View Javadoc
1   /*
2    * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
3    * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4    *
5    * This code is free software; you can redistribute it and/or modify it
6    * under the terms of the GNU General Public License version 2 only, as
7    * published by the Free Software Foundation.  Oracle designates this
8    * particular file as subject to the "Classpath" exception as provided
9    * by Oracle in the LICENSE file that accompanied this code.
10   *
11   * This code is distributed in the hope that it will be useful, but WITHOUT
12   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13   * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
14   * version 2 for more details (a copy is included in the LICENSE file that
15   * accompanied this code).
16   *
17   * You should have received a copy of the GNU General Public License version
18   * 2 along with this work; if not, write to the Free Software Foundation,
19   * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20   *
21   * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22   * or visit www.oracle.com if you need additional information or have any
23   * questions.
24   */
25  
26  package java.lang;
27  
28  import java.lang.annotation.Native;
29  import java.math.*;
30  
31  
32  /**
33   * The {@code Long} class wraps a value of the primitive type {@code
34   * long} in an object. An object of type {@code Long} contains a
35   * single field whose type is {@code long}.
36   *
37   * <p> In addition, this class provides several methods for converting
38   * a {@code long} to a {@code String} and a {@code String} to a {@code
39   * long}, as well as other constants and methods useful when dealing
40   * with a {@code long}.
41   *
42   * <p>Implementation note: The implementations of the "bit twiddling"
43   * methods (such as {@link #highestOneBit(long) highestOneBit} and
44   * {@link #numberOfTrailingZeros(long) numberOfTrailingZeros}) are
45   * based on material from Henry S. Warren, Jr.'s <i>Hacker's
46   * Delight</i>, (Addison Wesley, 2002).
47   *
48   * @author  Lee Boynton
49   * @author  Arthur van Hoff
50   * @author  Josh Bloch
51   * @author  Joseph D. Darcy
52   * @since   JDK1.0
53   */
54  public final class Long extends Number implements Comparable<Long> {
55      /**
56       * A constant holding the minimum value a {@code long} can
57       * have, -2<sup>63</sup>.
58       */
59      @Native public static final long MIN_VALUE = 0x8000000000000000L;
60  
61      /**
62       * A constant holding the maximum value a {@code long} can
63       * have, 2<sup>63</sup>-1.
64       */
65      @Native public static final long MAX_VALUE = 0x7fffffffffffffffL;
66  
67      /**
68       * The {@code Class} instance representing the primitive type
69       * {@code long}.
70       *
71       * @since   JDK1.1
72       */
73      @SuppressWarnings("unchecked")
74      public static final Class<Long>     TYPE = (Class<Long>) Class.getPrimitiveClass("long");
75  
76      /**
77       * Returns a string representation of the first argument in the
78       * radix specified by the second argument.
79       *
80       * <p>If the radix is smaller than {@code Character.MIN_RADIX}
81       * or larger than {@code Character.MAX_RADIX}, then the radix
82       * {@code 10} is used instead.
83       *
84       * <p>If the first argument is negative, the first element of the
85       * result is the ASCII minus sign {@code '-'}
86       * ({@code '\u005Cu002d'}). If the first argument is not
87       * negative, no sign character appears in the result.
88       *
89       * <p>The remaining characters of the result represent the magnitude
90       * of the first argument. If the magnitude is zero, it is
91       * represented by a single zero character {@code '0'}
92       * ({@code '\u005Cu0030'}); otherwise, the first character of
93       * the representation of the magnitude will not be the zero
94       * character.  The following ASCII characters are used as digits:
95       *
96       * <blockquote>
97       *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
98       * </blockquote>
99       *
100      * These are {@code '\u005Cu0030'} through
101      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
102      * {@code '\u005Cu007a'}. If {@code radix} is
103      * <var>N</var>, then the first <var>N</var> of these characters
104      * are used as radix-<var>N</var> digits in the order shown. Thus,
105      * the digits for hexadecimal (radix 16) are
106      * {@code 0123456789abcdef}. If uppercase letters are
107      * desired, the {@link java.lang.String#toUpperCase()} method may
108      * be called on the result:
109      *
110      * <blockquote>
111      *  {@code Long.toString(n, 16).toUpperCase()}
112      * </blockquote>
113      *
114      * @param   i       a {@code long} to be converted to a string.
115      * @param   radix   the radix to use in the string representation.
116      * @return  a string representation of the argument in the specified radix.
117      * @see     java.lang.Character#MAX_RADIX
118      * @see     java.lang.Character#MIN_RADIX
119      */
120     public static String toString(long i, int radix) {
121         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
122             radix = 10;
123         if (radix == 10)
124             return toString(i);
125         char[] buf = new char[65];
126         int charPos = 64;
127         boolean negative = (i < 0);
128 
129         if (!negative) {
130             i = -i;
131         }
132 
133         while (i <= -radix) {
134             buf[charPos--] = Integer.digits[(int)(-(i % radix))];
135             i = i / radix;
136         }
137         buf[charPos] = Integer.digits[(int)(-i)];
138 
139         if (negative) {
140             buf[--charPos] = '-';
141         }
142 
143         return new String(buf, charPos, (65 - charPos));
144     }
145 
146     /**
147      * Returns a string representation of the first argument as an
148      * unsigned integer value in the radix specified by the second
149      * argument.
150      *
151      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
152      * or larger than {@code Character.MAX_RADIX}, then the radix
153      * {@code 10} is used instead.
154      *
155      * <p>Note that since the first argument is treated as an unsigned
156      * value, no leading sign character is printed.
157      *
158      * <p>If the magnitude is zero, it is represented by a single zero
159      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
160      * the first character of the representation of the magnitude will
161      * not be the zero character.
162      *
163      * <p>The behavior of radixes and the characters used as digits
164      * are the same as {@link #toString(long, int) toString}.
165      *
166      * @param   i       an integer to be converted to an unsigned string.
167      * @param   radix   the radix to use in the string representation.
168      * @return  an unsigned string representation of the argument in the specified radix.
169      * @see     #toString(long, int)
170      * @since 1.8
171      */
172     public static String toUnsignedString(long i, int radix) {
173         if (i >= 0)
174             return toString(i, radix);
175         else {
176             switch (radix) {
177             case 2:
178                 return toBinaryString(i);
179 
180             case 4:
181                 return toUnsignedString0(i, 2);
182 
183             case 8:
184                 return toOctalString(i);
185 
186             case 10:
187                 /*
188                  * We can get the effect of an unsigned division by 10
189                  * on a long value by first shifting right, yielding a
190                  * positive value, and then dividing by 5.  This
191                  * allows the last digit and preceding digits to be
192                  * isolated more quickly than by an initial conversion
193                  * to BigInteger.
194                  */
195                 long quot = (i >>> 1) / 5;
196                 long rem = i - quot * 10;
197                 return toString(quot) + rem;
198 
199             case 16:
200                 return toHexString(i);
201 
202             case 32:
203                 return toUnsignedString0(i, 5);
204 
205             default:
206                 return toUnsignedBigInteger(i).toString(radix);
207             }
208         }
209     }
210 
211     /**
212      * Return a BigInteger equal to the unsigned value of the
213      * argument.
214      */
215     private static BigInteger toUnsignedBigInteger(long i) {
216         if (i >= 0L)
217             return BigInteger.valueOf(i);
218         else {
219             int upper = (int) (i >>> 32);
220             int lower = (int) i;
221 
222             // return (upper << 32) + lower
223             return (BigInteger.valueOf(Integer.toUnsignedLong(upper))).shiftLeft(32).
224                 add(BigInteger.valueOf(Integer.toUnsignedLong(lower)));
225         }
226     }
227 
228     /**
229      * Returns a string representation of the {@code long}
230      * argument as an unsigned integer in base&nbsp;16.
231      *
232      * <p>The unsigned {@code long} value is the argument plus
233      * 2<sup>64</sup> if the argument is negative; otherwise, it is
234      * equal to the argument.  This value is converted to a string of
235      * ASCII digits in hexadecimal (base&nbsp;16) with no extra
236      * leading {@code 0}s.
237      *
238      * <p>The value of the argument can be recovered from the returned
239      * string {@code s} by calling {@link
240      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
241      * 16)}.
242      *
243      * <p>If the unsigned magnitude is zero, it is represented by a
244      * single zero character {@code '0'} ({@code '\u005Cu0030'});
245      * otherwise, the first character of the representation of the
246      * unsigned magnitude will not be the zero character. The
247      * following characters are used as hexadecimal digits:
248      *
249      * <blockquote>
250      *  {@code 0123456789abcdef}
251      * </blockquote>
252      *
253      * These are the characters {@code '\u005Cu0030'} through
254      * {@code '\u005Cu0039'} and  {@code '\u005Cu0061'} through
255      * {@code '\u005Cu0066'}.  If uppercase letters are desired,
256      * the {@link java.lang.String#toUpperCase()} method may be called
257      * on the result:
258      *
259      * <blockquote>
260      *  {@code Long.toHexString(n).toUpperCase()}
261      * </blockquote>
262      *
263      * @param   i   a {@code long} to be converted to a string.
264      * @return  the string representation of the unsigned {@code long}
265      *          value represented by the argument in hexadecimal
266      *          (base&nbsp;16).
267      * @see #parseUnsignedLong(String, int)
268      * @see #toUnsignedString(long, int)
269      * @since   JDK 1.0.2
270      */
271     public static String toHexString(long i) {
272         return toUnsignedString0(i, 4);
273     }
274 
275     /**
276      * Returns a string representation of the {@code long}
277      * argument as an unsigned integer in base&nbsp;8.
278      *
279      * <p>The unsigned {@code long} value is the argument plus
280      * 2<sup>64</sup> if the argument is negative; otherwise, it is
281      * equal to the argument.  This value is converted to a string of
282      * ASCII digits in octal (base&nbsp;8) with no extra leading
283      * {@code 0}s.
284      *
285      * <p>The value of the argument can be recovered from the returned
286      * string {@code s} by calling {@link
287      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
288      * 8)}.
289      *
290      * <p>If the unsigned magnitude is zero, it is represented by a
291      * single zero character {@code '0'} ({@code '\u005Cu0030'});
292      * otherwise, the first character of the representation of the
293      * unsigned magnitude will not be the zero character. The
294      * following characters are used as octal digits:
295      *
296      * <blockquote>
297      *  {@code 01234567}
298      * </blockquote>
299      *
300      * These are the characters {@code '\u005Cu0030'} through
301      * {@code '\u005Cu0037'}.
302      *
303      * @param   i   a {@code long} to be converted to a string.
304      * @return  the string representation of the unsigned {@code long}
305      *          value represented by the argument in octal (base&nbsp;8).
306      * @see #parseUnsignedLong(String, int)
307      * @see #toUnsignedString(long, int)
308      * @since   JDK 1.0.2
309      */
310     public static String toOctalString(long i) {
311         return toUnsignedString0(i, 3);
312     }
313 
314     /**
315      * Returns a string representation of the {@code long}
316      * argument as an unsigned integer in base&nbsp;2.
317      *
318      * <p>The unsigned {@code long} value is the argument plus
319      * 2<sup>64</sup> if the argument is negative; otherwise, it is
320      * equal to the argument.  This value is converted to a string of
321      * ASCII digits in binary (base&nbsp;2) with no extra leading
322      * {@code 0}s.
323      *
324      * <p>The value of the argument can be recovered from the returned
325      * string {@code s} by calling {@link
326      * Long#parseUnsignedLong(String, int) Long.parseUnsignedLong(s,
327      * 2)}.
328      *
329      * <p>If the unsigned magnitude is zero, it is represented by a
330      * single zero character {@code '0'} ({@code '\u005Cu0030'});
331      * otherwise, the first character of the representation of the
332      * unsigned magnitude will not be the zero character. The
333      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
334      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
335      *
336      * @param   i   a {@code long} to be converted to a string.
337      * @return  the string representation of the unsigned {@code long}
338      *          value represented by the argument in binary (base&nbsp;2).
339      * @see #parseUnsignedLong(String, int)
340      * @see #toUnsignedString(long, int)
341      * @since   JDK 1.0.2
342      */
343     public static String toBinaryString(long i) {
344         return toUnsignedString0(i, 1);
345     }
346 
347     /**
348      * Format a long (treated as unsigned) into a String.
349      * @param val the value to format
350      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
351      */
352     static String toUnsignedString0(long val, int shift) {
353         // assert shift > 0 && shift <=5 : "Illegal shift value";
354         int mag = Long.SIZE - Long.numberOfLeadingZeros(val);
355         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
356         char[] buf = new char[chars];
357 
358         formatUnsignedLong(val, shift, buf, 0, chars);
359         return new String(buf, true);
360     }
361 
362     /**
363      * Format a long (treated as unsigned) into a character buffer.
364      * @param val the unsigned long to format
365      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
366      * @param buf the character buffer to write to
367      * @param offset the offset in the destination buffer to start at
368      * @param len the number of characters to write
369      * @return the lowest character location used
370      */
371      static int formatUnsignedLong(long val, int shift, char[] buf, int offset, int len) {
372         int charPos = len;
373         int radix = 1 << shift;
374         int mask = radix - 1;
375         do {
376             buf[offset + --charPos] = Integer.digits[((int) val) & mask];
377             val >>>= shift;
378         } while (val != 0 && charPos > 0);
379 
380         return charPos;
381     }
382 
383     /**
384      * Returns a {@code String} object representing the specified
385      * {@code long}.  The argument is converted to signed decimal
386      * representation and returned as a string, exactly as if the
387      * argument and the radix 10 were given as arguments to the {@link
388      * #toString(long, int)} method.
389      *
390      * @param   i   a {@code long} to be converted.
391      * @return  a string representation of the argument in base&nbsp;10.
392      */
393     public static String toString(long i) {
394         if (i == Long.MIN_VALUE)
395             return "-9223372036854775808";
396         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
397         char[] buf = new char[size];
398         getChars(i, size, buf);
399         return new String(buf, true);
400     }
401 
402     /**
403      * Returns a string representation of the argument as an unsigned
404      * decimal value.
405      *
406      * The argument is converted to unsigned decimal representation
407      * and returned as a string exactly as if the argument and radix
408      * 10 were given as arguments to the {@link #toUnsignedString(long,
409      * int)} method.
410      *
411      * @param   i  an integer to be converted to an unsigned string.
412      * @return  an unsigned string representation of the argument.
413      * @see     #toUnsignedString(long, int)
414      * @since 1.8
415      */
416     public static String toUnsignedString(long i) {
417         return toUnsignedString(i, 10);
418     }
419 
420     /**
421      * Places characters representing the integer i into the
422      * character array buf. The characters are placed into
423      * the buffer backwards starting with the least significant
424      * digit at the specified index (exclusive), and working
425      * backwards from there.
426      *
427      * Will fail if i == Long.MIN_VALUE
428      */
429     static void getChars(long i, int index, char[] buf) {
430         long q;
431         int r;
432         int charPos = index;
433         char sign = 0;
434 
435         if (i < 0) {
436             sign = '-';
437             i = -i;
438         }
439 
440         // Get 2 digits/iteration using longs until quotient fits into an int
441         while (i > Integer.MAX_VALUE) {
442             q = i / 100;
443             // really: r = i - (q * 100);
444             r = (int)(i - ((q << 6) + (q << 5) + (q << 2)));
445             i = q;
446             buf[--charPos] = Integer.DigitOnes[r];
447             buf[--charPos] = Integer.DigitTens[r];
448         }
449 
450         // Get 2 digits/iteration using ints
451         int q2;
452         int i2 = (int)i;
453         while (i2 >= 65536) {
454             q2 = i2 / 100;
455             // really: r = i2 - (q * 100);
456             r = i2 - ((q2 << 6) + (q2 << 5) + (q2 << 2));
457             i2 = q2;
458             buf[--charPos] = Integer.DigitOnes[r];
459             buf[--charPos] = Integer.DigitTens[r];
460         }
461 
462         // Fall thru to fast mode for smaller numbers
463         // assert(i2 <= 65536, i2);
464         for (;;) {
465             q2 = (i2 * 52429) >>> (16+3);
466             r = i2 - ((q2 << 3) + (q2 << 1));  // r = i2-(q2*10) ...
467             buf[--charPos] = Integer.digits[r];
468             i2 = q2;
469             if (i2 == 0) break;
470         }
471         if (sign != 0) {
472             buf[--charPos] = sign;
473         }
474     }
475 
476     // Requires positive x
477     static int stringSize(long x) {
478         long p = 10;
479         for (int i=1; i<19; i++) {
480             if (x < p)
481                 return i;
482             p = 10*p;
483         }
484         return 19;
485     }
486 
487     /**
488      * Parses the string argument as a signed {@code long} in the
489      * radix specified by the second argument. The characters in the
490      * string must all be digits of the specified radix (as determined
491      * by whether {@link java.lang.Character#digit(char, int)} returns
492      * a nonnegative value), except that the first character may be an
493      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
494      * indicate a negative value or an ASCII plus sign {@code '+'}
495      * ({@code '\u005Cu002B'}) to indicate a positive value. The
496      * resulting {@code long} value is returned.
497      *
498      * <p>Note that neither the character {@code L}
499      * ({@code '\u005Cu004C'}) nor {@code l}
500      * ({@code '\u005Cu006C'}) is permitted to appear at the end
501      * of the string as a type indicator, as would be permitted in
502      * Java programming language source code - except that either
503      * {@code L} or {@code l} may appear as a digit for a
504      * radix greater than or equal to 22.
505      *
506      * <p>An exception of type {@code NumberFormatException} is
507      * thrown if any of the following situations occurs:
508      * <ul>
509      *
510      * <li>The first argument is {@code null} or is a string of
511      * length zero.
512      *
513      * <li>The {@code radix} is either smaller than {@link
514      * java.lang.Character#MIN_RADIX} or larger than {@link
515      * java.lang.Character#MAX_RADIX}.
516      *
517      * <li>Any character of the string is not a digit of the specified
518      * radix, except that the first character may be a minus sign
519      * {@code '-'} ({@code '\u005Cu002d'}) or plus sign {@code
520      * '+'} ({@code '\u005Cu002B'}) provided that the string is
521      * longer than length 1.
522      *
523      * <li>The value represented by the string is not a value of type
524      *      {@code long}.
525      * </ul>
526      *
527      * <p>Examples:
528      * <blockquote><pre>
529      * parseLong("0", 10) returns 0L
530      * parseLong("473", 10) returns 473L
531      * parseLong("+42", 10) returns 42L
532      * parseLong("-0", 10) returns 0L
533      * parseLong("-FF", 16) returns -255L
534      * parseLong("1100110", 2) returns 102L
535      * parseLong("99", 8) throws a NumberFormatException
536      * parseLong("Hazelnut", 10) throws a NumberFormatException
537      * parseLong("Hazelnut", 36) returns 1356099454469L
538      * </pre></blockquote>
539      *
540      * @param      s       the {@code String} containing the
541      *                     {@code long} representation to be parsed.
542      * @param      radix   the radix to be used while parsing {@code s}.
543      * @return     the {@code long} represented by the string argument in
544      *             the specified radix.
545      * @throws     NumberFormatException  if the string does not contain a
546      *             parsable {@code long}.
547      */
548     public static long parseLong(String s, int radix)
549               throws NumberFormatException
550     {
551         if (s == null) {
552             throw new NumberFormatException("null");
553         }
554 
555         if (radix < Character.MIN_RADIX) {
556             throw new NumberFormatException("radix " + radix +
557                                             " less than Character.MIN_RADIX");
558         }
559         if (radix > Character.MAX_RADIX) {
560             throw new NumberFormatException("radix " + radix +
561                                             " greater than Character.MAX_RADIX");
562         }
563 
564         long result = 0;
565         boolean negative = false;
566         int i = 0, len = s.length();
567         long limit = -Long.MAX_VALUE;
568         long multmin;
569         int digit;
570 
571         if (len > 0) {
572             char firstChar = s.charAt(0);
573             if (firstChar < '0') { // Possible leading "+" or "-"
574                 if (firstChar == '-') {
575                     negative = true;
576                     limit = Long.MIN_VALUE;
577                 } else if (firstChar != '+')
578                     throw NumberFormatException.forInputString(s);
579 
580                 if (len == 1) // Cannot have lone "+" or "-"
581                     throw NumberFormatException.forInputString(s);
582                 i++;
583             }
584             multmin = limit / radix;
585             while (i < len) {
586                 // Accumulating negatively avoids surprises near MAX_VALUE
587                 digit = Character.digit(s.charAt(i++),radix);
588                 if (digit < 0) {
589                     throw NumberFormatException.forInputString(s);
590                 }
591                 if (result < multmin) {
592                     throw NumberFormatException.forInputString(s);
593                 }
594                 result *= radix;
595                 if (result < limit + digit) {
596                     throw NumberFormatException.forInputString(s);
597                 }
598                 result -= digit;
599             }
600         } else {
601             throw NumberFormatException.forInputString(s);
602         }
603         return negative ? result : -result;
604     }
605 
606     /**
607      * Parses the string argument as a signed decimal {@code long}.
608      * The characters in the string must all be decimal digits, except
609      * that the first character may be an ASCII minus sign {@code '-'}
610      * ({@code \u005Cu002D'}) to indicate a negative value or an
611      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
612      * indicate a positive value. The resulting {@code long} value is
613      * returned, exactly as if the argument and the radix {@code 10}
614      * were given as arguments to the {@link
615      * #parseLong(java.lang.String, int)} method.
616      *
617      * <p>Note that neither the character {@code L}
618      * ({@code '\u005Cu004C'}) nor {@code l}
619      * ({@code '\u005Cu006C'}) is permitted to appear at the end
620      * of the string as a type indicator, as would be permitted in
621      * Java programming language source code.
622      *
623      * @param      s   a {@code String} containing the {@code long}
624      *             representation to be parsed
625      * @return     the {@code long} represented by the argument in
626      *             decimal.
627      * @throws     NumberFormatException  if the string does not contain a
628      *             parsable {@code long}.
629      */
630     public static long parseLong(String s) throws NumberFormatException {
631         return parseLong(s, 10);
632     }
633 
634     /**
635      * Parses the string argument as an unsigned {@code long} in the
636      * radix specified by the second argument.  An unsigned integer
637      * maps the values usually associated with negative numbers to
638      * positive numbers larger than {@code MAX_VALUE}.
639      *
640      * The characters in the string must all be digits of the
641      * specified radix (as determined by whether {@link
642      * java.lang.Character#digit(char, int)} returns a nonnegative
643      * value), except that the first character may be an ASCII plus
644      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
645      * integer value is returned.
646      *
647      * <p>An exception of type {@code NumberFormatException} is
648      * thrown if any of the following situations occurs:
649      * <ul>
650      * <li>The first argument is {@code null} or is a string of
651      * length zero.
652      *
653      * <li>The radix is either smaller than
654      * {@link java.lang.Character#MIN_RADIX} or
655      * larger than {@link java.lang.Character#MAX_RADIX}.
656      *
657      * <li>Any character of the string is not a digit of the specified
658      * radix, except that the first character may be a plus sign
659      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
660      * string is longer than length 1.
661      *
662      * <li>The value represented by the string is larger than the
663      * largest unsigned {@code long}, 2<sup>64</sup>-1.
664      *
665      * </ul>
666      *
667      *
668      * @param      s   the {@code String} containing the unsigned integer
669      *                  representation to be parsed
670      * @param      radix   the radix to be used while parsing {@code s}.
671      * @return     the unsigned {@code long} represented by the string
672      *             argument in the specified radix.
673      * @throws     NumberFormatException if the {@code String}
674      *             does not contain a parsable {@code long}.
675      * @since 1.8
676      */
677     public static long parseUnsignedLong(String s, int radix)
678                 throws NumberFormatException {
679         if (s == null)  {
680             throw new NumberFormatException("null");
681         }
682 
683         int len = s.length();
684         if (len > 0) {
685             char firstChar = s.charAt(0);
686             if (firstChar == '-') {
687                 throw new
688                     NumberFormatException(String.format("Illegal leading minus sign " +
689                                                        "on unsigned string %s.", s));
690             } else {
691                 if (len <= 12 || // Long.MAX_VALUE in Character.MAX_RADIX is 13 digits
692                     (radix == 10 && len <= 18) ) { // Long.MAX_VALUE in base 10 is 19 digits
693                     return parseLong(s, radix);
694                 }
695 
696                 // No need for range checks on len due to testing above.
697                 long first = parseLong(s.substring(0, len - 1), radix);
698                 int second = Character.digit(s.charAt(len - 1), radix);
699                 if (second < 0) {
700                     throw new NumberFormatException("Bad digit at end of " + s);
701                 }
702                 long result = first * radix + second;
703                 if (compareUnsigned(result, first) < 0) {
704                     /*
705                      * The maximum unsigned value, (2^64)-1, takes at
706                      * most one more digit to represent than the
707                      * maximum signed value, (2^63)-1.  Therefore,
708                      * parsing (len - 1) digits will be appropriately
709                      * in-range of the signed parsing.  In other
710                      * words, if parsing (len -1) digits overflows
711                      * signed parsing, parsing len digits will
712                      * certainly overflow unsigned parsing.
713                      *
714                      * The compareUnsigned check above catches
715                      * situations where an unsigned overflow occurs
716                      * incorporating the contribution of the final
717                      * digit.
718                      */
719                     throw new NumberFormatException(String.format("String value %s exceeds " +
720                                                                   "range of unsigned long.", s));
721                 }
722                 return result;
723             }
724         } else {
725             throw NumberFormatException.forInputString(s);
726         }
727     }
728 
729     /**
730      * Parses the string argument as an unsigned decimal {@code long}. The
731      * characters in the string must all be decimal digits, except
732      * that the first character may be an an ASCII plus sign {@code
733      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
734      * is returned, exactly as if the argument and the radix 10 were
735      * given as arguments to the {@link
736      * #parseUnsignedLong(java.lang.String, int)} method.
737      *
738      * @param s   a {@code String} containing the unsigned {@code long}
739      *            representation to be parsed
740      * @return    the unsigned {@code long} value represented by the decimal string argument
741      * @throws    NumberFormatException  if the string does not contain a
742      *            parsable unsigned integer.
743      * @since 1.8
744      */
745     public static long parseUnsignedLong(String s) throws NumberFormatException {
746         return parseUnsignedLong(s, 10);
747     }
748 
749     /**
750      * Returns a {@code Long} object holding the value
751      * extracted from the specified {@code String} when parsed
752      * with the radix given by the second argument.  The first
753      * argument is interpreted as representing a signed
754      * {@code long} in the radix specified by the second
755      * argument, exactly as if the arguments were given to the {@link
756      * #parseLong(java.lang.String, int)} method. The result is a
757      * {@code Long} object that represents the {@code long}
758      * value specified by the string.
759      *
760      * <p>In other words, this method returns a {@code Long} object equal
761      * to the value of:
762      *
763      * <blockquote>
764      *  {@code new Long(Long.parseLong(s, radix))}
765      * </blockquote>
766      *
767      * @param      s       the string to be parsed
768      * @param      radix   the radix to be used in interpreting {@code s}
769      * @return     a {@code Long} object holding the value
770      *             represented by the string argument in the specified
771      *             radix.
772      * @throws     NumberFormatException  If the {@code String} does not
773      *             contain a parsable {@code long}.
774      */
775     public static Long valueOf(String s, int radix) throws NumberFormatException {
776         return Long.valueOf(parseLong(s, radix));
777     }
778 
779     /**
780      * Returns a {@code Long} object holding the value
781      * of the specified {@code String}. The argument is
782      * interpreted as representing a signed decimal {@code long},
783      * exactly as if the argument were given to the {@link
784      * #parseLong(java.lang.String)} method. The result is a
785      * {@code Long} object that represents the integer value
786      * specified by the string.
787      *
788      * <p>In other words, this method returns a {@code Long} object
789      * equal to the value of:
790      *
791      * <blockquote>
792      *  {@code new Long(Long.parseLong(s))}
793      * </blockquote>
794      *
795      * @param      s   the string to be parsed.
796      * @return     a {@code Long} object holding the value
797      *             represented by the string argument.
798      * @throws     NumberFormatException  If the string cannot be parsed
799      *             as a {@code long}.
800      */
801     public static Long valueOf(String s) throws NumberFormatException
802     {
803         return Long.valueOf(parseLong(s, 10));
804     }
805 
806     private static class LongCache {
807         private LongCache(){}
808 
809         static final Long cache[] = new Long[-(-128) + 127 + 1];
810 
811         static {
812             for(int i = 0; i < cache.length; i++)
813                 cache[i] = new Long(i - 128);
814         }
815     }
816 
817     /**
818      * Returns a {@code Long} instance representing the specified
819      * {@code long} value.
820      * If a new {@code Long} instance is not required, this method
821      * should generally be used in preference to the constructor
822      * {@link #Long(long)}, as this method is likely to yield
823      * significantly better space and time performance by caching
824      * frequently requested values.
825      *
826      * Note that unlike the {@linkplain Integer#valueOf(int)
827      * corresponding method} in the {@code Integer} class, this method
828      * is <em>not</em> required to cache values within a particular
829      * range.
830      *
831      * @param  l a long value.
832      * @return a {@code Long} instance representing {@code l}.
833      * @since  1.5
834      */
835     public static Long valueOf(long l) {
836         final int offset = 128;
837         if (l >= -128 && l <= 127) { // will cache
838             return LongCache.cache[(int)l + offset];
839         }
840         return new Long(l);
841     }
842 
843     /**
844      * Decodes a {@code String} into a {@code Long}.
845      * Accepts decimal, hexadecimal, and octal numbers given by the
846      * following grammar:
847      *
848      * <blockquote>
849      * <dl>
850      * <dt><i>DecodableString:</i>
851      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
852      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
853      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
854      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
855      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
856      *
857      * <dt><i>Sign:</i>
858      * <dd>{@code -}
859      * <dd>{@code +}
860      * </dl>
861      * </blockquote>
862      *
863      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
864      * are as defined in section 3.10.1 of
865      * <cite>The Java&trade; Language Specification</cite>,
866      * except that underscores are not accepted between digits.
867      *
868      * <p>The sequence of characters following an optional
869      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
870      * "{@code #}", or leading zero) is parsed as by the {@code
871      * Long.parseLong} method with the indicated radix (10, 16, or 8).
872      * This sequence of characters must represent a positive value or
873      * a {@link NumberFormatException} will be thrown.  The result is
874      * negated if first character of the specified {@code String} is
875      * the minus sign.  No whitespace characters are permitted in the
876      * {@code String}.
877      *
878      * @param     nm the {@code String} to decode.
879      * @return    a {@code Long} object holding the {@code long}
880      *            value represented by {@code nm}
881      * @throws    NumberFormatException  if the {@code String} does not
882      *            contain a parsable {@code long}.
883      * @see java.lang.Long#parseLong(String, int)
884      * @since 1.2
885      */
886     public static Long decode(String nm) throws NumberFormatException {
887         int radix = 10;
888         int index = 0;
889         boolean negative = false;
890         Long result;
891 
892         if (nm.length() == 0)
893             throw new NumberFormatException("Zero length string");
894         char firstChar = nm.charAt(0);
895         // Handle sign, if present
896         if (firstChar == '-') {
897             negative = true;
898             index++;
899         } else if (firstChar == '+')
900             index++;
901 
902         // Handle radix specifier, if present
903         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
904             index += 2;
905             radix = 16;
906         }
907         else if (nm.startsWith("#", index)) {
908             index ++;
909             radix = 16;
910         }
911         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
912             index ++;
913             radix = 8;
914         }
915 
916         if (nm.startsWith("-", index) || nm.startsWith("+", index))
917             throw new NumberFormatException("Sign character in wrong position");
918 
919         try {
920             result = Long.valueOf(nm.substring(index), radix);
921             result = negative ? Long.valueOf(-result.longValue()) : result;
922         } catch (NumberFormatException e) {
923             // If number is Long.MIN_VALUE, we'll end up here. The next line
924             // handles this case, and causes any genuine format error to be
925             // rethrown.
926             String constant = negative ? ("-" + nm.substring(index))
927                                        : nm.substring(index);
928             result = Long.valueOf(constant, radix);
929         }
930         return result;
931     }
932 
933     /**
934      * The value of the {@code Long}.
935      *
936      * @serial
937      */
938     private final long value;
939 
940     /**
941      * Constructs a newly allocated {@code Long} object that
942      * represents the specified {@code long} argument.
943      *
944      * @param   value   the value to be represented by the
945      *          {@code Long} object.
946      */
947     public Long(long value) {
948         this.value = value;
949     }
950 
951     /**
952      * Constructs a newly allocated {@code Long} object that
953      * represents the {@code long} value indicated by the
954      * {@code String} parameter. The string is converted to a
955      * {@code long} value in exactly the manner used by the
956      * {@code parseLong} method for radix 10.
957      *
958      * @param      s   the {@code String} to be converted to a
959      *             {@code Long}.
960      * @throws     NumberFormatException  if the {@code String} does not
961      *             contain a parsable {@code long}.
962      * @see        java.lang.Long#parseLong(java.lang.String, int)
963      */
964     public Long(String s) throws NumberFormatException {
965         this.value = parseLong(s, 10);
966     }
967 
968     /**
969      * Returns the value of this {@code Long} as a {@code byte} after
970      * a narrowing primitive conversion.
971      * @jls 5.1.3 Narrowing Primitive Conversions
972      */
973     public byte byteValue() {
974         return (byte)value;
975     }
976 
977     /**
978      * Returns the value of this {@code Long} as a {@code short} after
979      * a narrowing primitive conversion.
980      * @jls 5.1.3 Narrowing Primitive Conversions
981      */
982     public short shortValue() {
983         return (short)value;
984     }
985 
986     /**
987      * Returns the value of this {@code Long} as an {@code int} after
988      * a narrowing primitive conversion.
989      * @jls 5.1.3 Narrowing Primitive Conversions
990      */
991     public int intValue() {
992         return (int)value;
993     }
994 
995     /**
996      * Returns the value of this {@code Long} as a
997      * {@code long} value.
998      */
999     public long longValue() {
1000         return value;
1001     }
1002 
1003     /**
1004      * Returns the value of this {@code Long} as a {@code float} after
1005      * a widening primitive conversion.
1006      * @jls 5.1.2 Widening Primitive Conversions
1007      */
1008     public float floatValue() {
1009         return (float)value;
1010     }
1011 
1012     /**
1013      * Returns the value of this {@code Long} as a {@code double}
1014      * after a widening primitive conversion.
1015      * @jls 5.1.2 Widening Primitive Conversions
1016      */
1017     public double doubleValue() {
1018         return (double)value;
1019     }
1020 
1021     /**
1022      * Returns a {@code String} object representing this
1023      * {@code Long}'s value.  The value is converted to signed
1024      * decimal representation and returned as a string, exactly as if
1025      * the {@code long} value were given as an argument to the
1026      * {@link java.lang.Long#toString(long)} method.
1027      *
1028      * @return  a string representation of the value of this object in
1029      *          base&nbsp;10.
1030      */
1031     public String toString() {
1032         return toString(value);
1033     }
1034 
1035     /**
1036      * Returns a hash code for this {@code Long}. The result is
1037      * the exclusive OR of the two halves of the primitive
1038      * {@code long} value held by this {@code Long}
1039      * object. That is, the hashcode is the value of the expression:
1040      *
1041      * <blockquote>
1042      *  {@code (int)(this.longValue()^(this.longValue()>>>32))}
1043      * </blockquote>
1044      *
1045      * @return  a hash code value for this object.
1046      */
1047     @Override
1048     public int hashCode() {
1049         return Long.hashCode(value);
1050     }
1051 
1052     /**
1053      * Returns a hash code for a {@code long} value; compatible with
1054      * {@code Long.hashCode()}.
1055      *
1056      * @param value the value to hash
1057      * @return a hash code value for a {@code long} value.
1058      * @since 1.8
1059      */
1060     public static int hashCode(long value) {
1061         return (int)(value ^ (value >>> 32));
1062     }
1063 
1064     /**
1065      * Compares this object to the specified object.  The result is
1066      * {@code true} if and only if the argument is not
1067      * {@code null} and is a {@code Long} object that
1068      * contains the same {@code long} value as this object.
1069      *
1070      * @param   obj   the object to compare with.
1071      * @return  {@code true} if the objects are the same;
1072      *          {@code false} otherwise.
1073      */
1074     public boolean equals(Object obj) {
1075         if (obj instanceof Long) {
1076             return value == ((Long)obj).longValue();
1077         }
1078         return false;
1079     }
1080 
1081     /**
1082      * Determines the {@code long} value of the system property
1083      * with the specified name.
1084      *
1085      * <p>The first argument is treated as the name of a system
1086      * property.  System properties are accessible through the {@link
1087      * java.lang.System#getProperty(java.lang.String)} method. The
1088      * string value of this property is then interpreted as a {@code
1089      * long} value using the grammar supported by {@link Long#decode decode}
1090      * and a {@code Long} object representing this value is returned.
1091      *
1092      * <p>If there is no property with the specified name, if the
1093      * specified name is empty or {@code null}, or if the property
1094      * does not have the correct numeric format, then {@code null} is
1095      * returned.
1096      *
1097      * <p>In other words, this method returns a {@code Long} object
1098      * equal to the value of:
1099      *
1100      * <blockquote>
1101      *  {@code getLong(nm, null)}
1102      * </blockquote>
1103      *
1104      * @param   nm   property name.
1105      * @return  the {@code Long} value of the property.
1106      * @throws  SecurityException for the same reasons as
1107      *          {@link System#getProperty(String) System.getProperty}
1108      * @see     java.lang.System#getProperty(java.lang.String)
1109      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1110      */
1111     public static Long getLong(String nm) {
1112         return getLong(nm, null);
1113     }
1114 
1115     /**
1116      * Determines the {@code long} value of the system property
1117      * with the specified name.
1118      *
1119      * <p>The first argument is treated as the name of a system
1120      * property.  System properties are accessible through the {@link
1121      * java.lang.System#getProperty(java.lang.String)} method. The
1122      * string value of this property is then interpreted as a {@code
1123      * long} value using the grammar supported by {@link Long#decode decode}
1124      * and a {@code Long} object representing this value is returned.
1125      *
1126      * <p>The second argument is the default value. A {@code Long} object
1127      * that represents the value of the second argument is returned if there
1128      * is no property of the specified name, if the property does not have
1129      * the correct numeric format, or if the specified name is empty or null.
1130      *
1131      * <p>In other words, this method returns a {@code Long} object equal
1132      * to the value of:
1133      *
1134      * <blockquote>
1135      *  {@code getLong(nm, new Long(val))}
1136      * </blockquote>
1137      *
1138      * but in practice it may be implemented in a manner such as:
1139      *
1140      * <blockquote><pre>
1141      * Long result = getLong(nm, null);
1142      * return (result == null) ? new Long(val) : result;
1143      * </pre></blockquote>
1144      *
1145      * to avoid the unnecessary allocation of a {@code Long} object when
1146      * the default value is not needed.
1147      *
1148      * @param   nm    property name.
1149      * @param   val   default value.
1150      * @return  the {@code Long} value of the property.
1151      * @throws  SecurityException for the same reasons as
1152      *          {@link System#getProperty(String) System.getProperty}
1153      * @see     java.lang.System#getProperty(java.lang.String)
1154      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1155      */
1156     public static Long getLong(String nm, long val) {
1157         Long result = Long.getLong(nm, null);
1158         return (result == null) ? Long.valueOf(val) : result;
1159     }
1160 
1161     /**
1162      * Returns the {@code long} value of the system property with
1163      * the specified name.  The first argument is treated as the name
1164      * of a system property.  System properties are accessible through
1165      * the {@link java.lang.System#getProperty(java.lang.String)}
1166      * method. The string value of this property is then interpreted
1167      * as a {@code long} value, as per the
1168      * {@link Long#decode decode} method, and a {@code Long} object
1169      * representing this value is returned; in summary:
1170      *
1171      * <ul>
1172      * <li>If the property value begins with the two ASCII characters
1173      * {@code 0x} or the ASCII character {@code #}, not followed by
1174      * a minus sign, then the rest of it is parsed as a hexadecimal integer
1175      * exactly as for the method {@link #valueOf(java.lang.String, int)}
1176      * with radix 16.
1177      * <li>If the property value begins with the ASCII character
1178      * {@code 0} followed by another character, it is parsed as
1179      * an octal integer exactly as by the method {@link
1180      * #valueOf(java.lang.String, int)} with radix 8.
1181      * <li>Otherwise the property value is parsed as a decimal
1182      * integer exactly as by the method
1183      * {@link #valueOf(java.lang.String, int)} with radix 10.
1184      * </ul>
1185      *
1186      * <p>Note that, in every case, neither {@code L}
1187      * ({@code '\u005Cu004C'}) nor {@code l}
1188      * ({@code '\u005Cu006C'}) is permitted to appear at the end
1189      * of the property value as a type indicator, as would be
1190      * permitted in Java programming language source code.
1191      *
1192      * <p>The second argument is the default value. The default value is
1193      * returned if there is no property of the specified name, if the
1194      * property does not have the correct numeric format, or if the
1195      * specified name is empty or {@code null}.
1196      *
1197      * @param   nm   property name.
1198      * @param   val   default value.
1199      * @return  the {@code Long} value of the property.
1200      * @throws  SecurityException for the same reasons as
1201      *          {@link System#getProperty(String) System.getProperty}
1202      * @see     System#getProperty(java.lang.String)
1203      * @see     System#getProperty(java.lang.String, java.lang.String)
1204      */
1205     public static Long getLong(String nm, Long val) {
1206         String v = null;
1207         try {
1208             v = System.getProperty(nm);
1209         } catch (IllegalArgumentException | NullPointerException e) {
1210         }
1211         if (v != null) {
1212             try {
1213                 return Long.decode(v);
1214             } catch (NumberFormatException e) {
1215             }
1216         }
1217         return val;
1218     }
1219 
1220     /**
1221      * Compares two {@code Long} objects numerically.
1222      *
1223      * @param   anotherLong   the {@code Long} to be compared.
1224      * @return  the value {@code 0} if this {@code Long} is
1225      *          equal to the argument {@code Long}; a value less than
1226      *          {@code 0} if this {@code Long} is numerically less
1227      *          than the argument {@code Long}; and a value greater
1228      *          than {@code 0} if this {@code Long} is numerically
1229      *           greater than the argument {@code Long} (signed
1230      *           comparison).
1231      * @since   1.2
1232      */
1233     public int compareTo(Long anotherLong) {
1234         return compare(this.value, anotherLong.value);
1235     }
1236 
1237     /**
1238      * Compares two {@code long} values numerically.
1239      * The value returned is identical to what would be returned by:
1240      * <pre>
1241      *    Long.valueOf(x).compareTo(Long.valueOf(y))
1242      * </pre>
1243      *
1244      * @param  x the first {@code long} to compare
1245      * @param  y the second {@code long} to compare
1246      * @return the value {@code 0} if {@code x == y};
1247      *         a value less than {@code 0} if {@code x < y}; and
1248      *         a value greater than {@code 0} if {@code x > y}
1249      * @since 1.7
1250      */
1251     public static int compare(long x, long y) {
1252         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1253     }
1254 
1255     /**
1256      * Compares two {@code long} values numerically treating the values
1257      * as unsigned.
1258      *
1259      * @param  x the first {@code long} to compare
1260      * @param  y the second {@code long} to compare
1261      * @return the value {@code 0} if {@code x == y}; a value less
1262      *         than {@code 0} if {@code x < y} as unsigned values; and
1263      *         a value greater than {@code 0} if {@code x > y} as
1264      *         unsigned values
1265      * @since 1.8
1266      */
1267     public static int compareUnsigned(long x, long y) {
1268         return compare(x + MIN_VALUE, y + MIN_VALUE);
1269     }
1270 
1271 
1272     /**
1273      * Returns the unsigned quotient of dividing the first argument by
1274      * the second where each argument and the result is interpreted as
1275      * an unsigned value.
1276      *
1277      * <p>Note that in two's complement arithmetic, the three other
1278      * basic arithmetic operations of add, subtract, and multiply are
1279      * bit-wise identical if the two operands are regarded as both
1280      * being signed or both being unsigned.  Therefore separate {@code
1281      * addUnsigned}, etc. methods are not provided.
1282      *
1283      * @param dividend the value to be divided
1284      * @param divisor the value doing the dividing
1285      * @return the unsigned quotient of the first argument divided by
1286      * the second argument
1287      * @see #remainderUnsigned
1288      * @since 1.8
1289      */
1290     public static long divideUnsigned(long dividend, long divisor) {
1291         if (divisor < 0L) { // signed comparison
1292             // Answer must be 0 or 1 depending on relative magnitude
1293             // of dividend and divisor.
1294             return (compareUnsigned(dividend, divisor)) < 0 ? 0L :1L;
1295         }
1296 
1297         if (dividend > 0) //  Both inputs non-negative
1298             return dividend/divisor;
1299         else {
1300             /*
1301              * For simple code, leveraging BigInteger.  Longer and faster
1302              * code written directly in terms of operations on longs is
1303              * possible; see "Hacker's Delight" for divide and remainder
1304              * algorithms.
1305              */
1306             return toUnsignedBigInteger(dividend).
1307                 divide(toUnsignedBigInteger(divisor)).longValue();
1308         }
1309     }
1310 
1311     /**
1312      * Returns the unsigned remainder from dividing the first argument
1313      * by the second where each argument and the result is interpreted
1314      * as an unsigned value.
1315      *
1316      * @param dividend the value to be divided
1317      * @param divisor the value doing the dividing
1318      * @return the unsigned remainder of the first argument divided by
1319      * the second argument
1320      * @see #divideUnsigned
1321      * @since 1.8
1322      */
1323     public static long remainderUnsigned(long dividend, long divisor) {
1324         if (dividend > 0 && divisor > 0) { // signed comparisons
1325             return dividend % divisor;
1326         } else {
1327             if (compareUnsigned(dividend, divisor) < 0) // Avoid explicit check for 0 divisor
1328                 return dividend;
1329             else
1330                 return toUnsignedBigInteger(dividend).
1331                     remainder(toUnsignedBigInteger(divisor)).longValue();
1332         }
1333     }
1334 
1335     // Bit Twiddling
1336 
1337     /**
1338      * The number of bits used to represent a {@code long} value in two's
1339      * complement binary form.
1340      *
1341      * @since 1.5
1342      */
1343     @Native public static final int SIZE = 64;
1344 
1345     /**
1346      * The number of bytes used to represent a {@code long} value in two's
1347      * complement binary form.
1348      *
1349      * @since 1.8
1350      */
1351     public static final int BYTES = SIZE / Byte.SIZE;
1352 
1353     /**
1354      * Returns a {@code long} value with at most a single one-bit, in the
1355      * position of the highest-order ("leftmost") one-bit in the specified
1356      * {@code long} value.  Returns zero if the specified value has no
1357      * one-bits in its two's complement binary representation, that is, if it
1358      * is equal to zero.
1359      *
1360      * @param i the value whose highest one bit is to be computed
1361      * @return a {@code long} value with a single one-bit, in the position
1362      *     of the highest-order one-bit in the specified value, or zero if
1363      *     the specified value is itself equal to zero.
1364      * @since 1.5
1365      */
1366     public static long highestOneBit(long i) {
1367         // HD, Figure 3-1
1368         i |= (i >>  1);
1369         i |= (i >>  2);
1370         i |= (i >>  4);
1371         i |= (i >>  8);
1372         i |= (i >> 16);
1373         i |= (i >> 32);
1374         return i - (i >>> 1);
1375     }
1376 
1377     /**
1378      * Returns a {@code long} value with at most a single one-bit, in the
1379      * position of the lowest-order ("rightmost") one-bit in the specified
1380      * {@code long} value.  Returns zero if the specified value has no
1381      * one-bits in its two's complement binary representation, that is, if it
1382      * is equal to zero.
1383      *
1384      * @param i the value whose lowest one bit is to be computed
1385      * @return a {@code long} value with a single one-bit, in the position
1386      *     of the lowest-order one-bit in the specified value, or zero if
1387      *     the specified value is itself equal to zero.
1388      * @since 1.5
1389      */
1390     public static long lowestOneBit(long i) {
1391         // HD, Section 2-1
1392         return i & -i;
1393     }
1394 
1395     /**
1396      * Returns the number of zero bits preceding the highest-order
1397      * ("leftmost") one-bit in the two's complement binary representation
1398      * of the specified {@code long} value.  Returns 64 if the
1399      * specified value has no one-bits in its two's complement representation,
1400      * in other words if it is equal to zero.
1401      *
1402      * <p>Note that this method is closely related to the logarithm base 2.
1403      * For all positive {@code long} values x:
1404      * <ul>
1405      * <li>floor(log<sub>2</sub>(x)) = {@code 63 - numberOfLeadingZeros(x)}
1406      * <li>ceil(log<sub>2</sub>(x)) = {@code 64 - numberOfLeadingZeros(x - 1)}
1407      * </ul>
1408      *
1409      * @param i the value whose number of leading zeros is to be computed
1410      * @return the number of zero bits preceding the highest-order
1411      *     ("leftmost") one-bit in the two's complement binary representation
1412      *     of the specified {@code long} value, or 64 if the value
1413      *     is equal to zero.
1414      * @since 1.5
1415      */
1416     public static int numberOfLeadingZeros(long i) {
1417         // HD, Figure 5-6
1418          if (i == 0)
1419             return 64;
1420         int n = 1;
1421         int x = (int)(i >>> 32);
1422         if (x == 0) { n += 32; x = (int)i; }
1423         if (x >>> 16 == 0) { n += 16; x <<= 16; }
1424         if (x >>> 24 == 0) { n +=  8; x <<=  8; }
1425         if (x >>> 28 == 0) { n +=  4; x <<=  4; }
1426         if (x >>> 30 == 0) { n +=  2; x <<=  2; }
1427         n -= x >>> 31;
1428         return n;
1429     }
1430 
1431     /**
1432      * Returns the number of zero bits following the lowest-order ("rightmost")
1433      * one-bit in the two's complement binary representation of the specified
1434      * {@code long} value.  Returns 64 if the specified value has no
1435      * one-bits in its two's complement representation, in other words if it is
1436      * equal to zero.
1437      *
1438      * @param i the value whose number of trailing zeros is to be computed
1439      * @return the number of zero bits following the lowest-order ("rightmost")
1440      *     one-bit in the two's complement binary representation of the
1441      *     specified {@code long} value, or 64 if the value is equal
1442      *     to zero.
1443      * @since 1.5
1444      */
1445     public static int numberOfTrailingZeros(long i) {
1446         // HD, Figure 5-14
1447         int x, y;
1448         if (i == 0) return 64;
1449         int n = 63;
1450         y = (int)i; if (y != 0) { n = n -32; x = y; } else x = (int)(i>>>32);
1451         y = x <<16; if (y != 0) { n = n -16; x = y; }
1452         y = x << 8; if (y != 0) { n = n - 8; x = y; }
1453         y = x << 4; if (y != 0) { n = n - 4; x = y; }
1454         y = x << 2; if (y != 0) { n = n - 2; x = y; }
1455         return n - ((x << 1) >>> 31);
1456     }
1457 
1458     /**
1459      * Returns the number of one-bits in the two's complement binary
1460      * representation of the specified {@code long} value.  This function is
1461      * sometimes referred to as the <i>population count</i>.
1462      *
1463      * @param i the value whose bits are to be counted
1464      * @return the number of one-bits in the two's complement binary
1465      *     representation of the specified {@code long} value.
1466      * @since 1.5
1467      */
1468      public static int bitCount(long i) {
1469         // HD, Figure 5-14
1470         i = i - ((i >>> 1) & 0x5555555555555555L);
1471         i = (i & 0x3333333333333333L) + ((i >>> 2) & 0x3333333333333333L);
1472         i = (i + (i >>> 4)) & 0x0f0f0f0f0f0f0f0fL;
1473         i = i + (i >>> 8);
1474         i = i + (i >>> 16);
1475         i = i + (i >>> 32);
1476         return (int)i & 0x7f;
1477      }
1478 
1479     /**
1480      * Returns the value obtained by rotating the two's complement binary
1481      * representation of the specified {@code long} value left by the
1482      * specified number of bits.  (Bits shifted out of the left hand, or
1483      * high-order, side reenter on the right, or low-order.)
1484      *
1485      * <p>Note that left rotation with a negative distance is equivalent to
1486      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1487      * distance)}.  Note also that rotation by any multiple of 64 is a
1488      * no-op, so all but the last six bits of the rotation distance can be
1489      * ignored, even if the distance is negative: {@code rotateLeft(val,
1490      * distance) == rotateLeft(val, distance & 0x3F)}.
1491      *
1492      * @param i the value whose bits are to be rotated left
1493      * @param distance the number of bit positions to rotate left
1494      * @return the value obtained by rotating the two's complement binary
1495      *     representation of the specified {@code long} value left by the
1496      *     specified number of bits.
1497      * @since 1.5
1498      */
1499     public static long rotateLeft(long i, int distance) {
1500         return (i << distance) | (i >>> -distance);
1501     }
1502 
1503     /**
1504      * Returns the value obtained by rotating the two's complement binary
1505      * representation of the specified {@code long} value right by the
1506      * specified number of bits.  (Bits shifted out of the right hand, or
1507      * low-order, side reenter on the left, or high-order.)
1508      *
1509      * <p>Note that right rotation with a negative distance is equivalent to
1510      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1511      * distance)}.  Note also that rotation by any multiple of 64 is a
1512      * no-op, so all but the last six bits of the rotation distance can be
1513      * ignored, even if the distance is negative: {@code rotateRight(val,
1514      * distance) == rotateRight(val, distance & 0x3F)}.
1515      *
1516      * @param i the value whose bits are to be rotated right
1517      * @param distance the number of bit positions to rotate right
1518      * @return the value obtained by rotating the two's complement binary
1519      *     representation of the specified {@code long} value right by the
1520      *     specified number of bits.
1521      * @since 1.5
1522      */
1523     public static long rotateRight(long i, int distance) {
1524         return (i >>> distance) | (i << -distance);
1525     }
1526 
1527     /**
1528      * Returns the value obtained by reversing the order of the bits in the
1529      * two's complement binary representation of the specified {@code long}
1530      * value.
1531      *
1532      * @param i the value to be reversed
1533      * @return the value obtained by reversing order of the bits in the
1534      *     specified {@code long} value.
1535      * @since 1.5
1536      */
1537     public static long reverse(long i) {
1538         // HD, Figure 7-1
1539         i = (i & 0x5555555555555555L) << 1 | (i >>> 1) & 0x5555555555555555L;
1540         i = (i & 0x3333333333333333L) << 2 | (i >>> 2) & 0x3333333333333333L;
1541         i = (i & 0x0f0f0f0f0f0f0f0fL) << 4 | (i >>> 4) & 0x0f0f0f0f0f0f0f0fL;
1542         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1543         i = (i << 48) | ((i & 0xffff0000L) << 16) |
1544             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1545         return i;
1546     }
1547 
1548     /**
1549      * Returns the signum function of the specified {@code long} value.  (The
1550      * return value is -1 if the specified value is negative; 0 if the
1551      * specified value is zero; and 1 if the specified value is positive.)
1552      *
1553      * @param i the value whose signum is to be computed
1554      * @return the signum function of the specified {@code long} value.
1555      * @since 1.5
1556      */
1557     public static int signum(long i) {
1558         // HD, Section 2-7
1559         return (int) ((i >> 63) | (-i >>> 63));
1560     }
1561 
1562     /**
1563      * Returns the value obtained by reversing the order of the bytes in the
1564      * two's complement representation of the specified {@code long} value.
1565      *
1566      * @param i the value whose bytes are to be reversed
1567      * @return the value obtained by reversing the bytes in the specified
1568      *     {@code long} value.
1569      * @since 1.5
1570      */
1571     public static long reverseBytes(long i) {
1572         i = (i & 0x00ff00ff00ff00ffL) << 8 | (i >>> 8) & 0x00ff00ff00ff00ffL;
1573         return (i << 48) | ((i & 0xffff0000L) << 16) |
1574             ((i >>> 16) & 0xffff0000L) | (i >>> 48);
1575     }
1576 
1577     /**
1578      * Adds two {@code long} values together as per the + operator.
1579      *
1580      * @param a the first operand
1581      * @param b the second operand
1582      * @return the sum of {@code a} and {@code b}
1583      * @see java.util.function.BinaryOperator
1584      * @since 1.8
1585      */
1586     public static long sum(long a, long b) {
1587         return a + b;
1588     }
1589 
1590     /**
1591      * Returns the greater of two {@code long} values
1592      * as if by calling {@link Math#max(long, long) Math.max}.
1593      *
1594      * @param a the first operand
1595      * @param b the second operand
1596      * @return the greater of {@code a} and {@code b}
1597      * @see java.util.function.BinaryOperator
1598      * @since 1.8
1599      */
1600     public static long max(long a, long b) {
1601         return Math.max(a, b);
1602     }
1603 
1604     /**
1605      * Returns the smaller of two {@code long} values
1606      * as if by calling {@link Math#min(long, long) Math.min}.
1607      *
1608      * @param a the first operand
1609      * @param b the second operand
1610      * @return the smaller of {@code a} and {@code b}
1611      * @see java.util.function.BinaryOperator
1612      * @since 1.8
1613      */
1614     public static long min(long a, long b) {
1615         return Math.min(a, b);
1616     }
1617 
1618     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1619     @Native private static final long serialVersionUID = 4290774380558885855L;
1620 }