // rethrown.
1268             String constant = negative ? ("-" + nm.substring(index))
1269                                        : nm.substring(index);
1270             result = Long.valueOf(constant, radix);
1271         }
1272         return result;
1273     }
1274 
1275     /**
1276      * The value of the {@code Long}.
1277      *
1278      * @serial
1279      */
1280     private final long value;
1281 
1282     /**
1283      * Constructs a newly allocated {@code Long} object that
1284      * represents the specified {@code long} argument.
1285      *
1286      * @param   value   the value to be represented by the
1287      *          {@code Long} object.
1288      *
1289      * @deprecated
1290      * It is rarely appropriate to use this constructor. The static factory
1291      * {@link #valueOf(long)} is generally a better choice, as it is
1292      * likely to yield significantly better space and time performance.
1293      */
1294     @Deprecated(since="9")
1295     public Long(long value) {
1296         this.value = value;
1297     }
1298 
1299     /**
1300      * Constructs a newly allocated {@code Long} object that
1301      * represents the {@code long} value indicated by the
1302      * {@code String} parameter. The string is converted to a
1303      * {@code long} value in exactly the manner used by the
1304      * {@code parseLong} method for radix 10.
1305      *
1306      * @param      s   the {@code String} to be converted to a
1307      *             {@code Long}.
1308      * @throws     NumberFormatException  if the {@code String} does not
1309      *             contain a parsable {@code long}.
1310      *
1311      * @deprecated
1312      * It is rarely appropriate to use this constructor.
1313      * Use {@link #parseLong(String)} to convert a string to a
1314      * {@code long} primitive, or use {@link #valueOf(String)}
1315      * to convert a string to a {@code Long} object.
1316      */
1317     @Deprecated(since="9")
1318     public Long(String s) throws NumberFormatException {
1319         this.value = parseLong(s, 10);
1320     }
1321 
1322     /**
1323      * Returns the value of this {@code Long} as a {@code byte} after
1324      * a narrowing primitive conversion.
1325      * @jls 5.1.3 Narrowing Primitive Conversions
1326      */
1327     public byte byteValue() {
1328         return (byte)value;
1329     }
1330 
1331     /**
1332      * Returns the value of this {@code Long} as a {@code short} after
1333      * a narrowing primitive conversion.
1334      * @jls 5.1.3 Narrowing Primitive Conversions
1335      */
1336     public short shortValue() {
1337         return (short)value;
1338     }
1339 
1340     /**
1341      * Returns the value of this {@code Long} as an {@code int} after
1342      * a narrowing primitive conversion.
1343      * @jls 5.1.3 Narrowing Primitive Conversions
1344      */
1345     public int intValue() {
1346         return (int)value;
1347     }
1348 
1349     /**
1350      * Returns the value of this {@code Long} as a
1351      * {@code long} value.
1352      */
1353     @HotSpotIntrinsicCandidate
1354     public long longValue() {
1355         return value;
1356     }
1357 
1358     /**
1359      * Returns the value of this {@code Long} as a {@code float} after
1360      * a widening primitive conversion.
1361      * @jls 5.1.2 Widening Primitive Conversions
1362      */
1363     public float floatValue() {
1364         return (float)value;
1365     }
1366 
1367     /**
1368      * Returns the value of this {@code Long} as a {@code double}
1369      * after a widening primitive conversion.
1370      * @jls 5.1.2 Widening Primitive Conversions
1371      */
1372     public double doubleValue() {
1373         return (double)value;
1374     }
1375 
1376     /**
1377      * Returns a {@code String} object representing this
1378      * {@code Long}'s value.  The value is converted to signed
1379      * decimal representation and returned as a string, exactly as if
1380      * the {@code long} value were given as an argument to the
1381      * {@link java.lang.Long#toString(long)} method.
1382      *
1383      * @return  a string representation of the value of this object in
1384      *          base&nbsp;10.
1385      */
1386     public String toString() {
1387         return toString(value);
1388     }
1389 
1390     /**
1391      * Returns a hash code for this {@code Long}. The result is
1392      * the exclusive OR of the two halves of the primitive
1393      * {@code long} value held by this {@code Long}
1394      * object. That is, the hashcode is the value of the expression:
1395      *
1396      * <blockquote>
1397      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1398      * </blockquote>
1399      *
1400      * @return  a hash code value for this object.
1401      */
1402     @Override
1403     public int hashCode() {
1404         return Long.hashCode(value);
1405     }
1406 
1407     /**
1408      * Returns a hash code for a {@code long} value; compatible with
1409      * {@code Long.hashCode()}.
1410      *
1411      * @param value the value to hash
1412      * @return a hash code value for a {@code long} value.
1413      * @since 1.8
1414      */
1415     public static int hashCode(long value) {
1416         return (int)(value ^ (value >>> 32));
1417     }
1418 
1419     /**
1420      * Compares this object to the specified object.  The result is
1421      * {@code true} if and only if the argument is not
1422      * {@code null} and is a {@code Long} object that
1423      * contains the same {@code long} value as this object.
1424      *
1425      * @param   obj   the object to compare with.
1426      * @return  {@code true} if the objects are the same;
1427      *          {@code false} otherwise.
1428      */
1429     public boolean equals(Object obj) {
1430         if (obj instanceof Long) {
1431             return value == ((Long)obj).longValue();
1432         }
1433         return false;
1434     }
1435 
1436     /**
1437      * Determines the {@code long} value of the system property
1438      * with the specified name.
1439      *
1440      * <p>The first argument is treated as the name of a system
1441      * property.  System properties are accessible through the {@link
1442      * java.lang.System#getProperty(java.lang.String)} method. The
1443      * string value of this property is then interpreted as a {@code
1444      * long} value using the grammar supported by {@link Long#decode decode}
1445      * and a {@code Long} object representing this value is returned.
1446      *
1447      * <p>If there is no property with the specified name, if the
1448      * specified name is empty or {@code null}, or if the property
1449      * does not have the correct numeric format, then {@code null} is
1450      * returned.
1451      *
1452      * <p>In other words, this method returns a {@code Long} object
1453      * equal to the value of:
1454      *
1455      * <blockquote>
1456      *  {@code getLong(nm, null)}
1457      * </blockquote>
1458      *
1459      * @param   nm   property name.
1460      * @return  the {@code Long} value of the property.
1461      * @throws  SecurityException for the same reasons as
1462      *          {@link System#getProperty(String) System.getProperty}
1463      * @see     java.lang.System#getProperty(java.lang.String)
1464      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1465      */
1466     public static Long getLong(String nm) {
1467         return getLong(nm, null);
1468     }
1469 
1470     /**
1471      * Determines the {@code long} value of the system property
1472      * with the specified name.
1473      *
1474      * <p>The first argument is treated as the name of a system
1475      * property.  System properties are accessible through the {@link
1476      * java.lang.System#getProperty(java.lang.String)} method. The
1477      * string value of this property is then interpreted as a {@code
1478      * long} value using the grammar supported by {@link Long#decode decode}
1479      * and a {@code Long} object representing this value is returned.
1480      *
1481      * <p>The second argument is the default value. A {@code Long} object
1482      * that represents the value of the second argument is returned if there
1483      * is no property of the specified name, if the property does not have
1484      * the correct numeric format, or if the specified name is empty or null.
1485      *
1486      * <p>In other words, this method returns a {@code Long} object equal
1487      * to the value of:
1488      *
1489      * <blockquote>
1490      *  {@code getLong(nm, new Long(val))}
1491      * </blockquote>
1492      *
1493      * but in practice it may be implemented in a manner such as:
1494      *
1495      * <blockquote><pre>
1496      * Long result = getLong(nm, null);
1497      * return (result == null) ? new Long(val) : result;
1498      * </pre></blockquote>
1499      *
1500      * to avoid the unnecessary allocation of a {@code Long} object when
1501      * the default value is not needed.
1502      *
1503      * @param   nm    property name.
1504      * @param   val   default value.
1505      * @return  the {@code Long} value of the property.
1506      * @throws  SecurityException for the same reasons as
1507      *          {@link System#getProperty(String) System.getProperty}
1508      * @see     java.lang.System#getProperty(java.lang.String)
1509      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1510      */
1511     public static Long getLong(String nm, long val) {
1512         Long result = Long.getLong(nm, null);
1513         return (result == null) ? Long.valueOf(val) : result;
1514     }
1515 
1516     /**
1517      * Returns the {@code long} value of the system property with
1518      * the specified name.  The first argument is treated as the name
1519      * of a system property.  System properties are accessible through
1520      * the {@link java.lang.System#getProperty(java.lang.String)}
1521      * method. The string value of this property is then interpreted
1522      * as a {@code long} value, as per the
1523      * {@link Long#decode decode} method, and a {@code Long} object
1524      * representing this value is returned; in summary:
1525      *
1526      * <ul>
1527      * <li>If the property value begins with the two ASCII characters
1528      * {@code 0x} or the ASCII character {@code #}, not followed by
1529      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1530      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1531      * with radix 16.
1532      * <li>If the property value begins with the ASCII character
1533      * {@code 0} followed by another character, it is parsed as
1534      * an octal integer exactly as by the method {@link
1535      * #valueOf(java.lang.String, int)} with radix 8.
1536      * <li>Otherwise the property value is parsed as a decimal
1537      * integer exactly as by the method
1538      * {@link #valueOf(java.lang.String, int)} with radix 10.
1539      * </ul>
1540      *
1541      * <p>Note that, in every case, neither {@code L}
1542      * ({@code '\u005Cu004C'}) nor {@code l}
1543      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1544      * of the property value as a type indicator, as would be
1545      * permitted in Java programming language source code.
1546      *
1547      * <p>The second argument is the default value. The default value is
1548      * returned if there is no property of the specified name, if the
1549      * property does not have the correct numeric format, or if the
1550      * specified name is empty or {@code null}.
1551      *
1552      * @param   nm   property name.
1553      * @param   val   default value.
1554      * @return  the {@code Long} value of the property.
1555      * @throws  SecurityException for the same reasons as
1556      *          {@link System#getProperty(String) System.getProperty}
1557      * @see     System#getProperty(java.lang.String)
1558      * @see     System#getProperty(java.lang.String, java.lang.String)
1559      */
1560     public static Long getLong(String nm, Long val) {
1561         String v = null;
1562         try {
1563             v = System.getProperty(nm);
1564         } catch (IllegalArgumentException | NullPointerException e) {
1565         }
1566         if (v != null) {
1567             try {
1568                 return Long.decode(v);
1569             } catch (NumberFormatException e) {
1570             }
1571         }
1572         return val;
1573     }
1574 
1575     /**
1576      * Compares two {@code Long} objects numerically.
1577      *
1578      * @param   anotherLong   the {@code Long} to be compared.
1579      * @return  the value {@code 0} if this {@code Long} is
1580      *          equal to the argument {@code Long}; a value less than
1581      *          {@code 0} if this {@code Long} is numerically less
1582      *          than the argument {@code Long}; and a value greater
1583      *          than {@code 0} if this {@code Long} is numerically
1584      *           greater than the argument {@code Long} (signed
1585      *           comparison).
1586      * @since   1.2
1587      */
1588     public int compareTo(Long anotherLong) {
1589         return compare(this.value, anotherLong.value);
1590     }
1591 
1592     /**
1593      * Compares two {@code long} values numerically.
1594      * The value returned is identical to what would be returned by:
1595      * <pre>
1596      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1597      * </pre>
1598      *
1599      * @param  x the first {@code long} to compare
1600      * @param  y the second {@code long} to compare
1601      * @return the value {@code 0} if {@code x == y};
1602      *         a value less than {@code 0} if {@code x < y}; and
1603      *         a value greater than {@code 0} if {@code x > y}
1604      * @since 1.7
1605      */
1606     public static int compare(long x, long y) {
1607         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1608     }
1609 
1610     /**
1611      * Compares two {@code long} values numerically treating the values
1612      * as unsigned.
1613      *
1614      * @param  x the first {@code long} to compare
1615      * @param  y the second {@code long} to compare
1616      * @return the value {@code 0} if {@code x == y}; a value less
1617      *         than {@code 0} if {@code x < y} as unsigned values; and
1618      *         a value greater than {@code 0} if {@code x > y} as
1619      *         unsigned values
1620      * @since 1.8
1621      */
1622     public static int compareUnsigned(long x, long y) {
1623         return compare(x + MIN_VALUE, y + MIN_VALUE);
1624     }
1625 
1626 
1627     /**
1628      * Returns the unsigned quotient of dividing the first argument by
1629      * the second where each argument and the result is interpreted as
1630      * an unsigned value.
1631      *
1632      * <p>Note that in two's complement arithmetic, the three other
1633      * basic arithmetic operations of add, subtract, and multiply are
1634      * bit-wise identical if the two operands are regarded as both
1635      * being signed or both being unsigned.  Therefore separate {@code
1636      * addUnsigned}, etc. methods are not provided.
1637      *
1638      * @param dividend the value to be divided
1639      * @param divisor the value doing the dividing
1640      * @return the unsigned quotient of the first argument divided by
1641      * the second argument
1642      * @see #remainderUnsigned
1643      * @since 1.8
1644      */
1645     public static long divideUnsigned(long dividend, long divisor) {
1646         if (divisor < 0L) { // signed comparison
1647             // Answer must be 0 or 1 depending on relative magnitude
1648             // of dividend and divisor.
1649             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1650         }
1651 
1652         if (dividend > 0) //  Both inputs non-negative
1653             return dividend/divisor;
1654         else {
1655             /*
1656              * For simple code, leveraging BigInteger.  Longer and faster
1657              * code written directly in terms of operations on longs is
1658              * possible; see "Hacker's Delight" for divide and remainder
1659              * algorithms.
1660              */
1661             return toUnsignedBigInteger(dividend).
1662                 divide(toUnsignedBigInteger(divisor)).longValue();
1663         }
1664     }
1665 
1666     /**
1667      * Returns the unsigned remainder from dividing the first argument
1668      * by the second where each argument and the result is interpreted
1669      * as an unsigned value.
1670      *
1671      * @param dividend the value to be divided
1672      * @param divisor the value doing the dividing
1673      * @return the unsigned remainder of the first argument divided by
1674      * the second argument
1675      * @see #divideUnsigned
1676      * @since 1.8
1677      */
1678     public static long remainderUnsigned(long dividend, long divisor) {
1679         if (dividend > 0 && divisor > 0) { // signed comparisons
1680             return dividend % divisor;
1681         } else {
1682             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1683                 return dividend;
1684             else
1685                 return toUnsignedBigInteger(dividend).
1686                     remainder(toUnsignedBigInteger(divisor)).longValue();
1687         }
1688     }
1689 
1690     // Bit Twiddling
1691 
1692     /**
1693      * The number of bits used to represent a {@code long} value in two's
1694      * complement binary form.
1695      *
1696      * @since 1.5
1697      */
1698     @Native public static final int SIZE = 64;
1699 
1700     /**
1701      * The number of bytes used to represent a {@code long} value in two's
1702      * complement binary form.
1703      *
1704      * @since 1.8
1705      */
1706     public static final int BYTES = SIZE / Byte.SIZE;
1707 
1708     /**
1709      * Returns a {@code long} value with at most a single one-bit, in the
1710      * position of the highest-order ("leftmost") one-bit in the specified
1711      * {@code long} value.  Returns zero if the specified value has no
1712      * one-bits in its two's complement binary representation, that is, if it
1713      * is equal to zero.
1714      *
1715      * @param i the value whose highest one bit is to be computed
1716      * @return a {@code long} value with a single one-bit, in the position
1717      *     of the highest-order one-bit in the specified value, or zero if
1718      *     the specified value is itself equal to zero.
1719      * @since 1.5
1720      */
1721     public static long highestOneBit(long i) {
1722         // HD, Figure 3-1
1723         i |= (i >>  1);
1724         i |= (i >>  2);
1725         i |= (i >>  4);
1726         i |= (i >>  8);
1727         i |= (i >> 16);
1728         i |= (i >> 32);
1729         return i - (i >>> 1);
1730     }
1731 
1732     /**
1733      * Returns a {@code long} value with at most a single one-bit, in the
1734      * position of the lowest-order ("rightmost") one-bit in the specified
1735      * {@code long} value.  Returns zero if the specified value has no
1736      * one-bits in its two's complement binary representation, that is, if it
1737      * is equal to zero.
1738      *
1739      * @param i the value whose lowest one bit is to be computed
1740      * @return a {@code long} value with a single one-bit, in the position
1741      *     of the lowest-order one-bit in the specified value, or zero if
1742      *     the specified value is itself equal to zero.
1743      * @since 1.5
1744      */
1745     public static long lowestOneBit(long i) {
1746         // HD, Section 2-1
1747         return i & -i;
1748     }
1749 
1750     /**
1751      * Returns the number of zero bits preceding the highest-order
1752      * ("leftmost") one-bit in the two's complement binary representation
1753      * of the specified {@code long} value.  Returns 64 if the
1754      * specified value has no one-bits in its two's complement representation,
1755      * in other words if it is equal to zero.
1756      *
1757      * <p>Note that this method is closely related to the logarithm base 2.
1758      * For all positive {@code long} values x:
1759      * <ul>
1760      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1761      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1762      * </ul>
1763      *
1764      * @param i the value whose number of leading zeros is to be computed
1765      * @return the number of zero bits preceding the highest-order
1766      *     ("leftmost") one-bit in the two's complement binary representation
1767      *     of the specified {@code long} value, or 64 if the value
1768      *     is equal to zero.
1769      * @since 1.5
1770      */
1771     @HotSpotIntrinsicCandidate
1772     public static int numberOfLeadingZeros(long i) {
1773         // HD, Figure 5-6
1774          if (i == 0)
1775             return 64;
1776         int n = 1;
1777         int x = (int)(i >>> 32);
1778         if (x == 0) { n += 32; x = (int)i; }
1779         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1780         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1781         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1782         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1783         n -= x >>> 31;
1784         return n;
1785     }
1786 
1787     /**
1788      * Returns the number of zero bits following the lowest-order ("rightmost")
1789      * one-bit in the two's complement binary representation of the specified
1790      * {@code long} value.  Returns 64 if the specified value has no
1791      * one-bits in its two's complement representation, in other words if it is
1792      * equal to zero.
1793      *
1794      * @param i the value whose number of trailing zeros is to be computed
1795      * @return the number of zero bits following the lowest-order ("rightmost")
1796      *     one-bit in the two's complement binary representation of the
1797      *     specified {@code long} value, or 64 if the value is equal
1798      *     to zero.
1799      * @since 1.5
1800      */
1801     @HotSpotIntrinsicCandidate
1802     public static int numberOfTrailingZeros(long i) {
1803         // HD, Figure 5-14
1804         int x, y;
1805         if (i == 0) return 64;
1806         int n = 63;
1807         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1808         y = x <<16; if (y != 0) { n = n -16; x = y; }
1809         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1810         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1811         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1812         return n - ((x << 1) >>> 31);
1813     }
1814 
1815     /**
1816      * Returns the number of one-bits in the two's complement binary
1817      * representation of the specified {@code long} value.  This function is
1818      * sometimes referred to as the <i>population count</i>.
1819      *
1820      * @param i the value whose bits are to be counted
1821      * @return the number of one-bits in the two's complement binary
1822      *     representation of the specified {@code long} value.
1823      * @since 1.5
1824      */
1825      @HotSpotIntrinsicCandidate
1826      public static int bitCount(long i) {
1827         // HD, Figure 5-2
1828         i = i - ((i >>> 1) & 0x5555555555555555L);
1829         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1830         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1831         i = i + (i >>> 8);
1832         i = i + (i >>> 16);
1833         i = i + (i >>> 32);
1834         return (int)i & 0x7f;
1835      }
1836 
1837     /**
1838      * Returns the value obtained by rotating the two's complement binary
1839      * representation of the specified {@code long} value left by the
1840      * specified number of bits.  (Bits shifted out of the left hand, or
1841      * high-order, side reenter on the right, or low-order.)
1842      *
1843      * <p>Note that left rotation with a negative distance is equivalent to
1844      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1845      * distance)}.  Note also that rotation by any multiple of 64 is a
1846      * no-op, so all but the last six bits of the rotation distance can be
1847      * ignored, even if the distance is negative: {@code rotateLeft(val,
1848      * distance) == rotateLeft(val, distance & 0x3F)}.
1849      *
1850      * @param i the value whose bits are to be rotated left
1851      * @param distance the number of bit positions to rotate left
1852      * @return the value obtained by rotating the two's complement binary
1853      *     representation of the specified {@code long} value left by the
1854      *     specified number of bits.
1855      * @since 1.5
1856      */
1857     public static long rotateLeft(long i, int distance) {
1858         return (i << distance) | (i >>> -distance);
1859     }
1860 
1861     /**
1862      * Returns the value obtained by rotating the two's complement binary
1863      * representation of the specified {@code long} value right by the
1864      * specified number of bits.  (Bits shifted out of the right hand, or
1865      * low-order, side reenter on the left, or high-order.)
1866      *
1867      * <p>Note that right rotation with a negative distance is equivalent to
1868      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1869      * distance)}.  Note also that rotation by any multiple of 64 is a
1870      * no-op, so all but the last six bits of the rotation distance can be
1871      * ignored, even if the distance is negative: {@code rotateRight(val,
1872      * distance) == rotateRight(val, distance & 0x3F)}.
1873      *
1874      * @param i the value whose bits are to be rotated right
1875      * @param distance the number of bit positions to rotate right
1876      * @return the value obtained by rotating the two's complement binary
1877      *     representation of the specified {@code long} value right by the
1878      *     specified number of bits.
1879      * @since 1.5
1880      */
1881     public static long rotateRight(long i, int distance) {
1882         return (i >>> distance) | (i << -distance);
1883     }
1884 
1885     /**
1886      * Returns the value obtained by reversing the order of the bits in the
1887      * two's complement binary representation of the specified {@code long}
1888      * value.
1889      *
1890      * @param i the value to be reversed
1891      * @return the value obtained by reversing order of the bits in the
1892      *     specified {@code long} value.
1893      * @since 1.5
1894      */
1895     public static long reverse(long i) {
1896         // HD, Figure 7-1
1897         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1898         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1899         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1900 
1901         return reverseBytes(i);
1902     }
1903 
1904     /**
1905      * Returns the signum function of the specified {@code long} value.  (The
1906      * return value is -1 if the specified value is negative; 0 if the
1907      * specified value is zero; and 1 if the specified value is positive.)
1908      *
1909      * @param i the value whose signum is to be computed
1910      * @return the signum function of the specified {@code long} value.
1911      * @since 1.5
1912      */
1913     public static int signum(long i) {
1914         // HD, Section 2-7
1915         return (int) ((i >> 63) | (-i >>> 63));
1916     }
1917 
1918     /**
1919      * Returns the value obtained by reversing the order of the bytes in the
1920      * two's complement representation of the specified {@code long} value.
1921      *
1922      * @param i the value whose bytes are to be reversed
1923      * @return the value obtained by reversing the bytes in the specified
1924      *     {@code long} value.
1925      * @since 1.5
1926      */
1927     @HotSpotIntrinsicCandidate
1928     public static long reverseBytes(long i) {
1929         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1930         return (i << 48) | ((i & 0xffff0000L) << 16) |
1931             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1932     }
1933 
1934     /**
1935      * Adds two {@code long} values together as per the + operator.
1936      *
1937      * @param a the first operand
1938      * @param b the second operand
1939      * @return the sum of {@code a} and {@code b}
1940      * @see java.util.function.BinaryOperator
1941      * @since 1.8
1942      */
1943     public static long sum(long a, long b) {
1944         return a + b;
1945     }
1946 
1947     /**
1948      * Returns the greater of two {@code long} values
1949      * as if by calling {@link Math#max(long, long) Math.max}.
1950      *
1951      * @param a the first operand
1952      * @param b the second operand
1953      * @return the greater of {@code a} and {@code b}
1954      * @see java.util.function.BinaryOperator
1955      * @since 1.8
1956      */
1957     public static long max(long a, long b) {
1958         return Math.max(a, b);
1959     }
1960 
1961     /**
1962      * Returns the smaller of two {@code long} values
1963      * as if by calling {@link Math#min(long, long) Math.min}.
1964      *
1965      * @param a the first operand
1966      * @param b the second operand
1967      * @return the smaller of {@code a} and {@code b}
1968      * @see java.util.function.BinaryOperator
1969      * @since 1.8
1970      */
1971     public static long min(long a, long b) {
1972         return Math.min(a, b);
1973     }
1974 
1975     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1976     @Native private static final long serialVersionUID = 4290774380558885855L;
1977 }