1 /*
   2  * Copyright (c) 1994, 2012, 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.math.*;
  29 
  30 /**
  31  * The {@code Long} class wraps a value of the primitive type {@code
  32  * long} in an object. An object of type {@code Long} contains a
  33  * single field whose type is {@code long}.
  34  *
  35  * <p> In addition, this class provides several methods for converting
  36  * a {@code long} to a {@code String} and a {@code String} to a {@code
  37  * long}, as well as other constants and methods useful when dealing
  38  * with a {@code long}.
  39  *
  40  * <p>Implementation note: The implementations of the "bit twiddling"
  41  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  42  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  43  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  44  * Delight</i>, (Addison Wesley, 2002).
  45  *
  46  * @author  Lee Boynton
  47  * @author  Arthur van Hoff
  48  * @author  Josh Bloch
  49  * @author  Joseph D. Darcy
  50  * @since   JDK1.0
  51  */
  52 public final class Long extends Number implements Comparable<Long> {
  53     /**
  54      * A constant holding the minimum value a {@code long} can
  55      * have, -2<sup>63</sup>.
  56      */
  57     public static final long MIN_VALUE = 0x8000000000000000L;
  58 
  59     /**
  60      * A constant holding the maximum value a {@code long} can
  61      * have, 2<sup>63</sup>-1.
  62      */
  63     public static final long MAX_VALUE = 0x7fffffffffffffffL;
  64 
  65     /**
  66      * The {@code Class} instance representing the primitive type
  67      * {@code long}.
  68      *
  69      * @since   JDK1.1
  70      */
  71     @SuppressWarnings("unchecked")
  72     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  73 
  74     /**
  75      * Returns a string representation of the first argument in the
  76      * radix specified by the second argument.
  77      *
  78      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  79      * or larger than {@code Character.MAX_RADIX}, then the radix
  80      * {@code 10} is used instead.
  81      *
  82      * <p>If the first argument is negative, the first element of the
  83      * result is the ASCII minus sign {@code '-'}
  84      * (<code>'&#92;u002d'</code>). If the first argument is not
  85      * negative, no sign character appears in the result.
  86      *
  87      * <p>The remaining characters of the result represent the magnitude
  88      * of the first argument. If the magnitude is zero, it is
  89      * represented by a single zero character {@code '0'}
  90      * (<code>'&#92;u0030'</code>); otherwise, the first character of
  91      * the representation of the magnitude will not be the zero
  92      * character.  The following ASCII characters are used as digits:
  93      *
  94      * <blockquote>
  95      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
  96      * </blockquote>
  97      *
  98      * These are <code>'&#92;u0030'</code> through
  99      * <code>'&#92;u0039'</code> and <code>'&#92;u0061'</code> through
 100      * <code>'&#92;u007a'</code>. If {@code radix} is
 101      * <var>N</var>, then the first <var>N</var> of these characters
 102      * are used as radix-<var>N</var> digits in the order shown. Thus,
 103      * the digits for hexadecimal (radix 16) are
 104      * {@code 0123456789abcdef}. If uppercase letters are
 105      * desired, the {@link java.lang.String#toUpperCase()} method may
 106      * be called on the result:
 107      *
 108      * <blockquote>
 109      *  {@code Long.toString(n, 16).toUpperCase()}
 110      * </blockquote>
 111      *
 112      * @param   i       a {@code long} to be converted to a string.
 113      * @param   radix   the radix to use in the string representation.
 114      * @return  a string representation of the argument in the specified radix.
 115      * @see     java.lang.Character#MAX_RADIX
 116      * @see     java.lang.Character#MIN_RADIX
 117      */
 118     public static String toString(long i, int radix) {
 119         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 120             radix = 10;
 121         if (radix == 10)
 122             return toString(i);
 123         char[] buf = new char[65];
 124         int charPos = 64;
 125         boolean negative = (i < 0);
 126 
 127         if (!negative) {
 128             i = -i;
 129         }
 130 
 131         while (i <= -radix) {
 132             buf[charPos--] = Integer.digits[(int)(-(i % radix))];
 133             i = i / radix;
 134         }
 135         buf[charPos] = Integer.digits[(int)(-i)];
 136 
 137         if (negative) {
 138             buf[--charPos] = '-';
 139         }
 140 
 141         return new String(buf, charPos, (65 - charPos));
 142     }
 143 
 144     /**
 145      * Returns an unsigned string representation of the first argument
 146      * in the radix specified by the second argument.
 147      *
 148      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 149      * or larger than {@code Character.MAX_RADIX}, then the radix
 150      * {@code 10} is used instead.
 151      *
 152      * <p>Note that since the first argument is treated as an unsigned
 153      * value, no leading sign character is printed.
 154      *
 155      * <p>If the magnitude is zero, it is represented by a single zero
 156      * character {@code '0'} (<code>'&#92;u0030'</code>); otherwise,
 157      * the first character of the representation of the magnitude will
 158      * not be the zero character.
 159      *
 160      * <p>The characters used as digits and the behavior of radixes
 161      * is the same as {@link #toString(long, int) toString}.
 162      *
 163      * @param   i       an integer to be converted to an unsigned string.
 164      * @param   radix   the radix to use in the string representation.
 165      * @return  an unsigned string representation of the argument in the specified radix.
 166      * @see     #toString(long, int)
 167      * @since 1.8
 168      */
 169     public static String toUnsignedString(long i, int radix) {
 170         if (i >= 0)
 171             return toString(i, radix);
 172         else {
 173             switch (radix) {
 174             case 2:
 175                 return toBinaryString(i);
 176 
 177             case 4:
 178                 return toUnsignedString0(i, 2);
 179 
 180             case 8:
 181                 return toOctalString(i);
 182 
 183             case 10:
 184                 /*
 185                  * We can get the effect of an unsigned division by 10
 186                  * on a long value by first shifting right, yielding a
 187                  * positive value, and then dividing by 5.  This
 188                  * allows the last digit and preceding digits to be
 189                  * isolated more quickly than by an initial conversion
 190                  * to BigInteger.
 191                  */
 192                 long quot = (i >>> 1) / 5;
 193                 long rem = i - quot * 10;
 194                 return toString(quot) + rem;
 195 
 196             case 16:
 197                 return toHexString(i);
 198 
 199             case 32:
 200                 return toUnsignedString0(i, 5);
 201 
 202             default:
 203                 return toUnsignedBigInteger(i).toString(radix);
 204             }
 205         }
 206     }
 207 
 208     /**
 209      * Return a BigInteger equal to the unsigned value of the
 210      * argument.
 211      */
 212     private static BigInteger toUnsignedBigInteger(long i) {
 213         if (i >= 0L)
 214             return BigInteger.valueOf(i);
 215         else {
 216             int upper = (int) (i >>> 32);
 217             int lower = (int) i;
 218 
 219             // return (upper << 32) + lower
 220             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 221                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 222         }
 223     }
 224 
 225     /**
 226      * Returns a string representation of the {@code long}
 227      * argument as an unsigned integer in base&nbsp;16.
 228      *
 229      * <p>The unsigned {@code long} value is the argument plus
 230      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 231      * equal to the argument.  This value is converted to a string of
 232      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 233      * leading {@code 0}s.
 234      *
 235      * <p>The value of the argument can be recovered from the returned
 236      * string {@code s} by calling {@link
 237      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 238      * 16)}.
 239      *
 240      * <p>If the unsigned magnitude is zero, it is represented by a
 241      * single zero character {@code '0'} (<code>'&#92;u0030'</code>);
 242      * otherwise, the first character of the representation of the
 243      * unsigned magnitude will not be the zero character. The
 244      * following characters are used as hexadecimal digits:
 245      *
 246      * <blockquote>
 247      *  {@code 0123456789abcdef}
 248      * </blockquote>
 249      *
 250      * These are the characters <code>'&#92;u0030'</code> through
 251      * <code>'&#92;u0039'</code> and  <code>'&#92;u0061'</code> through
 252      * <code>'&#92;u0066'</code>.  If uppercase letters are desired,
 253      * the {@link java.lang.String#toUpperCase()} method may be called
 254      * on the result:
 255      *
 256      * <blockquote>
 257      *  {@code Long.toHexString(n).toUpperCase()}
 258      * </blockquote>
 259      *
 260      * @param   i   a {@code long} to be converted to a string.
 261      * @return  the string representation of the unsigned {@code long}
 262      *          value represented by the argument in hexadecimal
 263      *          (base&nbsp;16).
 264      * @see #parseUnsignedLong(String, int)
 265      * @see #toUnsignedString(long, int)
 266      * @since   JDK 1.0.2
 267      */
 268     public static String toHexString(long i) {
 269         return toUnsignedString0(i, 4);
 270     }
 271 
 272     /**
 273      * Returns a string representation of the {@code long}
 274      * argument as an unsigned integer in base&nbsp;8.
 275      *
 276      * <p>The unsigned {@code long} value is the argument plus
 277      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 278      * equal to the argument.  This value is converted to a string of
 279      * ASCII digits in octal (base&nbsp;8) with no extra leading
 280      * {@code 0}s.
 281      *
 282      * <p>The value of the argument can be recovered from the returned
 283      * string {@code s} by calling {@link
 284      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 285      * 8)}.
 286      *
 287      * <p>If the unsigned magnitude is zero, it is represented by a
 288      * single zero character {@code '0'} (<code>'&#92;u0030'</code>);
 289      * otherwise, the first character of the representation of the
 290      * unsigned magnitude will not be the zero character. The
 291      * following characters are used as octal digits:
 292      *
 293      * <blockquote>
 294      *  {@code 01234567}
 295      * </blockquote>
 296      *
 297      * These are the characters <code>'&#92;u0030'</code> through
 298      * <code>'&#92;u0037'</code>.
 299      *
 300      * @param   i   a {@code long} to be converted to a string.
 301      * @return  the string representation of the unsigned {@code long}
 302      *          value represented by the argument in octal (base&nbsp;8).
 303      * @see #parseUnsignedLong(String, int)
 304      * @see #toUnsignedString(long, int)
 305      * @since   JDK 1.0.2
 306      */
 307     public static String toOctalString(long i) {
 308         return toUnsignedString0(i, 3);
 309     }
 310 
 311     /**
 312      * Returns a string representation of the {@code long}
 313      * argument as an unsigned integer in base&nbsp;2.
 314      *
 315      * <p>The unsigned {@code long} value is the argument plus
 316      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 317      * equal to the argument.  This value is converted to a string of
 318      * ASCII digits in binary (base&nbsp;2) with no extra leading
 319      * {@code 0}s.
 320      *
 321      * <p>The value of the argument can be recovered from the returned
 322      * string {@code s} by calling {@link
 323      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 324      * 2)}.
 325      *
 326      * <p>If the unsigned magnitude is zero, it is represented by a
 327      * single zero character {@code '0'} (<code>'&#92;u0030'</code>);
 328      * otherwise, the first character of the representation of the
 329      * unsigned magnitude will not be the zero character. The
 330      * characters {@code '0'} (<code>'&#92;u0030'</code>) and {@code
 331      * '1'} (<code>'&#92;u0031'</code>) are used as binary digits.
 332      *
 333      * @param   i   a {@code long} to be converted to a string.
 334      * @return  the string representation of the unsigned {@code long}
 335      *          value represented by the argument in binary (base&nbsp;2).
 336      * @see #parseUnsignedLong(String, int)
 337      * @see #toUnsignedString(long, int)
 338      * @since   JDK 1.0.2
 339      */
 340     public static String toBinaryString(long i) {
 341         return toUnsignedString0(i, 1);
 342     }
 343 
 344     /**
 345      * Convert the integer to an unsigned number.
 346      */
 347     private static String toUnsignedString0(long i, int shift) {
 348         char[] buf = new char[64];
 349         int charPos = 64;
 350         int radix = 1 << shift;
 351         long mask = radix - 1;
 352         do {
 353             buf[--charPos] = Integer.digits[(int)(i & mask)];
 354             i >>>= shift;
 355         } while (i != 0);
 356         return new String(buf, charPos, (64 - charPos));
 357     }
 358 
 359     /**
 360      * Returns a {@code String} object representing the specified
 361      * {@code long}.  The argument is converted to signed decimal
 362      * representation and returned as a string, exactly as if the
 363      * argument and the radix 10 were given as arguments to the {@link
 364      * #toString(long, int)} method.
 365      *
 366      * @param   i   a {@code long} to be converted.
 367      * @return  a string representation of the argument in base&nbsp;10.
 368      */
 369     public static String toString(long i) {
 370         if (i == Long.MIN_VALUE)
 371             return "-9223372036854775808";
 372         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
 373         char[] buf = new char[size];
 374         getChars(i, size, buf);
 375         return new String(0, size, buf);
 376     }
 377 
 378     /**
 379      * Returns an unsigned string representation of the argument.
 380      *
 381      * The argument is converted to unsigned decimal representation
 382      * and returned as a string exactly as if the argument and radix
 383      * 10 were given as arguments to the {@link #toUnsignedString(long,
 384      * int)} method.
 385      *
 386      * @param   i  an integer to be converted to an unsigned string.
 387      * @return  an unsigned string representation of the argument.
 388      * @see     #toUnsignedString(long, int)
 389      * @since 1.8
 390      */
 391     public static String toUnsignedString(long i) {
 392         return toUnsignedString(i, 10);
 393     }
 394 
 395     /**
 396      * Places characters representing the integer i into the
 397      * character array buf. The characters are placed into
 398      * the buffer backwards starting with the least significant
 399      * digit at the specified index (exclusive), and working
 400      * backwards from there.
 401      *
 402      * Will fail if i == Long.MIN_VALUE
 403      */
 404     static void getChars(long i, int index, char[] buf) {
 405         long q;
 406         int r;
 407         int charPos = index;
 408         char sign = 0;
 409 
 410         if (i < 0) {
 411             sign = '-';
 412             i = -i;
 413         }
 414 
 415         // Get 2 digits/iteration using longs until quotient fits into an int
 416         while (i > Integer.MAX_VALUE) {
 417             q = i / 100;
 418             // really: r = i - (q * 100);
 419             r = (int)(i - ((q << 6) + (q << 5) + (q << 2)));
 420             i = q;
 421             buf[--charPos] = Integer.DigitOnes[r];
 422             buf[--charPos] = Integer.DigitTens[r];
 423         }
 424 
 425         // Get 2 digits/iteration using ints
 426         int q2;
 427         int i2 = (int)i;
 428         while (i2 >= 65536) {
 429             q2 = i2 / 100;
 430             // really: r = i2 - (q * 100);
 431             r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
 432             i2 = q2;
 433             buf[--charPos] = Integer.DigitOnes[r];
 434             buf[--charPos] = Integer.DigitTens[r];
 435         }
 436 
 437         // Fall thru to fast mode for smaller numbers
 438         // assert(i2 <= 65536, i2);
 439         for (;;) {
 440             q2 = (i2 * 52429) >>> (16+3);
 441             r = i2 - ((q2 << 3) + (q2 << 1));  // r = i2-(q2*10) ...
 442             buf[--charPos] = Integer.digits[r];
 443             i2 = q2;
 444             if (i2 == 0) break;
 445         }
 446         if (sign != 0) {
 447             buf[--charPos] = sign;
 448         }
 449     }
 450 
 451     // Requires positive x
 452     static int stringSize(long x) {
 453         long p = 10;
 454         for (int i=1; i<19; i++) {
 455             if (x < p)
 456                 return i;
 457             p = 10*p;
 458         }
 459         return 19;
 460     }
 461 
 462     /**
 463      * Parses the string argument as a signed {@code long} in the
 464      * radix specified by the second argument. The characters in the
 465      * string must all be digits of the specified radix (as determined
 466      * by whether {@link java.lang.Character#digit(char, int)} returns
 467      * a nonnegative value), except that the first character may be an
 468      * ASCII minus sign {@code '-'} (<code>'&#92;u002D'</code>) to
 469      * indicate a negative value or an ASCII plus sign {@code '+'}
 470      * (<code>'&#92;u002B'</code>) to indicate a positive value. The
 471      * resulting {@code long} value is returned.
 472      *
 473      * <p>Note that neither the character {@code L}
 474      * (<code>'&#92;u004C'</code>) nor {@code l}
 475      * (<code>'&#92;u006C'</code>) is permitted to appear at the end
 476      * of the string as a type indicator, as would be permitted in
 477      * Java programming language source code - except that either
 478      * {@code L} or {@code l} may appear as a digit for a
 479      * radix greater than 22.
 480      *
 481      * <p>An exception of type {@code NumberFormatException} is
 482      * thrown if any of the following situations occurs:
 483      * <ul>
 484      *
 485      * <li>The first argument is {@code null} or is a string of
 486      * length zero.
 487      *
 488      * <li>The {@code radix} is either smaller than {@link
 489      * java.lang.Character#MIN_RADIX} or larger than {@link
 490      * java.lang.Character#MAX_RADIX}.
 491      *
 492      * <li>Any character of the string is not a digit of the specified
 493      * radix, except that the first character may be a minus sign
 494      * {@code '-'} (<code>'&#92;u002d'</code>) or plus sign {@code
 495      * '+'} (<code>'&#92;u002B'</code>) provided that the string is
 496      * longer than length 1.
 497      *
 498      * <li>The value represented by the string is not a value of type
 499      *      {@code long}.
 500      * </ul>
 501      *
 502      * <p>Examples:
 503      * <blockquote><pre>
 504      * parseLong("0", 10) returns 0L
 505      * parseLong("473", 10) returns 473L
 506      * parseLong("+42", 10) returns 42L
 507      * parseLong("-0", 10) returns 0L
 508      * parseLong("-FF", 16) returns -255L
 509      * parseLong("1100110", 2) returns 102L
 510      * parseLong("99", 8) throws a NumberFormatException
 511      * parseLong("Hazelnut", 10) throws a NumberFormatException
 512      * parseLong("Hazelnut", 36) returns 1356099454469L
 513      * </pre></blockquote>
 514      *
 515      * @param      s       the {@code String} containing the
 516      *                     {@code long} representation to be parsed.
 517      * @param      radix   the radix to be used while parsing {@code s}.
 518      * @return     the {@code long} represented by the string argument in
 519      *             the specified radix.
 520      * @throws     NumberFormatException  if the string does not contain a
 521      *             parsable {@code long}.
 522      */
 523     public static long parseLong(String s, int radix)
 524               throws NumberFormatException
 525     {
 526         if (s == null) {
 527             throw new NumberFormatException("null");
 528         }
 529 
 530         if (radix < Character.MIN_RADIX) {
 531             throw new NumberFormatException("radix " + radix +
 532                                             " less than Character.MIN_RADIX");
 533         }
 534         if (radix > Character.MAX_RADIX) {
 535             throw new NumberFormatException("radix " + radix +
 536                                             " greater than Character.MAX_RADIX");
 537         }
 538 
 539         long result = 0;
 540         boolean negative = false;
 541         int i = 0, len = s.length();
 542         long limit = -Long.MAX_VALUE;
 543         long multmin;
 544         int digit;
 545 
 546         if (len > 0) {
 547             char firstChar = s.charAt(0);
 548             if (firstChar < '0') { // Possible leading "+" or "-"
 549                 if (firstChar == '-') {
 550                     negative = true;
 551                     limit = Long.MIN_VALUE;
 552                 } else if (firstChar != '+')
 553                     throw NumberFormatException.forInputString(s);
 554 
 555                 if (len == 1) // Cannot have lone "+" or "-"
 556                     throw NumberFormatException.forInputString(s);
 557                 i++;
 558             }
 559             multmin = limit / radix;
 560             while (i < len) {
 561                 // Accumulating negatively avoids surprises near MAX_VALUE
 562                 digit = Character.digit(s.charAt(i++),radix);
 563                 if (digit < 0) {
 564                     throw NumberFormatException.forInputString(s);
 565                 }
 566                 if (result < multmin) {
 567                     throw NumberFormatException.forInputString(s);
 568                 }
 569                 result *= radix;
 570                 if (result < limit + digit) {
 571                     throw NumberFormatException.forInputString(s);
 572                 }
 573                 result -= digit;
 574             }
 575         } else {
 576             throw NumberFormatException.forInputString(s);
 577         }
 578         return negative ? result : -result;
 579     }
 580 
 581     /**
 582      * Parses the string argument as a signed decimal {@code long}.
 583      * The characters in the string must all be decimal digits, except
 584      * that the first character may be an ASCII minus sign {@code '-'}
 585      * (<code>&#92;u002D'</code>) to indicate a negative value or an
 586      * ASCII plus sign {@code '+'} (<code>'&#92;u002B'</code>) to
 587      * indicate a positive value. The resulting {@code long} value is
 588      * returned, exactly as if the argument and the radix {@code 10}
 589      * were given as arguments to the {@link
 590      * #parseLong(java.lang.String, int)} method.
 591      *
 592      * <p>Note that neither the character {@code L}
 593      * (<code>'&#92;u004C'</code>) nor {@code l}
 594      * (<code>'&#92;u006C'</code>) is permitted to appear at the end
 595      * of the string as a type indicator, as would be permitted in
 596      * Java programming language source code.
 597      *
 598      * @param      s   a {@code String} containing the {@code long}
 599      *             representation to be parsed
 600      * @return     the {@code long} represented by the argument in
 601      *             decimal.
 602      * @throws     NumberFormatException  if the string does not contain a
 603      *             parsable {@code long}.
 604      */
 605     public static long parseLong(String s) throws NumberFormatException {
 606         return parseLong(s, 10);
 607     }
 608 
 609     /**
 610      * Parses the string argument as an unsigned {@code long} in the
 611      * radix specified by the second argument.
 612      *
 613      * The characters in the string must all be digits of the
 614      * specified radix (as determined by whether {@link
 615      * java.lang.Character#digit(char, int)} returns a nonnegative
 616      * value), except that the first character may be an ASCII plus
 617      * sign {@code '+'} (<code>'&#92;u002B'</code>). The resulting
 618      * integer value is returned.
 619      *
 620      * <p>An exception of type {@code NumberFormatException} is
 621      * thrown if any of the following situations occurs:
 622      * <ul>
 623      * <li>The first argument is {@code null} or is a string of
 624      * length zero.
 625      *
 626      * <li>The radix is either smaller than
 627      * {@link java.lang.Character#MIN_RADIX} or
 628      * larger than {@link java.lang.Character#MAX_RADIX}.
 629      *
 630      * <li>Any character of the string is not a digit of the specified
 631      * radix, except that the first character may be a plus sign
 632      * {@code '+'} (<code>'&#92;u002B'</code>) provided that the
 633      * string is longer than length 1.
 634      *
 635      * <li>The value represented by the string is larger than the
 636      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 637      *
 638      * </ul>
 639      *
 640      *
 641      * @param      s   the {@code String} containing the unsigned integer
 642      *                  representation to be parsed
 643      * @param      radix   the radix to be used while parsing {@code s}.
 644      * @return     the integer represented by the string argument in the
 645      *             specified radix.
 646      * @throws     NumberFormatException if the {@code String}
 647      *             does not contain a parsable {@code long}.
 648      * @since 1.8
 649      */
 650     public static long parseUnsignedLong(String s, int radix)
 651                 throws NumberFormatException {
 652         if (s == null)  {
 653             throw new NumberFormatException("null");
 654         }
 655 
 656         int len = s.length();
 657         if (len > 0) {
 658             char firstChar = s.charAt(0);
 659             if (firstChar == '-') {
 660                 throw new
 661                     NumberFormatException(String.format("Illegal leading minus sign " +
 662                                                        "on unsigned string %s.", s));
 663             } else {
 664                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 665                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 666                     return parseLong(s, radix);
 667                 }
 668 
 669                 // No need for range checks on len due to testing above.
 670                 long first = parseLong(s.substring(0, len - 1), radix);
 671                 int second = Character.digit(s.charAt(len - 1), radix);
 672                 if (second < 0) {
 673                     throw new NumberFormatException("Bad digit at end of " + s);
 674                 }
 675                 long result = first * radix + second;
 676                 if (compareUnsigned(result, first) < 0) {
 677                     /*
 678                      * The maximum unsigned value, (2^64)-1, takes at
 679                      * most one more digit to represent than the
 680                      * maximum signed value, (2^63)-1.  Therefore,
 681                      * parsing (len - 1) digits will be appropriately
 682                      * in-range of the signed parsing.  In other
 683                      * words, if parsing (len -1) digits overflows
 684                      * signed parsing, parsing len digits will
 685                      * certainly overflow unsigned parsing.
 686                      *
 687                      * The compareUnsigned check above catches
 688                      * situations where an unsigned overflow occurs
 689                      * incorporating the contribution of the final
 690                      * digit.
 691                      */
 692                     throw new NumberFormatException(String.format("String value %s exceeds " +
 693                                                                   "range of unsigned long.", s));
 694                 }
 695                 return result;
 696             }
 697         } else {
 698             throw NumberFormatException.forInputString(s);
 699         }
 700     }
 701 
 702     /**
 703      * Parses the string argument as an unsigned decimal {@code long}. The
 704      * characters in the string must all be decimal digits, except
 705      * that the first character may be an an ASCII plus sign {@code
 706      * '+'} (<code>'&#92;u002B'</code>). The resulting integer value
 707      * is returned, exactly as if the argument and the radix 10 were
 708      * given as arguments to the {@link
 709      * #parseUnsignedLong(java.lang.String, int)} method.
 710      *
 711      * @param s   a {@code String} containing the unsigned {@code long}
 712      *            representation to be parsed
 713      * @return    the unsigned integer value represented by the argument in decimal.
 714      * @throws    NumberFormatException  if the string does not contain a
 715      *            parsable unsigned integer.
 716      * @since 1.8
 717      */
 718     public static long parseUnsignedLong(String s) throws NumberFormatException {
 719         return parseUnsignedLong(s, 10);
 720     }
 721 
 722     /**
 723      * Returns a {@code Long} object holding the value
 724      * extracted from the specified {@code String} when parsed
 725      * with the radix given by the second argument.  The first
 726      * argument is interpreted as representing a signed
 727      * {@code long} in the radix specified by the second
 728      * argument, exactly as if the arguments were given to the {@link
 729      * #parseLong(java.lang.String, int)} method. The result is a
 730      * {@code Long} object that represents the {@code long}
 731      * value specified by the string.
 732      *
 733      * <p>In other words, this method returns a {@code Long} object equal
 734      * to the value of:
 735      *
 736      * <blockquote>
 737      *  {@code new Long(Long.parseLong(s, radix))}
 738      * </blockquote>
 739      *
 740      * @param      s       the string to be parsed
 741      * @param      radix   the radix to be used in interpreting {@code s}
 742      * @return     a {@code Long} object holding the value
 743      *             represented by the string argument in the specified
 744      *             radix.
 745      * @throws     NumberFormatException  If the {@code String} does not
 746      *             contain a parsable {@code long}.
 747      */
 748     public static Long valueOf(String s, int radix) throws NumberFormatException {
 749         return Long.valueOf(parseLong(s, radix));
 750     }
 751 
 752     /**
 753      * Returns a {@code Long} object holding the value
 754      * of the specified {@code String}. The argument is
 755      * interpreted as representing a signed decimal {@code long},
 756      * exactly as if the argument were given to the {@link
 757      * #parseLong(java.lang.String)} method. The result is a
 758      * {@code Long} object that represents the integer value
 759      * specified by the string.
 760      *
 761      * <p>In other words, this method returns a {@code Long} object
 762      * equal to the value of:
 763      *
 764      * <blockquote>
 765      *  {@code new Long(Long.parseLong(s))}
 766      * </blockquote>
 767      *
 768      * @param      s   the string to be parsed.
 769      * @return     a {@code Long} object holding the value
 770      *             represented by the string argument.
 771      * @throws     NumberFormatException  If the string cannot be parsed
 772      *             as a {@code long}.
 773      */
 774     public static Long valueOf(String s) throws NumberFormatException
 775     {
 776         return Long.valueOf(parseLong(s, 10));
 777     }
 778 
 779     private static class LongCache {
 780         private LongCache(){}
 781 
 782         static final Long cache[] = new Long[-(-128) + 127 + 1];
 783 
 784         static {
 785             for(int i = 0; i < cache.length; i++)
 786                 cache[i] = new Long(i - 128);
 787         }
 788     }
 789 
 790     /**
 791      * Returns a {@code Long} instance representing the specified
 792      * {@code long} value.
 793      * If a new {@code Long} instance is not required, this method
 794      * should generally be used in preference to the constructor
 795      * {@link #Long(long)}, as this method is likely to yield
 796      * significantly better space and time performance by caching
 797      * frequently requested values.
 798      *
 799      * Note that unlike the {@linkplain Integer#valueOf(int)
 800      * corresponding method} in the {@code Integer} class, this method
 801      * is <em>not</em> required to cache values within a particular
 802      * range.
 803      *
 804      * @param  l a long value.
 805      * @return a {@code Long} instance representing {@code l}.
 806      * @since  1.5
 807      */
 808     public static Long valueOf(long l) {
 809         final int offset = 128;
 810         if (l >= -128 && l <= 127) { // will cache
 811             return LongCache.cache[(int)l + offset];
 812         }
 813         return new Long(l);
 814     }
 815 
 816     /**
 817      * Decodes a {@code String} into a {@code Long}.
 818      * Accepts decimal, hexadecimal, and octal numbers given by the
 819      * following grammar:
 820      *
 821      * <blockquote>
 822      * <dl>
 823      * <dt><i>DecodableString:</i>
 824      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
 825      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
 826      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
 827      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
 828      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
 829      * <p>
 830      * <dt><i>Sign:</i>
 831      * <dd>{@code -}
 832      * <dd>{@code +}
 833      * </dl>
 834      * </blockquote>
 835      *
 836      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
 837      * are as defined in section 3.10.1 of
 838      * <cite>The Java&trade; Language Specification</cite>,
 839      * except that underscores are not accepted between digits.
 840      *
 841      * <p>The sequence of characters following an optional
 842      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
 843      * "{@code #}", or leading zero) is parsed as by the {@code
 844      * Long.parseLong} method with the indicated radix (10, 16, or 8).
 845      * This sequence of characters must represent a positive value or
 846      * a {@link NumberFormatException} will be thrown.  The result is
 847      * negated if first character of the specified {@code String} is
 848      * the minus sign.  No whitespace characters are permitted in the
 849      * {@code String}.
 850      *
 851      * @param     nm the {@code String} to decode.
 852      * @return    a {@code Long} object holding the {@code long}
 853      *            value represented by {@code nm}
 854      * @throws    NumberFormatException  if the {@code String} does not
 855      *            contain a parsable {@code long}.
 856      * @see java.lang.Long#parseLong(String, int)
 857      * @since 1.2
 858      */
 859     public static Long decode(String nm) throws NumberFormatException {
 860         int radix = 10;
 861         int index = 0;
 862         boolean negative = false;
 863         Long result;
 864 
 865         if (nm.length() == 0)
 866             throw new NumberFormatException("Zero length string");
 867         char firstChar = nm.charAt(0);
 868         // Handle sign, if present
 869         if (firstChar == '-') {
 870             negative = true;
 871             index++;
 872         } else if (firstChar == '+')
 873             index++;
 874 
 875         // Handle radix specifier, if present
 876         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
 877             index += 2;
 878             radix = 16;
 879         }
 880         else if (nm.startsWith("#", index)) {
 881             index ++;
 882             radix = 16;
 883         }
 884         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
 885             index ++;
 886             radix = 8;
 887         }
 888 
 889         if (nm.startsWith("-", index) || nm.startsWith("+", index))
 890             throw new NumberFormatException("Sign character in wrong position");
 891 
 892         try {
 893             result = Long.valueOf(nm.substring(index), radix);
 894             result = negative ? Long.valueOf(-result.longValue()) : result;
 895         } catch (NumberFormatException e) {
 896             // If number is Long.MIN_VALUE, we'll end up here. The next line
 897             // handles this case, and causes any genuine format error to be
 898             // rethrown.
 899             String constant = negative ? ("-" + nm.substring(index))
 900                                        : nm.substring(index);
 901             result = Long.valueOf(constant, radix);
 902         }
 903         return result;
 904     }
 905 
 906     /**
 907      * The value of the {@code Long}.
 908      *
 909      * @serial
 910      */
 911     private final long value;
 912 
 913     /**
 914      * Constructs a newly allocated {@code Long} object that
 915      * represents the specified {@code long} argument.
 916      *
 917      * @param   value   the value to be represented by the
 918      *          {@code Long} object.
 919      */
 920     public Long(long value) {
 921         this.value = value;
 922     }
 923 
 924     /**
 925      * Constructs a newly allocated {@code Long} object that
 926      * represents the {@code long} value indicated by the
 927      * {@code String} parameter. The string is converted to a
 928      * {@code long} value in exactly the manner used by the
 929      * {@code parseLong} method for radix 10.
 930      *
 931      * @param      s   the {@code String} to be converted to a
 932      *             {@code Long}.
 933      * @throws     NumberFormatException  if the {@code String} does not
 934      *             contain a parsable {@code long}.
 935      * @see        java.lang.Long#parseLong(java.lang.String, int)
 936      */
 937     public Long(String s) throws NumberFormatException {
 938         this.value = parseLong(s, 10);
 939     }
 940 
 941     /**
 942      * Returns the value of this {@code Long} as a {@code byte} after
 943      * a narrowing primitive conversion.
 944      * @jls 5.1.3 Narrowing Primitive Conversions
 945      */
 946     public byte byteValue() {
 947         return (byte)value;
 948     }
 949 
 950     /**
 951      * Returns the value of this {@code Long} as a {@code short} after
 952      * a narrowing primitive conversion.
 953      * @jls 5.1.3 Narrowing Primitive Conversions
 954      */
 955     public short shortValue() {
 956         return (short)value;
 957     }
 958 
 959     /**
 960      * Returns the value of this {@code Long} as an {@code int} after
 961      * a narrowing primitive conversion.
 962      * @jls 5.1.3 Narrowing Primitive Conversions
 963      */
 964     public int intValue() {
 965         return (int)value;
 966     }
 967 
 968     /**
 969      * Returns the value of this {@code Long} as a
 970      * {@code long} value.
 971      */
 972     public long longValue() {
 973         return value;
 974     }
 975 
 976     /**
 977      * Returns the value of this {@code Long} as a {@code float} after
 978      * a widening primitive conversion.
 979      * @jls 5.1.2 Widening Primitive Conversions
 980      */
 981     public float floatValue() {
 982         return (float)value;
 983     }
 984 
 985     /**
 986      * Returns the value of this {@code Long} as a {@code double}
 987      * after a widening primitive conversion.
 988      * @jls 5.1.2 Widening Primitive Conversions
 989      */
 990     public double doubleValue() {
 991         return (double)value;
 992     }
 993 
 994     /**
 995      * Returns a {@code String} object representing this
 996      * {@code Long}'s value.  The value is converted to signed
 997      * decimal representation and returned as a string, exactly as if
 998      * the {@code long} value were given as an argument to the
 999      * {@link java.lang.Long#toString(long)} method.
1000      *
1001      * @return  a string representation of the value of this object in
1002      *          base&nbsp;10.
1003      */
1004     public String toString() {
1005         return toString(value);
1006     }
1007 
1008     /**
1009      * Returns a hash code for this {@code Long}. The result is
1010      * the exclusive OR of the two halves of the primitive
1011      * {@code long} value held by this {@code Long}
1012      * object. That is, the hashcode is the value of the expression:
1013      *
1014      * <blockquote>
1015      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1016      * </blockquote>
1017      *
1018      * @return  a hash code value for this object.
1019      */
1020     public int hashCode() {
1021         return (int)(value ^ (value >>> 32));
1022     }
1023 
1024     /**
1025      * Compares this object to the specified object.  The result is
1026      * {@code true} if and only if the argument is not
1027      * {@code null} and is a {@code Long} object that
1028      * contains the same {@code long} value as this object.
1029      *
1030      * @param   obj   the object to compare with.
1031      * @return  {@code true} if the objects are the same;
1032      *          {@code false} otherwise.
1033      */
1034     public boolean equals(Object obj) {
1035         if (obj instanceof Long) {
1036             return value == ((Long)obj).longValue();
1037         }
1038         return false;
1039     }
1040 
1041     /**
1042      * Determines the {@code long} value of the system property
1043      * with the specified name.
1044      *
1045      * <p>The first argument is treated as the name of a system
1046      * property.  System properties are accessible through the {@link
1047      * java.lang.System#getProperty(java.lang.String)} method. The
1048      * string value of this property is then interpreted as a {@code
1049      * long} value using the grammar supported by {@link Long#decode decode}
1050      * and a {@code Long} object representing this value is returned.
1051      *
1052      * <p>If there is no property with the specified name, if the
1053      * specified name is empty or {@code null}, or if the property
1054      * does not have the correct numeric format, then {@code null} is
1055      * returned.
1056      *
1057      * <p>In other words, this method returns a {@code Long} object
1058      * equal to the value of:
1059      *
1060      * <blockquote>
1061      *  {@code getLong(nm, null)}
1062      * </blockquote>
1063      *
1064      * @param   nm   property name.
1065      * @return  the {@code Long} value of the property.
1066      * @throws  SecurityException for the same reasons as
1067      *          {@link System#getProperty(String) System.getProperty}
1068      * @see     java.lang.System#getProperty(java.lang.String)
1069      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1070      */
1071     public static Long getLong(String nm) {
1072         return getLong(nm, null);
1073     }
1074 
1075     /**
1076      * Determines the {@code long} value of the system property
1077      * with the specified name.
1078      *
1079      * <p>The first argument is treated as the name of a system
1080      * property.  System properties are accessible through the {@link
1081      * java.lang.System#getProperty(java.lang.String)} method. The
1082      * string value of this property is then interpreted as a {@code
1083      * long} value using the grammar supported by {@link Long#decode decode}
1084      * and a {@code Long} object representing this value is returned.
1085      *
1086      * <p>The second argument is the default value. A {@code Long} object
1087      * that represents the value of the second argument is returned if there
1088      * is no property of the specified name, if the property does not have
1089      * the correct numeric format, or if the specified name is empty or null.
1090      *
1091      * <p>In other words, this method returns a {@code Long} object equal
1092      * to the value of:
1093      *
1094      * <blockquote>
1095      *  {@code getLong(nm, new Long(val))}
1096      * </blockquote>
1097      *
1098      * but in practice it may be implemented in a manner such as:
1099      *
1100      * <blockquote><pre>
1101      * Long result = getLong(nm, null);
1102      * return (result == null) ? new Long(val) : result;
1103      * </pre></blockquote>
1104      *
1105      * to avoid the unnecessary allocation of a {@code Long} object when
1106      * the default value is not needed.
1107      *
1108      * @param   nm    property name.
1109      * @param   val   default value.
1110      * @return  the {@code Long} value of the property.
1111      * @throws  SecurityException for the same reasons as
1112      *          {@link System#getProperty(String) System.getProperty}
1113      * @see     java.lang.System#getProperty(java.lang.String)
1114      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1115      */
1116     public static Long getLong(String nm, long val) {
1117         Long result = Long.getLong(nm, null);
1118         return (result == null) ? Long.valueOf(val) : result;
1119     }
1120 
1121     /**
1122      * Returns the {@code long} value of the system property with
1123      * the specified name.  The first argument is treated as the name
1124      * of a system property.  System properties are accessible through
1125      * the {@link java.lang.System#getProperty(java.lang.String)}
1126      * method. The string value of this property is then interpreted
1127      * as a {@code long} value, as per the
1128      * {@link Long#decode decode} method, and a {@code Long} object
1129      * representing this value is returned; in summary:
1130      *
1131      * <ul>
1132      * <li>If the property value begins with the two ASCII characters
1133      * {@code 0x} or the ASCII character {@code #}, not followed by
1134      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1135      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1136      * with radix 16.
1137      * <li>If the property value begins with the ASCII character
1138      * {@code 0} followed by another character, it is parsed as
1139      * an octal integer exactly as by the method {@link
1140      * #valueOf(java.lang.String, int)} with radix 8.
1141      * <li>Otherwise the property value is parsed as a decimal
1142      * integer exactly as by the method
1143      * {@link #valueOf(java.lang.String, int)} with radix 10.
1144      * </ul>
1145      *
1146      * <p>Note that, in every case, neither {@code L}
1147      * (<code>'&#92;u004C'</code>) nor {@code l}
1148      * (<code>'&#92;u006C'</code>) is permitted to appear at the end
1149      * of the property value as a type indicator, as would be
1150      * permitted in Java programming language source code.
1151      *
1152      * <p>The second argument is the default value. The default value is
1153      * returned if there is no property of the specified name, if the
1154      * property does not have the correct numeric format, or if the
1155      * specified name is empty or {@code null}.
1156      *
1157      * @param   nm   property name.
1158      * @param   val   default value.
1159      * @return  the {@code Long} value of the property.
1160      * @throws  SecurityException for the same reasons as
1161      *          {@link System#getProperty(String) System.getProperty}
1162      * @see     System#getProperty(java.lang.String)
1163      * @see     System#getProperty(java.lang.String, java.lang.String)
1164      */
1165     public static Long getLong(String nm, Long val) {
1166         String v = null;
1167         try {
1168             v = System.getProperty(nm);
1169         } catch (IllegalArgumentException | NullPointerException e) {
1170         }
1171         if (v != null) {
1172             try {
1173                 return Long.decode(v);
1174             } catch (NumberFormatException e) {
1175             }
1176         }
1177         return val;
1178     }
1179 
1180     /**
1181      * Compares two {@code Long} objects numerically.
1182      *
1183      * @param   anotherLong   the {@code Long} to be compared.
1184      * @return  the value {@code 0} if this {@code Long} is
1185      *          equal to the argument {@code Long}; a value less than
1186      *          {@code 0} if this {@code Long} is numerically less
1187      *          than the argument {@code Long}; and a value greater
1188      *          than {@code 0} if this {@code Long} is numerically
1189      *           greater than the argument {@code Long} (signed
1190      *           comparison).
1191      * @since   1.2
1192      */
1193     public int compareTo(Long anotherLong) {
1194         return compare(this.value, anotherLong.value);
1195     }
1196 
1197     /**
1198      * Compares two {@code long} values numerically.
1199      * The value returned is identical to what would be returned by:
1200      * <pre>
1201      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1202      * </pre>
1203      *
1204      * @param  x the first {@code long} to compare
1205      * @param  y the second {@code long} to compare
1206      * @return the value {@code 0} if {@code x == y};
1207      *         a value less than {@code 0} if {@code x < y}; and
1208      *         a value greater than {@code 0} if {@code x > y}
1209      * @since 1.7
1210      */
1211     public static int compare(long x, long y) {
1212         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1213     }
1214 
1215     /**
1216      * Compares two {@code long} values numerically treating the values
1217      * as unsigned.
1218      *
1219      * @param  x the first {@code long} to compare
1220      * @param  y the second {@code long} to compare
1221      * @return the value {@code 0} if {@code x == y}; a value less
1222      *         than {@code 0} if {@code x < y} as unsigned values; and
1223      *         a value greater than {@code 0} if {@code x > y} as
1224      *         unsigned values
1225      * @since 1.8
1226      */
1227     public static int compareUnsigned(long x, long y) {
1228         return compare(x + MIN_VALUE, y + MIN_VALUE);
1229     }
1230 
1231 
1232     /**
1233      * Returns the unsigned quotient of dividing the first argument by
1234      * the second where each argument is interpreted as an unsigned
1235      * value.
1236      *
1237      * In other words, return the unsigned value of {@code
1238      * (dividend / divisor)}.
1239      *
1240      * @return the unsigned quotient of the first argument divided by
1241      * the second argument
1242      * @param dividend the value to be divided
1243      * @param divisor the value doing the dividing
1244      * @since 1.8
1245      */
1246     public static long divideUnsigned(long dividend, long divisor) {
1247         if (divisor < 0L) { // signed comparison
1248             // Answer must be 0 or 1 depending on relative magnitude
1249             // of dividend and divisor.
1250             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1251         }
1252 
1253         if (dividend > 0) //  Both inputs non-negative
1254             return dividend/divisor;
1255         else {
1256             /*
1257              * For simple code, leveraging BigInteger.  Longer and faster
1258              * code written directly in terms of operations on longs is
1259              * possible; see "Hacker's Delight" for divide and remainder
1260              * algorithms.
1261              */
1262             return toUnsignedBigInteger(dividend).
1263                 divide(toUnsignedBigInteger(divisor)).longValue();
1264         }
1265     }
1266 
1267     /**
1268      * Returns the unsigned remainder from dividing the first argument by
1269      * the second where each argument is interpreted as an unsigned
1270      * value.
1271      *
1272      * In other words, return the unsigned value of {@code
1273      * (dividend % divisor)}.
1274      *
1275      * @return the unsigned remainder of the first argument divided by
1276      * the second argument
1277      * @param dividend the value to be divided
1278      * @param divisor the value doing the dividing
1279      * @since 1.8
1280      */
1281     public static long remainderUnsigned(long dividend, long divisor) {
1282         if (dividend > 0 && divisor > 0) { // signed comparisons
1283             return dividend % divisor;
1284         } else {
1285             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1286                 return dividend;
1287             else
1288                 return toUnsignedBigInteger(dividend).
1289                     remainder(toUnsignedBigInteger(divisor)).longValue();
1290         }
1291     }
1292 
1293     // Bit Twiddling
1294 
1295     /**
1296      * The number of bits used to represent a {@code long} value in two's
1297      * complement binary form.
1298      *
1299      * @since 1.5
1300      */
1301     public static final int SIZE = 64;
1302 
1303     /**
1304      * Returns a {@code long} value with at most a single one-bit, in the
1305      * position of the highest-order ("leftmost") one-bit in the specified
1306      * {@code long} value.  Returns zero if the specified value has no
1307      * one-bits in its two's complement binary representation, that is, if it
1308      * is equal to zero.
1309      *
1310      * @return a {@code long} value with a single one-bit, in the position
1311      *     of the highest-order one-bit in the specified value, or zero if
1312      *     the specified value is itself equal to zero.
1313      * @since 1.5
1314      */
1315     public static long highestOneBit(long i) {
1316         // HD, Figure 3-1
1317         i |= (i >>  1);
1318         i |= (i >>  2);
1319         i |= (i >>  4);
1320         i |= (i >>  8);
1321         i |= (i >> 16);
1322         i |= (i >> 32);
1323         return i - (i >>> 1);
1324     }
1325 
1326     /**
1327      * Returns a {@code long} value with at most a single one-bit, in the
1328      * position of the lowest-order ("rightmost") one-bit in the specified
1329      * {@code long} value.  Returns zero if the specified value has no
1330      * one-bits in its two's complement binary representation, that is, if it
1331      * is equal to zero.
1332      *
1333      * @return a {@code long} value with a single one-bit, in the position
1334      *     of the lowest-order one-bit in the specified value, or zero if
1335      *     the specified value is itself equal to zero.
1336      * @since 1.5
1337      */
1338     public static long lowestOneBit(long i) {
1339         // HD, Section 2-1
1340         return i & -i;
1341     }
1342 
1343     /**
1344      * Returns the number of zero bits preceding the highest-order
1345      * ("leftmost") one-bit in the two's complement binary representation
1346      * of the specified {@code long} value.  Returns 64 if the
1347      * specified value has no one-bits in its two's complement representation,
1348      * in other words if it is equal to zero.
1349      *
1350      * <p>Note that this method is closely related to the logarithm base 2.
1351      * For all positive {@code long} values x:
1352      * <ul>
1353      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1354      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1355      * </ul>
1356      *
1357      * @return the number of zero bits preceding the highest-order
1358      *     ("leftmost") one-bit in the two's complement binary representation
1359      *     of the specified {@code long} value, or 64 if the value
1360      *     is equal to zero.
1361      * @since 1.5
1362      */
1363     public static int numberOfLeadingZeros(long i) {
1364         // HD, Figure 5-6
1365          if (i == 0)
1366             return 64;
1367         int n = 1;
1368         int x = (int)(i >>> 32);
1369         if (x == 0) { n += 32; x = (int)i; }
1370         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1371         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1372         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1373         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1374         n -= x >>> 31;
1375         return n;
1376     }
1377 
1378     /**
1379      * Returns the number of zero bits following the lowest-order ("rightmost")
1380      * one-bit in the two's complement binary representation of the specified
1381      * {@code long} value.  Returns 64 if the specified value has no
1382      * one-bits in its two's complement representation, in other words if it is
1383      * equal to zero.
1384      *
1385      * @return the number of zero bits following the lowest-order ("rightmost")
1386      *     one-bit in the two's complement binary representation of the
1387      *     specified {@code long} value, or 64 if the value is equal
1388      *     to zero.
1389      * @since 1.5
1390      */
1391     public static int numberOfTrailingZeros(long i) {
1392         // HD, Figure 5-14
1393         int x, y;
1394         if (i == 0) return 64;
1395         int n = 63;
1396         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1397         y = x <<16; if (y != 0) { n = n -16; x = y; }
1398         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1399         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1400         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1401         return n - ((x << 1) >>> 31);
1402     }
1403 
1404     /**
1405      * Returns the number of one-bits in the two's complement binary
1406      * representation of the specified {@code long} value.  This function is
1407      * sometimes referred to as the <i>population count</i>.
1408      *
1409      * @return the number of one-bits in the two's complement binary
1410      *     representation of the specified {@code long} value.
1411      * @since 1.5
1412      */
1413      public static int bitCount(long i) {
1414         // HD, Figure 5-14
1415         i = i - ((i >>> 1) & 0x5555555555555555L);
1416         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1417         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1418         i = i + (i >>> 8);
1419         i = i + (i >>> 16);
1420         i = i + (i >>> 32);
1421         return (int)i & 0x7f;
1422      }
1423 
1424     /**
1425      * Returns the value obtained by rotating the two's complement binary
1426      * representation of the specified {@code long} value left by the
1427      * specified number of bits.  (Bits shifted out of the left hand, or
1428      * high-order, side reenter on the right, or low-order.)
1429      *
1430      * <p>Note that left rotation with a negative distance is equivalent to
1431      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1432      * distance)}.  Note also that rotation by any multiple of 64 is a
1433      * no-op, so all but the last six bits of the rotation distance can be
1434      * ignored, even if the distance is negative: {@code rotateLeft(val,
1435      * distance) == rotateLeft(val, distance & 0x3F)}.
1436      *
1437      * @return the value obtained by rotating the two's complement binary
1438      *     representation of the specified {@code long} value left by the
1439      *     specified number of bits.
1440      * @since 1.5
1441      */
1442     public static long rotateLeft(long i, int distance) {
1443         return (i << distance) | (i >>> -distance);
1444     }
1445 
1446     /**
1447      * Returns the value obtained by rotating the two's complement binary
1448      * representation of the specified {@code long} value right by the
1449      * specified number of bits.  (Bits shifted out of the right hand, or
1450      * low-order, side reenter on the left, or high-order.)
1451      *
1452      * <p>Note that right rotation with a negative distance is equivalent to
1453      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1454      * distance)}.  Note also that rotation by any multiple of 64 is a
1455      * no-op, so all but the last six bits of the rotation distance can be
1456      * ignored, even if the distance is negative: {@code rotateRight(val,
1457      * distance) == rotateRight(val, distance & 0x3F)}.
1458      *
1459      * @return the value obtained by rotating the two's complement binary
1460      *     representation of the specified {@code long} value right by the
1461      *     specified number of bits.
1462      * @since 1.5
1463      */
1464     public static long rotateRight(long i, int distance) {
1465         return (i >>> distance) | (i << -distance);
1466     }
1467 
1468     /**
1469      * Returns the value obtained by reversing the order of the bits in the
1470      * two's complement binary representation of the specified {@code long}
1471      * value.
1472      *
1473      * @return the value obtained by reversing order of the bits in the
1474      *     specified {@code long} value.
1475      * @since 1.5
1476      */
1477     public static long reverse(long i) {
1478         // HD, Figure 7-1
1479         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1480         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1481         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1482         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1483         i = (i << 48) | ((i & 0xffff0000L) << 16) |
1484             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1485         return i;
1486     }
1487 
1488     /**
1489      * Returns the signum function of the specified {@code long} value.  (The
1490      * return value is -1 if the specified value is negative; 0 if the
1491      * specified value is zero; and 1 if the specified value is positive.)
1492      *
1493      * @return the signum function of the specified {@code long} value.
1494      * @since 1.5
1495      */
1496     public static int signum(long i) {
1497         // HD, Section 2-7
1498         return (int) ((i >> 63) | (-i >>> 63));
1499     }
1500 
1501     /**
1502      * Returns the value obtained by reversing the order of the bytes in the
1503      * two's complement representation of the specified {@code long} value.
1504      *
1505      * @return the value obtained by reversing the bytes in the specified
1506      *     {@code long} value.
1507      * @since 1.5
1508      */
1509     public static long reverseBytes(long i) {
1510         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1511         return (i << 48) | ((i & 0xffff0000L) << 16) |
1512             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1513     }
1514 
1515     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1516     private static final long serialVersionUID = 4290774380558885855L;
1517 }