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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
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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
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24   */
25  
26  package java.lang;
27  
28  import java.lang.annotation.Native;
29  
30  /**
31   * The {@code Integer} class wraps a value of the primitive type
32   * {@code int} in an object. An object of type {@code Integer}
33   * contains a single field whose type is {@code int}.
34   *
35   * <p>In addition, this class provides several methods for converting
36   * an {@code int} to a {@code String} and a {@code String} to an
37   * {@code int}, as well as other constants and methods useful when
38   * dealing with an {@code int}.
39   *
40   * <p>Implementation note: The implementations of the "bit twiddling"
41   * methods (such as {@link #highestOneBit(int) highestOneBit} and
42   * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
43   * based on material from Henry S. Warren, Jr.'s <i>Hacker's
44   * Delight</i>, (Addison Wesley, 2002).
45   *
46   * @author  Lee Boynton
47   * @author  Arthur van Hoff
48   * @author  Josh Bloch
49   * @author  Joseph D. Darcy
50   * @since JDK1.0
51   */
52  public final class Integer extends Number implements Comparable<Integer> {
53      /**
54       * A constant holding the minimum value an {@code int} can
55       * have, -2<sup>31</sup>.
56       */
57      @Native public static final int   MIN_VALUE = 0x80000000;
58  
59      /**
60       * A constant holding the maximum value an {@code int} can
61       * have, 2<sup>31</sup>-1.
62       */
63      @Native public static final int   MAX_VALUE = 0x7fffffff;
64  
65      /**
66       * The {@code Class} instance representing the primitive type
67       * {@code int}.
68       *
69       * @since   JDK1.1
70       */
71      @SuppressWarnings("unchecked")
72      public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");
73  
74      /**
75       * All possible chars for representing a number as a String
76       */
77      final static char[] digits = {
78          '0' , '1' , '2' , '3' , '4' , '5' ,
79          '6' , '7' , '8' , '9' , 'a' , 'b' ,
80          'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
81          'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
82          'o' , 'p' , 'q' , 'r' , 's' , 't' ,
83          'u' , 'v' , 'w' , 'x' , 'y' , 'z'
84      };
85  
86      /**
87       * Returns a string representation of the first argument in the
88       * radix specified by the second argument.
89       *
90       * <p>If the radix is smaller than {@code Character.MIN_RADIX}
91       * or larger than {@code Character.MAX_RADIX}, then the radix
92       * {@code 10} is used instead.
93       *
94       * <p>If the first argument is negative, the first element of the
95       * result is the ASCII minus character {@code '-'}
96       * ({@code '\u005Cu002D'}). If the first argument is not
97       * negative, no sign character appears in the result.
98       *
99       * <p>The remaining characters of the result represent the magnitude
100      * of the first argument. If the magnitude is zero, it is
101      * represented by a single zero character {@code '0'}
102      * ({@code '\u005Cu0030'}); otherwise, the first character of
103      * the representation of the magnitude will not be the zero
104      * character.  The following ASCII characters are used as digits:
105      *
106      * <blockquote>
107      *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
108      * </blockquote>
109      *
110      * These are {@code '\u005Cu0030'} through
111      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
112      * {@code '\u005Cu007A'}. If {@code radix} is
113      * <var>N</var>, then the first <var>N</var> of these characters
114      * are used as radix-<var>N</var> digits in the order shown. Thus,
115      * the digits for hexadecimal (radix 16) are
116      * {@code 0123456789abcdef}. If uppercase letters are
117      * desired, the {@link java.lang.String#toUpperCase()} method may
118      * be called on the result:
119      *
120      * <blockquote>
121      *  {@code Integer.toString(n, 16).toUpperCase()}
122      * </blockquote>
123      *
124      * @param   i       an integer to be converted to a string.
125      * @param   radix   the radix to use in the string representation.
126      * @return  a string representation of the argument in the specified radix.
127      * @see     java.lang.Character#MAX_RADIX
128      * @see     java.lang.Character#MIN_RADIX
129      */
130     public static String toString(int i, int radix) {
131         if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
132             radix = 10;
133 
134         /* Use the faster version */
135         if (radix == 10) {
136             return toString(i);
137         }
138 
139         char buf[] = new char[33];
140         boolean negative = (i < 0);
141         int charPos = 32;
142 
143         if (!negative) {
144             i = -i;
145         }
146 
147         while (i <= -radix) {
148             buf[charPos--] = digits[-(i % radix)];
149             i = i / radix;
150         }
151         buf[charPos] = digits[-i];
152 
153         if (negative) {
154             buf[--charPos] = '-';
155         }
156 
157         return new String(buf, charPos, (33 - charPos));
158     }
159 
160     /**
161      * Returns a string representation of the first argument as an
162      * unsigned integer value in the radix specified by the second
163      * argument.
164      *
165      * <p>If the radix is smaller than {@code Character.MIN_RADIX}
166      * or larger than {@code Character.MAX_RADIX}, then the radix
167      * {@code 10} is used instead.
168      *
169      * <p>Note that since the first argument is treated as an unsigned
170      * value, no leading sign character is printed.
171      *
172      * <p>If the magnitude is zero, it is represented by a single zero
173      * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
174      * the first character of the representation of the magnitude will
175      * not be the zero character.
176      *
177      * <p>The behavior of radixes and the characters used as digits
178      * are the same as {@link #toString(int, int) toString}.
179      *
180      * @param   i       an integer to be converted to an unsigned string.
181      * @param   radix   the radix to use in the string representation.
182      * @return  an unsigned string representation of the argument in the specified radix.
183      * @see     #toString(int, int)
184      * @since 1.8
185      */
186     public static String toUnsignedString(int i, int radix) {
187         return Long.toUnsignedString(toUnsignedLong(i), radix);
188     }
189 
190     /**
191      * Returns a string representation of the integer argument as an
192      * unsigned integer in base&nbsp;16.
193      *
194      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
195      * if the argument is negative; otherwise, it is equal to the
196      * argument.  This value is converted to a string of ASCII digits
197      * in hexadecimal (base&nbsp;16) with no extra leading
198      * {@code 0}s.
199      *
200      * <p>The value of the argument can be recovered from the returned
201      * string {@code s} by calling {@link
202      * Integer#parseUnsignedInt(String, int)
203      * Integer.parseUnsignedInt(s, 16)}.
204      *
205      * <p>If the unsigned magnitude is zero, it is represented by a
206      * single zero character {@code '0'} ({@code '\u005Cu0030'});
207      * otherwise, the first character of the representation of the
208      * unsigned magnitude will not be the zero character. The
209      * following characters are used as hexadecimal digits:
210      *
211      * <blockquote>
212      *  {@code 0123456789abcdef}
213      * </blockquote>
214      *
215      * These are the characters {@code '\u005Cu0030'} through
216      * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
217      * {@code '\u005Cu0066'}. If uppercase letters are
218      * desired, the {@link java.lang.String#toUpperCase()} method may
219      * be called on the result:
220      *
221      * <blockquote>
222      *  {@code Integer.toHexString(n).toUpperCase()}
223      * </blockquote>
224      *
225      * @param   i   an integer to be converted to a string.
226      * @return  the string representation of the unsigned integer value
227      *          represented by the argument in hexadecimal (base&nbsp;16).
228      * @see #parseUnsignedInt(String, int)
229      * @see #toUnsignedString(int, int)
230      * @since   JDK1.0.2
231      */
232     public static String toHexString(int i) {
233         return toUnsignedString0(i, 4);
234     }
235 
236     /**
237      * Returns a string representation of the integer argument as an
238      * unsigned integer in base&nbsp;8.
239      *
240      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
241      * if the argument is negative; otherwise, it is equal to the
242      * argument.  This value is converted to a string of ASCII digits
243      * in octal (base&nbsp;8) with no extra leading {@code 0}s.
244      *
245      * <p>The value of the argument can be recovered from the returned
246      * string {@code s} by calling {@link
247      * Integer#parseUnsignedInt(String, int)
248      * Integer.parseUnsignedInt(s, 8)}.
249      *
250      * <p>If the unsigned magnitude is zero, it is represented by a
251      * single zero character {@code '0'} ({@code '\u005Cu0030'});
252      * otherwise, the first character of the representation of the
253      * unsigned magnitude will not be the zero character. The
254      * following characters are used as octal digits:
255      *
256      * <blockquote>
257      * {@code 01234567}
258      * </blockquote>
259      *
260      * These are the characters {@code '\u005Cu0030'} through
261      * {@code '\u005Cu0037'}.
262      *
263      * @param   i   an integer to be converted to a string.
264      * @return  the string representation of the unsigned integer value
265      *          represented by the argument in octal (base&nbsp;8).
266      * @see #parseUnsignedInt(String, int)
267      * @see #toUnsignedString(int, int)
268      * @since   JDK1.0.2
269      */
270     public static String toOctalString(int i) {
271         return toUnsignedString0(i, 3);
272     }
273 
274     /**
275      * Returns a string representation of the integer argument as an
276      * unsigned integer in base&nbsp;2.
277      *
278      * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
279      * if the argument is negative; otherwise it is equal to the
280      * argument.  This value is converted to a string of ASCII digits
281      * in binary (base&nbsp;2) with no extra leading {@code 0}s.
282      *
283      * <p>The value of the argument can be recovered from the returned
284      * string {@code s} by calling {@link
285      * Integer#parseUnsignedInt(String, int)
286      * Integer.parseUnsignedInt(s, 2)}.
287      *
288      * <p>If the unsigned magnitude is zero, it is represented by a
289      * single zero character {@code '0'} ({@code '\u005Cu0030'});
290      * otherwise, the first character of the representation of the
291      * unsigned magnitude will not be the zero character. The
292      * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
293      * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
294      *
295      * @param   i   an integer to be converted to a string.
296      * @return  the string representation of the unsigned integer value
297      *          represented by the argument in binary (base&nbsp;2).
298      * @see #parseUnsignedInt(String, int)
299      * @see #toUnsignedString(int, int)
300      * @since   JDK1.0.2
301      */
302     public static String toBinaryString(int i) {
303         return toUnsignedString0(i, 1);
304     }
305 
306     /**
307      * Convert the integer to an unsigned number.
308      */
309     private static String toUnsignedString0(int val, int shift) {
310         // assert shift > 0 && shift <=5 : "Illegal shift value";
311         int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
312         int chars = Math.max(((mag + (shift - 1)) / shift), 1);
313         char[] buf = new char[chars];
314 
315         formatUnsignedInt(val, shift, buf, 0, chars);
316 
317         // Use special constructor which takes over "buf".
318         return new String(buf, true);
319     }
320 
321     /**
322      * Format a long (treated as unsigned) into a character buffer.
323      * @param val the unsigned int to format
324      * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
325      * @param buf the character buffer to write to
326      * @param offset the offset in the destination buffer to start at
327      * @param len the number of characters to write
328      * @return the lowest character  location used
329      */
330      static int formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
331         int charPos = len;
332         int radix = 1 << shift;
333         int mask = radix - 1;
334         do {
335             buf[offset + --charPos] = Integer.digits[val & mask];
336             val >>>= shift;
337         } while (val != 0 && charPos > 0);
338 
339         return charPos;
340     }
341 
342     final static char [] DigitTens = {
343         '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
344         '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
345         '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
346         '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
347         '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
348         '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
349         '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
350         '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
351         '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
352         '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
353         } ;
354 
355     final static char [] DigitOnes = {
356         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
357         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
358         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
359         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
360         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
361         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
362         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
363         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
364         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
365         '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
366         } ;
367 
368         // I use the "invariant division by multiplication" trick to
369         // accelerate Integer.toString.  In particular we want to
370         // avoid division by 10.
371         //
372         // The "trick" has roughly the same performance characteristics
373         // as the "classic" Integer.toString code on a non-JIT VM.
374         // The trick avoids .rem and .div calls but has a longer code
375         // path and is thus dominated by dispatch overhead.  In the
376         // JIT case the dispatch overhead doesn't exist and the
377         // "trick" is considerably faster than the classic code.
378         //
379         // TODO-FIXME: convert (x * 52429) into the equiv shift-add
380         // sequence.
381         //
382         // RE:  Division by Invariant Integers using Multiplication
383         //      T Gralund, P Montgomery
384         //      ACM PLDI 1994
385         //
386 
387     /**
388      * Returns a {@code String} object representing the
389      * specified integer. The argument is converted to signed decimal
390      * representation and returned as a string, exactly as if the
391      * argument and radix 10 were given as arguments to the {@link
392      * #toString(int, int)} method.
393      *
394      * @param   i   an integer to be converted.
395      * @return  a string representation of the argument in base&nbsp;10.
396      */
397     public static String toString(int i) {
398         if (i == Integer.MIN_VALUE)
399             return "-2147483648";
400         int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
401         char[] buf = new char[size];
402         getChars(i, size, buf);
403         return new String(buf, true);
404     }
405 
406     /**
407      * Returns a string representation of the argument as an unsigned
408      * decimal value.
409      *
410      * The argument is converted to unsigned decimal representation
411      * and returned as a string exactly as if the argument and radix
412      * 10 were given as arguments to the {@link #toUnsignedString(int,
413      * int)} method.
414      *
415      * @param   i  an integer to be converted to an unsigned string.
416      * @return  an unsigned string representation of the argument.
417      * @see     #toUnsignedString(int, int)
418      * @since 1.8
419      */
420     public static String toUnsignedString(int i) {
421         return Long.toString(toUnsignedLong(i));
422     }
423 
424     /**
425      * Places characters representing the integer i into the
426      * character array buf. The characters are placed into
427      * the buffer backwards starting with the least significant
428      * digit at the specified index (exclusive), and working
429      * backwards from there.
430      *
431      * Will fail if i == Integer.MIN_VALUE
432      */
433     static void getChars(int i, int index, char[] buf) {
434         int q, r;
435         int charPos = index;
436         char sign = 0;
437 
438         if (i < 0) {
439             sign = '-';
440             i = -i;
441         }
442 
443         // Generate two digits per iteration
444         while (i >= 65536) {
445             q = i / 100;
446         // really: r = i - (q * 100);
447             r = i - ((q << 6) + (q << 5) + (q << 2));
448             i = q;
449             buf [--charPos] = DigitOnes[r];
450             buf [--charPos] = DigitTens[r];
451         }
452 
453         // Fall thru to fast mode for smaller numbers
454         // assert(i <= 65536, i);
455         for (;;) {
456             q = (i * 52429) >>> (16+3);
457             r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
458             buf [--charPos] = digits [r];
459             i = q;
460             if (i == 0) break;
461         }
462         if (sign != 0) {
463             buf [--charPos] = sign;
464         }
465     }
466 
467     final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
468                                       99999999, 999999999, Integer.MAX_VALUE };
469 
470     // Requires positive x
471     static int stringSize(int x) {
472         for (int i=0; ; i++)
473             if (x <= sizeTable[i])
474                 return i+1;
475     }
476 
477     /**
478      * Parses the string argument as a signed integer in the radix
479      * specified by the second argument. The characters in the string
480      * must all be digits of the specified radix (as determined by
481      * whether {@link java.lang.Character#digit(char, int)} returns a
482      * nonnegative value), except that the first character may be an
483      * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
484      * indicate a negative value or an ASCII plus sign {@code '+'}
485      * ({@code '\u005Cu002B'}) to indicate a positive value. The
486      * resulting integer value is returned.
487      *
488      * <p>An exception of type {@code NumberFormatException} is
489      * thrown if any of the following situations occurs:
490      * <ul>
491      * <li>The first argument is {@code null} or is a string of
492      * length zero.
493      *
494      * <li>The radix is either smaller than
495      * {@link java.lang.Character#MIN_RADIX} or
496      * larger than {@link java.lang.Character#MAX_RADIX}.
497      *
498      * <li>Any character of the string is not a digit of the specified
499      * radix, except that the first character may be a minus sign
500      * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
501      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
502      * string is longer than length 1.
503      *
504      * <li>The value represented by the string is not a value of type
505      * {@code int}.
506      * </ul>
507      *
508      * <p>Examples:
509      * <blockquote><pre>
510      * parseInt("0", 10) returns 0
511      * parseInt("473", 10) returns 473
512      * parseInt("+42", 10) returns 42
513      * parseInt("-0", 10) returns 0
514      * parseInt("-FF", 16) returns -255
515      * parseInt("1100110", 2) returns 102
516      * parseInt("2147483647", 10) returns 2147483647
517      * parseInt("-2147483648", 10) returns -2147483648
518      * parseInt("2147483648", 10) throws a NumberFormatException
519      * parseInt("99", 8) throws a NumberFormatException
520      * parseInt("Kona", 10) throws a NumberFormatException
521      * parseInt("Kona", 27) returns 411787
522      * </pre></blockquote>
523      *
524      * @param      s   the {@code String} containing the integer
525      *                  representation to be parsed
526      * @param      radix   the radix to be used while parsing {@code s}.
527      * @return     the integer represented by the string argument in the
528      *             specified radix.
529      * @exception  NumberFormatException if the {@code String}
530      *             does not contain a parsable {@code int}.
531      */
532     public static int parseInt(String s, int radix)
533                 throws NumberFormatException
534     {
535         /*
536          * WARNING: This method may be invoked early during VM initialization
537          * before IntegerCache is initialized. Care must be taken to not use
538          * the valueOf method.
539          */
540 
541         if (s == null) {
542             throw new NumberFormatException("null");
543         }
544 
545         if (radix < Character.MIN_RADIX) {
546             throw new NumberFormatException("radix " + radix +
547                                             " less than Character.MIN_RADIX");
548         }
549 
550         if (radix > Character.MAX_RADIX) {
551             throw new NumberFormatException("radix " + radix +
552                                             " greater than Character.MAX_RADIX");
553         }
554 
555         int result = 0;
556         boolean negative = false;
557         int i = 0, len = s.length();
558         int limit = -Integer.MAX_VALUE;
559         int multmin;
560         int digit;
561 
562         if (len > 0) {
563             char firstChar = s.charAt(0);
564             if (firstChar < '0') { // Possible leading "+" or "-"
565                 if (firstChar == '-') {
566                     negative = true;
567                     limit = Integer.MIN_VALUE;
568                 } else if (firstChar != '+')
569                     throw NumberFormatException.forInputString(s);
570 
571                 if (len == 1) // Cannot have lone "+" or "-"
572                     throw NumberFormatException.forInputString(s);
573                 i++;
574             }
575             multmin = limit / radix;
576             while (i < len) {
577                 // Accumulating negatively avoids surprises near MAX_VALUE
578                 digit = Character.digit(s.charAt(i++),radix);
579                 if (digit < 0) {
580                     throw NumberFormatException.forInputString(s);
581                 }
582                 if (result < multmin) {
583                     throw NumberFormatException.forInputString(s);
584                 }
585                 result *= radix;
586                 if (result < limit + digit) {
587                     throw NumberFormatException.forInputString(s);
588                 }
589                 result -= digit;
590             }
591         } else {
592             throw NumberFormatException.forInputString(s);
593         }
594         return negative ? result : -result;
595     }
596 
597     /**
598      * Parses the string argument as a signed decimal integer. The
599      * characters in the string must all be decimal digits, except
600      * that the first character may be an ASCII minus sign {@code '-'}
601      * ({@code '\u005Cu002D'}) to indicate a negative value or an
602      * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
603      * indicate a positive value. The resulting integer value is
604      * returned, exactly as if the argument and the radix 10 were
605      * given as arguments to the {@link #parseInt(java.lang.String,
606      * int)} method.
607      *
608      * @param s    a {@code String} containing the {@code int}
609      *             representation to be parsed
610      * @return     the integer value represented by the argument in decimal.
611      * @exception  NumberFormatException  if the string does not contain a
612      *               parsable integer.
613      */
614     public static int parseInt(String s) throws NumberFormatException {
615         return parseInt(s,10);
616     }
617 
618     /**
619      * Parses the string argument as an unsigned integer in the radix
620      * specified by the second argument.  An unsigned integer maps the
621      * values usually associated with negative numbers to positive
622      * numbers larger than {@code MAX_VALUE}.
623      *
624      * The characters in the string must all be digits of the
625      * specified radix (as determined by whether {@link
626      * java.lang.Character#digit(char, int)} returns a nonnegative
627      * value), except that the first character may be an ASCII plus
628      * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
629      * integer value is returned.
630      *
631      * <p>An exception of type {@code NumberFormatException} is
632      * thrown if any of the following situations occurs:
633      * <ul>
634      * <li>The first argument is {@code null} or is a string of
635      * length zero.
636      *
637      * <li>The radix is either smaller than
638      * {@link java.lang.Character#MIN_RADIX} or
639      * larger than {@link java.lang.Character#MAX_RADIX}.
640      *
641      * <li>Any character of the string is not a digit of the specified
642      * radix, except that the first character may be a plus sign
643      * {@code '+'} ({@code '\u005Cu002B'}) provided that the
644      * string is longer than length 1.
645      *
646      * <li>The value represented by the string is larger than the
647      * largest unsigned {@code int}, 2<sup>32</sup>-1.
648      *
649      * </ul>
650      *
651      *
652      * @param      s   the {@code String} containing the unsigned integer
653      *                  representation to be parsed
654      * @param      radix   the radix to be used while parsing {@code s}.
655      * @return     the integer represented by the string argument in the
656      *             specified radix.
657      * @throws     NumberFormatException if the {@code String}
658      *             does not contain a parsable {@code int}.
659      * @since 1.8
660      */
661     public static int parseUnsignedInt(String s, int radix)
662                 throws NumberFormatException {
663         if (s == null)  {
664             throw new NumberFormatException("null");
665         }
666 
667         int len = s.length();
668         if (len > 0) {
669             char firstChar = s.charAt(0);
670             if (firstChar == '-') {
671                 throw new
672                     NumberFormatException(String.format("Illegal leading minus sign " +
673                                                        "on unsigned string %s.", s));
674             } else {
675                 if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
676                     (radix == 10 && len <= 9) ) { // Integer.MAX_VALUE in base 10 is 10 digits
677                     return parseInt(s, radix);
678                 } else {
679                     long ell = Long.parseLong(s, radix);
680                     if ((ell & 0xffff_ffff_0000_0000L) == 0) {
681                         return (int) ell;
682                     } else {
683                         throw new
684                             NumberFormatException(String.format("String value %s exceeds " +
685                                                                 "range of unsigned int.", s));
686                     }
687                 }
688             }
689         } else {
690             throw NumberFormatException.forInputString(s);
691         }
692     }
693 
694     /**
695      * Parses the string argument as an unsigned decimal integer. The
696      * characters in the string must all be decimal digits, except
697      * that the first character may be an an ASCII plus sign {@code
698      * '+'} ({@code '\u005Cu002B'}). The resulting integer value
699      * is returned, exactly as if the argument and the radix 10 were
700      * given as arguments to the {@link
701      * #parseUnsignedInt(java.lang.String, int)} method.
702      *
703      * @param s   a {@code String} containing the unsigned {@code int}
704      *            representation to be parsed
705      * @return    the unsigned integer value represented by the argument in decimal.
706      * @throws    NumberFormatException  if the string does not contain a
707      *            parsable unsigned integer.
708      * @since 1.8
709      */
710     public static int parseUnsignedInt(String s) throws NumberFormatException {
711         return parseUnsignedInt(s, 10);
712     }
713 
714     /**
715      * Returns an {@code Integer} object holding the value
716      * extracted from the specified {@code String} when parsed
717      * with the radix given by the second argument. The first argument
718      * is interpreted as representing a signed integer in the radix
719      * specified by the second argument, exactly as if the arguments
720      * were given to the {@link #parseInt(java.lang.String, int)}
721      * method. The result is an {@code Integer} object that
722      * represents the integer value specified by the string.
723      *
724      * <p>In other words, this method returns an {@code Integer}
725      * object equal to the value of:
726      *
727      * <blockquote>
728      *  {@code new Integer(Integer.parseInt(s, radix))}
729      * </blockquote>
730      *
731      * @param      s   the string to be parsed.
732      * @param      radix the radix to be used in interpreting {@code s}
733      * @return     an {@code Integer} object holding the value
734      *             represented by the string argument in the specified
735      *             radix.
736      * @exception NumberFormatException if the {@code String}
737      *            does not contain a parsable {@code int}.
738      */
739     public static Integer valueOf(String s, int radix) throws NumberFormatException {
740         return Integer.valueOf(parseInt(s,radix));
741     }
742 
743     /**
744      * Returns an {@code Integer} object holding the
745      * value of the specified {@code String}. The argument is
746      * interpreted as representing a signed decimal integer, exactly
747      * as if the argument were given to the {@link
748      * #parseInt(java.lang.String)} method. The result is an
749      * {@code Integer} object that represents the integer value
750      * specified by the string.
751      *
752      * <p>In other words, this method returns an {@code Integer}
753      * object equal to the value of:
754      *
755      * <blockquote>
756      *  {@code new Integer(Integer.parseInt(s))}
757      * </blockquote>
758      *
759      * @param      s   the string to be parsed.
760      * @return     an {@code Integer} object holding the value
761      *             represented by the string argument.
762      * @exception  NumberFormatException  if the string cannot be parsed
763      *             as an integer.
764      */
765     public static Integer valueOf(String s) throws NumberFormatException {
766         return Integer.valueOf(parseInt(s, 10));
767     }
768 
769     /**
770      * Cache to support the object identity semantics of autoboxing for values between
771      * -128 and 127 (inclusive) as required by JLS.
772      *
773      * The cache is initialized on first usage.  The size of the cache
774      * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
775      * During VM initialization, java.lang.Integer.IntegerCache.high property
776      * may be set and saved in the private system properties in the
777      * sun.misc.VM class.
778      */
779 
780     private static class IntegerCache {
781         static final int low = -128;
782         static final int high;
783         static final Integer cache[];
784 
785         static {
786             // high value may be configured by property
787             int h = 127;
788             String integerCacheHighPropValue =
789                 sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
790             if (integerCacheHighPropValue != null) {
791                 try {
792                     int i = parseInt(integerCacheHighPropValue);
793                     i = Math.max(i, 127);
794                     // Maximum array size is Integer.MAX_VALUE
795                     h = Math.min(i, Integer.MAX_VALUE - (-low) -1);
796                 } catch( NumberFormatException nfe) {
797                     // If the property cannot be parsed into an int, ignore it.
798                 }
799             }
800             high = h;
801 
802             cache = new Integer[(high - low) + 1];
803             int j = low;
804             for(int k = 0; k < cache.length; k++)
805                 cache[k] = new Integer(j++);
806 
807             // range [-128, 127] must be interned (JLS7 5.1.7)
808             assert IntegerCache.high >= 127;
809         }
810 
811         private IntegerCache() {}
812     }
813 
814     /**
815      * Returns an {@code Integer} instance representing the specified
816      * {@code int} value.  If a new {@code Integer} instance is not
817      * required, this method should generally be used in preference to
818      * the constructor {@link #Integer(int)}, as this method is likely
819      * to yield significantly better space and time performance by
820      * caching frequently requested values.
821      *
822      * This method will always cache values in the range -128 to 127,
823      * inclusive, and may cache other values outside of this range.
824      *
825      * @param  i an {@code int} value.
826      * @return an {@code Integer} instance representing {@code i}.
827      * @since  1.5
828      */
829     public static Integer valueOf(int i) {
830         if (i >= IntegerCache.low && i <= IntegerCache.high)
831             return IntegerCache.cache[i + (-IntegerCache.low)];
832         return new Integer(i);
833     }
834 
835     /**
836      * The value of the {@code Integer}.
837      *
838      * @serial
839      */
840     private final int value;
841 
842     /**
843      * Constructs a newly allocated {@code Integer} object that
844      * represents the specified {@code int} value.
845      *
846      * @param   value   the value to be represented by the
847      *                  {@code Integer} object.
848      */
849     public Integer(int value) {
850         this.value = value;
851     }
852 
853     /**
854      * Constructs a newly allocated {@code Integer} object that
855      * represents the {@code int} value indicated by the
856      * {@code String} parameter. The string is converted to an
857      * {@code int} value in exactly the manner used by the
858      * {@code parseInt} method for radix 10.
859      *
860      * @param      s   the {@code String} to be converted to an
861      *                 {@code Integer}.
862      * @exception  NumberFormatException  if the {@code String} does not
863      *               contain a parsable integer.
864      * @see        java.lang.Integer#parseInt(java.lang.String, int)
865      */
866     public Integer(String s) throws NumberFormatException {
867         this.value = parseInt(s, 10);
868     }
869 
870     /**
871      * Returns the value of this {@code Integer} as a {@code byte}
872      * after a narrowing primitive conversion.
873      * @jls 5.1.3 Narrowing Primitive Conversions
874      */
875     public byte byteValue() {
876         return (byte)value;
877     }
878 
879     /**
880      * Returns the value of this {@code Integer} as a {@code short}
881      * after a narrowing primitive conversion.
882      * @jls 5.1.3 Narrowing Primitive Conversions
883      */
884     public short shortValue() {
885         return (short)value;
886     }
887 
888     /**
889      * Returns the value of this {@code Integer} as an
890      * {@code int}.
891      */
892     public int intValue() {
893         return value;
894     }
895 
896     /**
897      * Returns the value of this {@code Integer} as a {@code long}
898      * after a widening primitive conversion.
899      * @jls 5.1.2 Widening Primitive Conversions
900      * @see Integer#toUnsignedLong(int)
901      */
902     public long longValue() {
903         return (long)value;
904     }
905 
906     /**
907      * Returns the value of this {@code Integer} as a {@code float}
908      * after a widening primitive conversion.
909      * @jls 5.1.2 Widening Primitive Conversions
910      */
911     public float floatValue() {
912         return (float)value;
913     }
914 
915     /**
916      * Returns the value of this {@code Integer} as a {@code double}
917      * after a widening primitive conversion.
918      * @jls 5.1.2 Widening Primitive Conversions
919      */
920     public double doubleValue() {
921         return (double)value;
922     }
923 
924     /**
925      * Returns a {@code String} object representing this
926      * {@code Integer}'s value. The value is converted to signed
927      * decimal representation and returned as a string, exactly as if
928      * the integer value were given as an argument to the {@link
929      * java.lang.Integer#toString(int)} method.
930      *
931      * @return  a string representation of the value of this object in
932      *          base&nbsp;10.
933      */
934     public String toString() {
935         return toString(value);
936     }
937 
938     /**
939      * Returns a hash code for this {@code Integer}.
940      *
941      * @return  a hash code value for this object, equal to the
942      *          primitive {@code int} value represented by this
943      *          {@code Integer} object.
944      */
945     @Override
946     public int hashCode() {
947         return Integer.hashCode(value);
948     }
949 
950     /**
951      * Returns a hash code for a {@code int} value; compatible with
952      * {@code Integer.hashCode()}.
953      *
954      * @param value the value to hash
955      * @since 1.8
956      *
957      * @return a hash code value for a {@code int} value.
958      */
959     public static int hashCode(int value) {
960         return value;
961     }
962 
963     /**
964      * Compares this object to the specified object.  The result is
965      * {@code true} if and only if the argument is not
966      * {@code null} and is an {@code Integer} object that
967      * contains the same {@code int} value as this object.
968      *
969      * @param   obj   the object to compare with.
970      * @return  {@code true} if the objects are the same;
971      *          {@code false} otherwise.
972      */
973     public boolean equals(Object obj) {
974         if (obj instanceof Integer) {
975             return value == ((Integer)obj).intValue();
976         }
977         return false;
978     }
979 
980     /**
981      * Determines the integer value of the system property with the
982      * specified name.
983      *
984      * <p>The first argument is treated as the name of a system
985      * property.  System properties are accessible through the {@link
986      * java.lang.System#getProperty(java.lang.String)} method. The
987      * string value of this property is then interpreted as an integer
988      * value using the grammar supported by {@link Integer#decode decode} and
989      * an {@code Integer} object representing this value is returned.
990      *
991      * <p>If there is no property with the specified name, if the
992      * specified name is empty or {@code null}, or if the property
993      * does not have the correct numeric format, then {@code null} is
994      * returned.
995      *
996      * <p>In other words, this method returns an {@code Integer}
997      * object equal to the value of:
998      *
999      * <blockquote>
1000      *  {@code getInteger(nm, null)}
1001      * </blockquote>
1002      *
1003      * @param   nm   property name.
1004      * @return  the {@code Integer} value of the property.
1005      * @throws  SecurityException for the same reasons as
1006      *          {@link System#getProperty(String) System.getProperty}
1007      * @see     java.lang.System#getProperty(java.lang.String)
1008      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1009      */
1010     public static Integer getInteger(String nm) {
1011         return getInteger(nm, null);
1012     }
1013 
1014     /**
1015      * Determines the integer value of the system property with the
1016      * specified name.
1017      *
1018      * <p>The first argument is treated as the name of a system
1019      * property.  System properties are accessible through the {@link
1020      * java.lang.System#getProperty(java.lang.String)} method. The
1021      * string value of this property is then interpreted as an integer
1022      * value using the grammar supported by {@link Integer#decode decode} and
1023      * an {@code Integer} object representing this value is returned.
1024      *
1025      * <p>The second argument is the default value. An {@code Integer} object
1026      * that represents the value of the second argument is returned if there
1027      * is no property of the specified name, if the property does not have
1028      * the correct numeric format, or if the specified name is empty or
1029      * {@code null}.
1030      *
1031      * <p>In other words, this method returns an {@code Integer} object
1032      * equal to the value of:
1033      *
1034      * <blockquote>
1035      *  {@code getInteger(nm, new Integer(val))}
1036      * </blockquote>
1037      *
1038      * but in practice it may be implemented in a manner such as:
1039      *
1040      * <blockquote><pre>
1041      * Integer result = getInteger(nm, null);
1042      * return (result == null) ? new Integer(val) : result;
1043      * </pre></blockquote>
1044      *
1045      * to avoid the unnecessary allocation of an {@code Integer}
1046      * object when the default value is not needed.
1047      *
1048      * @param   nm   property name.
1049      * @param   val   default value.
1050      * @return  the {@code Integer} value of the property.
1051      * @throws  SecurityException for the same reasons as
1052      *          {@link System#getProperty(String) System.getProperty}
1053      * @see     java.lang.System#getProperty(java.lang.String)
1054      * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
1055      */
1056     public static Integer getInteger(String nm, int val) {
1057         Integer result = getInteger(nm, null);
1058         return (result == null) ? Integer.valueOf(val) : result;
1059     }
1060 
1061     /**
1062      * Returns the integer value of the system property with the
1063      * specified name.  The first argument is treated as the name of a
1064      * system property.  System properties are accessible through the
1065      * {@link java.lang.System#getProperty(java.lang.String)} method.
1066      * The string value of this property is then interpreted as an
1067      * integer value, as per the {@link Integer#decode decode} method,
1068      * and an {@code Integer} object representing this value is
1069      * returned; in summary:
1070      *
1071      * <ul><li>If the property value begins with the two ASCII characters
1072      *         {@code 0x} or the ASCII character {@code #}, not
1073      *      followed by a minus sign, then the rest of it is parsed as a
1074      *      hexadecimal integer exactly as by the method
1075      *      {@link #valueOf(java.lang.String, int)} with radix 16.
1076      * <li>If the property value begins with the ASCII character
1077      *     {@code 0} followed by another character, it is parsed as an
1078      *     octal integer exactly as by the method
1079      *     {@link #valueOf(java.lang.String, int)} with radix 8.
1080      * <li>Otherwise, the property value is parsed as a decimal integer
1081      * exactly as by the method {@link #valueOf(java.lang.String, int)}
1082      * with radix 10.
1083      * </ul>
1084      *
1085      * <p>The second argument is the default value. The default value is
1086      * returned if there is no property of the specified name, if the
1087      * property does not have the correct numeric format, or if the
1088      * specified name is empty or {@code null}.
1089      *
1090      * @param   nm   property name.
1091      * @param   val   default value.
1092      * @return  the {@code Integer} value of the property.
1093      * @throws  SecurityException for the same reasons as
1094      *          {@link System#getProperty(String) System.getProperty}
1095      * @see     System#getProperty(java.lang.String)
1096      * @see     System#getProperty(java.lang.String, java.lang.String)
1097      */
1098     public static Integer getInteger(String nm, Integer val) {
1099         String v = null;
1100         try {
1101             v = System.getProperty(nm);
1102         } catch (IllegalArgumentException | NullPointerException e) {
1103         }
1104         if (v != null) {
1105             try {
1106                 return Integer.decode(v);
1107             } catch (NumberFormatException e) {
1108             }
1109         }
1110         return val;
1111     }
1112 
1113     /**
1114      * Decodes a {@code String} into an {@code Integer}.
1115      * Accepts decimal, hexadecimal, and octal numbers given
1116      * by the following grammar:
1117      *
1118      * <blockquote>
1119      * <dl>
1120      * <dt><i>DecodableString:</i>
1121      * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
1122      * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
1123      * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
1124      * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
1125      * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
1126      *
1127      * <dt><i>Sign:</i>
1128      * <dd>{@code -}
1129      * <dd>{@code +}
1130      * </dl>
1131      * </blockquote>
1132      *
1133      * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
1134      * are as defined in section 3.10.1 of
1135      * <cite>The Java&trade; Language Specification</cite>,
1136      * except that underscores are not accepted between digits.
1137      *
1138      * <p>The sequence of characters following an optional
1139      * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
1140      * "{@code #}", or leading zero) is parsed as by the {@code
1141      * Integer.parseInt} method with the indicated radix (10, 16, or
1142      * 8).  This sequence of characters must represent a positive
1143      * value or a {@link NumberFormatException} will be thrown.  The
1144      * result is negated if first character of the specified {@code
1145      * String} is the minus sign.  No whitespace characters are
1146      * permitted in the {@code String}.
1147      *
1148      * @param     nm the {@code String} to decode.
1149      * @return    an {@code Integer} object holding the {@code int}
1150      *             value represented by {@code nm}
1151      * @exception NumberFormatException  if the {@code String} does not
1152      *            contain a parsable integer.
1153      * @see java.lang.Integer#parseInt(java.lang.String, int)
1154      */
1155     public static Integer decode(String nm) throws NumberFormatException {
1156         int radix = 10;
1157         int index = 0;
1158         boolean negative = false;
1159         Integer result;
1160 
1161         if (nm.length() == 0)
1162             throw new NumberFormatException("Zero length string");
1163         char firstChar = nm.charAt(0);
1164         // Handle sign, if present
1165         if (firstChar == '-') {
1166             negative = true;
1167             index++;
1168         } else if (firstChar == '+')
1169             index++;
1170 
1171         // Handle radix specifier, if present
1172         if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
1173             index += 2;
1174             radix = 16;
1175         }
1176         else if (nm.startsWith("#", index)) {
1177             index ++;
1178             radix = 16;
1179         }
1180         else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
1181             index ++;
1182             radix = 8;
1183         }
1184 
1185         if (nm.startsWith("-", index) || nm.startsWith("+", index))
1186             throw new NumberFormatException("Sign character in wrong position");
1187 
1188         try {
1189             result = Integer.valueOf(nm.substring(index), radix);
1190             result = negative ? Integer.valueOf(-result.intValue()) : result;
1191         } catch (NumberFormatException e) {
1192             // If number is Integer.MIN_VALUE, we'll end up here. The next line
1193             // handles this case, and causes any genuine format error to be
1194             // rethrown.
1195             String constant = negative ? ("-" + nm.substring(index))
1196                                        : nm.substring(index);
1197             result = Integer.valueOf(constant, radix);
1198         }
1199         return result;
1200     }
1201 
1202     /**
1203      * Compares two {@code Integer} objects numerically.
1204      *
1205      * @param   anotherInteger   the {@code Integer} to be compared.
1206      * @return  the value {@code 0} if this {@code Integer} is
1207      *          equal to the argument {@code Integer}; a value less than
1208      *          {@code 0} if this {@code Integer} is numerically less
1209      *          than the argument {@code Integer}; and a value greater
1210      *          than {@code 0} if this {@code Integer} is numerically
1211      *           greater than the argument {@code Integer} (signed
1212      *           comparison).
1213      * @since   1.2
1214      */
1215     public int compareTo(Integer anotherInteger) {
1216         return compare(this.value, anotherInteger.value);
1217     }
1218 
1219     /**
1220      * Compares two {@code int} values numerically.
1221      * The value returned is identical to what would be returned by:
1222      * <pre>
1223      *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
1224      * </pre>
1225      *
1226      * @param  x the first {@code int} to compare
1227      * @param  y the second {@code int} to compare
1228      * @return the value {@code 0} if {@code x == y};
1229      *         a value less than {@code 0} if {@code x < y}; and
1230      *         a value greater than {@code 0} if {@code x > y}
1231      * @since 1.7
1232      */
1233     public static int compare(int x, int y) {
1234         return (x < y) ? -1 : ((x == y) ? 0 : 1);
1235     }
1236 
1237     /**
1238      * Compares two {@code int} values numerically treating the values
1239      * as unsigned.
1240      *
1241      * @param  x the first {@code int} to compare
1242      * @param  y the second {@code int} to compare
1243      * @return the value {@code 0} if {@code x == y}; a value less
1244      *         than {@code 0} if {@code x < y} as unsigned values; and
1245      *         a value greater than {@code 0} if {@code x > y} as
1246      *         unsigned values
1247      * @since 1.8
1248      */
1249     public static int compareUnsigned(int x, int y) {
1250         return compare(x + MIN_VALUE, y + MIN_VALUE);
1251     }
1252 
1253     /**
1254      * Converts the argument to a {@code long} by an unsigned
1255      * conversion.  In an unsigned conversion to a {@code long}, the
1256      * high-order 32 bits of the {@code long} are zero and the
1257      * low-order 32 bits are equal to the bits of the integer
1258      * argument.
1259      *
1260      * Consequently, zero and positive {@code int} values are mapped
1261      * to a numerically equal {@code long} value and negative {@code
1262      * int} values are mapped to a {@code long} value equal to the
1263      * input plus 2<sup>32</sup>.
1264      *
1265      * @param  x the value to convert to an unsigned {@code long}
1266      * @return the argument converted to {@code long} by an unsigned
1267      *         conversion
1268      * @since 1.8
1269      */
1270     public static long toUnsignedLong(int x) {
1271         return ((long) x) & 0xffffffffL;
1272     }
1273 
1274     /**
1275      * Returns the unsigned quotient of dividing the first argument by
1276      * the second where each argument and the result is interpreted as
1277      * an unsigned value.
1278      *
1279      * <p>Note that in two's complement arithmetic, the three other
1280      * basic arithmetic operations of add, subtract, and multiply are
1281      * bit-wise identical if the two operands are regarded as both
1282      * being signed or both being unsigned.  Therefore separate {@code
1283      * addUnsigned}, etc. methods are not provided.
1284      *
1285      * @param dividend the value to be divided
1286      * @param divisor the value doing the dividing
1287      * @return the unsigned quotient of the first argument divided by
1288      * the second argument
1289      * @see #remainderUnsigned
1290      * @since 1.8
1291      */
1292     public static int divideUnsigned(int dividend, int divisor) {
1293         // In lieu of tricky code, for now just use long arithmetic.
1294         return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
1295     }
1296 
1297     /**
1298      * Returns the unsigned remainder from dividing the first argument
1299      * by the second where each argument and the result is interpreted
1300      * as an unsigned value.
1301      *
1302      * @param dividend the value to be divided
1303      * @param divisor the value doing the dividing
1304      * @return the unsigned remainder of the first argument divided by
1305      * the second argument
1306      * @see #divideUnsigned
1307      * @since 1.8
1308      */
1309     public static int remainderUnsigned(int dividend, int divisor) {
1310         // In lieu of tricky code, for now just use long arithmetic.
1311         return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
1312     }
1313 
1314 
1315     // Bit twiddling
1316 
1317     /**
1318      * The number of bits used to represent an {@code int} value in two's
1319      * complement binary form.
1320      *
1321      * @since 1.5
1322      */
1323     @Native public static final int SIZE = 32;
1324 
1325     /**
1326      * The number of bytes used to represent a {@code int} value in two's
1327      * complement binary form.
1328      *
1329      * @since 1.8
1330      */
1331     public static final int BYTES = SIZE / Byte.SIZE;
1332 
1333     /**
1334      * Returns an {@code int} value with at most a single one-bit, in the
1335      * position of the highest-order ("leftmost") one-bit in the specified
1336      * {@code int} value.  Returns zero if the specified value has no
1337      * one-bits in its two's complement binary representation, that is, if it
1338      * is equal to zero.
1339      *
1340      * @param i the value whose highest one bit is to be computed
1341      * @return an {@code int} value with a single one-bit, in the position
1342      *     of the highest-order one-bit in the specified value, or zero if
1343      *     the specified value is itself equal to zero.
1344      * @since 1.5
1345      */
1346     public static int highestOneBit(int i) {
1347         // HD, Figure 3-1
1348         i |= (i >>  1);
1349         i |= (i >>  2);
1350         i |= (i >>  4);
1351         i |= (i >>  8);
1352         i |= (i >> 16);
1353         return i - (i >>> 1);
1354     }
1355 
1356     /**
1357      * Returns an {@code int} value with at most a single one-bit, in the
1358      * position of the lowest-order ("rightmost") one-bit in the specified
1359      * {@code int} value.  Returns zero if the specified value has no
1360      * one-bits in its two's complement binary representation, that is, if it
1361      * is equal to zero.
1362      *
1363      * @param i the value whose lowest one bit is to be computed
1364      * @return an {@code int} value with a single one-bit, in the position
1365      *     of the lowest-order one-bit in the specified value, or zero if
1366      *     the specified value is itself equal to zero.
1367      * @since 1.5
1368      */
1369     public static int lowestOneBit(int i) {
1370         // HD, Section 2-1
1371         return i & -i;
1372     }
1373 
1374     /**
1375      * Returns the number of zero bits preceding the highest-order
1376      * ("leftmost") one-bit in the two's complement binary representation
1377      * of the specified {@code int} value.  Returns 32 if the
1378      * specified value has no one-bits in its two's complement representation,
1379      * in other words if it is equal to zero.
1380      *
1381      * <p>Note that this method is closely related to the logarithm base 2.
1382      * For all positive {@code int} values x:
1383      * <ul>
1384      * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
1385      * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
1386      * </ul>
1387      *
1388      * @param i the value whose number of leading zeros is to be computed
1389      * @return the number of zero bits preceding the highest-order
1390      *     ("leftmost") one-bit in the two's complement binary representation
1391      *     of the specified {@code int} value, or 32 if the value
1392      *     is equal to zero.
1393      * @since 1.5
1394      */
1395     public static int numberOfLeadingZeros(int i) {
1396         // HD, Figure 5-6
1397         if (i == 0)
1398             return 32;
1399         int n = 1;
1400         if (i >>> 16 == 0) { n += 16; i <<= 16; }
1401         if (i >>> 24 == 0) { n +=  8; i <<=  8; }
1402         if (i >>> 28 == 0) { n +=  4; i <<=  4; }
1403         if (i >>> 30 == 0) { n +=  2; i <<=  2; }
1404         n -= i >>> 31;
1405         return n;
1406     }
1407 
1408     /**
1409      * Returns the number of zero bits following the lowest-order ("rightmost")
1410      * one-bit in the two's complement binary representation of the specified
1411      * {@code int} value.  Returns 32 if the specified value has no
1412      * one-bits in its two's complement representation, in other words if it is
1413      * equal to zero.
1414      *
1415      * @param i the value whose number of trailing zeros is to be computed
1416      * @return the number of zero bits following the lowest-order ("rightmost")
1417      *     one-bit in the two's complement binary representation of the
1418      *     specified {@code int} value, or 32 if the value is equal
1419      *     to zero.
1420      * @since 1.5
1421      */
1422     public static int numberOfTrailingZeros(int i) {
1423         // HD, Figure 5-14
1424         int y;
1425         if (i == 0) return 32;
1426         int n = 31;
1427         y = i <<16; if (y != 0) { n = n -16; i = y; }
1428         y = i << 8; if (y != 0) { n = n - 8; i = y; }
1429         y = i << 4; if (y != 0) { n = n - 4; i = y; }
1430         y = i << 2; if (y != 0) { n = n - 2; i = y; }
1431         return n - ((i << 1) >>> 31);
1432     }
1433 
1434     /**
1435      * Returns the number of one-bits in the two's complement binary
1436      * representation of the specified {@code int} value.  This function is
1437      * sometimes referred to as the <i>population count</i>.
1438      *
1439      * @param i the value whose bits are to be counted
1440      * @return the number of one-bits in the two's complement binary
1441      *     representation of the specified {@code int} value.
1442      * @since 1.5
1443      */
1444     public static int bitCount(int i) {
1445         // HD, Figure 5-2
1446         i = i - ((i >>> 1) & 0x55555555);
1447         i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
1448         i = (i + (i >>> 4)) & 0x0f0f0f0f;
1449         i = i + (i >>> 8);
1450         i = i + (i >>> 16);
1451         return i & 0x3f;
1452     }
1453 
1454     /**
1455      * Returns the value obtained by rotating the two's complement binary
1456      * representation of the specified {@code int} value left by the
1457      * specified number of bits.  (Bits shifted out of the left hand, or
1458      * high-order, side reenter on the right, or low-order.)
1459      *
1460      * <p>Note that left rotation with a negative distance is equivalent to
1461      * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
1462      * distance)}.  Note also that rotation by any multiple of 32 is a
1463      * no-op, so all but the last five bits of the rotation distance can be
1464      * ignored, even if the distance is negative: {@code rotateLeft(val,
1465      * distance) == rotateLeft(val, distance & 0x1F)}.
1466      *
1467      * @param i the value whose bits are to be rotated left
1468      * @param distance the number of bit positions to rotate left
1469      * @return the value obtained by rotating the two's complement binary
1470      *     representation of the specified {@code int} value left by the
1471      *     specified number of bits.
1472      * @since 1.5
1473      */
1474     public static int rotateLeft(int i, int distance) {
1475         return (i << distance) | (i >>> -distance);
1476     }
1477 
1478     /**
1479      * Returns the value obtained by rotating the two's complement binary
1480      * representation of the specified {@code int} value right by the
1481      * specified number of bits.  (Bits shifted out of the right hand, or
1482      * low-order, side reenter on the left, or high-order.)
1483      *
1484      * <p>Note that right rotation with a negative distance is equivalent to
1485      * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
1486      * distance)}.  Note also that rotation by any multiple of 32 is a
1487      * no-op, so all but the last five bits of the rotation distance can be
1488      * ignored, even if the distance is negative: {@code rotateRight(val,
1489      * distance) == rotateRight(val, distance & 0x1F)}.
1490      *
1491      * @param i the value whose bits are to be rotated right
1492      * @param distance the number of bit positions to rotate right
1493      * @return the value obtained by rotating the two's complement binary
1494      *     representation of the specified {@code int} value right by the
1495      *     specified number of bits.
1496      * @since 1.5
1497      */
1498     public static int rotateRight(int i, int distance) {
1499         return (i >>> distance) | (i << -distance);
1500     }
1501 
1502     /**
1503      * Returns the value obtained by reversing the order of the bits in the
1504      * two's complement binary representation of the specified {@code int}
1505      * value.
1506      *
1507      * @param i the value to be reversed
1508      * @return the value obtained by reversing order of the bits in the
1509      *     specified {@code int} value.
1510      * @since 1.5
1511      */
1512     public static int reverse(int i) {
1513         // HD, Figure 7-1
1514         i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
1515         i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
1516         i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
1517         i = (i << 24) | ((i & 0xff00) << 8) |
1518             ((i >>> 8) & 0xff00) | (i >>> 24);
1519         return i;
1520     }
1521 
1522     /**
1523      * Returns the signum function of the specified {@code int} value.  (The
1524      * return value is -1 if the specified value is negative; 0 if the
1525      * specified value is zero; and 1 if the specified value is positive.)
1526      *
1527      * @param i the value whose signum is to be computed
1528      * @return the signum function of the specified {@code int} value.
1529      * @since 1.5
1530      */
1531     public static int signum(int i) {
1532         // HD, Section 2-7
1533         return (i >> 31) | (-i >>> 31);
1534     }
1535 
1536     /**
1537      * Returns the value obtained by reversing the order of the bytes in the
1538      * two's complement representation of the specified {@code int} value.
1539      *
1540      * @param i the value whose bytes are to be reversed
1541      * @return the value obtained by reversing the bytes in the specified
1542      *     {@code int} value.
1543      * @since 1.5
1544      */
1545     public static int reverseBytes(int i) {
1546         return ((i >>> 24)           ) |
1547                ((i >>   8) &   0xFF00) |
1548                ((i <<   8) & 0xFF0000) |
1549                ((i << 24));
1550     }
1551 
1552     /**
1553      * Adds two integers together as per the + operator.
1554      *
1555      * @param a the first operand
1556      * @param b the second operand
1557      * @return the sum of {@code a} and {@code b}
1558      * @see java.util.function.BinaryOperator
1559      * @since 1.8
1560      */
1561     public static int sum(int a, int b) {
1562         return a + b;
1563     }
1564 
1565     /**
1566      * Returns the greater of two {@code int} values
1567      * as if by calling {@link Math#max(int, int) Math.max}.
1568      *
1569      * @param a the first operand
1570      * @param b the second operand
1571      * @return the greater of {@code a} and {@code b}
1572      * @see java.util.function.BinaryOperator
1573      * @since 1.8
1574      */
1575     public static int max(int a, int b) {
1576         return Math.max(a, b);
1577     }
1578 
1579     /**
1580      * Returns the smaller of two {@code int} values
1581      * as if by calling {@link Math#min(int, int) Math.min}.
1582      *
1583      * @param a the first operand
1584      * @param b the second operand
1585      * @return the smaller of {@code a} and {@code b}
1586      * @see java.util.function.BinaryOperator
1587      * @since 1.8
1588      */
1589     public static int min(int a, int b) {
1590         return Math.min(a, b);
1591     }
1592 
1593     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1594     @Native private static final long serialVersionUID = 1360826667806852920L;
1595 }