1 /*
   2  * Copyright (c) 1994, 2016, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.lang;
  27 
  28 import java.lang.annotation.Native;
  29 import java.math.*;
  30 import java.util.Objects;
  31 import jdk.internal.HotSpotIntrinsicCandidate;
  32 
  33 import static java.lang.String.COMPACT_STRINGS;
  34 import static java.lang.String.LATIN1;
  35 import static java.lang.String.UTF16;
  36 
  37 /**
  38  * The {@code Long} class wraps a value of the primitive type {@code
  39  * long} in an object. An object of type {@code Long} contains a
  40  * single field whose type is {@code long}.
  41  *
  42  * <p> In addition, this class provides several methods for converting
  43  * a {@code long} to a {@code String} and a {@code String} to a {@code
  44  * long}, as well as other constants and methods useful when dealing
  45  * with a {@code long}.
  46  *
  47  * <p>Implementation note: The implementations of the "bit twiddling"
  48  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  49  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  50  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  51  * Delight</i>, (Addison Wesley, 2002).
  52  *
  53  * @author  Lee Boynton
  54  * @author  Arthur van Hoff
  55  * @author  Josh Bloch
  56  * @author  Joseph D. Darcy
  57  * @since   1.0
  58  */
  59 public final class Long extends Number implements Comparable<Long> {
  60     /**
  61      * A constant holding the minimum value a {@code long} can
  62      * have, -2<sup>63</sup>.
  63      */
  64     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  65 
  66     /**
  67      * A constant holding the maximum value a {@code long} can
  68      * have, 2<sup>63</sup>-1.
  69      */
  70     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  71 
  72     /**
  73      * The {@code Class} instance representing the primitive type
  74      * {@code long}.
  75      *
  76      * @since   1.1
  77      */
  78     @SuppressWarnings("unchecked")
  79     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  80 
  81     /**
  82      * Returns a string representation of the first argument in the
  83      * radix specified by the second argument.
  84      *
  85      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  86      * or larger than {@code Character.MAX_RADIX}, then the radix
  87      * {@code 10} is used instead.
  88      *
  89      * <p>If the first argument is negative, the first element of the
  90      * result is the ASCII minus sign {@code '-'}
  91      * ({@code '\u005Cu002d'}). If the first argument is not
  92      * negative, no sign character appears in the result.
  93      *
  94      * <p>The remaining characters of the result represent the magnitude
  95      * of the first argument. If the magnitude is zero, it is
  96      * represented by a single zero character {@code '0'}
  97      * ({@code '\u005Cu0030'}); otherwise, the first character of
  98      * the representation of the magnitude will not be the zero
  99      * character.  The following ASCII characters are used as digits:
 100      *
 101      * <blockquote>
 102      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 103      * </blockquote>
 104      *
 105      * These are {@code '\u005Cu0030'} through
 106      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 107      * {@code '\u005Cu007a'}. If {@code radix} is
 108      * <var>N</var>, then the first <var>N</var> of these characters
 109      * are used as radix-<var>N</var> digits in the order shown. Thus,
 110      * the digits for hexadecimal (radix 16) are
 111      * {@code 0123456789abcdef}. If uppercase letters are
 112      * desired, the {@link java.lang.String#toUpperCase()} method may
 113      * be called on the result:
 114      *
 115      * <blockquote>
 116      *  {@code Long.toString(n, 16).toUpperCase()}
 117      * </blockquote>
 118      *
 119      * @param   i       a {@code long} to be converted to a string.
 120      * @param   radix   the radix to use in the string representation.
 121      * @return  a string representation of the argument in the specified radix.
 122      * @see     java.lang.Character#MAX_RADIX
 123      * @see     java.lang.Character#MIN_RADIX
 124      */
 125     public static String toString(long i, int radix) {
 126         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 127             radix = 10;
 128         if (radix == 10)
 129             return toString(i);
 130 
 131         if (COMPACT_STRINGS) {
 132             byte[] buf = new byte[65];
 133             int charPos = 64;
 134             boolean negative = (i < 0);
 135 
 136             if (!negative) {
 137                 i = -i;
 138             }
 139 
 140             while (i <= -radix) {
 141                 buf[charPos--] = (byte)Integer.digits[(int)(-(i % radix))];
 142                 i = i / radix;
 143             }
 144             buf[charPos] = (byte)Integer.digits[(int)(-i)];
 145 
 146             if (negative) {
 147                 buf[--charPos] = '-';
 148             }
 149             return StringLatin1.newString(buf, charPos, (65 - charPos));
 150         }
 151         return toStringUTF16(i, radix);
 152     }
 153 
 154     private static String toStringUTF16(long i, int radix) {
 155         byte[] buf = new byte[65 * 2];
 156         int charPos = 64;
 157         boolean negative = (i < 0);
 158         if (!negative) {
 159             i = -i;
 160         }
 161         while (i <= -radix) {
 162             StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 163             i = i / radix;
 164         }
 165         StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 166         if (negative) {
 167             StringUTF16.putChar(buf, --charPos, '-');
 168         }
 169         return StringUTF16.newString(buf, charPos, (65 - charPos));
 170     }
 171 
 172     /**
 173      * Returns a string representation of the first argument as an
 174      * unsigned integer value in the radix specified by the second
 175      * argument.
 176      *
 177      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 178      * or larger than {@code Character.MAX_RADIX}, then the radix
 179      * {@code 10} is used instead.
 180      *
 181      * <p>Note that since the first argument is treated as an unsigned
 182      * value, no leading sign character is printed.
 183      *
 184      * <p>If the magnitude is zero, it is represented by a single zero
 185      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 186      * the first character of the representation of the magnitude will
 187      * not be the zero character.
 188      *
 189      * <p>The behavior of radixes and the characters used as digits
 190      * are the same as {@link #toString(long, int) toString}.
 191      *
 192      * @param   i       an integer to be converted to an unsigned string.
 193      * @param   radix   the radix to use in the string representation.
 194      * @return  an unsigned string representation of the argument in the specified radix.
 195      * @see     #toString(long, int)
 196      * @since 1.8
 197      */
 198     public static String toUnsignedString(long i, int radix) {
 199         if (i >= 0)
 200             return toString(i, radix);
 201         else {
 202             switch (radix) {
 203             case 2:
 204                 return toBinaryString(i);
 205 
 206             case 4:
 207                 return toUnsignedString0(i, 2);
 208 
 209             case 8:
 210                 return toOctalString(i);
 211 
 212             case 10:
 213                 /*
 214                  * We can get the effect of an unsigned division by 10
 215                  * on a long value by first shifting right, yielding a
 216                  * positive value, and then dividing by 5.  This
 217                  * allows the last digit and preceding digits to be
 218                  * isolated more quickly than by an initial conversion
 219                  * to BigInteger.
 220                  */
 221                 long quot = (i >>> 1) / 5;
 222                 long rem = i - quot * 10;
 223                 return toString(quot) + rem;
 224 
 225             case 16:
 226                 return toHexString(i);
 227 
 228             case 32:
 229                 return toUnsignedString0(i, 5);
 230 
 231             default:
 232                 return toUnsignedBigInteger(i).toString(radix);
 233             }
 234         }
 235     }
 236 
 237     /**
 238      * Return a BigInteger equal to the unsigned value of the
 239      * argument.
 240      */
 241     private static BigInteger toUnsignedBigInteger(long i) {
 242         if (i >= 0L)
 243             return BigInteger.valueOf(i);
 244         else {
 245             int upper = (int) (i >>> 32);
 246             int lower = (int) i;
 247 
 248             // return (upper << 32) + lower
 249             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 250                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 251         }
 252     }
 253 
 254     /**
 255      * Returns a string representation of the {@code long}
 256      * argument as an unsigned integer in base&nbsp;16.
 257      *
 258      * <p>The unsigned {@code long} value is the argument plus
 259      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 260      * equal to the argument.  This value is converted to a string of
 261      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 262      * leading {@code 0}s.
 263      *
 264      * <p>The value of the argument can be recovered from the returned
 265      * string {@code s} by calling {@link
 266      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 267      * 16)}.
 268      *
 269      * <p>If the unsigned magnitude is zero, it is represented by a
 270      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 271      * otherwise, the first character of the representation of the
 272      * unsigned magnitude will not be the zero character. The
 273      * following characters are used as hexadecimal digits:
 274      *
 275      * <blockquote>
 276      *  {@code 0123456789abcdef}
 277      * </blockquote>
 278      *
 279      * These are the characters {@code '\u005Cu0030'} through
 280      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 281      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 282      * the {@link java.lang.String#toUpperCase()} method may be called
 283      * on the result:
 284      *
 285      * <blockquote>
 286      *  {@code Long.toHexString(n).toUpperCase()}
 287      * </blockquote>
 288      *
 289      * @param   i   a {@code long} to be converted to a string.
 290      * @return  the string representation of the unsigned {@code long}
 291      *          value represented by the argument in hexadecimal
 292      *          (base&nbsp;16).
 293      * @see #parseUnsignedLong(String, int)
 294      * @see #toUnsignedString(long, int)
 295      * @since   1.0.2
 296      */
 297     public static String toHexString(long i) {
 298         return toUnsignedString0(i, 4);
 299     }
 300 
 301     /**
 302      * Returns a string representation of the {@code long}
 303      * argument as an unsigned integer in base&nbsp;8.
 304      *
 305      * <p>The unsigned {@code long} value is the argument plus
 306      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 307      * equal to the argument.  This value is converted to a string of
 308      * ASCII digits in octal (base&nbsp;8) with no extra leading
 309      * {@code 0}s.
 310      *
 311      * <p>The value of the argument can be recovered from the returned
 312      * string {@code s} by calling {@link
 313      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 314      * 8)}.
 315      *
 316      * <p>If the unsigned magnitude is zero, it is represented by a
 317      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 318      * otherwise, the first character of the representation of the
 319      * unsigned magnitude will not be the zero character. The
 320      * following characters are used as octal digits:
 321      *
 322      * <blockquote>
 323      *  {@code 01234567}
 324      * </blockquote>
 325      *
 326      * These are the characters {@code '\u005Cu0030'} through
 327      * {@code '\u005Cu0037'}.
 328      *
 329      * @param   i   a {@code long} to be converted to a string.
 330      * @return  the string representation of the unsigned {@code long}
 331      *          value represented by the argument in octal (base&nbsp;8).
 332      * @see #parseUnsignedLong(String, int)
 333      * @see #toUnsignedString(long, int)
 334      * @since   1.0.2
 335      */
 336     public static String toOctalString(long i) {
 337         return toUnsignedString0(i, 3);
 338     }
 339 
 340     /**
 341      * Returns a string representation of the {@code long}
 342      * argument as an unsigned integer in base&nbsp;2.
 343      *
 344      * <p>The unsigned {@code long} value is the argument plus
 345      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 346      * equal to the argument.  This value is converted to a string of
 347      * ASCII digits in binary (base&nbsp;2) with no extra leading
 348      * {@code 0}s.
 349      *
 350      * <p>The value of the argument can be recovered from the returned
 351      * string {@code s} by calling {@link
 352      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 353      * 2)}.
 354      *
 355      * <p>If the unsigned magnitude is zero, it is represented by a
 356      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 357      * otherwise, the first character of the representation of the
 358      * unsigned magnitude will not be the zero character. The
 359      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 360      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 361      *
 362      * @param   i   a {@code long} to be converted to a string.
 363      * @return  the string representation of the unsigned {@code long}
 364      *          value represented by the argument in binary (base&nbsp;2).
 365      * @see #parseUnsignedLong(String, int)
 366      * @see #toUnsignedString(long, int)
 367      * @since   1.0.2
 368      */
 369     public static String toBinaryString(long i) {
 370         return toUnsignedString0(i, 1);
 371     }
 372 
 373     /**
 374      * Format a long (treated as unsigned) into a String.
 375      * @param val the value to format
 376      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 377      */
 378     static String toUnsignedString0(long val, int shift) {
 379         // assert shift > 0 && shift <=5 : "Illegal shift value";
 380         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 381         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 382         if (COMPACT_STRINGS) {
 383             byte[] buf = new byte[chars];
 384             formatUnsignedLong0(val, shift, buf, 0, chars);
 385             return new String(buf, LATIN1);
 386         } else {
 387             byte[] buf = new byte[chars * 2];
 388             formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
 389             return new String(buf, UTF16);
 390         }
 391     }
 392 
 393     /**
 394      * Format a long (treated as unsigned) into a character buffer. If
 395      * {@code len} exceeds the formatted ASCII representation of {@code val},
 396      * {@code buf} will be padded with leading zeroes.
 397      *
 398      * @param val the unsigned long to format
 399      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 400      * @param buf the character buffer to write to
 401      * @param offset the offset in the destination buffer to start at
 402      * @param len the number of characters to write
 403      */
 404 
 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     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.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.putChar(buf, 23, '-');
 452             StringUTF16.putChar(buf, 18, '-');
 453             StringUTF16.putChar(buf, 13, '-');
 454             StringUTF16.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             getCharsUTF16(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      * This is a variant of {@link #getChars(long, int, byte[])}, but for
 566      * UTF-16 coder.
 567      *
 568      * @param i     value to convert
 569      * @param index next index, after the least significant digit
 570      * @param buf   target buffer, UTF16-coded.
 571      * @return index of the most significant digit or minus sign, if present
 572      */
 573     static int getCharsUTF16(long i, int index, byte[] buf) {
 574         long q;
 575         int r;
 576         int charPos = index;
 577 
 578         boolean negative = (i < 0);
 579         if (!negative) {
 580             i = -i;
 581         }
 582 
 583         // Get 2 digits/iteration using longs until quotient fits into an int
 584         while (i <= Integer.MIN_VALUE) {
 585             q = i / 100;
 586             r = (int)((q * 100) - i);
 587             i = q;
 588             StringUTF16.putChar(buf, --charPos, Integer.DigitOnes[r]);
 589             StringUTF16.putChar(buf, --charPos, Integer.DigitTens[r]);
 590         }
 591 
 592         // Get 2 digits/iteration using ints
 593         int q2;
 594         int i2 = (int)i;
 595         while (i2 <= -100) {
 596             q2 = i2 / 100;
 597             r  = (q2 * 100) - i2;
 598             i2 = q2;
 599             StringUTF16.putChar(buf, --charPos, Integer.DigitOnes[r]);
 600             StringUTF16.putChar(buf, --charPos, Integer.DigitTens[r]);
 601         }
 602 
 603         // We know there are at most two digits left at this point.
 604         q2 = i2 / 10;
 605         r  = (q2 * 10) - i2;
 606         StringUTF16.putChar(buf, --charPos, '0' + r);
 607 
 608         // Whatever left is the remaining digit.
 609         if (q2 < 0) {
 610             StringUTF16.putChar(buf, --charPos, '0' - q2);
 611         }
 612 
 613         if (negative) {
 614             StringUTF16.putChar(buf, --charPos, '-');
 615         }
 616         return charPos;
 617     }
 618 
 619     /**
 620      * Returns the string representation size for a given long value.
 621      *
 622      * @param x long value
 623      * @return string size
 624      *
 625      * @implNote There are other ways to compute this: e.g. binary search,
 626      * but values are biased heavily towards zero, and therefore linear search
 627      * wins. The iteration results are also routinely inlined in the generated
 628      * code after loop unrolling.
 629      */
 630     static int stringSize(long x) {
 631         int d = 1;
 632         if (x >= 0) {
 633             d = 0;
 634             x = -x;
 635         }
 636         long p = -10;
 637         for (int i = 1; i < 19; i++) {
 638             if (x > p)
 639                 return i + d;
 640             p = 10 * p;
 641         }
 642         return 19 + d;
 643     }
 644 
 645     /**
 646      * Parses the string argument as a signed {@code long} in the
 647      * radix specified by the second argument. The characters in the
 648      * string must all be digits of the specified radix (as determined
 649      * by whether {@link java.lang.Character#digit(char, int)} returns
 650      * a nonnegative value), except that the first character may be an
 651      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 652      * indicate a negative value or an ASCII plus sign {@code '+'}
 653      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 654      * resulting {@code long} value is returned.
 655      *
 656      * <p>Note that neither the character {@code L}
 657      * ({@code '\u005Cu004C'}) nor {@code l}
 658      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 659      * of the string as a type indicator, as would be permitted in
 660      * Java programming language source code - except that either
 661      * {@code L} or {@code l} may appear as a digit for a
 662      * radix greater than or equal to 22.
 663      *
 664      * <p>An exception of type {@code NumberFormatException} is
 665      * thrown if any of the following situations occurs:
 666      * <ul>
 667      *
 668      * <li>The first argument is {@code null} or is a string of
 669      * length zero.
 670      *
 671      * <li>The {@code radix} is either smaller than {@link
 672      * java.lang.Character#MIN_RADIX} or larger than {@link
 673      * java.lang.Character#MAX_RADIX}.
 674      *
 675      * <li>Any character of the string is not a digit of the specified
 676      * radix, except that the first character may be a minus sign
 677      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 678      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 679      * longer than length 1.
 680      *
 681      * <li>The value represented by the string is not a value of type
 682      *      {@code long}.
 683      * </ul>
 684      *
 685      * <p>Examples:
 686      * <blockquote><pre>
 687      * parseLong("0", 10) returns 0L
 688      * parseLong("473", 10) returns 473L
 689      * parseLong("+42", 10) returns 42L
 690      * parseLong("-0", 10) returns 0L
 691      * parseLong("-FF", 16) returns -255L
 692      * parseLong("1100110", 2) returns 102L
 693      * parseLong("99", 8) throws a NumberFormatException
 694      * parseLong("Hazelnut", 10) throws a NumberFormatException
 695      * parseLong("Hazelnut", 36) returns 1356099454469L
 696      * </pre></blockquote>
 697      *
 698      * @param      s       the {@code String} containing the
 699      *                     {@code long} representation to be parsed.
 700      * @param      radix   the radix to be used while parsing {@code s}.
 701      * @return     the {@code long} represented by the string argument in
 702      *             the specified radix.
 703      * @throws     NumberFormatException  if the string does not contain a
 704      *             parsable {@code long}.
 705      */
 706     public static long parseLong(String s, int radix)
 707               throws NumberFormatException
 708     {
 709         if (s == null) {
 710             throw new NumberFormatException("null");
 711         }
 712 
 713         if (radix < Character.MIN_RADIX) {
 714             throw new NumberFormatException("radix " + radix +
 715                                             " less than Character.MIN_RADIX");
 716         }
 717         if (radix > Character.MAX_RADIX) {
 718             throw new NumberFormatException("radix " + radix +
 719                                             " greater than Character.MAX_RADIX");
 720         }
 721 
 722         boolean negative = false;
 723         int i = 0, len = s.length();
 724         long limit = -Long.MAX_VALUE;
 725 
 726         if (len > 0) {
 727             char firstChar = s.charAt(0);
 728             if (firstChar < '0') { // Possible leading "+" or "-"
 729                 if (firstChar == '-') {
 730                     negative = true;
 731                     limit = Long.MIN_VALUE;
 732                 } else if (firstChar != '+') {
 733                     throw NumberFormatException.forInputString(s);
 734                 }
 735 
 736                 if (len == 1) { // Cannot have lone "+" or "-"
 737                     throw NumberFormatException.forInputString(s);
 738                 }
 739                 i++;
 740             }
 741             long multmin = limit / radix;
 742             long result = 0;
 743             while (i < len) {
 744                 // Accumulating negatively avoids surprises near MAX_VALUE
 745                 int digit = Character.digit(s.charAt(i++),radix);
 746                 if (digit < 0 || result < multmin) {
 747                     throw NumberFormatException.forInputString(s);
 748                 }
 749                 result *= radix;
 750                 if (result < limit + digit) {
 751                     throw NumberFormatException.forInputString(s);
 752                 }
 753                 result -= digit;
 754             }
 755             return negative ? result : -result;
 756         } else {
 757             throw NumberFormatException.forInputString(s);
 758         }
 759     }
 760 
 761     /**
 762      * Parses the {@link CharSequence} argument as a signed {@code long} in
 763      * the specified {@code radix}, beginning at the specified
 764      * {@code beginIndex} and extending to {@code endIndex - 1}.
 765      *
 766      * <p>The method does not take steps to guard against the
 767      * {@code CharSequence} being mutated while parsing.
 768      *
 769      * @param      s   the {@code CharSequence} containing the {@code long}
 770      *                  representation to be parsed
 771      * @param      beginIndex   the beginning index, inclusive.
 772      * @param      endIndex     the ending index, exclusive.
 773      * @param      radix   the radix to be used while parsing {@code s}.
 774      * @return     the signed {@code long} represented by the subsequence in
 775      *             the specified radix.
 776      * @throws     NullPointerException  if {@code s} is null.
 777      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 778      *             negative, or if {@code beginIndex} is greater than
 779      *             {@code endIndex} or if {@code endIndex} is greater than
 780      *             {@code s.length()}.
 781      * @throws     NumberFormatException  if the {@code CharSequence} does not
 782      *             contain a parsable {@code int} in the specified
 783      *             {@code radix}, or if {@code radix} is either smaller than
 784      *             {@link java.lang.Character#MIN_RADIX} or larger than
 785      *             {@link java.lang.Character#MAX_RADIX}.
 786      * @since  9
 787      */
 788     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 789                 throws NumberFormatException {
 790         s = Objects.requireNonNull(s);
 791 
 792         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 793             throw new IndexOutOfBoundsException();
 794         }
 795         if (radix < Character.MIN_RADIX) {
 796             throw new NumberFormatException("radix " + radix +
 797                     " less than Character.MIN_RADIX");
 798         }
 799         if (radix > Character.MAX_RADIX) {
 800             throw new NumberFormatException("radix " + radix +
 801                     " greater than Character.MAX_RADIX");
 802         }
 803 
 804         boolean negative = false;
 805         int i = beginIndex;
 806         long limit = -Long.MAX_VALUE;
 807 
 808         if (i < endIndex) {
 809             char firstChar = s.charAt(i);
 810             if (firstChar < '0') { // Possible leading "+" or "-"
 811                 if (firstChar == '-') {
 812                     negative = true;
 813                     limit = Long.MIN_VALUE;
 814                 } else if (firstChar != '+') {
 815                     throw NumberFormatException.forCharSequence(s, beginIndex,
 816                             endIndex, i);
 817                 }
 818                 i++;
 819             }
 820             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 821                 throw NumberFormatException.forCharSequence(s, beginIndex,
 822                         endIndex, i);
 823             }
 824             long multmin = limit / radix;
 825             long result = 0;
 826             while (i < endIndex) {
 827                 // Accumulating negatively avoids surprises near MAX_VALUE
 828                 int digit = Character.digit(s.charAt(i), radix);
 829                 if (digit < 0 || result < multmin) {
 830                     throw NumberFormatException.forCharSequence(s, beginIndex,
 831                             endIndex, i);
 832                 }
 833                 result *= radix;
 834                 if (result < limit + digit) {
 835                     throw NumberFormatException.forCharSequence(s, beginIndex,
 836                             endIndex, i);
 837                 }
 838                 i++;
 839                 result -= digit;
 840             }
 841             return negative ? result : -result;
 842         } else {
 843             throw new NumberFormatException("");
 844         }
 845     }
 846 
 847     /**
 848      * Parses the string argument as a signed decimal {@code long}.
 849      * The characters in the string must all be decimal digits, except
 850      * that the first character may be an ASCII minus sign {@code '-'}
 851      * ({@code \u005Cu002D'}) to indicate a negative value or an
 852      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 853      * indicate a positive value. The resulting {@code long} value is
 854      * returned, exactly as if the argument and the radix {@code 10}
 855      * were given as arguments to the {@link
 856      * #parseLong(java.lang.String, int)} method.
 857      *
 858      * <p>Note that neither the character {@code L}
 859      * ({@code '\u005Cu004C'}) nor {@code l}
 860      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 861      * of the string as a type indicator, as would be permitted in
 862      * Java programming language source code.
 863      *
 864      * @param      s   a {@code String} containing the {@code long}
 865      *             representation to be parsed
 866      * @return     the {@code long} represented by the argument in
 867      *             decimal.
 868      * @throws     NumberFormatException  if the string does not contain a
 869      *             parsable {@code long}.
 870      */
 871     public static long parseLong(String s) throws NumberFormatException {
 872         return parseLong(s, 10);
 873     }
 874 
 875     /**
 876      * Parses the string argument as an unsigned {@code long} in the
 877      * radix specified by the second argument.  An unsigned integer
 878      * maps the values usually associated with negative numbers to
 879      * positive numbers larger than {@code MAX_VALUE}.
 880      *
 881      * The characters in the string must all be digits of the
 882      * specified radix (as determined by whether {@link
 883      * java.lang.Character#digit(char, int)} returns a nonnegative
 884      * value), except that the first character may be an ASCII plus
 885      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 886      * integer value is returned.
 887      *
 888      * <p>An exception of type {@code NumberFormatException} is
 889      * thrown if any of the following situations occurs:
 890      * <ul>
 891      * <li>The first argument is {@code null} or is a string of
 892      * length zero.
 893      *
 894      * <li>The radix is either smaller than
 895      * {@link java.lang.Character#MIN_RADIX} or
 896      * larger than {@link java.lang.Character#MAX_RADIX}.
 897      *
 898      * <li>Any character of the string is not a digit of the specified
 899      * radix, except that the first character may be a plus sign
 900      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 901      * string is longer than length 1.
 902      *
 903      * <li>The value represented by the string is larger than the
 904      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 905      *
 906      * </ul>
 907      *
 908      *
 909      * @param      s   the {@code String} containing the unsigned integer
 910      *                  representation to be parsed
 911      * @param      radix   the radix to be used while parsing {@code s}.
 912      * @return     the unsigned {@code long} represented by the string
 913      *             argument in the specified radix.
 914      * @throws     NumberFormatException if the {@code String}
 915      *             does not contain a parsable {@code long}.
 916      * @since 1.8
 917      */
 918     public static long parseUnsignedLong(String s, int radix)
 919                 throws NumberFormatException {
 920         if (s == null)  {
 921             throw new NumberFormatException("null");
 922         }
 923 
 924         int len = s.length();
 925         if (len > 0) {
 926             char firstChar = s.charAt(0);
 927             if (firstChar == '-') {
 928                 throw new
 929                     NumberFormatException(String.format("Illegal leading minus sign " +
 930                                                        "on unsigned string %s.", s));
 931             } else {
 932                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 933                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 934                     return parseLong(s, radix);
 935                 }
 936 
 937                 // No need for range checks on len due to testing above.
 938                 long first = parseLong(s, 0, len - 1, radix);
 939                 int second = Character.digit(s.charAt(len - 1), radix);
 940                 if (second < 0) {
 941                     throw new NumberFormatException("Bad digit at end of " + s);
 942                 }
 943                 long result = first * radix + second;
 944 
 945                 /*
 946                  * Test leftmost bits of multiprecision extension of first*radix
 947                  * for overflow. The number of bits needed is defined by
 948                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 949                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 950                  * overflow is tested by splitting guard in the ranges
 951                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 952                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 953                  * on a value which does not include a prime factor in the legal
 954                  * radix range.
 955                  */
 956                 int guard = radix * (int) (first >>> 57);
 957                 if (guard >= 128 ||
 958                     (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 959                     /*
 960                      * For purposes of exposition, the programmatic statements
 961                      * below should be taken to be multi-precision, i.e., not
 962                      * subject to overflow.
 963                      *
 964                      * A) Condition guard >= 128:
 965                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 966                      * hence always overflow.
 967                      *
 968                      * B) Condition guard < 92:
 969                      * Define left7 = first >>> 57.
 970                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 971                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 972                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 973                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 974                      * never overflow.
 975                      *
 976                      * C) Condition 92 <= guard < 128:
 977                      * first*radix + second >= radix*left7*2^57 + second
 978                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 979                      *
 980                      * D) Condition guard < 128:
 981                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 982                      * so
 983                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 984                      * thus
 985                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 986                      * whence
 987                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 988                      *
 989                      * E) Conditions C, D, and result >= 0:
 990                      * C and D combined imply the mathematical result
 991                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 992                      * bound is therefore negative as a signed long, but the
 993                      * upper bound is too small to overflow again after the
 994                      * signed long overflows to positive above 2^64 - 1. Hence
 995                      * result >= 0 implies overflow given C and D.
 996                      */
 997                     throw new NumberFormatException(String.format("String value %s exceeds " +
 998                                                                   "range of unsigned long.", s));
 999                 }
1000                 return result;
1001             }
1002         } else {
1003             throw NumberFormatException.forInputString(s);
1004         }
1005     }
1006 
1007     /**
1008      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
1009      * the specified {@code radix}, beginning at the specified
1010      * {@code beginIndex} and extending to {@code endIndex - 1}.
1011      *
1012      * <p>The method does not take steps to guard against the
1013      * {@code CharSequence} being mutated while parsing.
1014      *
1015      * @param      s   the {@code CharSequence} containing the unsigned
1016      *                 {@code long} representation to be parsed
1017      * @param      beginIndex   the beginning index, inclusive.
1018      * @param      endIndex     the ending index, exclusive.
1019      * @param      radix   the radix to be used while parsing {@code s}.
1020      * @return     the unsigned {@code long} represented by the subsequence in
1021      *             the specified radix.
1022      * @throws     NullPointerException  if {@code s} is null.
1023      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
1024      *             negative, or if {@code beginIndex} is greater than
1025      *             {@code endIndex} or if {@code endIndex} is greater than
1026      *             {@code s.length()}.
1027      * @throws     NumberFormatException  if the {@code CharSequence} does not
1028      *             contain a parsable unsigned {@code long} in the specified
1029      *             {@code radix}, or if {@code radix} is either smaller than
1030      *             {@link java.lang.Character#MIN_RADIX} or larger than
1031      *             {@link java.lang.Character#MAX_RADIX}.
1032      * @since  9
1033      */
1034     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
1035                 throws NumberFormatException {
1036         s = Objects.requireNonNull(s);
1037 
1038         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
1039             throw new IndexOutOfBoundsException();
1040         }
1041         int start = beginIndex, len = endIndex - beginIndex;
1042 
1043         if (len > 0) {
1044             char firstChar = s.charAt(start);
1045             if (firstChar == '-') {
1046                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
1047                         "on unsigned string %s.", s.subSequence(start, start + len)));
1048             } else {
1049                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
1050                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
1051                     return parseLong(s, start, start + len, radix);
1052                 }
1053 
1054                 // No need for range checks on end due to testing above.
1055                 long first = parseLong(s, start, start + len - 1, radix);
1056                 int second = Character.digit(s.charAt(start + len - 1), radix);
1057                 if (second < 0) {
1058                     throw new NumberFormatException("Bad digit at end of " +
1059                             s.subSequence(start, start + len));
1060                 }
1061                 long result = first * radix + second;
1062 
1063                 /*
1064                  * Test leftmost bits of multiprecision extension of first*radix
1065                  * for overflow. The number of bits needed is defined by
1066                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
1067                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
1068                  * overflow is tested by splitting guard in the ranges
1069                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
1070                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
1071                  * on a value which does not include a prime factor in the legal
1072                  * radix range.
1073                  */
1074                 int guard = radix * (int) (first >>> 57);
1075                 if (guard >= 128 ||
1076                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
1077                     /*
1078                      * For purposes of exposition, the programmatic statements
1079                      * below should be taken to be multi-precision, i.e., not
1080                      * subject to overflow.
1081                      *
1082                      * A) Condition guard >= 128:
1083                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
1084                      * hence always overflow.
1085                      *
1086                      * B) Condition guard < 92:
1087                      * Define left7 = first >>> 57.
1088                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
1089                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
1090                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
1091                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
1092                      * never overflow.
1093                      *
1094                      * C) Condition 92 <= guard < 128:
1095                      * first*radix + second >= radix*left7*2^57 + second
1096                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
1097                      *
1098                      * D) Condition guard < 128:
1099                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
1100                      * so
1101                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
1102                      * thus
1103                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
1104                      * whence
1105                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
1106                      *
1107                      * E) Conditions C, D, and result >= 0:
1108                      * C and D combined imply the mathematical result
1109                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
1110                      * bound is therefore negative as a signed long, but the
1111                      * upper bound is too small to overflow again after the
1112                      * signed long overflows to positive above 2^64 - 1. Hence
1113                      * result >= 0 implies overflow given C and D.
1114                      */
1115                     throw new NumberFormatException(String.format("String value %s exceeds " +
1116                             "range of unsigned long.", s.subSequence(start, start + len)));
1117                 }
1118                 return result;
1119             }
1120         } else {
1121             throw NumberFormatException.forInputString("");
1122         }
1123     }
1124 
1125     /**
1126      * Parses the string argument as an unsigned decimal {@code long}. The
1127      * characters in the string must all be decimal digits, except
1128      * that the first character may be an ASCII plus sign {@code
1129      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
1130      * is returned, exactly as if the argument and the radix 10 were
1131      * given as arguments to the {@link
1132      * #parseUnsignedLong(java.lang.String, int)} method.
1133      *
1134      * @param s   a {@code String} containing the unsigned {@code long}
1135      *            representation to be parsed
1136      * @return    the unsigned {@code long} value represented by the decimal string argument
1137      * @throws    NumberFormatException  if the string does not contain a
1138      *            parsable unsigned integer.
1139      * @since 1.8
1140      */
1141     public static long parseUnsignedLong(String s) throws NumberFormatException {
1142         return parseUnsignedLong(s, 10);
1143     }
1144 
1145     /**
1146      * Returns a {@code Long} object holding the value
1147      * extracted from the specified {@code String} when parsed
1148      * with the radix given by the second argument.  The first
1149      * argument is interpreted as representing a signed
1150      * {@code long} in the radix specified by the second
1151      * argument, exactly as if the arguments were given to the {@link
1152      * #parseLong(java.lang.String, int)} method. The result is a
1153      * {@code Long} object that represents the {@code long}
1154      * value specified by the string.
1155      *
1156      * <p>In other words, this method returns a {@code Long} object equal
1157      * to the value of:
1158      *
1159      * <blockquote>
1160      *  {@code new Long(Long.parseLong(s, radix))}
1161      * </blockquote>
1162      *
1163      * @param      s       the string to be parsed
1164      * @param      radix   the radix to be used in interpreting {@code s}
1165      * @return     a {@code Long} object holding the value
1166      *             represented by the string argument in the specified
1167      *             radix.
1168      * @throws     NumberFormatException  If the {@code String} does not
1169      *             contain a parsable {@code long}.
1170      */
1171     public static Long valueOf(String s, int radix) throws NumberFormatException {
1172         return Long.valueOf(parseLong(s, radix));
1173     }
1174 
1175     /**
1176      * Returns a {@code Long} object holding the value
1177      * of the specified {@code String}. The argument is
1178      * interpreted as representing a signed decimal {@code long},
1179      * exactly as if the argument were given to the {@link
1180      * #parseLong(java.lang.String)} method. The result is a
1181      * {@code Long} object that represents the integer value
1182      * specified by the string.
1183      *
1184      * <p>In other words, this method returns a {@code Long} object
1185      * equal to the value of:
1186      *
1187      * <blockquote>
1188      *  {@code new Long(Long.parseLong(s))}
1189      * </blockquote>
1190      *
1191      * @param      s   the string to be parsed.
1192      * @return     a {@code Long} object holding the value
1193      *             represented by the string argument.
1194      * @throws     NumberFormatException  If the string cannot be parsed
1195      *             as a {@code long}.
1196      */
1197     public static Long valueOf(String s) throws NumberFormatException
1198     {
1199         return Long.valueOf(parseLong(s, 10));
1200     }
1201 
1202     private static class LongCache {
1203         private LongCache(){}
1204 
1205         static final Long cache[] = new Long[-(-128) + 127 + 1];
1206 
1207         static {
1208             for(int i = 0; i < cache.length; i++)
1209                 cache[i] = new Long(i - 128);
1210         }
1211     }
1212 
1213     /**
1214      * Returns a {@code Long} instance representing the specified
1215      * {@code long} value.
1216      * If a new {@code Long} instance is not required, this method
1217      * should generally be used in preference to the constructor
1218      * {@link #Long(long)}, as this method is likely to yield
1219      * significantly better space and time performance by caching
1220      * frequently requested values.
1221      *
1222      * Note that unlike the {@linkplain Integer#valueOf(int)
1223      * corresponding method} in the {@code Integer} class, this method
1224      * is <em>not</em> required to cache values within a particular
1225      * range.
1226      *
1227      * @param  l a long value.
1228      * @return a {@code Long} instance representing {@code l}.
1229      * @since  1.5
1230      */
1231     @HotSpotIntrinsicCandidate
1232     public static Long valueOf(long l) {
1233         final int offset = 128;
1234         if (l >= -128 && l <= 127) { // will cache
1235             return LongCache.cache[(int)l + offset];
1236         }
1237         return new Long(l);
1238     }
1239 
1240     /**
1241      * Decodes a {@code String} into a {@code Long}.
1242      * Accepts decimal, hexadecimal, and octal numbers given by the
1243      * following grammar:
1244      *
1245      * <blockquote>
1246      * <dl>
1247      * <dt><i>DecodableString:</i>
1248      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1249      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1250      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1251      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1252      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1253      *
1254      * <dt><i>Sign:</i>
1255      * <dd>{@code -}
1256      * <dd>{@code +}
1257      * </dl>
1258      * </blockquote>
1259      *
1260      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1261      * are as defined in section 3.10.1 of
1262      * <cite>The Java&trade; Language Specification</cite>,
1263      * except that underscores are not accepted between digits.
1264      *
1265      * <p>The sequence of characters following an optional
1266      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1267      * "{@code #}", or leading zero) is parsed as by the {@code
1268      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1269      * This sequence of characters must represent a positive value or
1270      * a {@link NumberFormatException} will be thrown.  The result is
1271      * negated if first character of the specified {@code String} is
1272      * the minus sign.  No whitespace characters are permitted in the
1273      * {@code String}.
1274      *
1275      * @param     nm the {@code String} to decode.
1276      * @return    a {@code Long} object holding the {@code long}
1277      *            value represented by {@code nm}
1278      * @throws    NumberFormatException  if the {@code String} does not
1279      *            contain a parsable {@code long}.
1280      * @see java.lang.Long#parseLong(String, int)
1281      * @since 1.2
1282      */
1283     public static Long decode(String nm) throws NumberFormatException {
1284         int radix = 10;
1285         int index = 0;
1286         boolean negative = false;
1287         Long result;
1288 
1289         if (nm.length() == 0)
1290             throw new NumberFormatException("Zero length string");
1291         char firstChar = nm.charAt(0);
1292         // Handle sign, if present
1293         if (firstChar == '-') {
1294             negative = true;
1295             index++;
1296         } else if (firstChar == '+')
1297             index++;
1298 
1299         // Handle radix specifier, if present
1300         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1301             index += 2;
1302             radix = 16;
1303         }
1304         else if (nm.startsWith("#", index)) {
1305             index ++;
1306             radix = 16;
1307         }
1308         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1309             index ++;
1310             radix = 8;
1311         }
1312 
1313         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1314             throw new NumberFormatException("Sign character in wrong position");
1315 
1316         try {
1317             result = Long.valueOf(nm.substring(index), radix);
1318             result = negative ? Long.valueOf(-result.longValue()) : result;
1319         } catch (NumberFormatException e) {
1320             // If number is Long.MIN_VALUE, we'll end up here. The next line
1321             // handles this case, and causes any genuine format error to be
1322             // rethrown.
1323             String constant = negative ? ("-" + nm.substring(index))
1324                                        : nm.substring(index);
1325             result = Long.valueOf(constant, radix);
1326         }
1327         return result;
1328     }
1329 
1330     /**
1331      * The value of the {@code Long}.
1332      *
1333      * @serial
1334      */
1335     private final long value;
1336 
1337     /**
1338      * Constructs a newly allocated {@code Long} object that
1339      * represents the specified {@code long} argument.
1340      *
1341      * @param   value   the value to be represented by the
1342      *          {@code Long} object.
1343      */
1344     public Long(long value) {
1345         this.value = value;
1346     }
1347 
1348     /**
1349      * Constructs a newly allocated {@code Long} object that
1350      * represents the {@code long} value indicated by the
1351      * {@code String} parameter. The string is converted to a
1352      * {@code long} value in exactly the manner used by the
1353      * {@code parseLong} method for radix 10.
1354      *
1355      * @param      s   the {@code String} to be converted to a
1356      *             {@code Long}.
1357      * @throws     NumberFormatException  if the {@code String} does not
1358      *             contain a parsable {@code long}.
1359      * @see        java.lang.Long#parseLong(java.lang.String, int)
1360      */
1361     public Long(String s) throws NumberFormatException {
1362         this.value = parseLong(s, 10);
1363     }
1364 
1365     /**
1366      * Returns the value of this {@code Long} as a {@code byte} after
1367      * a narrowing primitive conversion.
1368      * @jls 5.1.3 Narrowing Primitive Conversions
1369      */
1370     public byte byteValue() {
1371         return (byte)value;
1372     }
1373 
1374     /**
1375      * Returns the value of this {@code Long} as a {@code short} after
1376      * a narrowing primitive conversion.
1377      * @jls 5.1.3 Narrowing Primitive Conversions
1378      */
1379     public short shortValue() {
1380         return (short)value;
1381     }
1382 
1383     /**
1384      * Returns the value of this {@code Long} as an {@code int} after
1385      * a narrowing primitive conversion.
1386      * @jls 5.1.3 Narrowing Primitive Conversions
1387      */
1388     public int intValue() {
1389         return (int)value;
1390     }
1391 
1392     /**
1393      * Returns the value of this {@code Long} as a
1394      * {@code long} value.
1395      */
1396     @HotSpotIntrinsicCandidate
1397     public long longValue() {
1398         return value;
1399     }
1400 
1401     /**
1402      * Returns the value of this {@code Long} as a {@code float} after
1403      * a widening primitive conversion.
1404      * @jls 5.1.2 Widening Primitive Conversions
1405      */
1406     public float floatValue() {
1407         return (float)value;
1408     }
1409 
1410     /**
1411      * Returns the value of this {@code Long} as a {@code double}
1412      * after a widening primitive conversion.
1413      * @jls 5.1.2 Widening Primitive Conversions
1414      */
1415     public double doubleValue() {
1416         return (double)value;
1417     }
1418 
1419     /**
1420      * Returns a {@code String} object representing this
1421      * {@code Long}'s value.  The value is converted to signed
1422      * decimal representation and returned as a string, exactly as if
1423      * the {@code long} value were given as an argument to the
1424      * {@link java.lang.Long#toString(long)} method.
1425      *
1426      * @return  a string representation of the value of this object in
1427      *          base&nbsp;10.
1428      */
1429     public String toString() {
1430         return toString(value);
1431     }
1432 
1433     /**
1434      * Returns a hash code for this {@code Long}. The result is
1435      * the exclusive OR of the two halves of the primitive
1436      * {@code long} value held by this {@code Long}
1437      * object. That is, the hashcode is the value of the expression:
1438      *
1439      * <blockquote>
1440      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1441      * </blockquote>
1442      *
1443      * @return  a hash code value for this object.
1444      */
1445     @Override
1446     public int hashCode() {
1447         return Long.hashCode(value);
1448     }
1449 
1450     /**
1451      * Returns a hash code for a {@code long} value; compatible with
1452      * {@code Long.hashCode()}.
1453      *
1454      * @param value the value to hash
1455      * @return a hash code value for a {@code long} value.
1456      * @since 1.8
1457      */
1458     public static int hashCode(long value) {
1459         return (int)(value ^ (value >>> 32));
1460     }
1461 
1462     /**
1463      * Compares this object to the specified object.  The result is
1464      * {@code true} if and only if the argument is not
1465      * {@code null} and is a {@code Long} object that
1466      * contains the same {@code long} value as this object.
1467      *
1468      * @param   obj   the object to compare with.
1469      * @return  {@code true} if the objects are the same;
1470      *          {@code false} otherwise.
1471      */
1472     public boolean equals(Object obj) {
1473         if (obj instanceof Long) {
1474             return value == ((Long)obj).longValue();
1475         }
1476         return false;
1477     }
1478 
1479     /**
1480      * Determines the {@code long} value of the system property
1481      * with the specified name.
1482      *
1483      * <p>The first argument is treated as the name of a system
1484      * property.  System properties are accessible through the {@link
1485      * java.lang.System#getProperty(java.lang.String)} method. The
1486      * string value of this property is then interpreted as a {@code
1487      * long} value using the grammar supported by {@link Long#decode decode}
1488      * and a {@code Long} object representing this value is returned.
1489      *
1490      * <p>If there is no property with the specified name, if the
1491      * specified name is empty or {@code null}, or if the property
1492      * does not have the correct numeric format, then {@code null} is
1493      * returned.
1494      *
1495      * <p>In other words, this method returns a {@code Long} object
1496      * equal to the value of:
1497      *
1498      * <blockquote>
1499      *  {@code getLong(nm, null)}
1500      * </blockquote>
1501      *
1502      * @param   nm   property name.
1503      * @return  the {@code Long} value of the property.
1504      * @throws  SecurityException for the same reasons as
1505      *          {@link System#getProperty(String) System.getProperty}
1506      * @see     java.lang.System#getProperty(java.lang.String)
1507      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1508      */
1509     public static Long getLong(String nm) {
1510         return getLong(nm, null);
1511     }
1512 
1513     /**
1514      * Determines the {@code long} value of the system property
1515      * with the specified name.
1516      *
1517      * <p>The first argument is treated as the name of a system
1518      * property.  System properties are accessible through the {@link
1519      * java.lang.System#getProperty(java.lang.String)} method. The
1520      * string value of this property is then interpreted as a {@code
1521      * long} value using the grammar supported by {@link Long#decode decode}
1522      * and a {@code Long} object representing this value is returned.
1523      *
1524      * <p>The second argument is the default value. A {@code Long} object
1525      * that represents the value of the second argument is returned if there
1526      * is no property of the specified name, if the property does not have
1527      * the correct numeric format, or if the specified name is empty or null.
1528      *
1529      * <p>In other words, this method returns a {@code Long} object equal
1530      * to the value of:
1531      *
1532      * <blockquote>
1533      *  {@code getLong(nm, new Long(val))}
1534      * </blockquote>
1535      *
1536      * but in practice it may be implemented in a manner such as:
1537      *
1538      * <blockquote><pre>
1539      * Long result = getLong(nm, null);
1540      * return (result == null) ? new Long(val) : result;
1541      * </pre></blockquote>
1542      *
1543      * to avoid the unnecessary allocation of a {@code Long} object when
1544      * the default value is not needed.
1545      *
1546      * @param   nm    property name.
1547      * @param   val   default value.
1548      * @return  the {@code Long} value of the property.
1549      * @throws  SecurityException for the same reasons as
1550      *          {@link System#getProperty(String) System.getProperty}
1551      * @see     java.lang.System#getProperty(java.lang.String)
1552      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1553      */
1554     public static Long getLong(String nm, long val) {
1555         Long result = Long.getLong(nm, null);
1556         return (result == null) ? Long.valueOf(val) : result;
1557     }
1558 
1559     /**
1560      * Returns the {@code long} value of the system property with
1561      * the specified name.  The first argument is treated as the name
1562      * of a system property.  System properties are accessible through
1563      * the {@link java.lang.System#getProperty(java.lang.String)}
1564      * method. The string value of this property is then interpreted
1565      * as a {@code long} value, as per the
1566      * {@link Long#decode decode} method, and a {@code Long} object
1567      * representing this value is returned; in summary:
1568      *
1569      * <ul>
1570      * <li>If the property value begins with the two ASCII characters
1571      * {@code 0x} or the ASCII character {@code #}, not followed by
1572      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1573      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1574      * with radix 16.
1575      * <li>If the property value begins with the ASCII character
1576      * {@code 0} followed by another character, it is parsed as
1577      * an octal integer exactly as by the method {@link
1578      * #valueOf(java.lang.String, int)} with radix 8.
1579      * <li>Otherwise the property value is parsed as a decimal
1580      * integer exactly as by the method
1581      * {@link #valueOf(java.lang.String, int)} with radix 10.
1582      * </ul>
1583      *
1584      * <p>Note that, in every case, neither {@code L}
1585      * ({@code '\u005Cu004C'}) nor {@code l}
1586      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1587      * of the property value as a type indicator, as would be
1588      * permitted in Java programming language source code.
1589      *
1590      * <p>The second argument is the default value. The default value is
1591      * returned if there is no property of the specified name, if the
1592      * property does not have the correct numeric format, or if the
1593      * specified name is empty or {@code null}.
1594      *
1595      * @param   nm   property name.
1596      * @param   val   default value.
1597      * @return  the {@code Long} value of the property.
1598      * @throws  SecurityException for the same reasons as
1599      *          {@link System#getProperty(String) System.getProperty}
1600      * @see     System#getProperty(java.lang.String)
1601      * @see     System#getProperty(java.lang.String, java.lang.String)
1602      */
1603     public static Long getLong(String nm, Long val) {
1604         String v = null;
1605         try {
1606             v = System.getProperty(nm);
1607         } catch (IllegalArgumentException | NullPointerException e) {
1608         }
1609         if (v != null) {
1610             try {
1611                 return Long.decode(v);
1612             } catch (NumberFormatException e) {
1613             }
1614         }
1615         return val;
1616     }
1617 
1618     /**
1619      * Compares two {@code Long} objects numerically.
1620      *
1621      * @param   anotherLong   the {@code Long} to be compared.
1622      * @return  the value {@code 0} if this {@code Long} is
1623      *          equal to the argument {@code Long}; a value less than
1624      *          {@code 0} if this {@code Long} is numerically less
1625      *          than the argument {@code Long}; and a value greater
1626      *          than {@code 0} if this {@code Long} is numerically
1627      *           greater than the argument {@code Long} (signed
1628      *           comparison).
1629      * @since   1.2
1630      */
1631     public int compareTo(Long anotherLong) {
1632         return compare(this.value, anotherLong.value);
1633     }
1634 
1635     /**
1636      * Compares two {@code long} values numerically.
1637      * The value returned is identical to what would be returned by:
1638      * <pre>
1639      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1640      * </pre>
1641      *
1642      * @param  x the first {@code long} to compare
1643      * @param  y the second {@code long} to compare
1644      * @return the value {@code 0} if {@code x == y};
1645      *         a value less than {@code 0} if {@code x < y}; and
1646      *         a value greater than {@code 0} if {@code x > y}
1647      * @since 1.7
1648      */
1649     public static int compare(long x, long y) {
1650         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1651     }
1652 
1653     /**
1654      * Compares two {@code long} values numerically treating the values
1655      * as unsigned.
1656      *
1657      * @param  x the first {@code long} to compare
1658      * @param  y the second {@code long} to compare
1659      * @return the value {@code 0} if {@code x == y}; a value less
1660      *         than {@code 0} if {@code x < y} as unsigned values; and
1661      *         a value greater than {@code 0} if {@code x > y} as
1662      *         unsigned values
1663      * @since 1.8
1664      */
1665     public static int compareUnsigned(long x, long y) {
1666         return compare(x + MIN_VALUE, y + MIN_VALUE);
1667     }
1668 
1669 
1670     /**
1671      * Returns the unsigned quotient of dividing the first argument by
1672      * the second where each argument and the result is interpreted as
1673      * an unsigned value.
1674      *
1675      * <p>Note that in two's complement arithmetic, the three other
1676      * basic arithmetic operations of add, subtract, and multiply are
1677      * bit-wise identical if the two operands are regarded as both
1678      * being signed or both being unsigned.  Therefore separate {@code
1679      * addUnsigned}, etc. methods are not provided.
1680      *
1681      * @param dividend the value to be divided
1682      * @param divisor the value doing the dividing
1683      * @return the unsigned quotient of the first argument divided by
1684      * the second argument
1685      * @see #remainderUnsigned
1686      * @since 1.8
1687      */
1688     public static long divideUnsigned(long dividend, long divisor) {
1689         if (divisor < 0L) { // signed comparison
1690             // Answer must be 0 or 1 depending on relative magnitude
1691             // of dividend and divisor.
1692             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1693         }
1694 
1695         if (dividend > 0) //  Both inputs non-negative
1696             return dividend/divisor;
1697         else {
1698             /*
1699              * For simple code, leveraging BigInteger.  Longer and faster
1700              * code written directly in terms of operations on longs is
1701              * possible; see "Hacker's Delight" for divide and remainder
1702              * algorithms.
1703              */
1704             return toUnsignedBigInteger(dividend).
1705                 divide(toUnsignedBigInteger(divisor)).longValue();
1706         }
1707     }
1708 
1709     /**
1710      * Returns the unsigned remainder from dividing the first argument
1711      * by the second where each argument and the result is interpreted
1712      * as an unsigned value.
1713      *
1714      * @param dividend the value to be divided
1715      * @param divisor the value doing the dividing
1716      * @return the unsigned remainder of the first argument divided by
1717      * the second argument
1718      * @see #divideUnsigned
1719      * @since 1.8
1720      */
1721     public static long remainderUnsigned(long dividend, long divisor) {
1722         if (dividend > 0 && divisor > 0) { // signed comparisons
1723             return dividend % divisor;
1724         } else {
1725             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1726                 return dividend;
1727             else
1728                 return toUnsignedBigInteger(dividend).
1729                     remainder(toUnsignedBigInteger(divisor)).longValue();
1730         }
1731     }
1732 
1733     // Bit Twiddling
1734 
1735     /**
1736      * The number of bits used to represent a {@code long} value in two's
1737      * complement binary form.
1738      *
1739      * @since 1.5
1740      */
1741     @Native public static final int SIZE = 64;
1742 
1743     /**
1744      * The number of bytes used to represent a {@code long} value in two's
1745      * complement binary form.
1746      *
1747      * @since 1.8
1748      */
1749     public static final int BYTES = SIZE / Byte.SIZE;
1750 
1751     /**
1752      * Returns a {@code long} value with at most a single one-bit, in the
1753      * position of the highest-order ("leftmost") one-bit in the specified
1754      * {@code long} value.  Returns zero if the specified value has no
1755      * one-bits in its two's complement binary representation, that is, if it
1756      * is equal to zero.
1757      *
1758      * @param i the value whose highest one bit is to be computed
1759      * @return a {@code long} value with a single one-bit, in the position
1760      *     of the highest-order one-bit in the specified value, or zero if
1761      *     the specified value is itself equal to zero.
1762      * @since 1.5
1763      */
1764     public static long highestOneBit(long i) {
1765         // HD, Figure 3-1
1766         i |= (i >>  1);
1767         i |= (i >>  2);
1768         i |= (i >>  4);
1769         i |= (i >>  8);
1770         i |= (i >> 16);
1771         i |= (i >> 32);
1772         return i - (i >>> 1);
1773     }
1774 
1775     /**
1776      * Returns a {@code long} value with at most a single one-bit, in the
1777      * position of the lowest-order ("rightmost") one-bit in the specified
1778      * {@code long} value.  Returns zero if the specified value has no
1779      * one-bits in its two's complement binary representation, that is, if it
1780      * is equal to zero.
1781      *
1782      * @param i the value whose lowest one bit is to be computed
1783      * @return a {@code long} value with a single one-bit, in the position
1784      *     of the lowest-order one-bit in the specified value, or zero if
1785      *     the specified value is itself equal to zero.
1786      * @since 1.5
1787      */
1788     public static long lowestOneBit(long i) {
1789         // HD, Section 2-1
1790         return i & -i;
1791     }
1792 
1793     /**
1794      * Returns the number of zero bits preceding the highest-order
1795      * ("leftmost") one-bit in the two's complement binary representation
1796      * of the specified {@code long} value.  Returns 64 if the
1797      * specified value has no one-bits in its two's complement representation,
1798      * in other words if it is equal to zero.
1799      *
1800      * <p>Note that this method is closely related to the logarithm base 2.
1801      * For all positive {@code long} values x:
1802      * <ul>
1803      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1804      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1805      * </ul>
1806      *
1807      * @param i the value whose number of leading zeros is to be computed
1808      * @return the number of zero bits preceding the highest-order
1809      *     ("leftmost") one-bit in the two's complement binary representation
1810      *     of the specified {@code long} value, or 64 if the value
1811      *     is equal to zero.
1812      * @since 1.5
1813      */
1814     @HotSpotIntrinsicCandidate
1815     public static int numberOfLeadingZeros(long i) {
1816         // HD, Figure 5-6
1817          if (i == 0)
1818             return 64;
1819         int n = 1;
1820         int x = (int)(i >>> 32);
1821         if (x == 0) { n += 32; x = (int)i; }
1822         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1823         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1824         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1825         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1826         n -= x >>> 31;
1827         return n;
1828     }
1829 
1830     /**
1831      * Returns the number of zero bits following the lowest-order ("rightmost")
1832      * one-bit in the two's complement binary representation of the specified
1833      * {@code long} value.  Returns 64 if the specified value has no
1834      * one-bits in its two's complement representation, in other words if it is
1835      * equal to zero.
1836      *
1837      * @param i the value whose number of trailing zeros is to be computed
1838      * @return the number of zero bits following the lowest-order ("rightmost")
1839      *     one-bit in the two's complement binary representation of the
1840      *     specified {@code long} value, or 64 if the value is equal
1841      *     to zero.
1842      * @since 1.5
1843      */
1844     @HotSpotIntrinsicCandidate
1845     public static int numberOfTrailingZeros(long i) {
1846         // HD, Figure 5-14
1847         int x, y;
1848         if (i == 0) return 64;
1849         int n = 63;
1850         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1851         y = x <<16; if (y != 0) { n = n -16; x = y; }
1852         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1853         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1854         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1855         return n - ((x << 1) >>> 31);
1856     }
1857 
1858     /**
1859      * Returns the number of one-bits in the two's complement binary
1860      * representation of the specified {@code long} value.  This function is
1861      * sometimes referred to as the <i>population count</i>.
1862      *
1863      * @param i the value whose bits are to be counted
1864      * @return the number of one-bits in the two's complement binary
1865      *     representation of the specified {@code long} value.
1866      * @since 1.5
1867      */
1868      @HotSpotIntrinsicCandidate
1869      public static int bitCount(long i) {
1870         // HD, Figure 5-2
1871         i = i - ((i >>> 1) & 0x5555555555555555L);
1872         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1873         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1874         i = i + (i >>> 8);
1875         i = i + (i >>> 16);
1876         i = i + (i >>> 32);
1877         return (int)i & 0x7f;
1878      }
1879 
1880     /**
1881      * Returns the value obtained by rotating the two's complement binary
1882      * representation of the specified {@code long} value left by the
1883      * specified number of bits.  (Bits shifted out of the left hand, or
1884      * high-order, side reenter on the right, or low-order.)
1885      *
1886      * <p>Note that left rotation with a negative distance is equivalent to
1887      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1888      * distance)}.  Note also that rotation by any multiple of 64 is a
1889      * no-op, so all but the last six bits of the rotation distance can be
1890      * ignored, even if the distance is negative: {@code rotateLeft(val,
1891      * distance) == rotateLeft(val, distance & 0x3F)}.
1892      *
1893      * @param i the value whose bits are to be rotated left
1894      * @param distance the number of bit positions to rotate left
1895      * @return the value obtained by rotating the two's complement binary
1896      *     representation of the specified {@code long} value left by the
1897      *     specified number of bits.
1898      * @since 1.5
1899      */
1900     public static long rotateLeft(long i, int distance) {
1901         return (i << distance) | (i >>> -distance);
1902     }
1903 
1904     /**
1905      * Returns the value obtained by rotating the two's complement binary
1906      * representation of the specified {@code long} value right by the
1907      * specified number of bits.  (Bits shifted out of the right hand, or
1908      * low-order, side reenter on the left, or high-order.)
1909      *
1910      * <p>Note that right rotation with a negative distance is equivalent to
1911      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1912      * distance)}.  Note also that rotation by any multiple of 64 is a
1913      * no-op, so all but the last six bits of the rotation distance can be
1914      * ignored, even if the distance is negative: {@code rotateRight(val,
1915      * distance) == rotateRight(val, distance & 0x3F)}.
1916      *
1917      * @param i the value whose bits are to be rotated right
1918      * @param distance the number of bit positions to rotate right
1919      * @return the value obtained by rotating the two's complement binary
1920      *     representation of the specified {@code long} value right by the
1921      *     specified number of bits.
1922      * @since 1.5
1923      */
1924     public static long rotateRight(long i, int distance) {
1925         return (i >>> distance) | (i << -distance);
1926     }
1927 
1928     /**
1929      * Returns the value obtained by reversing the order of the bits in the
1930      * two's complement binary representation of the specified {@code long}
1931      * value.
1932      *
1933      * @param i the value to be reversed
1934      * @return the value obtained by reversing order of the bits in the
1935      *     specified {@code long} value.
1936      * @since 1.5
1937      */
1938     public static long reverse(long i) {
1939         // HD, Figure 7-1
1940         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1941         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1942         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1943         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1944         i = (i << 48) | ((i & 0xffff0000L) << 16) |
1945             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1946         return i;
1947     }
1948 
1949     /**
1950      * Returns the signum function of the specified {@code long} value.  (The
1951      * return value is -1 if the specified value is negative; 0 if the
1952      * specified value is zero; and 1 if the specified value is positive.)
1953      *
1954      * @param i the value whose signum is to be computed
1955      * @return the signum function of the specified {@code long} value.
1956      * @since 1.5
1957      */
1958     public static int signum(long i) {
1959         // HD, Section 2-7
1960         return (int) ((i >> 63) | (-i >>> 63));
1961     }
1962 
1963     /**
1964      * Returns the value obtained by reversing the order of the bytes in the
1965      * two's complement representation of the specified {@code long} value.
1966      *
1967      * @param i the value whose bytes are to be reversed
1968      * @return the value obtained by reversing the bytes in the specified
1969      *     {@code long} value.
1970      * @since 1.5
1971      */
1972     @HotSpotIntrinsicCandidate
1973     public static long reverseBytes(long i) {
1974         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1975         return (i << 48) | ((i & 0xffff0000L) << 16) |
1976             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1977     }
1978 
1979     /**
1980      * Adds two {@code long} values together as per the + operator.
1981      *
1982      * @param a the first operand
1983      * @param b the second operand
1984      * @return the sum of {@code a} and {@code b}
1985      * @see java.util.function.BinaryOperator
1986      * @since 1.8
1987      */
1988     public static long sum(long a, long b) {
1989         return a + b;
1990     }
1991 
1992     /**
1993      * Returns the greater of two {@code long} values
1994      * as if by calling {@link Math#max(long, long) Math.max}.
1995      *
1996      * @param a the first operand
1997      * @param b the second operand
1998      * @return the greater of {@code a} and {@code b}
1999      * @see java.util.function.BinaryOperator
2000      * @since 1.8
2001      */
2002     public static long max(long a, long b) {
2003         return Math.max(a, b);
2004     }
2005 
2006     /**
2007      * Returns the smaller of two {@code long} values
2008      * as if by calling {@link Math#min(long, long) Math.min}.
2009      *
2010      * @param a the first operand
2011      * @param b the second operand
2012      * @return the smaller of {@code a} and {@code b}
2013      * @see java.util.function.BinaryOperator
2014      * @since 1.8
2015      */
2016     public static long min(long a, long b) {
2017         return Math.min(a, b);
2018     }
2019 
2020     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2021     @Native private static final long serialVersionUID = 4290774380558885855L;
2022 }