In addition, this class provides several methods for converting + * an {@code int} to a {@code String} and a {@code String} to an + * {@code int}, as well as other constants and methods useful when + * dealing with an {@code int}. + * + *
Implementation note: The implementations of the "bit twiddling"
+ * methods (such as {@link #highestOneBit(int) highestOneBit} and
+ * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
+ * based on material from Henry S. Warren, Jr.'s Hacker's
+ * Delight, (Addison Wesley, 2002).
+ *
+ * @author Lee Boynton
+ * @author Arthur van Hoff
+ * @author Josh Bloch
+ * @author Joseph D. Darcy
+ * @since 1.0
+ */
+public final class Integer extends Number implements Comparable If the radix is smaller than {@code Character.MIN_RADIX}
+ * or larger than {@code Character.MAX_RADIX}, then the radix
+ * {@code 10} is used instead.
+ *
+ * If the first argument is negative, the first element of the
+ * result is the ASCII minus character {@code '-'}
+ * ({@code '\u005Cu002D'}). If the first argument is not
+ * negative, no sign character appears in the result.
+ *
+ * The remaining characters of the result represent the magnitude
+ * of the first argument. If the magnitude is zero, it is
+ * represented by a single zero character {@code '0'}
+ * ({@code '\u005Cu0030'}); otherwise, the first character of
+ * the representation of the magnitude will not be the zero
+ * character. The following ASCII characters are used as digits:
+ *
+ * If the radix is smaller than {@code Character.MIN_RADIX}
+ * or larger than {@code Character.MAX_RADIX}, then the radix
+ * {@code 10} is used instead.
+ *
+ * Note that since the first argument is treated as an unsigned
+ * value, no leading sign character is printed.
+ *
+ * If the magnitude is zero, it is represented by a single zero
+ * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
+ * the first character of the representation of the magnitude will
+ * not be the zero character.
+ *
+ * The behavior of radixes and the characters used as digits
+ * are the same as {@link #toString(int, int) toString}.
+ *
+ * @param i an integer to be converted to an unsigned string.
+ * @param radix the radix to use in the string representation.
+ * @return an unsigned string representation of the argument in the specified radix.
+ * @see #toString(int, int)
+ * @since 1.8
+ */
+ public static String toUnsignedString(int i, int radix) {
+ return Long.toUnsignedString(toUnsignedLong(i), radix);
+ }
+
+ /**
+ * Returns a string representation of the integer argument as an
+ * unsigned integer in base 16.
+ *
+ * The unsigned integer value is the argument plus 232
+ * if the argument is negative; otherwise, it is equal to the
+ * argument. This value is converted to a string of ASCII digits
+ * in hexadecimal (base 16) with no extra leading
+ * {@code 0}s.
+ *
+ * The value of the argument can be recovered from the returned
+ * string {@code s} by calling {@link
+ * Integer#parseUnsignedInt(String, int)
+ * Integer.parseUnsignedInt(s, 16)}.
+ *
+ * If the unsigned magnitude is zero, it is represented by a
+ * single zero character {@code '0'} ({@code '\u005Cu0030'});
+ * otherwise, the first character of the representation of the
+ * unsigned magnitude will not be the zero character. The
+ * following characters are used as hexadecimal digits:
+ *
+ * The unsigned integer value is the argument plus 232
+ * if the argument is negative; otherwise, it is equal to the
+ * argument. This value is converted to a string of ASCII digits
+ * in octal (base 8) with no extra leading {@code 0}s.
+ *
+ * The value of the argument can be recovered from the returned
+ * string {@code s} by calling {@link
+ * Integer#parseUnsignedInt(String, int)
+ * Integer.parseUnsignedInt(s, 8)}.
+ *
+ * If the unsigned magnitude is zero, it is represented by a
+ * single zero character {@code '0'} ({@code '\u005Cu0030'});
+ * otherwise, the first character of the representation of the
+ * unsigned magnitude will not be the zero character. The
+ * following characters are used as octal digits:
+ *
+ * The unsigned integer value is the argument plus 232
+ * if the argument is negative; otherwise it is equal to the
+ * argument. This value is converted to a string of ASCII digits
+ * in binary (base 2) with no extra leading {@code 0}s.
+ *
+ * The value of the argument can be recovered from the returned
+ * string {@code s} by calling {@link
+ * Integer#parseUnsignedInt(String, int)
+ * Integer.parseUnsignedInt(s, 2)}.
+ *
+ * If the unsigned magnitude is zero, it is represented by a
+ * single zero character {@code '0'} ({@code '\u005Cu0030'});
+ * otherwise, the first character of the representation of the
+ * unsigned magnitude will not be the zero character. The
+ * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
+ * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
+ *
+ * @param i an integer to be converted to a string.
+ * @return the string representation of the unsigned integer value
+ * represented by the argument in binary (base 2).
+ * @see #parseUnsignedInt(String, int)
+ * @see #toUnsignedString(int, int)
+ * @since 1.0.2
+ */
+ public static String toBinaryString(int i) {
+ return toUnsignedString0(i, 1);
+ }
+
+ /**
+ * Convert the integer to an unsigned number.
+ */
+ private static String toUnsignedString0(int val, int shift) {
+ // assert shift > 0 && shift <=5 : "Illegal shift value";
+ int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
+ int chars = Math.max(((mag + (shift - 1)) / shift), 1);
+ char[] buf = new char[chars];
+
+ formatUnsignedInt(val, shift, buf, 0, chars);
+
+ // Use special constructor which takes over "buf".
+ return new String(buf, true);
+ }
+
+ /**
+ * Format an {@code int} (treated as unsigned) into a character buffer. If
+ * {@code len} exceeds the formatted ASCII representation of {@code val},
+ * {@code buf} will be padded with leading zeroes.
+ *
+ * @param val the unsigned int to format
+ * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
+ * @param buf the character buffer to write to
+ * @param offset the offset in the destination buffer to start at
+ * @param len the number of characters to write
+ */
+ static void formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
+ // assert shift > 0 && shift <=5 : "Illegal shift value";
+ // assert offset >= 0 && offset < buf.length : "illegal offset";
+ // assert len > 0 && (offset + len) <= buf.length : "illegal length";
+ int charPos = offset + len;
+ int radix = 1 << shift;
+ int mask = radix - 1;
+ do {
+ buf[--charPos] = Integer.digits[val & mask];
+ val >>>= shift;
+ } while (charPos > offset);
+ }
+
+ final static char [] DigitTens = {
+ '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
+ '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
+ '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
+ '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
+ '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
+ '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
+ '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
+ '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
+ '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
+ '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
+ } ;
+
+ final static char [] DigitOnes = {
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
+ } ;
+
+ // I use the "invariant division by multiplication" trick to
+ // accelerate Integer.toString. In particular we want to
+ // avoid division by 10.
+ //
+ // The "trick" has roughly the same performance characteristics
+ // as the "classic" Integer.toString code on a non-JIT VM.
+ // The trick avoids .rem and .div calls but has a longer code
+ // path and is thus dominated by dispatch overhead. In the
+ // JIT case the dispatch overhead doesn't exist and the
+ // "trick" is considerably faster than the classic code.
+ //
+ // RE: Division by Invariant Integers using Multiplication
+ // T Gralund, P Montgomery
+ // ACM PLDI 1994
+ //
+
+ /**
+ * Returns a {@code String} object representing the
+ * specified integer. The argument is converted to signed decimal
+ * representation and returned as a string, exactly as if the
+ * argument and radix 10 were given as arguments to the {@link
+ * #toString(int, int)} method.
+ *
+ * @param i an integer to be converted.
+ * @return a string representation of the argument in base 10.
+ */
+ public static String toString(int i) {
+ if (i == Integer.MIN_VALUE)
+ return "-2147483648";
+ int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
+ char[] buf = new char[size];
+ getChars(i, size, buf);
+ return new String(buf, true);
+ }
+
+ /**
+ * Returns a string representation of the argument as an unsigned
+ * decimal value.
+ *
+ * The argument is converted to unsigned decimal representation
+ * and returned as a string exactly as if the argument and radix
+ * 10 were given as arguments to the {@link #toUnsignedString(int,
+ * int)} method.
+ *
+ * @param i an integer to be converted to an unsigned string.
+ * @return an unsigned string representation of the argument.
+ * @see #toUnsignedString(int, int)
+ * @since 1.8
+ */
+ public static String toUnsignedString(int i) {
+ return Long.toString(toUnsignedLong(i));
+ }
+
+ /**
+ * Places characters representing the integer i into the
+ * character array buf. The characters are placed into
+ * the buffer backwards starting with the least significant
+ * digit at the specified index (exclusive), and working
+ * backwards from there.
+ *
+ * Will fail if i == Integer.MIN_VALUE
+ */
+ static void getChars(int i, int index, char[] buf) {
+ int q, r;
+ int charPos = index;
+ char sign = 0;
+
+ if (i < 0) {
+ sign = '-';
+ i = -i;
+ }
+
+ // Generate two digits per iteration
+ while (i >= 65536) {
+ q = i / 100;
+ // really: r = i - (q * 100);
+ r = i - ((q << 6) + (q << 5) + (q << 2));
+ i = q;
+ buf [--charPos] = DigitOnes[r];
+ buf [--charPos] = DigitTens[r];
+ }
+
+ // Fall thru to fast mode for smaller numbers
+ // assert(i <= 65536, i);
+ for (;;) {
+ q = (i * 52429) >>> (16+3);
+ r = i - ((q << 3) + (q << 1)); // r = i-(q*10) ...
+ buf [--charPos] = digits [r];
+ i = q;
+ if (i == 0) break;
+ }
+ if (sign != 0) {
+ buf [--charPos] = sign;
+ }
+ }
+
+ final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
+ 99999999, 999999999, Integer.MAX_VALUE };
+
+ // Requires positive x
+ static int stringSize(int x) {
+ for (int i=0; ; i++)
+ if (x <= sizeTable[i])
+ return i+1;
+ }
+
+ /**
+ * Parses the string argument as a signed integer in the radix
+ * specified by the second argument. The characters in the string
+ * must all be digits of the specified radix (as determined by
+ * whether {@link java.lang.Character#digit(char, int)} returns a
+ * nonnegative value), except that the first character may be an
+ * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
+ * indicate a negative value or an ASCII plus sign {@code '+'}
+ * ({@code '\u005Cu002B'}) to indicate a positive value. The
+ * resulting integer value is returned.
+ *
+ * An exception of type {@code NumberFormatException} is
+ * thrown if any of the following situations occurs:
+ * Examples:
+ * The method does not take steps to guard against the
+ * {@code CharSequence} being mutated while parsing.
+ *
+ * @param s the {@code CharSequence} containing the {@code int}
+ * representation to be parsed
+ * @param radix the radix to be used while parsing {@code s}.
+ * @param beginIndex the beginning index, inclusive.
+ * @return the signed {@code int} represented by the subsequence in
+ * the specified radix.
+ * @throws NullPointerException if {@code s} is null.
+ * @throws IndexOutOfBoundsException if {@code beginIndex} is
+ * negative, or if {@code beginIndex} is greater than
+ * {@code s.length()}.
+ * @throws NumberFormatException if the {@code CharSequence} does not
+ * contain a parsable {@code int} in the specified
+ * {@code radix}, or if {@code radix} is either smaller than
+ * {@link java.lang.Character#MIN_RADIX} or larger than
+ * {@link java.lang.Character#MAX_RADIX}.
+ * @since 1.9
+ */
+ public static int parseInt(CharSequence s, int radix, int beginIndex)
+ throws NumberFormatException {
+ // forces an implicit null check of s
+ return parseInt(s, radix, beginIndex, s.length());
+ }
+
+ /**
+ * Parses the {@link CharSequence} argument as a signed {@code int} in the
+ * specified {@code radix}, beginning at the specified {@code beginIndex}
+ * and extending to {@code endIndex - 1}.
+ *
+ * The method does not take steps to guard against the
+ * {@code CharSequence} being mutated while parsing.
+ *
+ * @param s the {@code CharSequence} containing the {@code int}
+ * representation to be parsed
+ * @param radix the radix to be used while parsing {@code s}.
+ * @param beginIndex the beginning index, inclusive.
+ * @param endIndex the ending index, exclusive.
+ * @return the signed {@code int} represented by the subsequence in
+ * the specified radix.
+ * @throws NullPointerException if {@code s} is null.
+ * @throws IndexOutOfBoundsException if {@code beginIndex} is
+ * negative, or if {@code beginIndex} is greater than
+ * {@code endIndex} or if {@code endIndex} is greater than
+ * {@code s.length()}.
+ * @throws NumberFormatException if the {@code CharSequence} does not
+ * contain a parsable {@code int} in the specified
+ * {@code radix}, or if {@code radix} is either smaller than
+ * {@link java.lang.Character#MIN_RADIX} or larger than
+ * {@link java.lang.Character#MAX_RADIX}.
+ * @since 1.9
+ */
+ public static int parseInt(CharSequence s, int radix, int beginIndex, int endIndex)
+ throws NumberFormatException {
+ s = Objects.requireNonNull(s);
+
+ if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
+ throw new IndexOutOfBoundsException();
+ }
+ if (radix < Character.MIN_RADIX) {
+ throw new NumberFormatException("radix " + radix +
+ " less than Character.MIN_RADIX");
+ }
+ if (radix > Character.MAX_RADIX) {
+ throw new NumberFormatException("radix " + radix +
+ " greater than Character.MAX_RADIX");
+ }
+
+ boolean negative = false;
+ int i = beginIndex;
+ int limit = -Integer.MAX_VALUE;
+
+ if (i < endIndex) {
+ char firstChar = s.charAt(i);
+ if (firstChar < '0') { // Possible leading "+" or "-"
+ if (firstChar == '-') {
+ negative = true;
+ limit = Integer.MIN_VALUE;
+ } else if (firstChar != '+') {
+ throw NumberFormatException.forCharSequence(s, beginIndex,
+ endIndex, i);
+ }
+ i++;
+ if (i == endIndex) { // Cannot have lone "+" or "-"
+ throw NumberFormatException.forCharSequence(s, beginIndex,
+ endIndex, i);
+ }
+ }
+ int multmin = limit / radix;
+ int result = 0;
+ while (i < endIndex) {
+ // Accumulating negatively avoids surprises near MAX_VALUE
+ int digit = Character.digit(s.charAt(i++), radix);
+ if (digit < 0 || result < multmin) {
+ throw NumberFormatException.forCharSequence(s, beginIndex,
+ endIndex, i);
+ }
+ result *= radix;
+ if (result < limit + digit) {
+ throw NumberFormatException.forCharSequence(s, beginIndex,
+ endIndex, i);
+ }
+ result -= digit;
+ }
+ return negative ? result : -result;
+ } else {
+ throw NumberFormatException.forInputString("");
+ }
+ }
+
+ /**
+ * Parses the string argument as a signed decimal integer. The
+ * characters in the string must all be decimal digits, except
+ * that the first character may be an ASCII minus sign {@code '-'}
+ * ({@code '\u005Cu002D'}) to indicate a negative value or an
+ * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
+ * indicate a positive value. The resulting integer value is
+ * returned, exactly as if the argument and the radix 10 were
+ * given as arguments to the {@link #parseInt(java.lang.String,
+ * int)} method.
+ *
+ * @param s a {@code String} containing the {@code int}
+ * representation to be parsed
+ * @return the integer value represented by the argument in decimal.
+ * @exception NumberFormatException if the string does not contain a
+ * parsable integer.
+ */
+ public static int parseInt(String s) throws NumberFormatException {
+ return parseInt(s,10);
+ }
+
+ /**
+ * Parses the string argument as an unsigned integer in the radix
+ * specified by the second argument. An unsigned integer maps the
+ * values usually associated with negative numbers to positive
+ * numbers larger than {@code MAX_VALUE}.
+ *
+ * The characters in the string must all be digits of the
+ * specified radix (as determined by whether {@link
+ * java.lang.Character#digit(char, int)} returns a nonnegative
+ * value), except that the first character may be an ASCII plus
+ * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
+ * integer value is returned.
+ *
+ * An exception of type {@code NumberFormatException} is
+ * thrown if any of the following situations occurs:
+ * The method does not take steps to guard against the
+ * {@code CharSequence} being mutated while parsing.
+ *
+ * @param s the {@code CharSequence} containing the unsigned
+ * {@code int} representation to be parsed
+ * @param radix the radix to be used while parsing {@code s}.
+ * @param beginIndex the beginning index, inclusive.
+ * @return the unsigned {@code int} represented by the subsequence in
+ * the specified radix.
+ * @throws NullPointerException if {@code s} is null.
+ * @throws IndexOutOfBoundsException if {@code beginIndex} is
+ * negative, or if {@code beginIndex} is greater than
+ * {@code s.length()}.
+ * @throws NumberFormatException if the {@code CharSequence} does not
+ * contain a parsable unsigned {@code int} in the specified
+ * {@code radix}, or if {@code radix} is either smaller than
+ * {@link java.lang.Character#MIN_RADIX} or larger than
+ * {@link java.lang.Character#MAX_RADIX}.
+ * @since 1.9
+ */
+ public static int parseUnsignedInt(CharSequence s, int radix, int beginIndex)
+ throws NumberFormatException {
+ // forces an implicit null check of s
+ return parseUnsignedInt(s, radix, beginIndex, s.length());
+ }
+
+ /**
+ * Parses the {@link CharSequence} argument as an unsigned {@code int} in
+ * the specified {@code radix}, beginning at the specified
+ * {@code beginIndex} and extending to {@code endIndex - 1}.
+ *
+ * The method does not take steps to guard against the
+ * {@code CharSequence} being mutated while parsing.
+ *
+ * @param s the {@code CharSequence} containing the unsigned
+ * {@code int} representation to be parsed
+ * @param radix the radix to be used while parsing {@code s}.
+ * @param beginIndex the beginning index, inclusive.
+ * @param endIndex the ending index, exclusive.
+ * @return the unsigned {@code int} represented by the subsequence in
+ * the specified radix.
+ * @throws NullPointerException if {@code s} is null.
+ * @throws IndexOutOfBoundsException if {@code beginIndex} is
+ * negative, or if {@code beginIndex} is greater than
+ * {@code endIndex} or if {@code endIndex} is greater than
+ * {@code s.length()}.
+ * @throws NumberFormatException if the {@code CharSequence} does not
+ * contain a parsable unsigned {@code int} in the specified
+ * {@code radix}, or if {@code radix} is either smaller than
+ * {@link java.lang.Character#MIN_RADIX} or larger than
+ * {@link java.lang.Character#MAX_RADIX}.
+ * @since 1.9
+ */
+ public static int parseUnsignedInt(CharSequence s, int radix, int beginIndex, int endIndex)
+ throws NumberFormatException {
+ s = Objects.requireNonNull(s);
+
+ if (beginIndex < 0 || beginIndex > endIndex || endIndex > s.length()) {
+ throw new IndexOutOfBoundsException();
+ }
+ int start = beginIndex, len = endIndex - beginIndex;
+
+ if (len > 0) {
+ char firstChar = s.charAt(start);
+ if (firstChar == '-') {
+ throw new
+ NumberFormatException(String.format("Illegal leading minus sign " +
+ "on unsigned string %s.", s));
+ } else {
+ if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
+ (radix == 10 && len <= 9)) { // Integer.MAX_VALUE in base 10 is 10 digits
+ return parseInt(s, radix, start, start + len);
+ } else {
+ long ell = Long.parseLong(s, radix, start, start + len);
+ if ((ell & 0xffff_ffff_0000_0000L) == 0) {
+ return (int) ell;
+ } else {
+ throw new
+ NumberFormatException(String.format("String value %s exceeds " +
+ "range of unsigned int.", s));
+ }
+ }
+ }
+ } else {
+ throw new NumberFormatException("");
+ }
+ }
+
+ /**
+ * Parses the string argument as an unsigned decimal integer. The
+ * characters in the string must all be decimal digits, except
+ * that the first character may be an an ASCII plus sign {@code
+ * '+'} ({@code '\u005Cu002B'}). The resulting integer value
+ * is returned, exactly as if the argument and the radix 10 were
+ * given as arguments to the {@link
+ * #parseUnsignedInt(java.lang.String, int)} method.
+ *
+ * @param s a {@code String} containing the unsigned {@code int}
+ * representation to be parsed
+ * @return the unsigned integer value represented by the argument in decimal.
+ * @throws NumberFormatException if the string does not contain a
+ * parsable unsigned integer.
+ * @since 1.8
+ */
+ public static int parseUnsignedInt(String s) throws NumberFormatException {
+ return parseUnsignedInt(s, 10);
+ }
+
+ /**
+ * Returns an {@code Integer} object holding the value
+ * extracted from the specified {@code String} when parsed
+ * with the radix given by the second argument. The first argument
+ * is interpreted as representing a signed integer in the radix
+ * specified by the second argument, exactly as if the arguments
+ * were given to the {@link #parseInt(java.lang.String, int)}
+ * method. The result is an {@code Integer} object that
+ * represents the integer value specified by the string.
+ *
+ * In other words, this method returns an {@code Integer}
+ * object equal to the value of:
+ *
+ * In other words, this method returns an {@code Integer}
+ * object equal to the value of:
+ *
+ * The first argument is treated as the name of a system
+ * property. System properties are accessible through the {@link
+ * java.lang.System#getProperty(java.lang.String)} method. The
+ * string value of this property is then interpreted as an integer
+ * value using the grammar supported by {@link Integer#decode decode} and
+ * an {@code Integer} object representing this value is returned.
+ *
+ * If there is no property with the specified name, if the
+ * specified name is empty or {@code null}, or if the property
+ * does not have the correct numeric format, then {@code null} is
+ * returned.
+ *
+ * In other words, this method returns an {@code Integer}
+ * object equal to the value of:
+ *
+ * The first argument is treated as the name of a system
+ * property. System properties are accessible through the {@link
+ * java.lang.System#getProperty(java.lang.String)} method. The
+ * string value of this property is then interpreted as an integer
+ * value using the grammar supported by {@link Integer#decode decode} and
+ * an {@code Integer} object representing this value is returned.
+ *
+ * The second argument is the default value. An {@code Integer} object
+ * that represents the value of the second argument is returned if there
+ * is no property of the specified name, if the property does not have
+ * the correct numeric format, or if the specified name is empty or
+ * {@code null}.
+ *
+ * In other words, this method returns an {@code Integer} object
+ * equal to the value of:
+ *
+ * The second argument is the default value. The default value is
+ * returned if there is no property of the specified name, if the
+ * property does not have the correct numeric format, or if the
+ * specified name is empty or {@code null}.
+ *
+ * @param nm property name.
+ * @param val default value.
+ * @return the {@code Integer} value of the property.
+ * @throws SecurityException for the same reasons as
+ * {@link System#getProperty(String) System.getProperty}
+ * @see System#getProperty(java.lang.String)
+ * @see System#getProperty(java.lang.String, java.lang.String)
+ */
+ public static Integer getInteger(String nm, Integer val) {
+ String v = null;
+ try {
+ v = System.getProperty(nm);
+ } catch (IllegalArgumentException | NullPointerException e) {
+ }
+ if (v != null) {
+ try {
+ return Integer.decode(v);
+ } catch (NumberFormatException e) {
+ }
+ }
+ return val;
+ }
+
+ /**
+ * Decodes a {@code String} into an {@code Integer}.
+ * Accepts decimal, hexadecimal, and octal numbers given
+ * by the following grammar:
+ *
+ * The sequence of characters following an optional
+ * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
+ * "{@code #}", or leading zero) is parsed as by the {@code
+ * Integer.parseInt} method with the indicated radix (10, 16, or
+ * 8). This sequence of characters must represent a positive
+ * value or a {@link NumberFormatException} will be thrown. The
+ * result is negated if first character of the specified {@code
+ * String} is the minus sign. No whitespace characters are
+ * permitted in the {@code String}.
+ *
+ * @param nm the {@code String} to decode.
+ * @return an {@code Integer} object holding the {@code int}
+ * value represented by {@code nm}
+ * @exception NumberFormatException if the {@code String} does not
+ * contain a parsable integer.
+ * @see java.lang.Integer#parseInt(java.lang.String, int)
+ */
+ public static Integer decode(String nm) throws NumberFormatException {
+ int radix = 10;
+ int index = 0;
+ boolean negative = false;
+ Integer result;
+
+ if (nm.length() == 0)
+ throw new NumberFormatException("Zero length string");
+ char firstChar = nm.charAt(0);
+ // Handle sign, if present
+ if (firstChar == '-') {
+ negative = true;
+ index++;
+ } else if (firstChar == '+')
+ index++;
+
+ // Handle radix specifier, if present
+ if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
+ index += 2;
+ radix = 16;
+ }
+ else if (nm.startsWith("#", index)) {
+ index ++;
+ radix = 16;
+ }
+ else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
+ index ++;
+ radix = 8;
+ }
+
+ if (nm.startsWith("-", index) || nm.startsWith("+", index))
+ throw new NumberFormatException("Sign character in wrong position");
+
+ try {
+ result = Integer.valueOf(nm.substring(index), radix);
+ result = negative ? Integer.valueOf(-result.intValue()) : result;
+ } catch (NumberFormatException e) {
+ // If number is Integer.MIN_VALUE, we'll end up here. The next line
+ // handles this case, and causes any genuine format error to be
+ // rethrown.
+ String constant = negative ? ("-" + nm.substring(index))
+ : nm.substring(index);
+ result = Integer.valueOf(constant, radix);
+ }
+ return result;
+ }
+
+ /**
+ * Compares two {@code Integer} objects numerically.
+ *
+ * @param anotherInteger the {@code Integer} to be compared.
+ * @return the value {@code 0} if this {@code Integer} is
+ * equal to the argument {@code Integer}; a value less than
+ * {@code 0} if this {@code Integer} is numerically less
+ * than the argument {@code Integer}; and a value greater
+ * than {@code 0} if this {@code Integer} is numerically
+ * greater than the argument {@code Integer} (signed
+ * comparison).
+ * @since 1.2
+ */
+ public int compareTo(Integer anotherInteger) {
+ return compare(this.value, anotherInteger.value);
+ }
+
+ /**
+ * Compares two {@code int} values numerically.
+ * The value returned is identical to what would be returned by:
+ * Note that in two's complement arithmetic, the three other
+ * basic arithmetic operations of add, subtract, and multiply are
+ * bit-wise identical if the two operands are regarded as both
+ * being signed or both being unsigned. Therefore separate {@code
+ * addUnsigned}, etc. methods are not provided.
+ *
+ * @param dividend the value to be divided
+ * @param divisor the value doing the dividing
+ * @return the unsigned quotient of the first argument divided by
+ * the second argument
+ * @see #remainderUnsigned
+ * @since 1.8
+ */
+ public static int divideUnsigned(int dividend, int divisor) {
+ // In lieu of tricky code, for now just use long arithmetic.
+ return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
+ }
+
+ /**
+ * Returns the unsigned remainder from dividing the first argument
+ * by the second where each argument and the result is interpreted
+ * as an unsigned value.
+ *
+ * @param dividend the value to be divided
+ * @param divisor the value doing the dividing
+ * @return the unsigned remainder of the first argument divided by
+ * the second argument
+ * @see #divideUnsigned
+ * @since 1.8
+ */
+ public static int remainderUnsigned(int dividend, int divisor) {
+ // In lieu of tricky code, for now just use long arithmetic.
+ return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
+ }
+
+
+ // Bit twiddling
+
+ /**
+ * The number of bits used to represent an {@code int} value in two's
+ * complement binary form.
+ *
+ * @since 1.5
+ */
+ @Native public static final int SIZE = 32;
+
+ /**
+ * The number of bytes used to represent a {@code int} value in two's
+ * complement binary form.
+ *
+ * @since 1.8
+ */
+ public static final int BYTES = SIZE / Byte.SIZE;
+
+ /**
+ * Returns an {@code int} value with at most a single one-bit, in the
+ * position of the highest-order ("leftmost") one-bit in the specified
+ * {@code int} value. Returns zero if the specified value has no
+ * one-bits in its two's complement binary representation, that is, if it
+ * is equal to zero.
+ *
+ * @param i the value whose highest one bit is to be computed
+ * @return an {@code int} value with a single one-bit, in the position
+ * of the highest-order one-bit in the specified value, or zero if
+ * the specified value is itself equal to zero.
+ * @since 1.5
+ */
+ public static int highestOneBit(int i) {
+ // HD, Figure 3-1
+ i |= (i >> 1);
+ i |= (i >> 2);
+ i |= (i >> 4);
+ i |= (i >> 8);
+ i |= (i >> 16);
+ return i - (i >>> 1);
+ }
+
+ /**
+ * Returns an {@code int} value with at most a single one-bit, in the
+ * position of the lowest-order ("rightmost") one-bit in the specified
+ * {@code int} value. Returns zero if the specified value has no
+ * one-bits in its two's complement binary representation, that is, if it
+ * is equal to zero.
+ *
+ * @param i the value whose lowest one bit is to be computed
+ * @return an {@code int} value with a single one-bit, in the position
+ * of the lowest-order one-bit in the specified value, or zero if
+ * the specified value is itself equal to zero.
+ * @since 1.5
+ */
+ public static int lowestOneBit(int i) {
+ // HD, Section 2-1
+ return i & -i;
+ }
+
+ /**
+ * Returns the number of zero bits preceding the highest-order
+ * ("leftmost") one-bit in the two's complement binary representation
+ * of the specified {@code int} value. Returns 32 if the
+ * specified value has no one-bits in its two's complement representation,
+ * in other words if it is equal to zero.
+ *
+ * Note that this method is closely related to the logarithm base 2.
+ * For all positive {@code int} values x:
+ * Note that left rotation with a negative distance is equivalent to
+ * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
+ * distance)}. Note also that rotation by any multiple of 32 is a
+ * no-op, so all but the last five bits of the rotation distance can be
+ * ignored, even if the distance is negative: {@code rotateLeft(val,
+ * distance) == rotateLeft(val, distance & 0x1F)}.
+ *
+ * @param i the value whose bits are to be rotated left
+ * @param distance the number of bit positions to rotate left
+ * @return the value obtained by rotating the two's complement binary
+ * representation of the specified {@code int} value left by the
+ * specified number of bits.
+ * @since 1.5
+ */
+ public static int rotateLeft(int i, int distance) {
+ return (i << distance) | (i >>> -distance);
+ }
+
+ /**
+ * Returns the value obtained by rotating the two's complement binary
+ * representation of the specified {@code int} value right by the
+ * specified number of bits. (Bits shifted out of the right hand, or
+ * low-order, side reenter on the left, or high-order.)
+ *
+ * Note that right rotation with a negative distance is equivalent to
+ * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
+ * distance)}. Note also that rotation by any multiple of 32 is a
+ * no-op, so all but the last five bits of the rotation distance can be
+ * ignored, even if the distance is negative: {@code rotateRight(val,
+ * distance) == rotateRight(val, distance & 0x1F)}.
+ *
+ * @param i the value whose bits are to be rotated right
+ * @param distance the number of bit positions to rotate right
+ * @return the value obtained by rotating the two's complement binary
+ * representation of the specified {@code int} value right by the
+ * specified number of bits.
+ * @since 1.5
+ */
+ public static int rotateRight(int i, int distance) {
+ return (i >>> distance) | (i << -distance);
+ }
+
+ /**
+ * Returns the value obtained by reversing the order of the bits in the
+ * two's complement binary representation of the specified {@code int}
+ * value.
+ *
+ * @param i the value to be reversed
+ * @return the value obtained by reversing order of the bits in the
+ * specified {@code int} value.
+ * @since 1.5
+ */
+ public static int reverse(int i) {
+ // HD, Figure 7-1
+ i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
+ i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
+ i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
+ i = (i << 24) | ((i & 0xff00) << 8) |
+ ((i >>> 8) & 0xff00) | (i >>> 24);
+ return i;
+ }
+
+ /**
+ * Returns the signum function of the specified {@code int} value. (The
+ * return value is -1 if the specified value is negative; 0 if the
+ * specified value is zero; and 1 if the specified value is positive.)
+ *
+ * @param i the value whose signum is to be computed
+ * @return the signum function of the specified {@code int} value.
+ * @since 1.5
+ */
+ public static int signum(int i) {
+ // HD, Section 2-7
+ return (i >> 31) | (-i >>> 31);
+ }
+
+ /**
+ * Returns the value obtained by reversing the order of the bytes in the
+ * two's complement representation of the specified {@code int} value.
+ *
+ * @param i the value whose bytes are to be reversed
+ * @return the value obtained by reversing the bytes in the specified
+ * {@code int} value.
+ * @since 1.5
+ */
+ public static int reverseBytes(int i) {
+ return ((i >>> 24) ) |
+ ((i >> 8) & 0xFF00) |
+ ((i << 8) & 0xFF0000) |
+ ((i << 24));
+ }
+
+ /**
+ * Adds two integers together as per the + operator.
+ *
+ * @param a the first operand
+ * @param b the second operand
+ * @return the sum of {@code a} and {@code b}
+ * @see java.util.function.BinaryOperator
+ * @since 1.8
+ */
+ public static int sum(int a, int b) {
+ return a + b;
+ }
+
+ /**
+ * Returns the greater of two {@code int} values
+ * as if by calling {@link Math#max(int, int) Math.max}.
+ *
+ * @param a the first operand
+ * @param b the second operand
+ * @return the greater of {@code a} and {@code b}
+ * @see java.util.function.BinaryOperator
+ * @since 1.8
+ */
+ public static int max(int a, int b) {
+ return Math.max(a, b);
+ }
+
+ /**
+ * Returns the smaller of two {@code int} values
+ * as if by calling {@link Math#min(int, int) Math.min}.
+ *
+ * @param a the first operand
+ * @param b the second operand
+ * @return the smaller of {@code a} and {@code b}
+ * @see java.util.function.BinaryOperator
+ * @since 1.8
+ */
+ public static int min(int a, int b) {
+ return Math.min(a, b);
+ }
+
+ /** use serialVersionUID from JDK 1.0.2 for interoperability */
+ @Native private static final long serialVersionUID = 1360826667806852920L;
+}
+ * {@code 0123456789abcdefghijklmnopqrstuvwxyz}
+ *
+ *
+ * These are {@code '\u005Cu0030'} through
+ * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
+ * {@code '\u005Cu007A'}. If {@code radix} is
+ * N, then the first N of these characters
+ * are used as radix-N digits in the order shown. Thus,
+ * the digits for hexadecimal (radix 16) are
+ * {@code 0123456789abcdef}. If uppercase letters are
+ * desired, the {@link java.lang.String#toUpperCase()} method may
+ * be called on the result:
+ *
+ *
+ * {@code Integer.toString(n, 16).toUpperCase()}
+ *
+ *
+ * @param i an integer to be converted to a string.
+ * @param radix the radix to use in the string representation.
+ * @return a string representation of the argument in the specified radix.
+ * @see java.lang.Character#MAX_RADIX
+ * @see java.lang.Character#MIN_RADIX
+ */
+ public static String toString(int i, int radix) {
+ if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
+ radix = 10;
+
+ /* Use the faster version */
+ if (radix == 10) {
+ return toString(i);
+ }
+
+ char buf[] = new char[33];
+ boolean negative = (i < 0);
+ int charPos = 32;
+
+ if (!negative) {
+ i = -i;
+ }
+
+ while (i <= -radix) {
+ buf[charPos--] = digits[-(i % radix)];
+ i = i / radix;
+ }
+ buf[charPos] = digits[-i];
+
+ if (negative) {
+ buf[--charPos] = '-';
+ }
+
+ return new String(buf, charPos, (33 - charPos));
+ }
+
+ /**
+ * Returns a string representation of the first argument as an
+ * unsigned integer value in the radix specified by the second
+ * argument.
+ *
+ *
+ * {@code 0123456789abcdef}
+ *
+ *
+ * These are the characters {@code '\u005Cu0030'} through
+ * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
+ * {@code '\u005Cu0066'}. If uppercase letters are
+ * desired, the {@link java.lang.String#toUpperCase()} method may
+ * be called on the result:
+ *
+ *
+ * {@code Integer.toHexString(n).toUpperCase()}
+ *
+ *
+ * @param i an integer to be converted to a string.
+ * @return the string representation of the unsigned integer value
+ * represented by the argument in hexadecimal (base 16).
+ * @see #parseUnsignedInt(String, int)
+ * @see #toUnsignedString(int, int)
+ * @since 1.0.2
+ */
+ public static String toHexString(int i) {
+ return toUnsignedString0(i, 4);
+ }
+
+ /**
+ * Returns a string representation of the integer argument as an
+ * unsigned integer in base 8.
+ *
+ *
+ * {@code 01234567}
+ *
+ *
+ * These are the characters {@code '\u005Cu0030'} through
+ * {@code '\u005Cu0037'}.
+ *
+ * @param i an integer to be converted to a string.
+ * @return the string representation of the unsigned integer value
+ * represented by the argument in octal (base 8).
+ * @see #parseUnsignedInt(String, int)
+ * @see #toUnsignedString(int, int)
+ * @since 1.0.2
+ */
+ public static String toOctalString(int i) {
+ return toUnsignedString0(i, 3);
+ }
+
+ /**
+ * Returns a string representation of the integer argument as an
+ * unsigned integer in base 2.
+ *
+ *
+ *
+ *
+ *
+ *
+ * @param s the {@code String} containing the integer
+ * representation to be parsed
+ * @param radix the radix to be used while parsing {@code s}.
+ * @return the integer represented by the string argument in the
+ * specified radix.
+ * @exception NumberFormatException if the {@code String}
+ * does not contain a parsable {@code int}.
+ */
+ public static int parseInt(String s, int radix)
+ throws NumberFormatException
+ {
+ /*
+ * WARNING: This method may be invoked early during VM initialization
+ * before IntegerCache is initialized. Care must be taken to not use
+ * the valueOf method.
+ */
+
+ if (s == null) {
+ throw new NumberFormatException("null");
+ }
+
+ if (radix < Character.MIN_RADIX) {
+ throw new NumberFormatException("radix " + radix +
+ " less than Character.MIN_RADIX");
+ }
+
+ if (radix > Character.MAX_RADIX) {
+ throw new NumberFormatException("radix " + radix +
+ " greater than Character.MAX_RADIX");
+ }
+
+ boolean negative = false;
+ int i = 0, len = s.length();
+ int limit = -Integer.MAX_VALUE;
+
+ if (len > 0) {
+ char firstChar = s.charAt(0);
+ if (firstChar < '0') { // Possible leading "+" or "-"
+ if (firstChar == '-') {
+ negative = true;
+ limit = Integer.MIN_VALUE;
+ } else if (firstChar != '+') {
+ throw NumberFormatException.forInputString(s);
+ }
+
+ if (len == 1) { // Cannot have lone "+" or "-"
+ throw NumberFormatException.forInputString(s);
+ }
+ i++;
+ }
+ int multmin = limit / radix;
+ int result = 0;
+ while (i < len) {
+ // Accumulating negatively avoids surprises near MAX_VALUE
+ int digit = Character.digit(s.charAt(i++), radix);
+ if (digit < 0 || result < multmin) {
+ throw NumberFormatException.forInputString(s);
+ }
+ result *= radix;
+ if (result < limit + digit) {
+ throw NumberFormatException.forInputString(s);
+ }
+ result -= digit;
+ }
+ return negative ? result : -result;
+ } else {
+ throw NumberFormatException.forInputString(s);
+ }
+ }
+
+ /**
+ * Parses the {@link CharSequence} argument as a signed {@code int} in the
+ * specified {@code radix}, beginning at the specified {@code beginIndex}
+ * and extending to the end of the sequence.
+ *
+ *
+ * parseInt("0", 10) returns 0
+ * parseInt("473", 10) returns 473
+ * parseInt("+42", 10) returns 42
+ * parseInt("-0", 10) returns 0
+ * parseInt("-FF", 16) returns -255
+ * parseInt("1100110", 2) returns 102
+ * parseInt("2147483647", 10) returns 2147483647
+ * parseInt("-2147483648", 10) returns -2147483648
+ * parseInt("2147483648", 10) throws a NumberFormatException
+ * parseInt("99", 8) throws a NumberFormatException
+ * parseInt("Kona", 10) throws a NumberFormatException
+ * parseInt("Kona", 27) returns 411787
+ *
+ *
+ *
+ *
+ * @param s the {@code String} containing the unsigned integer
+ * representation to be parsed
+ * @param radix the radix to be used while parsing {@code s}.
+ * @return the integer represented by the string argument in the
+ * specified radix.
+ * @throws NumberFormatException if the {@code String}
+ * does not contain a parsable {@code int}.
+ * @since 1.8
+ */
+ public static int parseUnsignedInt(String s, int radix)
+ throws NumberFormatException {
+ if (s == null) {
+ throw new NumberFormatException("null");
+ }
+
+ int len = s.length();
+ if (len > 0) {
+ char firstChar = s.charAt(0);
+ if (firstChar == '-') {
+ throw new
+ NumberFormatException(String.format("Illegal leading minus sign " +
+ "on unsigned string %s.", s));
+ } else {
+ if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
+ (radix == 10 && len <= 9) ) { // Integer.MAX_VALUE in base 10 is 10 digits
+ return parseInt(s, radix);
+ } else {
+ long ell = Long.parseLong(s, radix);
+ if ((ell & 0xffff_ffff_0000_0000L) == 0) {
+ return (int) ell;
+ } else {
+ throw new
+ NumberFormatException(String.format("String value %s exceeds " +
+ "range of unsigned int.", s));
+ }
+ }
+ }
+ } else {
+ throw NumberFormatException.forInputString(s);
+ }
+ }
+
+ /**
+ * Parses the {@link CharSequence} argument as an unsigned {@code int} in
+ * the specified {@code radix}, beginning at the specified
+ * {@code beginIndex} and extending to the end of the sequence.
+ *
+ *
+ * {@code new Integer(Integer.parseInt(s, radix))}
+ *
+ *
+ * @param s the string to be parsed.
+ * @param radix the radix to be used in interpreting {@code s}
+ * @return an {@code Integer} object holding the value
+ * represented by the string argument in the specified
+ * radix.
+ * @exception NumberFormatException if the {@code String}
+ * does not contain a parsable {@code int}.
+ */
+ public static Integer valueOf(String s, int radix) throws NumberFormatException {
+ return Integer.valueOf(parseInt(s,radix));
+ }
+
+ /**
+ * Returns an {@code Integer} object holding the
+ * value of the specified {@code String}. The argument is
+ * interpreted as representing a signed decimal integer, exactly
+ * as if the argument were given to the {@link
+ * #parseInt(java.lang.String)} method. The result is an
+ * {@code Integer} object that represents the integer value
+ * specified by the string.
+ *
+ *
+ * {@code new Integer(Integer.parseInt(s))}
+ *
+ *
+ * @param s the string to be parsed.
+ * @return an {@code Integer} object holding the value
+ * represented by the string argument.
+ * @exception NumberFormatException if the string cannot be parsed
+ * as an integer.
+ */
+ public static Integer valueOf(String s) throws NumberFormatException {
+ return Integer.valueOf(parseInt(s, 10));
+ }
+
+ /**
+ * Cache to support the object identity semantics of autoboxing for values between
+ * -128 and 127 (inclusive) as required by JLS.
+ *
+ * The cache is initialized on first usage. The size of the cache
+ * may be controlled by the {@code -XX:AutoBoxCacheMax=
+ * {@code getInteger(nm, null)}
+ *
+ *
+ * @param nm property name.
+ * @return the {@code Integer} value of the property.
+ * @throws SecurityException for the same reasons as
+ * {@link System#getProperty(String) System.getProperty}
+ * @see java.lang.System#getProperty(java.lang.String)
+ * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
+ */
+ public static Integer getInteger(String nm) {
+ return getInteger(nm, null);
+ }
+
+ /**
+ * Determines the integer value of the system property with the
+ * specified name.
+ *
+ *
+ * {@code getInteger(nm, new Integer(val))}
+ *
+ *
+ * but in practice it may be implemented in a manner such as:
+ *
+ *
+ *
+ * to avoid the unnecessary allocation of an {@code Integer}
+ * object when the default value is not needed.
+ *
+ * @param nm property name.
+ * @param val default value.
+ * @return the {@code Integer} value of the property.
+ * @throws SecurityException for the same reasons as
+ * {@link System#getProperty(String) System.getProperty}
+ * @see java.lang.System#getProperty(java.lang.String)
+ * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
+ */
+ public static Integer getInteger(String nm, int val) {
+ Integer result = getInteger(nm, null);
+ return (result == null) ? Integer.valueOf(val) : result;
+ }
+
+ /**
+ * Returns the integer value of the system property with the
+ * specified name. The first argument is treated as the name of a
+ * system property. System properties are accessible through the
+ * {@link java.lang.System#getProperty(java.lang.String)} method.
+ * The string value of this property is then interpreted as an
+ * integer value, as per the {@link Integer#decode decode} method,
+ * and an {@code Integer} object representing this value is
+ * returned; in summary:
+ *
+ *
+ * Integer result = getInteger(nm, null);
+ * return (result == null) ? new Integer(val) : result;
+ *
+ *
+ *
+ *
+ *
+ * DecimalNumeral, HexDigits, and OctalDigits
+ * are as defined in section 3.10.1 of
+ * The Java™ Language Specification,
+ * except that underscores are not accepted between digits.
+ *
+ *
+ *
+ *
+ * Integer.valueOf(x).compareTo(Integer.valueOf(y))
+ *
+ *
+ * @param x the first {@code int} to compare
+ * @param y the second {@code int} to compare
+ * @return the value {@code 0} if {@code x == y};
+ * a value less than {@code 0} if {@code x < y}; and
+ * a value greater than {@code 0} if {@code x > y}
+ * @since 1.7
+ */
+ public static int compare(int x, int y) {
+ return (x < y) ? -1 : ((x == y) ? 0 : 1);
+ }
+
+ /**
+ * Compares two {@code int} values numerically treating the values
+ * as unsigned.
+ *
+ * @param x the first {@code int} to compare
+ * @param y the second {@code int} to compare
+ * @return the value {@code 0} if {@code x == y}; a value less
+ * than {@code 0} if {@code x < y} as unsigned values; and
+ * a value greater than {@code 0} if {@code x > y} as
+ * unsigned values
+ * @since 1.8
+ */
+ public static int compareUnsigned(int x, int y) {
+ return compare(x + MIN_VALUE, y + MIN_VALUE);
+ }
+
+ /**
+ * Converts the argument to a {@code long} by an unsigned
+ * conversion. In an unsigned conversion to a {@code long}, the
+ * high-order 32 bits of the {@code long} are zero and the
+ * low-order 32 bits are equal to the bits of the integer
+ * argument.
+ *
+ * Consequently, zero and positive {@code int} values are mapped
+ * to a numerically equal {@code long} value and negative {@code
+ * int} values are mapped to a {@code long} value equal to the
+ * input plus 232.
+ *
+ * @param x the value to convert to an unsigned {@code long}
+ * @return the argument converted to {@code long} by an unsigned
+ * conversion
+ * @since 1.8
+ */
+ public static long toUnsignedLong(int x) {
+ return ((long) x) & 0xffffffffL;
+ }
+
+ /**
+ * Returns the unsigned quotient of dividing the first argument by
+ * the second where each argument and the result is interpreted as
+ * an unsigned value.
+ *
+ *
+ *
+ *
+ * @param i the value whose number of leading zeros is to be computed
+ * @return the number of zero bits preceding the highest-order
+ * ("leftmost") one-bit in the two's complement binary representation
+ * of the specified {@code int} value, or 32 if the value
+ * is equal to zero.
+ * @since 1.5
+ */
+ public static int numberOfLeadingZeros(int i) {
+ // HD, Figure 5-6
+ if (i == 0)
+ return 32;
+ int n = 1;
+ if (i >>> 16 == 0) { n += 16; i <<= 16; }
+ if (i >>> 24 == 0) { n += 8; i <<= 8; }
+ if (i >>> 28 == 0) { n += 4; i <<= 4; }
+ if (i >>> 30 == 0) { n += 2; i <<= 2; }
+ n -= i >>> 31;
+ return n;
+ }
+
+ /**
+ * Returns the number of zero bits following the lowest-order ("rightmost")
+ * one-bit in the two's complement binary representation of the specified
+ * {@code int} value. Returns 32 if the specified value has no
+ * one-bits in its two's complement representation, in other words if it is
+ * equal to zero.
+ *
+ * @param i the value whose number of trailing zeros is to be computed
+ * @return the number of zero bits following the lowest-order ("rightmost")
+ * one-bit in the two's complement binary representation of the
+ * specified {@code int} value, or 32 if the value is equal
+ * to zero.
+ * @since 1.5
+ */
+ public static int numberOfTrailingZeros(int i) {
+ // HD, Figure 5-14
+ int y;
+ if (i == 0) return 32;
+ int n = 31;
+ y = i <<16; if (y != 0) { n = n -16; i = y; }
+ y = i << 8; if (y != 0) { n = n - 8; i = y; }
+ y = i << 4; if (y != 0) { n = n - 4; i = y; }
+ y = i << 2; if (y != 0) { n = n - 2; i = y; }
+ return n - ((i << 1) >>> 31);
+ }
+
+ /**
+ * Returns the number of one-bits in the two's complement binary
+ * representation of the specified {@code int} value. This function is
+ * sometimes referred to as the population count.
+ *
+ * @param i the value whose bits are to be counted
+ * @return the number of one-bits in the two's complement binary
+ * representation of the specified {@code int} value.
+ * @since 1.5
+ */
+ public static int bitCount(int i) {
+ // HD, Figure 5-2
+ i = i - ((i >>> 1) & 0x55555555);
+ i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
+ i = (i + (i >>> 4)) & 0x0f0f0f0f;
+ i = i + (i >>> 8);
+ i = i + (i >>> 16);
+ return i & 0x3f;
+ }
+
+ /**
+ * Returns the value obtained by rotating the two's complement binary
+ * representation of the specified {@code int} value left by the
+ * specified number of bits. (Bits shifted out of the left hand, or
+ * high-order, side reenter on the right, or low-order.)
+ *
+ *