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.lang.invoke.Constable;
  30 import java.lang.invoke.MethodHandles;
  31 import java.math.*;
  32 import java.util.Objects;
  33 import jdk.internal.HotSpotIntrinsicCandidate;
  34 
  35 import static java.lang.String.COMPACT_STRINGS;
  36 import static java.lang.String.LATIN1;
  37 import static java.lang.String.UTF16;
  38 
  39 /**
  40  * The {@code Long} class wraps a value of the primitive type {@code
  41  * long} in an object. An object of type {@code Long} contains a
  42  * single field whose type is {@code long}.
  43  *
  44  * <p> In addition, this class provides several methods for converting
  45  * a {@code long} to a {@code String} and a {@code String} to a {@code
  46  * long}, as well as other constants and methods useful when dealing
  47  * with a {@code long}.
  48  *
  49  * <p>Implementation note: The implementations of the "bit twiddling"
  50  * methods (such as {@link #highestOneBit(long) highestOneBit} and
  51  * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
  52  * based on material from Henry S. Warren, Jr.'s <i>Hacker's
  53  * Delight</i>, (Addison Wesley, 2002).
  54  *
  55  * @author  Lee Boynton
  56  * @author  Arthur van Hoff
  57  * @author  Josh Bloch
  58  * @author  Joseph D. Darcy
  59  * @since   1.0
  60  */
  61 public final class Long extends Number implements Comparable<Long>, Constable<Long> {
  62     /**
  63      * A constant holding the minimum value a {@code long} can
  64      * have, -2<sup>63</sup>.
  65      */
  66     @Native public static final long MIN_VALUE = 0x8000000000000000L;
  67 
  68     /**
  69      * A constant holding the maximum value a {@code long} can
  70      * have, 2<sup>63</sup>-1.
  71      */
  72     @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
  73 
  74     /**
  75      * The {@code Class} instance representing the primitive type
  76      * {@code long}.
  77      *
  78      * @since   1.1
  79      */
  80     @SuppressWarnings("unchecked")
  81     public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
  82 
  83     /**
  84      * Returns a string representation of the first argument in the
  85      * radix specified by the second argument.
  86      *
  87      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
  88      * or larger than {@code Character.MAX_RADIX}, then the radix
  89      * {@code 10} is used instead.
  90      *
  91      * <p>If the first argument is negative, the first element of the
  92      * result is the ASCII minus sign {@code '-'}
  93      * ({@code '\u005Cu002d'}). If the first argument is not
  94      * negative, no sign character appears in the result.
  95      *
  96      * <p>The remaining characters of the result represent the magnitude
  97      * of the first argument. If the magnitude is zero, it is
  98      * represented by a single zero character {@code '0'}
  99      * ({@code '\u005Cu0030'}); otherwise, the first character of
 100      * the representation of the magnitude will not be the zero
 101      * character.  The following ASCII characters are used as digits:
 102      *
 103      * <blockquote>
 104      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
 105      * </blockquote>
 106      *
 107      * These are {@code '\u005Cu0030'} through
 108      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
 109      * {@code '\u005Cu007a'}. If {@code radix} is
 110      * <var>N</var>, then the first <var>N</var> of these characters
 111      * are used as radix-<var>N</var> digits in the order shown. Thus,
 112      * the digits for hexadecimal (radix 16) are
 113      * {@code 0123456789abcdef}. If uppercase letters are
 114      * desired, the {@link java.lang.String#toUpperCase()} method may
 115      * be called on the result:
 116      *
 117      * <blockquote>
 118      *  {@code Long.toString(n, 16).toUpperCase()}
 119      * </blockquote>
 120      *
 121      * @param   i       a {@code long} to be converted to a string.
 122      * @param   radix   the radix to use in the string representation.
 123      * @return  a string representation of the argument in the specified radix.
 124      * @see     java.lang.Character#MAX_RADIX
 125      * @see     java.lang.Character#MIN_RADIX
 126      */
 127     public static String toString(long i, int radix) {
 128         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
 129             radix = 10;
 130         if (radix == 10)
 131             return toString(i);
 132 
 133         if (COMPACT_STRINGS) {
 134             byte[] buf = new byte[65];
 135             int charPos = 64;
 136             boolean negative = (i < 0);
 137 
 138             if (!negative) {
 139                 i = -i;
 140             }
 141 
 142             while (i <= -radix) {
 143                 buf[charPos--] = (byte)Integer.digits[(int)(-(i % radix))];
 144                 i = i / radix;
 145             }
 146             buf[charPos] = (byte)Integer.digits[(int)(-i)];
 147 
 148             if (negative) {
 149                 buf[--charPos] = '-';
 150             }
 151             return StringLatin1.newString(buf, charPos, (65 - charPos));
 152         }
 153         return toStringUTF16(i, radix);
 154     }
 155 
 156     private static String toStringUTF16(long i, int radix) {
 157         byte[] buf = new byte[65 * 2];
 158         int charPos = 64;
 159         boolean negative = (i < 0);
 160         if (!negative) {
 161             i = -i;
 162         }
 163         while (i <= -radix) {
 164             StringUTF16.putChar(buf, charPos--, Integer.digits[(int)(-(i % radix))]);
 165             i = i / radix;
 166         }
 167         StringUTF16.putChar(buf, charPos, Integer.digits[(int)(-i)]);
 168         if (negative) {
 169             StringUTF16.putChar(buf, --charPos, '-');
 170         }
 171         return StringUTF16.newString(buf, charPos, (65 - charPos));
 172     }
 173 
 174     /**
 175      * Returns a string representation of the first argument as an
 176      * unsigned integer value in the radix specified by the second
 177      * argument.
 178      *
 179      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
 180      * or larger than {@code Character.MAX_RADIX}, then the radix
 181      * {@code 10} is used instead.
 182      *
 183      * <p>Note that since the first argument is treated as an unsigned
 184      * value, no leading sign character is printed.
 185      *
 186      * <p>If the magnitude is zero, it is represented by a single zero
 187      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
 188      * the first character of the representation of the magnitude will
 189      * not be the zero character.
 190      *
 191      * <p>The behavior of radixes and the characters used as digits
 192      * are the same as {@link #toString(long, int) toString}.
 193      *
 194      * @param   i       an integer to be converted to an unsigned string.
 195      * @param   radix   the radix to use in the string representation.
 196      * @return  an unsigned string representation of the argument in the specified radix.
 197      * @see     #toString(long, int)
 198      * @since 1.8
 199      */
 200     public static String toUnsignedString(long i, int radix) {
 201         if (i >= 0)
 202             return toString(i, radix);
 203         else {
 204             switch (radix) {
 205             case 2:
 206                 return toBinaryString(i);
 207 
 208             case 4:
 209                 return toUnsignedString0(i, 2);
 210 
 211             case 8:
 212                 return toOctalString(i);
 213 
 214             case 10:
 215                 /*
 216                  * We can get the effect of an unsigned division by 10
 217                  * on a long value by first shifting right, yielding a
 218                  * positive value, and then dividing by 5.  This
 219                  * allows the last digit and preceding digits to be
 220                  * isolated more quickly than by an initial conversion
 221                  * to BigInteger.
 222                  */
 223                 long quot = (i >>> 1) / 5;
 224                 long rem = i - quot * 10;
 225                 return toString(quot) + rem;
 226 
 227             case 16:
 228                 return toHexString(i);
 229 
 230             case 32:
 231                 return toUnsignedString0(i, 5);
 232 
 233             default:
 234                 return toUnsignedBigInteger(i).toString(radix);
 235             }
 236         }
 237     }
 238 
 239     /**
 240      * Return a BigInteger equal to the unsigned value of the
 241      * argument.
 242      */
 243     private static BigInteger toUnsignedBigInteger(long i) {
 244         if (i >= 0L)
 245             return BigInteger.valueOf(i);
 246         else {
 247             int upper = (int) (i >>> 32);
 248             int lower = (int) i;
 249 
 250             // return (upper << 32) + lower
 251             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
 252                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
 253         }
 254     }
 255 
 256     /**
 257      * Returns a string representation of the {@code long}
 258      * argument as an unsigned integer in base&nbsp;16.
 259      *
 260      * <p>The unsigned {@code long} value is the argument plus
 261      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 262      * equal to the argument.  This value is converted to a string of
 263      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
 264      * leading {@code 0}s.
 265      *
 266      * <p>The value of the argument can be recovered from the returned
 267      * string {@code s} by calling {@link
 268      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 269      * 16)}.
 270      *
 271      * <p>If the unsigned magnitude is zero, it is represented by a
 272      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 273      * otherwise, the first character of the representation of the
 274      * unsigned magnitude will not be the zero character. The
 275      * following characters are used as hexadecimal digits:
 276      *
 277      * <blockquote>
 278      *  {@code 0123456789abcdef}
 279      * </blockquote>
 280      *
 281      * These are the characters {@code '\u005Cu0030'} through
 282      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
 283      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
 284      * the {@link java.lang.String#toUpperCase()} method may be called
 285      * on the result:
 286      *
 287      * <blockquote>
 288      *  {@code Long.toHexString(n).toUpperCase()}
 289      * </blockquote>
 290      *
 291      * @param   i   a {@code long} to be converted to a string.
 292      * @return  the string representation of the unsigned {@code long}
 293      *          value represented by the argument in hexadecimal
 294      *          (base&nbsp;16).
 295      * @see #parseUnsignedLong(String, int)
 296      * @see #toUnsignedString(long, int)
 297      * @since   1.0.2
 298      */
 299     public static String toHexString(long i) {
 300         return toUnsignedString0(i, 4);
 301     }
 302 
 303     /**
 304      * Returns a string representation of the {@code long}
 305      * argument as an unsigned integer in base&nbsp;8.
 306      *
 307      * <p>The unsigned {@code long} value is the argument plus
 308      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 309      * equal to the argument.  This value is converted to a string of
 310      * ASCII digits in octal (base&nbsp;8) with no extra leading
 311      * {@code 0}s.
 312      *
 313      * <p>The value of the argument can be recovered from the returned
 314      * string {@code s} by calling {@link
 315      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 316      * 8)}.
 317      *
 318      * <p>If the unsigned magnitude is zero, it is represented by a
 319      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 320      * otherwise, the first character of the representation of the
 321      * unsigned magnitude will not be the zero character. The
 322      * following characters are used as octal digits:
 323      *
 324      * <blockquote>
 325      *  {@code 01234567}
 326      * </blockquote>
 327      *
 328      * These are the characters {@code '\u005Cu0030'} through
 329      * {@code '\u005Cu0037'}.
 330      *
 331      * @param   i   a {@code long} to be converted to a string.
 332      * @return  the string representation of the unsigned {@code long}
 333      *          value represented by the argument in octal (base&nbsp;8).
 334      * @see #parseUnsignedLong(String, int)
 335      * @see #toUnsignedString(long, int)
 336      * @since   1.0.2
 337      */
 338     public static String toOctalString(long i) {
 339         return toUnsignedString0(i, 3);
 340     }
 341 
 342     /**
 343      * Returns a string representation of the {@code long}
 344      * argument as an unsigned integer in base&nbsp;2.
 345      *
 346      * <p>The unsigned {@code long} value is the argument plus
 347      * 2<sup>64</sup> if the argument is negative; otherwise, it is
 348      * equal to the argument.  This value is converted to a string of
 349      * ASCII digits in binary (base&nbsp;2) with no extra leading
 350      * {@code 0}s.
 351      *
 352      * <p>The value of the argument can be recovered from the returned
 353      * string {@code s} by calling {@link
 354      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
 355      * 2)}.
 356      *
 357      * <p>If the unsigned magnitude is zero, it is represented by a
 358      * single zero character {@code '0'} ({@code '\u005Cu0030'});
 359      * otherwise, the first character of the representation of the
 360      * unsigned magnitude will not be the zero character. The
 361      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
 362      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
 363      *
 364      * @param   i   a {@code long} to be converted to a string.
 365      * @return  the string representation of the unsigned {@code long}
 366      *          value represented by the argument in binary (base&nbsp;2).
 367      * @see #parseUnsignedLong(String, int)
 368      * @see #toUnsignedString(long, int)
 369      * @since   1.0.2
 370      */
 371     public static String toBinaryString(long i) {
 372         return toUnsignedString0(i, 1);
 373     }
 374 
 375     /**
 376      * Format a long (treated as unsigned) into a String.
 377      * @param val the value to format
 378      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 379      */
 380     static String toUnsignedString0(long val, int shift) {
 381         // assert shift > 0 && shift <=5 : "Illegal shift value";
 382         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
 383         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
 384         if (COMPACT_STRINGS) {
 385             byte[] buf = new byte[chars];
 386             formatUnsignedLong0(val, shift, buf, 0, chars);
 387             return new String(buf, LATIN1);
 388         } else {
 389             byte[] buf = new byte[chars * 2];
 390             formatUnsignedLong0UTF16(val, shift, buf, 0, chars);
 391             return new String(buf, UTF16);
 392         }
 393     }
 394 
 395     /**
 396      * Format a long (treated as unsigned) into a character buffer. If
 397      * {@code len} exceeds the formatted ASCII representation of {@code val},
 398      * {@code buf} will be padded with leading zeroes.
 399      *
 400      * @param val the unsigned long to format
 401      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
 402      * @param buf the character buffer to write to
 403      * @param offset the offset in the destination buffer to start at
 404      * @param len the number of characters to write
 405      */
 406 
 407     /** byte[]/LATIN1 version    */
 408     static void formatUnsignedLong0(long val, int shift, byte[] buf, int offset, int len) {
 409         int charPos = offset + len;
 410         int radix = 1 << shift;
 411         int mask = radix - 1;
 412         do {
 413             buf[--charPos] = (byte)Integer.digits[((int) val) & mask];
 414             val >>>= shift;
 415         } while (charPos > offset);
 416     }
 417 
 418     /** byte[]/UTF16 version    */
 419     static void formatUnsignedLong0UTF16(long val, int shift, byte[] buf, int offset, int len) {
 420         int charPos = offset + len;
 421         int radix = 1 << shift;
 422         int mask = radix - 1;
 423         do {
 424             StringUTF16.putChar(buf, --charPos, Integer.digits[((int) val) & mask]);
 425             val >>>= shift;
 426         } while (charPos > offset);
 427     }
 428 
 429     static String fastUUID(long lsb, long msb) {
 430         if (COMPACT_STRINGS) {
 431             byte[] buf = new byte[36];
 432             formatUnsignedLong0(lsb,        4, buf, 24, 12);
 433             formatUnsignedLong0(lsb >>> 48, 4, buf, 19, 4);
 434             formatUnsignedLong0(msb,        4, buf, 14, 4);
 435             formatUnsignedLong0(msb >>> 16, 4, buf, 9,  4);
 436             formatUnsignedLong0(msb >>> 32, 4, buf, 0,  8);
 437 
 438             buf[23] = '-';
 439             buf[18] = '-';
 440             buf[13] = '-';
 441             buf[8]  = '-';
 442 
 443             return new String(buf, LATIN1);
 444         } else {
 445             byte[] buf = new byte[72];
 446 
 447             formatUnsignedLong0UTF16(lsb,        4, buf, 24, 12);
 448             formatUnsignedLong0UTF16(lsb >>> 48, 4, buf, 19, 4);
 449             formatUnsignedLong0UTF16(msb,        4, buf, 14, 4);
 450             formatUnsignedLong0UTF16(msb >>> 16, 4, buf, 9,  4);
 451             formatUnsignedLong0UTF16(msb >>> 32, 4, buf, 0,  8);
 452 
 453             StringUTF16.putChar(buf, 23, '-');
 454             StringUTF16.putChar(buf, 18, '-');
 455             StringUTF16.putChar(buf, 13, '-');
 456             StringUTF16.putChar(buf,  8, '-');
 457 
 458             return new String(buf, UTF16);
 459         }
 460     }
 461 
 462     /**
 463      * Returns a {@code String} object representing the specified
 464      * {@code long}.  The argument is converted to signed decimal
 465      * representation and returned as a string, exactly as if the
 466      * argument and the radix 10 were given as arguments to the {@link
 467      * #toString(long, int)} method.
 468      *
 469      * @param   i   a {@code long} to be converted.
 470      * @return  a string representation of the argument in base&nbsp;10.
 471      */
 472     public static String toString(long i) {
 473         int size = stringSize(i);
 474         if (COMPACT_STRINGS) {
 475             byte[] buf = new byte[size];
 476             getChars(i, size, buf);
 477             return new String(buf, LATIN1);
 478         } else {
 479             byte[] buf = new byte[size * 2];
 480             getCharsUTF16(i, size, buf);
 481             return new String(buf, UTF16);
 482         }
 483     }
 484 
 485     /**
 486      * Returns a string representation of the argument as an unsigned
 487      * decimal value.
 488      *
 489      * The argument is converted to unsigned decimal representation
 490      * and returned as a string exactly as if the argument and radix
 491      * 10 were given as arguments to the {@link #toUnsignedString(long,
 492      * int)} method.
 493      *
 494      * @param   i  an integer to be converted to an unsigned string.
 495      * @return  an unsigned string representation of the argument.
 496      * @see     #toUnsignedString(long, int)
 497      * @since 1.8
 498      */
 499     public static String toUnsignedString(long i) {
 500         return toUnsignedString(i, 10);
 501     }
 502 
 503     /**
 504      * Places characters representing the long i into the
 505      * character array buf. The characters are placed into
 506      * the buffer backwards starting with the least significant
 507      * digit at the specified index (exclusive), and working
 508      * backwards from there.
 509      *
 510      * @implNote This method converts positive inputs into negative
 511      * values, to cover the Long.MIN_VALUE case. Converting otherwise
 512      * (negative to positive) will expose -Long.MIN_VALUE that overflows
 513      * long.
 514      *
 515      * @param i     value to convert
 516      * @param index next index, after the least significant digit
 517      * @param buf   target buffer, Latin1-encoded
 518      * @return index of the most significant digit or minus sign, if present
 519      */
 520     static int getChars(long i, int index, byte[] buf) {
 521         long q;
 522         int r;
 523         int charPos = index;
 524 
 525         boolean negative = (i < 0);
 526         if (!negative) {
 527             i = -i;
 528         }
 529 
 530         // Get 2 digits/iteration using longs until quotient fits into an int
 531         while (i <= Integer.MIN_VALUE) {
 532             q = i / 100;
 533             r = (int)((q * 100) - i);
 534             i = q;
 535             buf[--charPos] = Integer.DigitOnes[r];
 536             buf[--charPos] = Integer.DigitTens[r];
 537         }
 538 
 539         // Get 2 digits/iteration using ints
 540         int q2;
 541         int i2 = (int)i;
 542         while (i2 <= -100) {
 543             q2 = i2 / 100;
 544             r  = (q2 * 100) - i2;
 545             i2 = q2;
 546             buf[--charPos] = Integer.DigitOnes[r];
 547             buf[--charPos] = Integer.DigitTens[r];
 548         }
 549 
 550         // We know there are at most two digits left at this point.
 551         q2 = i2 / 10;
 552         r  = (q2 * 10) - i2;
 553         buf[--charPos] = (byte)('0' + r);
 554 
 555         // Whatever left is the remaining digit.
 556         if (q2 < 0) {
 557             buf[--charPos] = (byte)('0' - q2);
 558         }
 559 
 560         if (negative) {
 561             buf[--charPos] = (byte)'-';
 562         }
 563         return charPos;
 564     }
 565 
 566     /**
 567      * This is a variant of {@link #getChars(long, int, byte[])}, but for
 568      * UTF-16 coder.
 569      *
 570      * @param i     value to convert
 571      * @param index next index, after the least significant digit
 572      * @param buf   target buffer, UTF16-coded.
 573      * @return index of the most significant digit or minus sign, if present
 574      */
 575     static int getCharsUTF16(long i, int index, byte[] buf) {
 576         long q;
 577         int r;
 578         int charPos = index;
 579 
 580         boolean negative = (i < 0);
 581         if (!negative) {
 582             i = -i;
 583         }
 584 
 585         // Get 2 digits/iteration using longs until quotient fits into an int
 586         while (i <= Integer.MIN_VALUE) {
 587             q = i / 100;
 588             r = (int)((q * 100) - i);
 589             i = q;
 590             StringUTF16.putChar(buf, --charPos, Integer.DigitOnes[r]);
 591             StringUTF16.putChar(buf, --charPos, Integer.DigitTens[r]);
 592         }
 593 
 594         // Get 2 digits/iteration using ints
 595         int q2;
 596         int i2 = (int)i;
 597         while (i2 <= -100) {
 598             q2 = i2 / 100;
 599             r  = (q2 * 100) - i2;
 600             i2 = q2;
 601             StringUTF16.putChar(buf, --charPos, Integer.DigitOnes[r]);
 602             StringUTF16.putChar(buf, --charPos, Integer.DigitTens[r]);
 603         }
 604 
 605         // We know there are at most two digits left at this point.
 606         q2 = i2 / 10;
 607         r  = (q2 * 10) - i2;
 608         StringUTF16.putChar(buf, --charPos, '0' + r);
 609 
 610         // Whatever left is the remaining digit.
 611         if (q2 < 0) {
 612             StringUTF16.putChar(buf, --charPos, '0' - q2);
 613         }
 614 
 615         if (negative) {
 616             StringUTF16.putChar(buf, --charPos, '-');
 617         }
 618         return charPos;
 619     }
 620 
 621     /**
 622      * Returns the string representation size for a given long value.
 623      *
 624      * @param x long value
 625      * @return string size
 626      *
 627      * @implNote There are other ways to compute this: e.g. binary search,
 628      * but values are biased heavily towards zero, and therefore linear search
 629      * wins. The iteration results are also routinely inlined in the generated
 630      * code after loop unrolling.
 631      */
 632     static int stringSize(long x) {
 633         int d = 1;
 634         if (x >= 0) {
 635             d = 0;
 636             x = -x;
 637         }
 638         long p = -10;
 639         for (int i = 1; i < 19; i++) {
 640             if (x > p)
 641                 return i + d;
 642             p = 10 * p;
 643         }
 644         return 19 + d;
 645     }
 646 
 647     /**
 648      * Parses the string argument as a signed {@code long} in the
 649      * radix specified by the second argument. The characters in the
 650      * string must all be digits of the specified radix (as determined
 651      * by whether {@link java.lang.Character#digit(char, int)} returns
 652      * a nonnegative value), except that the first character may be an
 653      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
 654      * indicate a negative value or an ASCII plus sign {@code '+'}
 655      * ({@code '\u005Cu002B'}) to indicate a positive value. The
 656      * resulting {@code long} value is returned.
 657      *
 658      * <p>Note that neither the character {@code L}
 659      * ({@code '\u005Cu004C'}) nor {@code l}
 660      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 661      * of the string as a type indicator, as would be permitted in
 662      * Java programming language source code - except that either
 663      * {@code L} or {@code l} may appear as a digit for a
 664      * radix greater than or equal to 22.
 665      *
 666      * <p>An exception of type {@code NumberFormatException} is
 667      * thrown if any of the following situations occurs:
 668      * <ul>
 669      *
 670      * <li>The first argument is {@code null} or is a string of
 671      * length zero.
 672      *
 673      * <li>The {@code radix} is either smaller than {@link
 674      * java.lang.Character#MIN_RADIX} or larger than {@link
 675      * java.lang.Character#MAX_RADIX}.
 676      *
 677      * <li>Any character of the string is not a digit of the specified
 678      * radix, except that the first character may be a minus sign
 679      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
 680      * '+'} ({@code '\u005Cu002B'}) provided that the string is
 681      * longer than length 1.
 682      *
 683      * <li>The value represented by the string is not a value of type
 684      *      {@code long}.
 685      * </ul>
 686      *
 687      * <p>Examples:
 688      * <blockquote><pre>
 689      * parseLong("0", 10) returns 0L
 690      * parseLong("473", 10) returns 473L
 691      * parseLong("+42", 10) returns 42L
 692      * parseLong("-0", 10) returns 0L
 693      * parseLong("-FF", 16) returns -255L
 694      * parseLong("1100110", 2) returns 102L
 695      * parseLong("99", 8) throws a NumberFormatException
 696      * parseLong("Hazelnut", 10) throws a NumberFormatException
 697      * parseLong("Hazelnut", 36) returns 1356099454469L
 698      * </pre></blockquote>
 699      *
 700      * @param      s       the {@code String} containing the
 701      *                     {@code long} representation to be parsed.
 702      * @param      radix   the radix to be used while parsing {@code s}.
 703      * @return     the {@code long} represented by the string argument in
 704      *             the specified radix.
 705      * @throws     NumberFormatException  if the string does not contain a
 706      *             parsable {@code long}.
 707      */
 708     public static long parseLong(String s, int radix)
 709               throws NumberFormatException
 710     {
 711         if (s == null) {
 712             throw new NumberFormatException("null");
 713         }
 714 
 715         if (radix < Character.MIN_RADIX) {
 716             throw new NumberFormatException("radix " + radix +
 717                                             " less than Character.MIN_RADIX");
 718         }
 719         if (radix > Character.MAX_RADIX) {
 720             throw new NumberFormatException("radix " + radix +
 721                                             " greater than Character.MAX_RADIX");
 722         }
 723 
 724         boolean negative = false;
 725         int i = 0, len = s.length();
 726         long limit = -Long.MAX_VALUE;
 727 
 728         if (len > 0) {
 729             char firstChar = s.charAt(0);
 730             if (firstChar < '0') { // Possible leading "+" or "-"
 731                 if (firstChar == '-') {
 732                     negative = true;
 733                     limit = Long.MIN_VALUE;
 734                 } else if (firstChar != '+') {
 735                     throw NumberFormatException.forInputString(s);
 736                 }
 737 
 738                 if (len == 1) { // Cannot have lone "+" or "-"
 739                     throw NumberFormatException.forInputString(s);
 740                 }
 741                 i++;
 742             }
 743             long multmin = limit / radix;
 744             long result = 0;
 745             while (i < len) {
 746                 // Accumulating negatively avoids surprises near MAX_VALUE
 747                 int digit = Character.digit(s.charAt(i++),radix);
 748                 if (digit < 0 || result < multmin) {
 749                     throw NumberFormatException.forInputString(s);
 750                 }
 751                 result *= radix;
 752                 if (result < limit + digit) {
 753                     throw NumberFormatException.forInputString(s);
 754                 }
 755                 result -= digit;
 756             }
 757             return negative ? result : -result;
 758         } else {
 759             throw NumberFormatException.forInputString(s);
 760         }
 761     }
 762 
 763     /**
 764      * Parses the {@link CharSequence} argument as a signed {@code long} in
 765      * the specified {@code radix}, beginning at the specified
 766      * {@code beginIndex} and extending to {@code endIndex - 1}.
 767      *
 768      * <p>The method does not take steps to guard against the
 769      * {@code CharSequence} being mutated while parsing.
 770      *
 771      * @param      s   the {@code CharSequence} containing the {@code long}
 772      *                  representation to be parsed
 773      * @param      beginIndex   the beginning index, inclusive.
 774      * @param      endIndex     the ending index, exclusive.
 775      * @param      radix   the radix to be used while parsing {@code s}.
 776      * @return     the signed {@code long} represented by the subsequence in
 777      *             the specified radix.
 778      * @throws     NullPointerException  if {@code s} is null.
 779      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
 780      *             negative, or if {@code beginIndex} is greater than
 781      *             {@code endIndex} or if {@code endIndex} is greater than
 782      *             {@code s.length()}.
 783      * @throws     NumberFormatException  if the {@code CharSequence} does not
 784      *             contain a parsable {@code int} in the specified
 785      *             {@code radix}, or if {@code radix} is either smaller than
 786      *             {@link java.lang.Character#MIN_RADIX} or larger than
 787      *             {@link java.lang.Character#MAX_RADIX}.
 788      * @since  9
 789      */
 790     public static long parseLong(CharSequence s, int beginIndex, int endIndex, int radix)
 791                 throws NumberFormatException {
 792         s = Objects.requireNonNull(s);
 793 
 794         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
 795             throw new IndexOutOfBoundsException();
 796         }
 797         if (radix < Character.MIN_RADIX) {
 798             throw new NumberFormatException("radix " + radix +
 799                     " less than Character.MIN_RADIX");
 800         }
 801         if (radix > Character.MAX_RADIX) {
 802             throw new NumberFormatException("radix " + radix +
 803                     " greater than Character.MAX_RADIX");
 804         }
 805 
 806         boolean negative = false;
 807         int i = beginIndex;
 808         long limit = -Long.MAX_VALUE;
 809 
 810         if (i < endIndex) {
 811             char firstChar = s.charAt(i);
 812             if (firstChar < '0') { // Possible leading "+" or "-"
 813                 if (firstChar == '-') {
 814                     negative = true;
 815                     limit = Long.MIN_VALUE;
 816                 } else if (firstChar != '+') {
 817                     throw NumberFormatException.forCharSequence(s, beginIndex,
 818                             endIndex, i);
 819                 }
 820                 i++;
 821             }
 822             if (i >= endIndex) { // Cannot have lone "+", "-" or ""
 823                 throw NumberFormatException.forCharSequence(s, beginIndex,
 824                         endIndex, i);
 825             }
 826             long multmin = limit / radix;
 827             long result = 0;
 828             while (i < endIndex) {
 829                 // Accumulating negatively avoids surprises near MAX_VALUE
 830                 int digit = Character.digit(s.charAt(i), radix);
 831                 if (digit < 0 || result < multmin) {
 832                     throw NumberFormatException.forCharSequence(s, beginIndex,
 833                             endIndex, i);
 834                 }
 835                 result *= radix;
 836                 if (result < limit + digit) {
 837                     throw NumberFormatException.forCharSequence(s, beginIndex,
 838                             endIndex, i);
 839                 }
 840                 i++;
 841                 result -= digit;
 842             }
 843             return negative ? result : -result;
 844         } else {
 845             throw new NumberFormatException("");
 846         }
 847     }
 848 
 849     /**
 850      * Parses the string argument as a signed decimal {@code long}.
 851      * The characters in the string must all be decimal digits, except
 852      * that the first character may be an ASCII minus sign {@code '-'}
 853      * ({@code \u005Cu002D'}) to indicate a negative value or an
 854      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
 855      * indicate a positive value. The resulting {@code long} value is
 856      * returned, exactly as if the argument and the radix {@code 10}
 857      * were given as arguments to the {@link
 858      * #parseLong(java.lang.String, int)} method.
 859      *
 860      * <p>Note that neither the character {@code L}
 861      * ({@code '\u005Cu004C'}) nor {@code l}
 862      * ({@code '\u005Cu006C'}) is permitted to appear at the end
 863      * of the string as a type indicator, as would be permitted in
 864      * Java programming language source code.
 865      *
 866      * @param      s   a {@code String} containing the {@code long}
 867      *             representation to be parsed
 868      * @return     the {@code long} represented by the argument in
 869      *             decimal.
 870      * @throws     NumberFormatException  if the string does not contain a
 871      *             parsable {@code long}.
 872      */
 873     public static long parseLong(String s) throws NumberFormatException {
 874         return parseLong(s, 10);
 875     }
 876 
 877     /**
 878      * Parses the string argument as an unsigned {@code long} in the
 879      * radix specified by the second argument.  An unsigned integer
 880      * maps the values usually associated with negative numbers to
 881      * positive numbers larger than {@code MAX_VALUE}.
 882      *
 883      * The characters in the string must all be digits of the
 884      * specified radix (as determined by whether {@link
 885      * java.lang.Character#digit(char, int)} returns a nonnegative
 886      * value), except that the first character may be an ASCII plus
 887      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
 888      * integer value is returned.
 889      *
 890      * <p>An exception of type {@code NumberFormatException} is
 891      * thrown if any of the following situations occurs:
 892      * <ul>
 893      * <li>The first argument is {@code null} or is a string of
 894      * length zero.
 895      *
 896      * <li>The radix is either smaller than
 897      * {@link java.lang.Character#MIN_RADIX} or
 898      * larger than {@link java.lang.Character#MAX_RADIX}.
 899      *
 900      * <li>Any character of the string is not a digit of the specified
 901      * radix, except that the first character may be a plus sign
 902      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
 903      * string is longer than length 1.
 904      *
 905      * <li>The value represented by the string is larger than the
 906      * largest unsigned {@code long}, 2<sup>64</sup>-1.
 907      *
 908      * </ul>
 909      *
 910      *
 911      * @param      s   the {@code String} containing the unsigned integer
 912      *                  representation to be parsed
 913      * @param      radix   the radix to be used while parsing {@code s}.
 914      * @return     the unsigned {@code long} represented by the string
 915      *             argument in the specified radix.
 916      * @throws     NumberFormatException if the {@code String}
 917      *             does not contain a parsable {@code long}.
 918      * @since 1.8
 919      */
 920     public static long parseUnsignedLong(String s, int radix)
 921                 throws NumberFormatException {
 922         if (s == null)  {
 923             throw new NumberFormatException("null");
 924         }
 925 
 926         int len = s.length();
 927         if (len > 0) {
 928             char firstChar = s.charAt(0);
 929             if (firstChar == '-') {
 930                 throw new
 931                     NumberFormatException(String.format("Illegal leading minus sign " +
 932                                                        "on unsigned string %s.", s));
 933             } else {
 934                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
 935                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
 936                     return parseLong(s, radix);
 937                 }
 938 
 939                 // No need for range checks on len due to testing above.
 940                 long first = parseLong(s, 0, len - 1, radix);
 941                 int second = Character.digit(s.charAt(len - 1), radix);
 942                 if (second < 0) {
 943                     throw new NumberFormatException("Bad digit at end of " + s);
 944                 }
 945                 long result = first * radix + second;
 946 
 947                 /*
 948                  * Test leftmost bits of multiprecision extension of first*radix
 949                  * for overflow. The number of bits needed is defined by
 950                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
 951                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
 952                  * overflow is tested by splitting guard in the ranges
 953                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
 954                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
 955                  * on a value which does not include a prime factor in the legal
 956                  * radix range.
 957                  */
 958                 int guard = radix * (int) (first >>> 57);
 959                 if (guard >= 128 ||
 960                     (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
 961                     /*
 962                      * For purposes of exposition, the programmatic statements
 963                      * below should be taken to be multi-precision, i.e., not
 964                      * subject to overflow.
 965                      *
 966                      * A) Condition guard >= 128:
 967                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
 968                      * hence always overflow.
 969                      *
 970                      * B) Condition guard < 92:
 971                      * Define left7 = first >>> 57.
 972                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
 973                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
 974                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
 975                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
 976                      * never overflow.
 977                      *
 978                      * C) Condition 92 <= guard < 128:
 979                      * first*radix + second >= radix*left7*2^57 + second
 980                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
 981                      *
 982                      * D) Condition guard < 128:
 983                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
 984                      * so
 985                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
 986                      * thus
 987                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
 988                      * whence
 989                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
 990                      *
 991                      * E) Conditions C, D, and result >= 0:
 992                      * C and D combined imply the mathematical result
 993                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
 994                      * bound is therefore negative as a signed long, but the
 995                      * upper bound is too small to overflow again after the
 996                      * signed long overflows to positive above 2^64 - 1. Hence
 997                      * result >= 0 implies overflow given C and D.
 998                      */
 999                     throw new NumberFormatException(String.format("String value %s exceeds " +
1000                                                                   "range of unsigned long.", s));
1001                 }
1002                 return result;
1003             }
1004         } else {
1005             throw NumberFormatException.forInputString(s);
1006         }
1007     }
1008 
1009     /**
1010      * Parses the {@link CharSequence} argument as an unsigned {@code long} in
1011      * the specified {@code radix}, beginning at the specified
1012      * {@code beginIndex} and extending to {@code endIndex - 1}.
1013      *
1014      * <p>The method does not take steps to guard against the
1015      * {@code CharSequence} being mutated while parsing.
1016      *
1017      * @param      s   the {@code CharSequence} containing the unsigned
1018      *                 {@code long} representation to be parsed
1019      * @param      beginIndex   the beginning index, inclusive.
1020      * @param      endIndex     the ending index, exclusive.
1021      * @param      radix   the radix to be used while parsing {@code s}.
1022      * @return     the unsigned {@code long} represented by the subsequence in
1023      *             the specified radix.
1024      * @throws     NullPointerException  if {@code s} is null.
1025      * @throws     IndexOutOfBoundsException  if {@code beginIndex} is
1026      *             negative, or if {@code beginIndex} is greater than
1027      *             {@code endIndex} or if {@code endIndex} is greater than
1028      *             {@code s.length()}.
1029      * @throws     NumberFormatException  if the {@code CharSequence} does not
1030      *             contain a parsable unsigned {@code long} in the specified
1031      *             {@code radix}, or if {@code radix} is either smaller than
1032      *             {@link java.lang.Character#MIN_RADIX} or larger than
1033      *             {@link java.lang.Character#MAX_RADIX}.
1034      * @since  9
1035      */
1036     public static long parseUnsignedLong(CharSequence s, int beginIndex, int endIndex, int radix)
1037                 throws NumberFormatException {
1038         s = Objects.requireNonNull(s);
1039 
1040         if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
1041             throw new IndexOutOfBoundsException();
1042         }
1043         int start = beginIndex, len = endIndex - beginIndex;
1044 
1045         if (len > 0) {
1046             char firstChar = s.charAt(start);
1047             if (firstChar == '-') {
1048                 throw new NumberFormatException(String.format("Illegal leading minus sign " +
1049                         "on unsigned string %s.", s.subSequence(start, start + len)));
1050             } else {
1051                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
1052                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
1053                     return parseLong(s, start, start + len, radix);
1054                 }
1055 
1056                 // No need for range checks on end due to testing above.
1057                 long first = parseLong(s, start, start + len - 1, radix);
1058                 int second = Character.digit(s.charAt(start + len - 1), radix);
1059                 if (second < 0) {
1060                     throw new NumberFormatException("Bad digit at end of " +
1061                             s.subSequence(start, start + len));
1062                 }
1063                 long result = first * radix + second;
1064 
1065                 /*
1066                  * Test leftmost bits of multiprecision extension of first*radix
1067                  * for overflow. The number of bits needed is defined by
1068                  * GUARD_BIT = ceil(log2(Character.MAX_RADIX)) + 1 = 7. Then
1069                  * int guard = radix*(int)(first >>> (64 - GUARD_BIT)) and
1070                  * overflow is tested by splitting guard in the ranges
1071                  * guard < 92, 92 <= guard < 128, and 128 <= guard, where
1072                  * 92 = 128 - Character.MAX_RADIX. Note that guard cannot take
1073                  * on a value which does not include a prime factor in the legal
1074                  * radix range.
1075                  */
1076                 int guard = radix * (int) (first >>> 57);
1077                 if (guard >= 128 ||
1078                         (result >= 0 && guard >= 128 - Character.MAX_RADIX)) {
1079                     /*
1080                      * For purposes of exposition, the programmatic statements
1081                      * below should be taken to be multi-precision, i.e., not
1082                      * subject to overflow.
1083                      *
1084                      * A) Condition guard >= 128:
1085                      * If guard >= 128 then first*radix >= 2^7 * 2^57 = 2^64
1086                      * hence always overflow.
1087                      *
1088                      * B) Condition guard < 92:
1089                      * Define left7 = first >>> 57.
1090                      * Given first = (left7 * 2^57) + (first & (2^57 - 1)) then
1091                      * result <= (radix*left7)*2^57 + radix*(2^57 - 1) + second.
1092                      * Thus if radix*left7 < 92, radix <= 36, and second < 36,
1093                      * then result < 92*2^57 + 36*(2^57 - 1) + 36 = 2^64 hence
1094                      * never overflow.
1095                      *
1096                      * C) Condition 92 <= guard < 128:
1097                      * first*radix + second >= radix*left7*2^57 + second
1098                      * so that first*radix + second >= 92*2^57 + 0 > 2^63
1099                      *
1100                      * D) Condition guard < 128:
1101                      * radix*first <= (radix*left7) * 2^57 + radix*(2^57 - 1)
1102                      * so
1103                      * radix*first + second <= (radix*left7) * 2^57 + radix*(2^57 - 1) + 36
1104                      * thus
1105                      * radix*first + second < 128 * 2^57 + 36*2^57 - radix + 36
1106                      * whence
1107                      * radix*first + second < 2^64 + 2^6*2^57 = 2^64 + 2^63
1108                      *
1109                      * E) Conditions C, D, and result >= 0:
1110                      * C and D combined imply the mathematical result
1111                      * 2^63 < first*radix + second < 2^64 + 2^63. The lower
1112                      * bound is therefore negative as a signed long, but the
1113                      * upper bound is too small to overflow again after the
1114                      * signed long overflows to positive above 2^64 - 1. Hence
1115                      * result >= 0 implies overflow given C and D.
1116                      */
1117                     throw new NumberFormatException(String.format("String value %s exceeds " +
1118                             "range of unsigned long.", s.subSequence(start, start + len)));
1119                 }
1120                 return result;
1121             }
1122         } else {
1123             throw NumberFormatException.forInputString("");
1124         }
1125     }
1126 
1127     /**
1128      * Parses the string argument as an unsigned decimal {@code long}. The
1129      * characters in the string must all be decimal digits, except
1130      * that the first character may be an ASCII plus sign {@code
1131      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
1132      * is returned, exactly as if the argument and the radix 10 were
1133      * given as arguments to the {@link
1134      * #parseUnsignedLong(java.lang.String, int)} method.
1135      *
1136      * @param s   a {@code String} containing the unsigned {@code long}
1137      *            representation to be parsed
1138      * @return    the unsigned {@code long} value represented by the decimal string argument
1139      * @throws    NumberFormatException  if the string does not contain a
1140      *            parsable unsigned integer.
1141      * @since 1.8
1142      */
1143     public static long parseUnsignedLong(String s) throws NumberFormatException {
1144         return parseUnsignedLong(s, 10);
1145     }
1146 
1147     /**
1148      * Returns a {@code Long} object holding the value
1149      * extracted from the specified {@code String} when parsed
1150      * with the radix given by the second argument.  The first
1151      * argument is interpreted as representing a signed
1152      * {@code long} in the radix specified by the second
1153      * argument, exactly as if the arguments were given to the {@link
1154      * #parseLong(java.lang.String, int)} method. The result is a
1155      * {@code Long} object that represents the {@code long}
1156      * value specified by the string.
1157      *
1158      * <p>In other words, this method returns a {@code Long} object equal
1159      * to the value of:
1160      *
1161      * <blockquote>
1162      *  {@code new Long(Long.parseLong(s, radix))}
1163      * </blockquote>
1164      *
1165      * @param      s       the string to be parsed
1166      * @param      radix   the radix to be used in interpreting {@code s}
1167      * @return     a {@code Long} object holding the value
1168      *             represented by the string argument in the specified
1169      *             radix.
1170      * @throws     NumberFormatException  If the {@code String} does not
1171      *             contain a parsable {@code long}.
1172      */
1173     public static Long valueOf(String s, int radix) throws NumberFormatException {
1174         return Long.valueOf(parseLong(s, radix));
1175     }
1176 
1177     /**
1178      * Returns a {@code Long} object holding the value
1179      * of the specified {@code String}. The argument is
1180      * interpreted as representing a signed decimal {@code long},
1181      * exactly as if the argument were given to the {@link
1182      * #parseLong(java.lang.String)} method. The result is a
1183      * {@code Long} object that represents the integer value
1184      * specified by the string.
1185      *
1186      * <p>In other words, this method returns a {@code Long} object
1187      * equal to the value of:
1188      *
1189      * <blockquote>
1190      *  {@code new Long(Long.parseLong(s))}
1191      * </blockquote>
1192      *
1193      * @param      s   the string to be parsed.
1194      * @return     a {@code Long} object holding the value
1195      *             represented by the string argument.
1196      * @throws     NumberFormatException  If the string cannot be parsed
1197      *             as a {@code long}.
1198      */
1199     public static Long valueOf(String s) throws NumberFormatException
1200     {
1201         return Long.valueOf(parseLong(s, 10));
1202     }
1203 
1204     private static class LongCache {
1205         private LongCache(){}
1206 
1207         static final Long cache[] = new Long[-(-128) + 127 + 1];
1208 
1209         static {
1210             for(int i = 0; i < cache.length; i++)
1211                 cache[i] = new Long(i - 128);
1212         }
1213     }
1214 
1215     /**
1216      * Returns a {@code Long} instance representing the specified
1217      * {@code long} value.
1218      * If a new {@code Long} instance is not required, this method
1219      * should generally be used in preference to the constructor
1220      * {@link #Long(long)}, as this method is likely to yield
1221      * significantly better space and time performance by caching
1222      * frequently requested values.
1223      *
1224      * Note that unlike the {@linkplain Integer#valueOf(int)
1225      * corresponding method} in the {@code Integer} class, this method
1226      * is <em>not</em> required to cache values within a particular
1227      * range.
1228      *
1229      * @param  l a long value.
1230      * @return a {@code Long} instance representing {@code l}.
1231      * @since  1.5
1232      */
1233     @HotSpotIntrinsicCandidate
1234     public static Long valueOf(long l) {
1235         final int offset = 128;
1236         if (l >= -128 && l <= 127) { // will cache
1237             return LongCache.cache[(int)l + offset];
1238         }
1239         return new Long(l);
1240     }
1241 
1242     /**
1243      * Decodes a {@code String} into a {@code Long}.
1244      * Accepts decimal, hexadecimal, and octal numbers given by the
1245      * following grammar:
1246      *
1247      * <blockquote>
1248      * <dl>
1249      * <dt><i>DecodableString:</i>
1250      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1251      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1252      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1253      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1254      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1255      *
1256      * <dt><i>Sign:</i>
1257      * <dd>{@code -}
1258      * <dd>{@code +}
1259      * </dl>
1260      * </blockquote>
1261      *
1262      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1263      * are as defined in section 3.10.1 of
1264      * <cite>The Java&trade; Language Specification</cite>,
1265      * except that underscores are not accepted between digits.
1266      *
1267      * <p>The sequence of characters following an optional
1268      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1269      * "{@code #}", or leading zero) is parsed as by the {@code
1270      * Long.parseLong} method with the indicated radix (10, 16, or 8).
1271      * This sequence of characters must represent a positive value or
1272      * a {@link NumberFormatException} will be thrown.  The result is
1273      * negated if first character of the specified {@code String} is
1274      * the minus sign.  No whitespace characters are permitted in the
1275      * {@code String}.
1276      *
1277      * @param     nm the {@code String} to decode.
1278      * @return    a {@code Long} object holding the {@code long}
1279      *            value represented by {@code nm}
1280      * @throws    NumberFormatException  if the {@code String} does not
1281      *            contain a parsable {@code long}.
1282      * @see java.lang.Long#parseLong(String, int)
1283      * @since 1.2
1284      */
1285     public static Long decode(String nm) throws NumberFormatException {
1286         int radix = 10;
1287         int index = 0;
1288         boolean negative = false;
1289         Long result;
1290 
1291         if (nm.length() == 0)
1292             throw new NumberFormatException("Zero length string");
1293         char firstChar = nm.charAt(0);
1294         // Handle sign, if present
1295         if (firstChar == '-') {
1296             negative = true;
1297             index++;
1298         } else if (firstChar == '+')
1299             index++;
1300 
1301         // Handle radix specifier, if present
1302         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1303             index += 2;
1304             radix = 16;
1305         }
1306         else if (nm.startsWith("#", index)) {
1307             index ++;
1308             radix = 16;
1309         }
1310         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1311             index ++;
1312             radix = 8;
1313         }
1314 
1315         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1316             throw new NumberFormatException("Sign character in wrong position");
1317 
1318         try {
1319             result = Long.valueOf(nm.substring(index), radix);
1320             result = negative ? Long.valueOf(-result.longValue()) : result;
1321         } catch (NumberFormatException e) {
1322             // If number is Long.MIN_VALUE, we'll end up here. The next line
1323             // handles this case, and causes any genuine format error to be
1324             // rethrown.
1325             String constant = negative ? ("-" + nm.substring(index))
1326                                        : nm.substring(index);
1327             result = Long.valueOf(constant, radix);
1328         }
1329         return result;
1330     }
1331 
1332     /**
1333      * The value of the {@code Long}.
1334      *
1335      * @serial
1336      */
1337     private final long value;
1338 
1339     /**
1340      * Constructs a newly allocated {@code Long} object that
1341      * represents the specified {@code long} argument.
1342      *
1343      * @param   value   the value to be represented by the
1344      *          {@code Long} object.
1345      *
1346      * @deprecated
1347      * It is rarely appropriate to use this constructor. The static factory
1348      * {@link #valueOf(long)} is generally a better choice, as it is
1349      * likely to yield significantly better space and time performance.
1350      */
1351     @Deprecated(since="9")
1352     public Long(long value) {
1353         this.value = value;
1354     }
1355 
1356     /**
1357      * Constructs a newly allocated {@code Long} object that
1358      * represents the {@code long} value indicated by the
1359      * {@code String} parameter. The string is converted to a
1360      * {@code long} value in exactly the manner used by the
1361      * {@code parseLong} method for radix 10.
1362      *
1363      * @param      s   the {@code String} to be converted to a
1364      *             {@code Long}.
1365      * @throws     NumberFormatException  if the {@code String} does not
1366      *             contain a parsable {@code long}.
1367      *
1368      * @deprecated
1369      * It is rarely appropriate to use this constructor.
1370      * Use {@link #parseLong(String)} to convert a string to a
1371      * {@code long} primitive, or use {@link #valueOf(String)}
1372      * to convert a string to a {@code Long} object.
1373      */
1374     @Deprecated(since="9")
1375     public Long(String s) throws NumberFormatException {
1376         this.value = parseLong(s, 10);
1377     }
1378 
1379     /**
1380      * Returns the value of this {@code Long} as a {@code byte} after
1381      * a narrowing primitive conversion.
1382      * @jls 5.1.3 Narrowing Primitive Conversions
1383      */
1384     public byte byteValue() {
1385         return (byte)value;
1386     }
1387 
1388     /**
1389      * Returns the value of this {@code Long} as a {@code short} after
1390      * a narrowing primitive conversion.
1391      * @jls 5.1.3 Narrowing Primitive Conversions
1392      */
1393     public short shortValue() {
1394         return (short)value;
1395     }
1396 
1397     /**
1398      * Returns the value of this {@code Long} as an {@code int} after
1399      * a narrowing primitive conversion.
1400      * @jls 5.1.3 Narrowing Primitive Conversions
1401      */
1402     public int intValue() {
1403         return (int)value;
1404     }
1405 
1406     /**
1407      * Returns the value of this {@code Long} as a
1408      * {@code long} value.
1409      */
1410     @HotSpotIntrinsicCandidate
1411     public long longValue() {
1412         return value;
1413     }
1414 
1415     /**
1416      * Returns the value of this {@code Long} as a {@code float} after
1417      * a widening primitive conversion.
1418      * @jls 5.1.2 Widening Primitive Conversions
1419      */
1420     public float floatValue() {
1421         return (float)value;
1422     }
1423 
1424     /**
1425      * Returns the value of this {@code Long} as a {@code double}
1426      * after a widening primitive conversion.
1427      * @jls 5.1.2 Widening Primitive Conversions
1428      */
1429     public double doubleValue() {
1430         return (double)value;
1431     }
1432 
1433     /**
1434      * Returns a {@code String} object representing this
1435      * {@code Long}'s value.  The value is converted to signed
1436      * decimal representation and returned as a string, exactly as if
1437      * the {@code long} value were given as an argument to the
1438      * {@link java.lang.Long#toString(long)} method.
1439      *
1440      * @return  a string representation of the value of this object in
1441      *          base&nbsp;10.
1442      */
1443     public String toString() {
1444         return toString(value);
1445     }
1446 
1447     /**
1448      * Returns a hash code for this {@code Long}. The result is
1449      * the exclusive OR of the two halves of the primitive
1450      * {@code long} value held by this {@code Long}
1451      * object. That is, the hashcode is the value of the expression:
1452      *
1453      * <blockquote>
1454      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1455      * </blockquote>
1456      *
1457      * @return  a hash code value for this object.
1458      */
1459     @Override
1460     public int hashCode() {
1461         return Long.hashCode(value);
1462     }
1463 
1464     /**
1465      * Returns a hash code for a {@code long} value; compatible with
1466      * {@code Long.hashCode()}.
1467      *
1468      * @param value the value to hash
1469      * @return a hash code value for a {@code long} value.
1470      * @since 1.8
1471      */
1472     public static int hashCode(long value) {
1473         return (int)(value ^ (value >>> 32));
1474     }
1475 
1476     /**
1477      * Compares this object to the specified object.  The result is
1478      * {@code true} if and only if the argument is not
1479      * {@code null} and is a {@code Long} object that
1480      * contains the same {@code long} value as this object.
1481      *
1482      * @param   obj   the object to compare with.
1483      * @return  {@code true} if the objects are the same;
1484      *          {@code false} otherwise.
1485      */
1486     public boolean equals(Object obj) {
1487         if (obj instanceof Long) {
1488             return value == ((Long)obj).longValue();
1489         }
1490         return false;
1491     }
1492 
1493     /**
1494      * Determines the {@code long} value of the system property
1495      * with the specified name.
1496      *
1497      * <p>The first argument is treated as the name of a system
1498      * property.  System properties are accessible through the {@link
1499      * java.lang.System#getProperty(java.lang.String)} method. The
1500      * string value of this property is then interpreted as a {@code
1501      * long} value using the grammar supported by {@link Long#decode decode}
1502      * and a {@code Long} object representing this value is returned.
1503      *
1504      * <p>If there is no property with the specified name, if the
1505      * specified name is empty or {@code null}, or if the property
1506      * does not have the correct numeric format, then {@code null} is
1507      * returned.
1508      *
1509      * <p>In other words, this method returns a {@code Long} object
1510      * equal to the value of:
1511      *
1512      * <blockquote>
1513      *  {@code getLong(nm, null)}
1514      * </blockquote>
1515      *
1516      * @param   nm   property name.
1517      * @return  the {@code Long} value of the property.
1518      * @throws  SecurityException for the same reasons as
1519      *          {@link System#getProperty(String) System.getProperty}
1520      * @see     java.lang.System#getProperty(java.lang.String)
1521      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1522      */
1523     public static Long getLong(String nm) {
1524         return getLong(nm, null);
1525     }
1526 
1527     /**
1528      * Determines the {@code long} value of the system property
1529      * with the specified name.
1530      *
1531      * <p>The first argument is treated as the name of a system
1532      * property.  System properties are accessible through the {@link
1533      * java.lang.System#getProperty(java.lang.String)} method. The
1534      * string value of this property is then interpreted as a {@code
1535      * long} value using the grammar supported by {@link Long#decode decode}
1536      * and a {@code Long} object representing this value is returned.
1537      *
1538      * <p>The second argument is the default value. A {@code Long} object
1539      * that represents the value of the second argument is returned if there
1540      * is no property of the specified name, if the property does not have
1541      * the correct numeric format, or if the specified name is empty or null.
1542      *
1543      * <p>In other words, this method returns a {@code Long} object equal
1544      * to the value of:
1545      *
1546      * <blockquote>
1547      *  {@code getLong(nm, new Long(val))}
1548      * </blockquote>
1549      *
1550      * but in practice it may be implemented in a manner such as:
1551      *
1552      * <blockquote><pre>
1553      * Long result = getLong(nm, null);
1554      * return (result == null) ? new Long(val) : result;
1555      * </pre></blockquote>
1556      *
1557      * to avoid the unnecessary allocation of a {@code Long} object when
1558      * the default value is not needed.
1559      *
1560      * @param   nm    property name.
1561      * @param   val   default value.
1562      * @return  the {@code Long} value of the property.
1563      * @throws  SecurityException for the same reasons as
1564      *          {@link System#getProperty(String) System.getProperty}
1565      * @see     java.lang.System#getProperty(java.lang.String)
1566      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1567      */
1568     public static Long getLong(String nm, long val) {
1569         Long result = Long.getLong(nm, null);
1570         return (result == null) ? Long.valueOf(val) : result;
1571     }
1572 
1573     /**
1574      * Returns the {@code long} value of the system property with
1575      * the specified name.  The first argument is treated as the name
1576      * of a system property.  System properties are accessible through
1577      * the {@link java.lang.System#getProperty(java.lang.String)}
1578      * method. The string value of this property is then interpreted
1579      * as a {@code long} value, as per the
1580      * {@link Long#decode decode} method, and a {@code Long} object
1581      * representing this value is returned; in summary:
1582      *
1583      * <ul>
1584      * <li>If the property value begins with the two ASCII characters
1585      * {@code 0x} or the ASCII character {@code #}, not followed by
1586      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1587      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1588      * with radix 16.
1589      * <li>If the property value begins with the ASCII character
1590      * {@code 0} followed by another character, it is parsed as
1591      * an octal integer exactly as by the method {@link
1592      * #valueOf(java.lang.String, int)} with radix 8.
1593      * <li>Otherwise the property value is parsed as a decimal
1594      * integer exactly as by the method
1595      * {@link #valueOf(java.lang.String, int)} with radix 10.
1596      * </ul>
1597      *
1598      * <p>Note that, in every case, neither {@code L}
1599      * ({@code '\u005Cu004C'}) nor {@code l}
1600      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1601      * of the property value as a type indicator, as would be
1602      * permitted in Java programming language source code.
1603      *
1604      * <p>The second argument is the default value. The default value is
1605      * returned if there is no property of the specified name, if the
1606      * property does not have the correct numeric format, or if the
1607      * specified name is empty or {@code null}.
1608      *
1609      * @param   nm   property name.
1610      * @param   val   default value.
1611      * @return  the {@code Long} value of the property.
1612      * @throws  SecurityException for the same reasons as
1613      *          {@link System#getProperty(String) System.getProperty}
1614      * @see     System#getProperty(java.lang.String)
1615      * @see     System#getProperty(java.lang.String, java.lang.String)
1616      */
1617     public static Long getLong(String nm, Long val) {
1618         String v = null;
1619         try {
1620             v = System.getProperty(nm);
1621         } catch (IllegalArgumentException | NullPointerException e) {
1622         }
1623         if (v != null) {
1624             try {
1625                 return Long.decode(v);
1626             } catch (NumberFormatException e) {
1627             }
1628         }
1629         return val;
1630     }
1631 
1632     /**
1633      * Compares two {@code Long} objects numerically.
1634      *
1635      * @param   anotherLong   the {@code Long} to be compared.
1636      * @return  the value {@code 0} if this {@code Long} is
1637      *          equal to the argument {@code Long}; a value less than
1638      *          {@code 0} if this {@code Long} is numerically less
1639      *          than the argument {@code Long}; and a value greater
1640      *          than {@code 0} if this {@code Long} is numerically
1641      *           greater than the argument {@code Long} (signed
1642      *           comparison).
1643      * @since   1.2
1644      */
1645     public int compareTo(Long anotherLong) {
1646         return compare(this.value, anotherLong.value);
1647     }
1648 
1649     /**
1650      * Compares two {@code long} values numerically.
1651      * The value returned is identical to what would be returned by:
1652      * <pre>
1653      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1654      * </pre>
1655      *
1656      * @param  x the first {@code long} to compare
1657      * @param  y the second {@code long} to compare
1658      * @return the value {@code 0} if {@code x == y};
1659      *         a value less than {@code 0} if {@code x < y}; and
1660      *         a value greater than {@code 0} if {@code x > y}
1661      * @since 1.7
1662      */
1663     public static int compare(long x, long y) {
1664         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1665     }
1666 
1667     /**
1668      * Compares two {@code long} values numerically treating the values
1669      * as unsigned.
1670      *
1671      * @param  x the first {@code long} to compare
1672      * @param  y the second {@code long} to compare
1673      * @return the value {@code 0} if {@code x == y}; a value less
1674      *         than {@code 0} if {@code x < y} as unsigned values; and
1675      *         a value greater than {@code 0} if {@code x > y} as
1676      *         unsigned values
1677      * @since 1.8
1678      */
1679     public static int compareUnsigned(long x, long y) {
1680         return compare(x + MIN_VALUE, y + MIN_VALUE);
1681     }
1682 
1683 
1684     /**
1685      * Returns the unsigned quotient of dividing the first argument by
1686      * the second where each argument and the result is interpreted as
1687      * an unsigned value.
1688      *
1689      * <p>Note that in two's complement arithmetic, the three other
1690      * basic arithmetic operations of add, subtract, and multiply are
1691      * bit-wise identical if the two operands are regarded as both
1692      * being signed or both being unsigned.  Therefore separate {@code
1693      * addUnsigned}, etc. methods are not provided.
1694      *
1695      * @param dividend the value to be divided
1696      * @param divisor the value doing the dividing
1697      * @return the unsigned quotient of the first argument divided by
1698      * the second argument
1699      * @see #remainderUnsigned
1700      * @since 1.8
1701      */
1702     public static long divideUnsigned(long dividend, long divisor) {
1703         if (divisor < 0L) { // signed comparison
1704             // Answer must be 0 or 1 depending on relative magnitude
1705             // of dividend and divisor.
1706             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1707         }
1708 
1709         if (dividend > 0) //  Both inputs non-negative
1710             return dividend/divisor;
1711         else {
1712             /*
1713              * For simple code, leveraging BigInteger.  Longer and faster
1714              * code written directly in terms of operations on longs is
1715              * possible; see "Hacker's Delight" for divide and remainder
1716              * algorithms.
1717              */
1718             return toUnsignedBigInteger(dividend).
1719                 divide(toUnsignedBigInteger(divisor)).longValue();
1720         }
1721     }
1722 
1723     /**
1724      * Returns the unsigned remainder from dividing the first argument
1725      * by the second where each argument and the result is interpreted
1726      * as an unsigned value.
1727      *
1728      * @param dividend the value to be divided
1729      * @param divisor the value doing the dividing
1730      * @return the unsigned remainder of the first argument divided by
1731      * the second argument
1732      * @see #divideUnsigned
1733      * @since 1.8
1734      */
1735     public static long remainderUnsigned(long dividend, long divisor) {
1736         if (dividend > 0 && divisor > 0) { // signed comparisons
1737             return dividend % divisor;
1738         } else {
1739             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1740                 return dividend;
1741             else
1742                 return toUnsignedBigInteger(dividend).
1743                     remainder(toUnsignedBigInteger(divisor)).longValue();
1744         }
1745     }
1746 
1747     // Bit Twiddling
1748 
1749     /**
1750      * The number of bits used to represent a {@code long} value in two's
1751      * complement binary form.
1752      *
1753      * @since 1.5
1754      */
1755     @Native public static final int SIZE = 64;
1756 
1757     /**
1758      * The number of bytes used to represent a {@code long} value in two's
1759      * complement binary form.
1760      *
1761      * @since 1.8
1762      */
1763     public static final int BYTES = SIZE / Byte.SIZE;
1764 
1765     /**
1766      * Returns a {@code long} value with at most a single one-bit, in the
1767      * position of the highest-order ("leftmost") one-bit in the specified
1768      * {@code long} value.  Returns zero if the specified value has no
1769      * one-bits in its two's complement binary representation, that is, if it
1770      * is equal to zero.
1771      *
1772      * @param i the value whose highest one bit is to be computed
1773      * @return a {@code long} value with a single one-bit, in the position
1774      *     of the highest-order one-bit in the specified value, or zero if
1775      *     the specified value is itself equal to zero.
1776      * @since 1.5
1777      */
1778     public static long highestOneBit(long i) {
1779         // HD, Figure 3-1
1780         i |= (i >>  1);
1781         i |= (i >>  2);
1782         i |= (i >>  4);
1783         i |= (i >>  8);
1784         i |= (i >> 16);
1785         i |= (i >> 32);
1786         return i - (i >>> 1);
1787     }
1788 
1789     /**
1790      * Returns a {@code long} value with at most a single one-bit, in the
1791      * position of the lowest-order ("rightmost") one-bit in the specified
1792      * {@code long} value.  Returns zero if the specified value has no
1793      * one-bits in its two's complement binary representation, that is, if it
1794      * is equal to zero.
1795      *
1796      * @param i the value whose lowest one bit is to be computed
1797      * @return a {@code long} value with a single one-bit, in the position
1798      *     of the lowest-order one-bit in the specified value, or zero if
1799      *     the specified value is itself equal to zero.
1800      * @since 1.5
1801      */
1802     public static long lowestOneBit(long i) {
1803         // HD, Section 2-1
1804         return i & -i;
1805     }
1806 
1807     /**
1808      * Returns 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.  Returns 64 if the
1811      * specified value has no one-bits in its two's complement representation,
1812      * in other words if it is equal to zero.
1813      *
1814      * <p>Note that this method is closely related to the logarithm base 2.
1815      * For all positive {@code long} values x:
1816      * <ul>
1817      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1818      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1819      * </ul>
1820      *
1821      * @param i the value whose number of leading zeros is to be computed
1822      * @return the number of zero bits preceding the highest-order
1823      *     ("leftmost") one-bit in the two's complement binary representation
1824      *     of the specified {@code long} value, or 64 if the value
1825      *     is equal to zero.
1826      * @since 1.5
1827      */
1828     @HotSpotIntrinsicCandidate
1829     public static int numberOfLeadingZeros(long i) {
1830         // HD, Figure 5-6
1831          if (i == 0)
1832             return 64;
1833         int n = 1;
1834         int x = (int)(i >>> 32);
1835         if (x == 0) { n += 32; x = (int)i; }
1836         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1837         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1838         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1839         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1840         n -= x >>> 31;
1841         return n;
1842     }
1843 
1844     /**
1845      * Returns the number of zero bits following the lowest-order ("rightmost")
1846      * one-bit in the two's complement binary representation of the specified
1847      * {@code long} value.  Returns 64 if the specified value has no
1848      * one-bits in its two's complement representation, in other words if it is
1849      * equal to zero.
1850      *
1851      * @param i the value whose number of trailing zeros is to be computed
1852      * @return the number of zero bits following the lowest-order ("rightmost")
1853      *     one-bit in the two's complement binary representation of the
1854      *     specified {@code long} value, or 64 if the value is equal
1855      *     to zero.
1856      * @since 1.5
1857      */
1858     @HotSpotIntrinsicCandidate
1859     public static int numberOfTrailingZeros(long i) {
1860         // HD, Figure 5-14
1861         int x, y;
1862         if (i == 0) return 64;
1863         int n = 63;
1864         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1865         y = x <<16; if (y != 0) { n = n -16; x = y; }
1866         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1867         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1868         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1869         return n - ((x << 1) >>> 31);
1870     }
1871 
1872     /**
1873      * Returns the number of one-bits in the two's complement binary
1874      * representation of the specified {@code long} value.  This function is
1875      * sometimes referred to as the <i>population count</i>.
1876      *
1877      * @param i the value whose bits are to be counted
1878      * @return the number of one-bits in the two's complement binary
1879      *     representation of the specified {@code long} value.
1880      * @since 1.5
1881      */
1882      @HotSpotIntrinsicCandidate
1883      public static int bitCount(long i) {
1884         // HD, Figure 5-2
1885         i = i - ((i >>> 1) & 0x5555555555555555L);
1886         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1887         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1888         i = i + (i >>> 8);
1889         i = i + (i >>> 16);
1890         i = i + (i >>> 32);
1891         return (int)i & 0x7f;
1892      }
1893 
1894     /**
1895      * Returns 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.  (Bits shifted out of the left hand, or
1898      * high-order, side reenter on the right, or low-order.)
1899      *
1900      * <p>Note that left rotation with a negative distance is equivalent to
1901      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1902      * distance)}.  Note also that rotation by any multiple of 64 is a
1903      * no-op, so all but the last six bits of the rotation distance can be
1904      * ignored, even if the distance is negative: {@code rotateLeft(val,
1905      * distance) == rotateLeft(val, distance & 0x3F)}.
1906      *
1907      * @param i the value whose bits are to be rotated left
1908      * @param distance the number of bit positions to rotate left
1909      * @return the value obtained by rotating the two's complement binary
1910      *     representation of the specified {@code long} value left by the
1911      *     specified number of bits.
1912      * @since 1.5
1913      */
1914     public static long rotateLeft(long i, int distance) {
1915         return (i << distance) | (i >>> -distance);
1916     }
1917 
1918     /**
1919      * Returns 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.  (Bits shifted out of the right hand, or
1922      * low-order, side reenter on the left, or high-order.)
1923      *
1924      * <p>Note that right rotation with a negative distance is equivalent to
1925      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1926      * distance)}.  Note also that rotation by any multiple of 64 is a
1927      * no-op, so all but the last six bits of the rotation distance can be
1928      * ignored, even if the distance is negative: {@code rotateRight(val,
1929      * distance) == rotateRight(val, distance & 0x3F)}.
1930      *
1931      * @param i the value whose bits are to be rotated right
1932      * @param distance the number of bit positions to rotate right
1933      * @return the value obtained by rotating the two's complement binary
1934      *     representation of the specified {@code long} value right by the
1935      *     specified number of bits.
1936      * @since 1.5
1937      */
1938     public static long rotateRight(long i, int distance) {
1939         return (i >>> distance) | (i << -distance);
1940     }
1941 
1942     /**
1943      * Returns the value obtained by reversing the order of the bits in the
1944      * two's complement binary representation of the specified {@code long}
1945      * value.
1946      *
1947      * @param i the value to be reversed
1948      * @return the value obtained by reversing order of the bits in the
1949      *     specified {@code long} value.
1950      * @since 1.5
1951      */
1952     public static long reverse(long i) {
1953         // HD, Figure 7-1
1954         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1955         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1956         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1957 
1958         return reverseBytes(i);
1959     }
1960 
1961     /**
1962      * Returns the signum function of the specified {@code long} value.  (The
1963      * return value is -1 if the specified value is negative; 0 if the
1964      * specified value is zero; and 1 if the specified value is positive.)
1965      *
1966      * @param i the value whose signum is to be computed
1967      * @return the signum function of the specified {@code long} value.
1968      * @since 1.5
1969      */
1970     public static int signum(long i) {
1971         // HD, Section 2-7
1972         return (int) ((i >> 63) | (-i >>> 63));
1973     }
1974 
1975     /**
1976      * Returns the value obtained by reversing the order of the bytes in the
1977      * two's complement representation of the specified {@code long} value.
1978      *
1979      * @param i the value whose bytes are to be reversed
1980      * @return the value obtained by reversing the bytes in the specified
1981      *     {@code long} value.
1982      * @since 1.5
1983      */
1984     @HotSpotIntrinsicCandidate
1985     public static long reverseBytes(long i) {
1986         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1987         return (i << 48) | ((i & 0xffff0000L) << 16) |
1988             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1989     }
1990 
1991     /**
1992      * Adds two {@code long} values together as per the + operator.
1993      *
1994      * @param a the first operand
1995      * @param b the second operand
1996      * @return the sum of {@code a} and {@code b}
1997      * @see java.util.function.BinaryOperator
1998      * @since 1.8
1999      */
2000     public static long sum(long a, long b) {
2001         return a + b;
2002     }
2003 
2004     /**
2005      * Returns the greater of two {@code long} values
2006      * as if by calling {@link Math#max(long, long) Math.max}.
2007      *
2008      * @param a the first operand
2009      * @param b the second operand
2010      * @return the greater of {@code a} and {@code b}
2011      * @see java.util.function.BinaryOperator
2012      * @since 1.8
2013      */
2014     public static long max(long a, long b) {
2015         return Math.max(a, b);
2016     }
2017 
2018     /**
2019      * Returns the smaller of two {@code long} values
2020      * as if by calling {@link Math#min(long, long) Math.min}.
2021      *
2022      * @param a the first operand
2023      * @param b the second operand
2024      * @return the smaller of {@code a} and {@code b}
2025      * @see java.util.function.BinaryOperator
2026      * @since 1.8
2027      */
2028     public static long min(long a, long b) {
2029         return Math.min(a, b);
2030     }
2031 
2032     @Override
2033     public Long resolveConstant(MethodHandles.Lookup lookup) {
2034         return this;
2035     }
2036 
2037     /** use serialVersionUID from JDK 1.0.2 for interoperability */
2038     @Native private static final long serialVersionUID = 4290774380558885855L;
2039 }