/*
* Copyright (C) 2011 The Guava Authors
*
* Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
* in compliance with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software distributed under the
* License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
* express or implied. See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.google.common.primitives;
import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.base.Preconditions.checkNotNull;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Comparator;
import com.google.common.annotations.Beta;
import com.google.common.annotations.GwtCompatible;
/**
* Static utility methods pertaining to {@code long} primitives that interpret values as
* <i>unsigned</i> (that is, any negative value {@code x} is treated as the positive value
* {@code 2^64 + x}). The methods for which signedness is not an issue are in {@link Longs}, as
* well as signed versions of methods for which signedness is an issue.
*
* <p>In addition, this class provides several static methods for converting a {@code long} to a
* {@code String} and a {@code String} to a {@code long} that treat the {@code long} as an unsigned
* number.
*
* <p>Users of these utilities must be <i>extremely careful</i> not to mix up signed and unsigned
* {@code long} values. When possible, it is recommended that the {@link UnsignedLong} wrapper
* class be used, at a small efficiency penalty, to enforce the distinction in the type system.
*
* @author Louis Wasserman
* @author Brian Milch
* @author Colin Evans
* @since 10.0
*/
@Beta
@GwtCompatible
public final class UnsignedLongs {
private UnsignedLongs() {}
public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1
/**
* A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on
* longs, that is, {@code a <= b} as unsigned longs if and only if {@code rotate(a) <= rotate(b)}
* as signed longs.
*/
private static long flip(long a) {
return a ^ Long.MIN_VALUE;
}
/**
* Compares the two specified {@code long} values, treating them as unsigned values between
* {@code 0} and {@code 2^64 - 1} inclusive.
*
* @param a the first unsigned {@code long} to compare
* @param b the second unsigned {@code long} to compare
* @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
* greater than {@code b}; or zero if they are equal
*/
public static int compare(long a, long b) {
return Longs.compare(flip(a), flip(b));
}
/**
* Returns the least value present in {@code array}.
*
* @param array a <i>nonempty</i> array of unsigned {@code long} values
* @return the value present in {@code array} that is less than or equal to every other value in
* the array according to {@link #compare}
* @throws IllegalArgumentException if {@code array} is empty
*/
public static long min(long... array) {
checkArgument(array.length > 0);
long min = flip(array[0]);
for (int i = 1; i < array.length; i++) {
long next = flip(array[i]);
if (next < min) {
min = next;
}
}
return flip(min);
}
/**
* Returns the greatest value present in {@code array}.
*
* @param array a <i>nonempty</i> array of unsigned {@code long} values
* @return the value present in {@code array} that is greater than or equal to every other value
* in the array according to {@link #compare}
* @throws IllegalArgumentException if {@code array} is empty
*/
public static long max(long... array) {
checkArgument(array.length > 0);
long max = flip(array[0]);
for (int i = 1; i < array.length; i++) {
long next = flip(array[i]);
if (next > max) {
max = next;
}
}
return flip(max);
}
/**
* Returns a string containing the supplied unsigned {@code long} values separated by
* {@code separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
*
* @param separator the text that should appear between consecutive values in the resulting
* string (but not at the start or end)
* @param array an array of unsigned {@code long} values, possibly empty
*/
public static String join(String separator, long... array) {
checkNotNull(separator);
if (array.length == 0) {
return "";
}
// For pre-sizing a builder, just get the right order of magnitude
StringBuilder builder = new StringBuilder(array.length * 5);
builder.append(array[0]);
for (int i = 1; i < array.length; i++) {
builder.append(separator).append(toString(array[i]));
}
return builder.toString();
}
/**
* Returns a comparator that compares two {@code long} arrays lexicographically. That is, it
* compares, using {@link #compare(long, long)}), the first pair of values that follow any common
* prefix, or when one array is a prefix of the other, treats the shorter array as the lesser.
* For example, {@code [] < [1L] < [1L, 2L] < [2L]}. Values are treated as unsigned.
*
* <p>
* The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
* support only identity equality), but it is consistent with
* {@link Arrays#equals(long[], long[])}.
*
* @see <a href="http://en.wikipedia.org/wiki/Lexicographical_order">Lexicographical order
* article at Wikipedia</a>
*/
public static Comparator<long[]> lexicographicalComparator() {
return LexicographicalComparator.INSTANCE;
}
enum LexicographicalComparator implements Comparator<long[]> {
INSTANCE;
@Override
public int compare(long[] left, long[] right) {
int minLength = Math.min(left.length, right.length);
for (int i = 0; i < minLength; i++) {
if (left[i] != right[i]) {
return UnsignedLongs.compare(left[i], right[i]);
}
}
return left.length - right.length;
}
}
/**
* Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
* quantities.
*
* @param dividend the dividend (numerator)
* @param divisor the divisor (denominator)
* @throws ArithmeticException if divisor is 0
*/
public static long divide(long dividend, long divisor) {
if (divisor < 0) { // i.e., divisor >= 2^63:
if (compare(dividend, divisor) < 0) {
return 0; // dividend < divisor
} else {
return 1; // dividend >= divisor
}
}
// Optimization - use signed division if dividend < 2^63
if (dividend >= 0) {
return dividend / divisor;
}
/*
* Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
* guaranteed to be either exact or one less than the correct value. This follows from fact
* that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
* quite trivial.
*/
long quotient = ((dividend >>> 1) / divisor) << 1;
long rem = dividend - quotient * divisor;
return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
}
/**
* Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
* quantities.
*
* @param dividend the dividend (numerator)
* @param divisor the divisor (denominator)
* @throws ArithmeticException if divisor is 0
*/
public static long remainder(long dividend, long divisor) {
if (divisor < 0) { // i.e., divisor >= 2^63:
if (compare(dividend, divisor) < 0) {
return dividend; // dividend < divisor
} else {
return dividend - divisor; // dividend >= divisor
}
}
// Optimization - use signed modulus if dividend < 2^63
if (dividend >= 0) {
return dividend % divisor;
}
/*
* Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
* guaranteed to be either exact or one less than the correct value. This follows from fact
* that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
* quite trivial.
*/
long quotient = ((dividend >>> 1) / divisor) << 1;
long rem = dividend - quotient * divisor;
return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
}
/**
* Returns the unsigned {@code long} value represented by the given decimal string.
*
* @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
* value
*/
public static long parseUnsignedLong(String s) {
return parseUnsignedLong(s, 10);
}
/**
* Returns the unsigned {@code long} value represented by a string with the given radix.
*
* @param s the string containing the unsigned {@code long} representation to be parsed.
* @param radix the radix to use while parsing {@code s}
* @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
* with the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX}
* and {@link Character#MAX_RADIX}.
*/
public static long parseUnsignedLong(String s, int radix) {
checkNotNull(s);
if (s.length() == 0) {
throw new NumberFormatException("empty string");
}
if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
throw new NumberFormatException("illegal radix:" + radix);
}
int max_safe_pos = maxSafeDigits[radix] - 1;
long value = 0;
for (int pos = 0; pos < s.length(); pos++) {
int digit = Character.digit(s.charAt(pos), radix);
if (digit == -1) {
throw new NumberFormatException(s);
}
if (pos > max_safe_pos && overflowInParse(value, digit, radix)) {
throw new NumberFormatException("Too large for unsigned long: " + s);
}
value = (value * radix) + digit;
}
return value;
}
/**
* Returns true if (current * radix) + digit is a number too large to be represented by an
* unsigned long. This is useful for detecting overflow while parsing a string representation of
* a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
* undefined results or an ArrayIndexOutOfBoundsException.
*/
private static boolean overflowInParse(long current, int digit, int radix) {
if (current >= 0) {
if (current < maxValueDivs[radix]) {
return false;
}
if (current > maxValueDivs[radix]) {
return true;
}
// current == maxValueDivs[radix]
return (digit > maxValueMods[radix]);
}
// current < 0: high bit is set
return true;
}
/**
* Returns a string representation of x, where x is treated as unsigned.
*/
public static String toString(long x) {
return toString(x, 10);
}
/**
* Returns a string representation of {@code x} for the given radix, where {@code x} is treated
* as unsigned.
*
* @param x the value to convert to a string.
* @param radix the radix to use while working with {@code x}
* @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
* and {@link Character#MAX_RADIX}.
*/
public static String toString(long x, int radix) {
checkArgument(radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
"radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX", radix);
if (x == 0) {
// Simply return "0"
return "0";
} else {
char[] buf = new char[64];
int i = buf.length;
if (x < 0) {
// Split x into high-order and low-order halves.
// Individual digits are generated from the bottom half into which
// bits are moved continously from the top half.
long top = x >>> 32;
long bot = (x & 0xffffffffl) + ((top % radix) << 32);
top /= radix;
while ((bot > 0) || (top > 0)) {
buf[--i] = Character.forDigit((int) (bot % radix), radix);
bot = (bot / radix) + ((top % radix) << 32);
top /= radix;
}
} else {
// Simple modulo/division approach
while (x > 0) {
buf[--i] = Character.forDigit((int) (x % radix), radix);
x /= radix;
}
}
// Generate string
return new String(buf, i, buf.length - i);
}
}
// calculated as 0xffffffffffffffff / radix
private static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
private static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
private static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];
static {
BigInteger overflow = new BigInteger("10000000000000000", 16);
for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
maxValueDivs[i] = divide(MAX_VALUE, i);
maxValueMods[i] = (int) remainder(MAX_VALUE, i);
maxSafeDigits[i] = overflow.toString(i).length() - 1;
}
}
}
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