jaroslav@49: /* jaroslav@49: * Copyright (c) 1994, 2010, Oracle and/or its affiliates. All rights reserved. jaroslav@49: * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. jaroslav@49: * jaroslav@49: * This code is free software; you can redistribute it and/or modify it jaroslav@49: * under the terms of the GNU General Public License version 2 only, as jaroslav@49: * published by the Free Software Foundation. Oracle designates this jaroslav@49: * particular file as subject to the "Classpath" exception as provided jaroslav@49: * by Oracle in the LICENSE file that accompanied this code. jaroslav@49: * jaroslav@49: * This code is distributed in the hope that it will be useful, but WITHOUT jaroslav@49: * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or jaroslav@49: * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License jaroslav@49: * version 2 for more details (a copy is included in the LICENSE file that jaroslav@49: * accompanied this code). jaroslav@49: * jaroslav@49: * You should have received a copy of the GNU General Public License version jaroslav@49: * 2 along with this work; if not, write to the Free Software Foundation, jaroslav@49: * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. jaroslav@49: * jaroslav@49: * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA jaroslav@49: * or visit www.oracle.com if you need additional information or have any jaroslav@49: * questions. jaroslav@49: */ jaroslav@49: jaroslav@49: package java.lang; jaroslav@49: jaroslav@49: import java.util.Properties; jaroslav@49: jaroslav@49: /** jaroslav@49: * The {@code Integer} class wraps a value of the primitive type jaroslav@49: * {@code int} in an object. An object of type {@code Integer} jaroslav@49: * contains a single field whose type is {@code int}. jaroslav@49: * jaroslav@49: *
In addition, this class provides several methods for converting jaroslav@49: * an {@code int} to a {@code String} and a {@code String} to an jaroslav@49: * {@code int}, as well as other constants and methods useful when jaroslav@49: * dealing with an {@code int}. jaroslav@49: * jaroslav@49: *
Implementation note: The implementations of the "bit twiddling"
jaroslav@49: * methods (such as {@link #highestOneBit(int) highestOneBit} and
jaroslav@49: * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
jaroslav@49: * based on material from Henry S. Warren, Jr.'s Hacker's
jaroslav@49: * Delight, (Addison Wesley, 2002).
jaroslav@49: *
jaroslav@49: * @author Lee Boynton
jaroslav@49: * @author Arthur van Hoff
jaroslav@49: * @author Josh Bloch
jaroslav@49: * @author Joseph D. Darcy
jaroslav@49: * @since JDK1.0
jaroslav@49: */
jaroslav@49: public final class Integer extends Number implements Comparable If the radix is smaller than {@code Character.MIN_RADIX}
jaroslav@49: * or larger than {@code Character.MAX_RADIX}, then the radix
jaroslav@49: * {@code 10} is used instead.
jaroslav@49: *
jaroslav@49: * If the first argument is negative, the first element of the
jaroslav@49: * result is the ASCII minus character {@code '-'}
jaroslav@49: * ( The remaining characters of the result represent the magnitude
jaroslav@49: * of the first argument. If the magnitude is zero, it is
jaroslav@49: * represented by a single zero character {@code '0'}
jaroslav@49: * ( The unsigned integer value is the argument plus 232
jaroslav@49: * if the argument is negative; otherwise, it is equal to the
jaroslav@49: * argument. This value is converted to a string of ASCII digits
jaroslav@49: * in hexadecimal (base 16) with no extra leading
jaroslav@49: * {@code 0}s. If the unsigned magnitude is zero, it is
jaroslav@49: * represented by a single zero character {@code '0'}
jaroslav@49: * ( The unsigned integer value is the argument plus 232
jaroslav@49: * if the argument is negative; otherwise, it is equal to the
jaroslav@49: * argument. This value is converted to a string of ASCII digits
jaroslav@49: * in octal (base 8) with no extra leading {@code 0}s.
jaroslav@49: *
jaroslav@49: * If the unsigned magnitude is zero, it is represented by a
jaroslav@49: * single zero character {@code '0'}
jaroslav@49: * ( The unsigned integer value is the argument plus 232
jaroslav@49: * if the argument is negative; otherwise it is equal to the
jaroslav@49: * argument. This value is converted to a string of ASCII digits
jaroslav@49: * in binary (base 2) with no extra leading {@code 0}s.
jaroslav@49: * If the unsigned magnitude is zero, it is represented by a
jaroslav@49: * single zero character {@code '0'}
jaroslav@49: * ( An exception of type {@code NumberFormatException} is
jaroslav@49: * thrown if any of the following situations occurs:
jaroslav@49: * Examples:
jaroslav@49: * In other words, this method returns an {@code Integer}
jaroslav@49: * object equal to the value of:
jaroslav@49: *
jaroslav@49: * In other words, this method returns an {@code Integer}
jaroslav@49: * object equal to the value of:
jaroslav@49: *
jaroslav@49: * The first argument is treated as the name of a system property.
jaroslav@49: * System properties are accessible through the
jaroslav@49: * {@link java.lang.System#getProperty(java.lang.String)} method. The
jaroslav@49: * string value of this property is then interpreted as an integer
jaroslav@49: * value and an {@code Integer} object representing this value is
jaroslav@49: * returned. Details of possible numeric formats can be found with
jaroslav@49: * the definition of {@code getProperty}.
jaroslav@49: *
jaroslav@49: * If there is no property with the specified name, if the specified name
jaroslav@49: * is empty or {@code null}, or if the property does not have
jaroslav@49: * the correct numeric format, then {@code null} is returned.
jaroslav@49: *
jaroslav@49: * In other words, this method returns an {@code Integer}
jaroslav@49: * object equal to the value of:
jaroslav@49: *
jaroslav@49: * The first argument is treated as the name of a system property.
jaroslav@49: * System properties are accessible through the {@link
jaroslav@49: * java.lang.System#getProperty(java.lang.String)} method. The
jaroslav@49: * string value of this property is then interpreted as an integer
jaroslav@49: * value and an {@code Integer} object representing this value is
jaroslav@49: * returned. Details of possible numeric formats can be found with
jaroslav@49: * the definition of {@code getProperty}.
jaroslav@49: *
jaroslav@49: * The second argument is the default value. An {@code Integer} object
jaroslav@49: * that represents the value of the second argument is returned if there
jaroslav@49: * is no property of the specified name, if the property does not have
jaroslav@49: * the correct numeric format, or if the specified name is empty or
jaroslav@49: * {@code null}.
jaroslav@49: *
jaroslav@49: * In other words, this method returns an {@code Integer} object
jaroslav@49: * equal to the value of:
jaroslav@49: *
jaroslav@49: * The second argument is the default value. The default value is
jaroslav@49: * returned if there is no property of the specified name, if the
jaroslav@49: * property does not have the correct numeric format, or if the
jaroslav@49: * specified name is empty or {@code null}.
jaroslav@49: *
jaroslav@49: * @param nm property name.
jaroslav@49: * @param val default value.
jaroslav@49: * @return the {@code Integer} value of the property.
jaroslav@49: * @see java.lang.System#getProperty(java.lang.String)
jaroslav@49: * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
jaroslav@49: * @see java.lang.Integer#decode
jaroslav@49: */
jaroslav@49: public static Integer getInteger(String nm, Integer val) {
jaroslav@49: String v = null;
jaroslav@49: try {
jaroslav@49: v = System.getProperty(nm);
jaroslav@49: } catch (IllegalArgumentException e) {
jaroslav@49: } catch (NullPointerException e) {
jaroslav@49: }
jaroslav@49: if (v != null) {
jaroslav@49: try {
jaroslav@49: return Integer.decode(v);
jaroslav@49: } catch (NumberFormatException e) {
jaroslav@49: }
jaroslav@49: }
jaroslav@49: return val;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Decodes a {@code String} into an {@code Integer}.
jaroslav@49: * Accepts decimal, hexadecimal, and octal numbers given
jaroslav@49: * by the following grammar:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * The sequence of characters following an optional
jaroslav@49: * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
jaroslav@49: * "{@code #}", or leading zero) is parsed as by the {@code
jaroslav@49: * Integer.parseInt} method with the indicated radix (10, 16, or
jaroslav@49: * 8). This sequence of characters must represent a positive
jaroslav@49: * value or a {@link NumberFormatException} will be thrown. The
jaroslav@49: * result is negated if first character of the specified {@code
jaroslav@49: * String} is the minus sign. No whitespace characters are
jaroslav@49: * permitted in the {@code String}.
jaroslav@49: *
jaroslav@49: * @param nm the {@code String} to decode.
jaroslav@49: * @return an {@code Integer} object holding the {@code int}
jaroslav@49: * value represented by {@code nm}
jaroslav@49: * @exception NumberFormatException if the {@code String} does not
jaroslav@49: * contain a parsable integer.
jaroslav@49: * @see java.lang.Integer#parseInt(java.lang.String, int)
jaroslav@49: */
jaroslav@49: public static Integer decode(String nm) throws NumberFormatException {
jaroslav@49: int radix = 10;
jaroslav@49: int index = 0;
jaroslav@49: boolean negative = false;
jaroslav@49: Integer result;
jaroslav@49:
jaroslav@49: if (nm.length() == 0)
jaroslav@49: throw new NumberFormatException("Zero length string");
jaroslav@49: char firstChar = nm.charAt(0);
jaroslav@49: // Handle sign, if present
jaroslav@49: if (firstChar == '-') {
jaroslav@49: negative = true;
jaroslav@49: index++;
jaroslav@49: } else if (firstChar == '+')
jaroslav@49: index++;
jaroslav@49:
jaroslav@49: // Handle radix specifier, if present
jaroslav@49: if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
jaroslav@49: index += 2;
jaroslav@49: radix = 16;
jaroslav@49: }
jaroslav@49: else if (nm.startsWith("#", index)) {
jaroslav@49: index ++;
jaroslav@49: radix = 16;
jaroslav@49: }
jaroslav@49: else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
jaroslav@49: index ++;
jaroslav@49: radix = 8;
jaroslav@49: }
jaroslav@49:
jaroslav@49: if (nm.startsWith("-", index) || nm.startsWith("+", index))
jaroslav@49: throw new NumberFormatException("Sign character in wrong position");
jaroslav@49:
jaroslav@49: try {
jaroslav@49: result = Integer.valueOf(nm.substring(index), radix);
jaroslav@49: result = negative ? Integer.valueOf(-result.intValue()) : result;
jaroslav@49: } catch (NumberFormatException e) {
jaroslav@49: // If number is Integer.MIN_VALUE, we'll end up here. The next line
jaroslav@49: // handles this case, and causes any genuine format error to be
jaroslav@49: // rethrown.
jaroslav@49: String constant = negative ? ("-" + nm.substring(index))
jaroslav@49: : nm.substring(index);
jaroslav@49: result = Integer.valueOf(constant, radix);
jaroslav@49: }
jaroslav@49: return result;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Compares two {@code Integer} objects numerically.
jaroslav@49: *
jaroslav@49: * @param anotherInteger the {@code Integer} to be compared.
jaroslav@49: * @return the value {@code 0} if this {@code Integer} is
jaroslav@49: * equal to the argument {@code Integer}; a value less than
jaroslav@49: * {@code 0} if this {@code Integer} is numerically less
jaroslav@49: * than the argument {@code Integer}; and a value greater
jaroslav@49: * than {@code 0} if this {@code Integer} is numerically
jaroslav@49: * greater than the argument {@code Integer} (signed
jaroslav@49: * comparison).
jaroslav@49: * @since 1.2
jaroslav@49: */
jaroslav@49: public int compareTo(Integer anotherInteger) {
jaroslav@49: return compare(this.value, anotherInteger.value);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Compares two {@code int} values numerically.
jaroslav@49: * The value returned is identical to what would be returned by:
jaroslav@49: * Note that this method is closely related to the logarithm base 2.
jaroslav@49: * For all positive {@code int} values x:
jaroslav@49: * Note that left rotation with a negative distance is equivalent to
jaroslav@49: * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
jaroslav@49: * distance)}. Note also that rotation by any multiple of 32 is a
jaroslav@49: * no-op, so all but the last five bits of the rotation distance can be
jaroslav@49: * ignored, even if the distance is negative: {@code rotateLeft(val,
jaroslav@49: * distance) == rotateLeft(val, distance & 0x1F)}.
jaroslav@49: *
jaroslav@49: * @return the value obtained by rotating the two's complement binary
jaroslav@49: * representation of the specified {@code int} value left by the
jaroslav@49: * specified number of bits.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int rotateLeft(int i, int distance) {
jaroslav@49: return (i << distance) | (i >>> -distance);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the value obtained by rotating the two's complement binary
jaroslav@49: * representation of the specified {@code int} value right by the
jaroslav@49: * specified number of bits. (Bits shifted out of the right hand, or
jaroslav@49: * low-order, side reenter on the left, or high-order.)
jaroslav@49: *
jaroslav@49: * Note that right rotation with a negative distance is equivalent to
jaroslav@49: * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
jaroslav@49: * distance)}. Note also that rotation by any multiple of 32 is a
jaroslav@49: * no-op, so all but the last five bits of the rotation distance can be
jaroslav@49: * ignored, even if the distance is negative: {@code rotateRight(val,
jaroslav@49: * distance) == rotateRight(val, distance & 0x1F)}.
jaroslav@49: *
jaroslav@49: * @return the value obtained by rotating the two's complement binary
jaroslav@49: * representation of the specified {@code int} value right by the
jaroslav@49: * specified number of bits.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int rotateRight(int i, int distance) {
jaroslav@49: return (i >>> distance) | (i << -distance);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the value obtained by reversing the order of the bits in the
jaroslav@49: * two's complement binary representation of the specified {@code int}
jaroslav@49: * value.
jaroslav@49: *
jaroslav@49: * @return the value obtained by reversing order of the bits in the
jaroslav@49: * specified {@code int} value.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int reverse(int i) {
jaroslav@49: // HD, Figure 7-1
jaroslav@49: i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
jaroslav@49: i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
jaroslav@49: i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
jaroslav@49: i = (i << 24) | ((i & 0xff00) << 8) |
jaroslav@49: ((i >>> 8) & 0xff00) | (i >>> 24);
jaroslav@49: return i;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the signum function of the specified {@code int} value. (The
jaroslav@49: * return value is -1 if the specified value is negative; 0 if the
jaroslav@49: * specified value is zero; and 1 if the specified value is positive.)
jaroslav@49: *
jaroslav@49: * @return the signum function of the specified {@code int} value.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int signum(int i) {
jaroslav@49: // HD, Section 2-7
jaroslav@49: return (i >> 31) | (-i >>> 31);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the value obtained by reversing the order of the bytes in the
jaroslav@49: * two's complement representation of the specified {@code int} value.
jaroslav@49: *
jaroslav@49: * @return the value obtained by reversing the bytes in the specified
jaroslav@49: * {@code int} value.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int reverseBytes(int i) {
jaroslav@49: return ((i >>> 24) ) |
jaroslav@49: ((i >> 8) & 0xFF00) |
jaroslav@49: ((i << 8) & 0xFF0000) |
jaroslav@49: ((i << 24));
jaroslav@49: }
jaroslav@49:
jaroslav@49: /** use serialVersionUID from JDK 1.0.2 for interoperability */
jaroslav@49: private static final long serialVersionUID = 1360826667806852920L;
jaroslav@49: }
'\u002D'
). If the first argument is not
jaroslav@49: * negative, no sign character appears in the result.
jaroslav@49: *
jaroslav@49: * '\u0030'
); otherwise, the first character of
jaroslav@49: * the representation of the magnitude will not be the zero
jaroslav@49: * character. The following ASCII characters are used as digits:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code 0123456789abcdefghijklmnopqrstuvwxyz}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * These are '\u0030'
through
jaroslav@49: * '\u0039'
and '\u0061'
through
jaroslav@49: * '\u007A'
. If {@code radix} is
jaroslav@49: * N, then the first N of these characters
jaroslav@49: * are used as radix-N digits in the order shown. Thus,
jaroslav@49: * the digits for hexadecimal (radix 16) are
jaroslav@49: * {@code 0123456789abcdef}. If uppercase letters are
jaroslav@49: * desired, the {@link java.lang.String#toUpperCase()} method may
jaroslav@49: * be called on the result:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code Integer.toString(n, 16).toUpperCase()}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param i an integer to be converted to a string.
jaroslav@49: * @param radix the radix to use in the string representation.
jaroslav@49: * @return a string representation of the argument in the specified radix.
jaroslav@49: * @see java.lang.Character#MAX_RADIX
jaroslav@49: * @see java.lang.Character#MIN_RADIX
jaroslav@49: */
jaroslav@49: public static String toString(int i, int radix) {
jaroslav@49:
jaroslav@49: if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
jaroslav@49: radix = 10;
jaroslav@49:
jaroslav@49: /* Use the faster version */
jaroslav@49: if (radix == 10) {
jaroslav@49: return toString(i);
jaroslav@49: }
jaroslav@49:
jaroslav@49: char buf[] = new char[33];
jaroslav@49: boolean negative = (i < 0);
jaroslav@49: int charPos = 32;
jaroslav@49:
jaroslav@49: if (!negative) {
jaroslav@49: i = -i;
jaroslav@49: }
jaroslav@49:
jaroslav@49: while (i <= -radix) {
jaroslav@49: buf[charPos--] = digits[-(i % radix)];
jaroslav@49: i = i / radix;
jaroslav@49: }
jaroslav@49: buf[charPos] = digits[-i];
jaroslav@49:
jaroslav@49: if (negative) {
jaroslav@49: buf[--charPos] = '-';
jaroslav@49: }
jaroslav@49:
jaroslav@49: return new String(buf, charPos, (33 - charPos));
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns a string representation of the integer argument as an
jaroslav@49: * unsigned integer in base 16.
jaroslav@49: *
jaroslav@49: * '\u0030'
); otherwise, the first character of
jaroslav@49: * the representation of the unsigned magnitude will not be the
jaroslav@49: * zero character. The following characters are used as
jaroslav@49: * hexadecimal digits:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code 0123456789abcdef}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * These are the characters '\u0030'
through
jaroslav@49: * '\u0039'
and '\u0061'
through
jaroslav@49: * '\u0066'
. If uppercase letters are
jaroslav@49: * desired, the {@link java.lang.String#toUpperCase()} method may
jaroslav@49: * be called on the result:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code Integer.toHexString(n).toUpperCase()}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param i an integer to be converted to a string.
jaroslav@49: * @return the string representation of the unsigned integer value
jaroslav@49: * represented by the argument in hexadecimal (base 16).
jaroslav@49: * @since JDK1.0.2
jaroslav@49: */
jaroslav@49: public static String toHexString(int i) {
jaroslav@49: return toUnsignedString(i, 4);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns a string representation of the integer argument as an
jaroslav@49: * unsigned integer in base 8.
jaroslav@49: *
jaroslav@49: * '\u0030'
); otherwise, the first character of
jaroslav@49: * the representation of the unsigned magnitude will not be the
jaroslav@49: * zero character. The following characters are used as octal
jaroslav@49: * digits:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code 01234567}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * These are the characters '\u0030'
through
jaroslav@49: * '\u0037'
.
jaroslav@49: *
jaroslav@49: * @param i an integer to be converted to a string.
jaroslav@49: * @return the string representation of the unsigned integer value
jaroslav@49: * represented by the argument in octal (base 8).
jaroslav@49: * @since JDK1.0.2
jaroslav@49: */
jaroslav@49: public static String toOctalString(int i) {
jaroslav@49: return toUnsignedString(i, 3);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns a string representation of the integer argument as an
jaroslav@49: * unsigned integer in base 2.
jaroslav@49: *
jaroslav@49: * '\u0030'
); otherwise, the first character of
jaroslav@49: * the representation of the unsigned magnitude will not be the
jaroslav@49: * zero character. The characters {@code '0'}
jaroslav@49: * ('\u0030'
) and {@code '1'}
jaroslav@49: * ('\u0031'
) are used as binary digits.
jaroslav@49: *
jaroslav@49: * @param i an integer to be converted to a string.
jaroslav@49: * @return the string representation of the unsigned integer value
jaroslav@49: * represented by the argument in binary (base 2).
jaroslav@49: * @since JDK1.0.2
jaroslav@49: */
jaroslav@49: public static String toBinaryString(int i) {
jaroslav@49: return toUnsignedString(i, 1);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Convert the integer to an unsigned number.
jaroslav@49: */
jaroslav@49: private static String toUnsignedString(int i, int shift) {
jaroslav@49: char[] buf = new char[32];
jaroslav@49: int charPos = 32;
jaroslav@49: int radix = 1 << shift;
jaroslav@49: int mask = radix - 1;
jaroslav@49: do {
jaroslav@49: buf[--charPos] = digits[i & mask];
jaroslav@49: i >>>= shift;
jaroslav@49: } while (i != 0);
jaroslav@49:
jaroslav@49: return new String(buf, charPos, (32 - charPos));
jaroslav@49: }
jaroslav@49:
jaroslav@49:
jaroslav@49: final static char [] DigitTens = {
jaroslav@49: '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
jaroslav@49: '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
jaroslav@49: '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
jaroslav@49: '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
jaroslav@49: '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
jaroslav@49: '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
jaroslav@49: '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
jaroslav@49: '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
jaroslav@49: '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
jaroslav@49: '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
jaroslav@49: } ;
jaroslav@49:
jaroslav@49: final static char [] DigitOnes = {
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
jaroslav@49: } ;
jaroslav@49:
jaroslav@49: // I use the "invariant division by multiplication" trick to
jaroslav@49: // accelerate Integer.toString. In particular we want to
jaroslav@49: // avoid division by 10.
jaroslav@49: //
jaroslav@49: // The "trick" has roughly the same performance characteristics
jaroslav@49: // as the "classic" Integer.toString code on a non-JIT VM.
jaroslav@49: // The trick avoids .rem and .div calls but has a longer code
jaroslav@49: // path and is thus dominated by dispatch overhead. In the
jaroslav@49: // JIT case the dispatch overhead doesn't exist and the
jaroslav@49: // "trick" is considerably faster than the classic code.
jaroslav@49: //
jaroslav@49: // TODO-FIXME: convert (x * 52429) into the equiv shift-add
jaroslav@49: // sequence.
jaroslav@49: //
jaroslav@49: // RE: Division by Invariant Integers using Multiplication
jaroslav@49: // T Gralund, P Montgomery
jaroslav@49: // ACM PLDI 1994
jaroslav@49: //
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns a {@code String} object representing the
jaroslav@49: * specified integer. The argument is converted to signed decimal
jaroslav@49: * representation and returned as a string, exactly as if the
jaroslav@49: * argument and radix 10 were given as arguments to the {@link
jaroslav@49: * #toString(int, int)} method.
jaroslav@49: *
jaroslav@49: * @param i an integer to be converted.
jaroslav@49: * @return a string representation of the argument in base 10.
jaroslav@49: */
jaroslav@49: public static String toString(int i) {
jaroslav@49: if (i == Integer.MIN_VALUE)
jaroslav@49: return "-2147483648";
jaroslav@49: int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
jaroslav@49: char[] buf = new char[size];
jaroslav@49: getChars(i, size, buf);
jaroslav@49: return new String(0, size, buf);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Places characters representing the integer i into the
jaroslav@49: * character array buf. The characters are placed into
jaroslav@49: * the buffer backwards starting with the least significant
jaroslav@49: * digit at the specified index (exclusive), and working
jaroslav@49: * backwards from there.
jaroslav@49: *
jaroslav@49: * Will fail if i == Integer.MIN_VALUE
jaroslav@49: */
jaroslav@49: static void getChars(int i, int index, char[] buf) {
jaroslav@49: int q, r;
jaroslav@49: int charPos = index;
jaroslav@49: char sign = 0;
jaroslav@49:
jaroslav@49: if (i < 0) {
jaroslav@49: sign = '-';
jaroslav@49: i = -i;
jaroslav@49: }
jaroslav@49:
jaroslav@49: // Generate two digits per iteration
jaroslav@49: while (i >= 65536) {
jaroslav@49: q = i / 100;
jaroslav@49: // really: r = i - (q * 100);
jaroslav@49: r = i - ((q << 6) + (q << 5) + (q << 2));
jaroslav@49: i = q;
jaroslav@49: buf [--charPos] = DigitOnes[r];
jaroslav@49: buf [--charPos] = DigitTens[r];
jaroslav@49: }
jaroslav@49:
jaroslav@49: // Fall thru to fast mode for smaller numbers
jaroslav@49: // assert(i <= 65536, i);
jaroslav@49: for (;;) {
jaroslav@49: q = (i * 52429) >>> (16+3);
jaroslav@49: r = i - ((q << 3) + (q << 1)); // r = i-(q*10) ...
jaroslav@49: buf [--charPos] = digits [r];
jaroslav@49: i = q;
jaroslav@49: if (i == 0) break;
jaroslav@49: }
jaroslav@49: if (sign != 0) {
jaroslav@49: buf [--charPos] = sign;
jaroslav@49: }
jaroslav@49: }
jaroslav@49:
jaroslav@49: final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
jaroslav@49: 99999999, 999999999, Integer.MAX_VALUE };
jaroslav@49:
jaroslav@49: // Requires positive x
jaroslav@49: static int stringSize(int x) {
jaroslav@49: for (int i=0; ; i++)
jaroslav@49: if (x <= sizeTable[i])
jaroslav@49: return i+1;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Parses the string argument as a signed integer in the radix
jaroslav@49: * specified by the second argument. The characters in the string
jaroslav@49: * must all be digits of the specified radix (as determined by
jaroslav@49: * whether {@link java.lang.Character#digit(char, int)} returns a
jaroslav@49: * nonnegative value), except that the first character may be an
jaroslav@49: * ASCII minus sign {@code '-'} ('\u002D'
) to
jaroslav@49: * indicate a negative value or an ASCII plus sign {@code '+'}
jaroslav@49: * ('\u002B'
) to indicate a positive value. The
jaroslav@49: * resulting integer value is returned.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * '\u002D'
) or plus sign
jaroslav@49: * {@code '+'} ('\u002B'
) provided that the
jaroslav@49: * string is longer than length 1.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param s the {@code String} containing the integer
jaroslav@49: * representation to be parsed
jaroslav@49: * @param radix the radix to be used while parsing {@code s}.
jaroslav@49: * @return the integer represented by the string argument in the
jaroslav@49: * specified radix.
jaroslav@49: * @exception NumberFormatException if the {@code String}
jaroslav@49: * does not contain a parsable {@code int}.
jaroslav@49: */
jaroslav@49: public static int parseInt(String s, int radix)
jaroslav@49: throws NumberFormatException
jaroslav@49: {
jaroslav@49: /*
jaroslav@49: * WARNING: This method may be invoked early during VM initialization
jaroslav@49: * before IntegerCache is initialized. Care must be taken to not use
jaroslav@49: * the valueOf method.
jaroslav@49: */
jaroslav@49:
jaroslav@49: if (s == null) {
jaroslav@49: throw new NumberFormatException("null");
jaroslav@49: }
jaroslav@49:
jaroslav@49: if (radix < Character.MIN_RADIX) {
jaroslav@49: throw new NumberFormatException("radix " + radix +
jaroslav@49: " less than Character.MIN_RADIX");
jaroslav@49: }
jaroslav@49:
jaroslav@49: if (radix > Character.MAX_RADIX) {
jaroslav@49: throw new NumberFormatException("radix " + radix +
jaroslav@49: " greater than Character.MAX_RADIX");
jaroslav@49: }
jaroslav@49:
jaroslav@49: int result = 0;
jaroslav@49: boolean negative = false;
jaroslav@49: int i = 0, len = s.length();
jaroslav@49: int limit = -Integer.MAX_VALUE;
jaroslav@49: int multmin;
jaroslav@49: int digit;
jaroslav@49:
jaroslav@49: if (len > 0) {
jaroslav@49: char firstChar = s.charAt(0);
jaroslav@49: if (firstChar < '0') { // Possible leading "+" or "-"
jaroslav@49: if (firstChar == '-') {
jaroslav@49: negative = true;
jaroslav@49: limit = Integer.MIN_VALUE;
jaroslav@49: } else if (firstChar != '+')
jaroslav@49: throw NumberFormatException.forInputString(s);
jaroslav@49:
jaroslav@49: if (len == 1) // Cannot have lone "+" or "-"
jaroslav@49: throw NumberFormatException.forInputString(s);
jaroslav@49: i++;
jaroslav@49: }
jaroslav@49: multmin = limit / radix;
jaroslav@49: while (i < len) {
jaroslav@49: // Accumulating negatively avoids surprises near MAX_VALUE
jaroslav@49: digit = Character.digit(s.charAt(i++),radix);
jaroslav@49: if (digit < 0) {
jaroslav@49: throw NumberFormatException.forInputString(s);
jaroslav@49: }
jaroslav@49: if (result < multmin) {
jaroslav@49: throw NumberFormatException.forInputString(s);
jaroslav@49: }
jaroslav@49: result *= radix;
jaroslav@49: if (result < limit + digit) {
jaroslav@49: throw NumberFormatException.forInputString(s);
jaroslav@49: }
jaroslav@49: result -= digit;
jaroslav@49: }
jaroslav@49: } else {
jaroslav@49: throw NumberFormatException.forInputString(s);
jaroslav@49: }
jaroslav@49: return negative ? result : -result;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Parses the string argument as a signed decimal integer. The
jaroslav@49: * characters in the string must all be decimal digits, except
jaroslav@49: * that the first character may be an ASCII minus sign {@code '-'}
jaroslav@49: * (
jaroslav@49: * parseInt("0", 10) returns 0
jaroslav@49: * parseInt("473", 10) returns 473
jaroslav@49: * parseInt("+42", 10) returns 42
jaroslav@49: * parseInt("-0", 10) returns 0
jaroslav@49: * parseInt("-FF", 16) returns -255
jaroslav@49: * parseInt("1100110", 2) returns 102
jaroslav@49: * parseInt("2147483647", 10) returns 2147483647
jaroslav@49: * parseInt("-2147483648", 10) returns -2147483648
jaroslav@49: * parseInt("2147483648", 10) throws a NumberFormatException
jaroslav@49: * parseInt("99", 8) throws a NumberFormatException
jaroslav@49: * parseInt("Kona", 10) throws a NumberFormatException
jaroslav@49: * parseInt("Kona", 27) returns 411787
jaroslav@49: *
'\u002D'
) to indicate a negative value or an
jaroslav@49: * ASCII plus sign {@code '+'} ('\u002B'
) to
jaroslav@49: * indicate a positive value. The resulting integer value is
jaroslav@49: * returned, exactly as if the argument and the radix 10 were
jaroslav@49: * given as arguments to the {@link #parseInt(java.lang.String,
jaroslav@49: * int)} method.
jaroslav@49: *
jaroslav@49: * @param s a {@code String} containing the {@code int}
jaroslav@49: * representation to be parsed
jaroslav@49: * @return the integer value represented by the argument in decimal.
jaroslav@49: * @exception NumberFormatException if the string does not contain a
jaroslav@49: * parsable integer.
jaroslav@49: */
jaroslav@49: public static int parseInt(String s) throws NumberFormatException {
jaroslav@49: return parseInt(s,10);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns an {@code Integer} object holding the value
jaroslav@49: * extracted from the specified {@code String} when parsed
jaroslav@49: * with the radix given by the second argument. The first argument
jaroslav@49: * is interpreted as representing a signed integer in the radix
jaroslav@49: * specified by the second argument, exactly as if the arguments
jaroslav@49: * were given to the {@link #parseInt(java.lang.String, int)}
jaroslav@49: * method. The result is an {@code Integer} object that
jaroslav@49: * represents the integer value specified by the string.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code new Integer(Integer.parseInt(s, radix))}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param s the string to be parsed.
jaroslav@49: * @param radix the radix to be used in interpreting {@code s}
jaroslav@49: * @return an {@code Integer} object holding the value
jaroslav@49: * represented by the string argument in the specified
jaroslav@49: * radix.
jaroslav@49: * @exception NumberFormatException if the {@code String}
jaroslav@49: * does not contain a parsable {@code int}.
jaroslav@49: */
jaroslav@49: public static Integer valueOf(String s, int radix) throws NumberFormatException {
jaroslav@49: return Integer.valueOf(parseInt(s,radix));
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns an {@code Integer} object holding the
jaroslav@49: * value of the specified {@code String}. The argument is
jaroslav@49: * interpreted as representing a signed decimal integer, exactly
jaroslav@49: * as if the argument were given to the {@link
jaroslav@49: * #parseInt(java.lang.String)} method. The result is an
jaroslav@49: * {@code Integer} object that represents the integer value
jaroslav@49: * specified by the string.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code new Integer(Integer.parseInt(s))}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param s the string to be parsed.
jaroslav@49: * @return an {@code Integer} object holding the value
jaroslav@49: * represented by the string argument.
jaroslav@49: * @exception NumberFormatException if the string cannot be parsed
jaroslav@49: * as an integer.
jaroslav@49: */
jaroslav@49: public static Integer valueOf(String s) throws NumberFormatException {
jaroslav@49: return Integer.valueOf(parseInt(s, 10));
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Cache to support the object identity semantics of autoboxing for values between
jaroslav@49: * -128 and 127 (inclusive) as required by JLS.
jaroslav@49: *
jaroslav@49: * The cache is initialized on first usage. The size of the cache
jaroslav@49: * may be controlled by the -XX:AutoBoxCacheMax=
jaroslav@49: * {@code getInteger(nm, null)}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param nm property name.
jaroslav@49: * @return the {@code Integer} value of the property.
jaroslav@49: * @see java.lang.System#getProperty(java.lang.String)
jaroslav@49: * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
jaroslav@49: */
jaroslav@49: public static Integer getInteger(String nm) {
jaroslav@49: return getInteger(nm, null);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Determines the integer value of the system property with the
jaroslav@49: * specified name.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * {@code getInteger(nm, new Integer(val))}
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * but in practice it may be implemented in a manner such as:
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * to avoid the unnecessary allocation of an {@code Integer}
jaroslav@49: * object when the default value is not needed.
jaroslav@49: *
jaroslav@49: * @param nm property name.
jaroslav@49: * @param val default value.
jaroslav@49: * @return the {@code Integer} value of the property.
jaroslav@49: * @see java.lang.System#getProperty(java.lang.String)
jaroslav@49: * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
jaroslav@49: */
jaroslav@49: public static Integer getInteger(String nm, int val) {
jaroslav@49: Integer result = getInteger(nm, null);
jaroslav@49: return (result == null) ? Integer.valueOf(val) : result;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the integer value of the system property with the
jaroslav@49: * specified name. The first argument is treated as the name of a
jaroslav@49: * system property. System properties are accessible through the
jaroslav@49: * {@link java.lang.System#getProperty(java.lang.String)} method.
jaroslav@49: * The string value of this property is then interpreted as an
jaroslav@49: * integer value, as per the {@code Integer.decode} method,
jaroslav@49: * and an {@code Integer} object representing this value is
jaroslav@49: * returned.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * Integer result = getInteger(nm, null);
jaroslav@49: * return (result == null) ? new Integer(val) : result;
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * DecimalNumeral, HexDigits, and OctalDigits
jaroslav@49: * are as defined in section 3.10.1 of
jaroslav@49: * The Java™ Language Specification,
jaroslav@49: * except that underscores are not accepted between digits.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * Integer.valueOf(x).compareTo(Integer.valueOf(y))
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @param x the first {@code int} to compare
jaroslav@49: * @param y the second {@code int} to compare
jaroslav@49: * @return the value {@code 0} if {@code x == y};
jaroslav@49: * a value less than {@code 0} if {@code x < y}; and
jaroslav@49: * a value greater than {@code 0} if {@code x > y}
jaroslav@49: * @since 1.7
jaroslav@49: */
jaroslav@49: public static int compare(int x, int y) {
jaroslav@49: return (x < y) ? -1 : ((x == y) ? 0 : 1);
jaroslav@49: }
jaroslav@49:
jaroslav@49:
jaroslav@49: // Bit twiddling
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * The number of bits used to represent an {@code int} value in two's
jaroslav@49: * complement binary form.
jaroslav@49: *
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static final int SIZE = 32;
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns an {@code int} value with at most a single one-bit, in the
jaroslav@49: * position of the highest-order ("leftmost") one-bit in the specified
jaroslav@49: * {@code int} value. Returns zero if the specified value has no
jaroslav@49: * one-bits in its two's complement binary representation, that is, if it
jaroslav@49: * is equal to zero.
jaroslav@49: *
jaroslav@49: * @return an {@code int} value with a single one-bit, in the position
jaroslav@49: * of the highest-order one-bit in the specified value, or zero if
jaroslav@49: * the specified value is itself equal to zero.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int highestOneBit(int i) {
jaroslav@49: // HD, Figure 3-1
jaroslav@49: i |= (i >> 1);
jaroslav@49: i |= (i >> 2);
jaroslav@49: i |= (i >> 4);
jaroslav@49: i |= (i >> 8);
jaroslav@49: i |= (i >> 16);
jaroslav@49: return i - (i >>> 1);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns an {@code int} value with at most a single one-bit, in the
jaroslav@49: * position of the lowest-order ("rightmost") one-bit in the specified
jaroslav@49: * {@code int} value. Returns zero if the specified value has no
jaroslav@49: * one-bits in its two's complement binary representation, that is, if it
jaroslav@49: * is equal to zero.
jaroslav@49: *
jaroslav@49: * @return an {@code int} value with a single one-bit, in the position
jaroslav@49: * of the lowest-order one-bit in the specified value, or zero if
jaroslav@49: * the specified value is itself equal to zero.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int lowestOneBit(int i) {
jaroslav@49: // HD, Section 2-1
jaroslav@49: return i & -i;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the number of zero bits preceding the highest-order
jaroslav@49: * ("leftmost") one-bit in the two's complement binary representation
jaroslav@49: * of the specified {@code int} value. Returns 32 if the
jaroslav@49: * specified value has no one-bits in its two's complement representation,
jaroslav@49: * in other words if it is equal to zero.
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: *
jaroslav@49: * @return the number of zero bits preceding the highest-order
jaroslav@49: * ("leftmost") one-bit in the two's complement binary representation
jaroslav@49: * of the specified {@code int} value, or 32 if the value
jaroslav@49: * is equal to zero.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int numberOfLeadingZeros(int i) {
jaroslav@49: // HD, Figure 5-6
jaroslav@49: if (i == 0)
jaroslav@49: return 32;
jaroslav@49: int n = 1;
jaroslav@49: if (i >>> 16 == 0) { n += 16; i <<= 16; }
jaroslav@49: if (i >>> 24 == 0) { n += 8; i <<= 8; }
jaroslav@49: if (i >>> 28 == 0) { n += 4; i <<= 4; }
jaroslav@49: if (i >>> 30 == 0) { n += 2; i <<= 2; }
jaroslav@49: n -= i >>> 31;
jaroslav@49: return n;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the number of zero bits following the lowest-order ("rightmost")
jaroslav@49: * one-bit in the two's complement binary representation of the specified
jaroslav@49: * {@code int} value. Returns 32 if the specified value has no
jaroslav@49: * one-bits in its two's complement representation, in other words if it is
jaroslav@49: * equal to zero.
jaroslav@49: *
jaroslav@49: * @return the number of zero bits following the lowest-order ("rightmost")
jaroslav@49: * one-bit in the two's complement binary representation of the
jaroslav@49: * specified {@code int} value, or 32 if the value is equal
jaroslav@49: * to zero.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int numberOfTrailingZeros(int i) {
jaroslav@49: // HD, Figure 5-14
jaroslav@49: int y;
jaroslav@49: if (i == 0) return 32;
jaroslav@49: int n = 31;
jaroslav@49: y = i <<16; if (y != 0) { n = n -16; i = y; }
jaroslav@49: y = i << 8; if (y != 0) { n = n - 8; i = y; }
jaroslav@49: y = i << 4; if (y != 0) { n = n - 4; i = y; }
jaroslav@49: y = i << 2; if (y != 0) { n = n - 2; i = y; }
jaroslav@49: return n - ((i << 1) >>> 31);
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the number of one-bits in the two's complement binary
jaroslav@49: * representation of the specified {@code int} value. This function is
jaroslav@49: * sometimes referred to as the population count.
jaroslav@49: *
jaroslav@49: * @return the number of one-bits in the two's complement binary
jaroslav@49: * representation of the specified {@code int} value.
jaroslav@49: * @since 1.5
jaroslav@49: */
jaroslav@49: public static int bitCount(int i) {
jaroslav@49: // HD, Figure 5-2
jaroslav@49: i = i - ((i >>> 1) & 0x55555555);
jaroslav@49: i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
jaroslav@49: i = (i + (i >>> 4)) & 0x0f0f0f0f;
jaroslav@49: i = i + (i >>> 8);
jaroslav@49: i = i + (i >>> 16);
jaroslav@49: return i & 0x3f;
jaroslav@49: }
jaroslav@49:
jaroslav@49: /**
jaroslav@49: * Returns the value obtained by rotating the two's complement binary
jaroslav@49: * representation of the specified {@code int} value left by the
jaroslav@49: * specified number of bits. (Bits shifted out of the left hand, or
jaroslav@49: * high-order, side reenter on the right, or low-order.)
jaroslav@49: *
jaroslav@49: *