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001 /*
002 * Copyright (C) 2011 The Guava Authors
003 *
004 * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
005 * in compliance with the License. You may obtain a copy of the License at
006 *
007 * http://www.apache.org/licenses/LICENSE-2.0
008 *
009 * Unless required by applicable law or agreed to in writing, software distributed under the
010 * License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
011 * express or implied. See the License for the specific language governing permissions and
012 * limitations under the License.
013 */
014
015 package com.google.common.primitives;
016
017 import static com.google.common.base.Preconditions.checkArgument;
018 import static com.google.common.base.Preconditions.checkNotNull;
019
020 import java.math.BigInteger;
021 import java.util.Arrays;
022 import java.util.Comparator;
023
024 import com.google.common.annotations.Beta;
025 import com.google.common.annotations.GwtCompatible;
026
027 /**
028 * Static utility methods pertaining to {@code long} primitives that interpret values as
029 * <i>unsigned</i> (that is, any negative value {@code x} is treated as the positive value
030 * {@code 2^64 + x}). The methods for which signedness is not an issue are in {@link Longs}, as
031 * well as signed versions of methods for which signedness is an issue.
032 *
033 * <p>In addition, this class provides several static methods for converting a {@code long} to a
034 * {@code String} and a {@code String} to a {@code long} that treat the {@code long} as an unsigned
035 * number.
036 *
037 * <p>Users of these utilities must be <i>extremely careful</i> not to mix up signed and unsigned
038 * {@code long} values. When possible, it is recommended that the {@link UnsignedLong} wrapper
039 * class be used, at a small efficiency penalty, to enforce the distinction in the type system.
040 *
041 * @author Louis Wasserman
042 * @author Brian Milch
043 * @author Colin Evans
044 * @since 10.0
045 */
046 @Beta
047 @GwtCompatible
048 public final class UnsignedLongs {
049 private UnsignedLongs() {}
050
051 public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1
052
053 /**
054 * A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on
055 * longs, that is, {@code a <= b} as unsigned longs if and only if {@code rotate(a) <= rotate(b)}
056 * as signed longs.
057 */
058 private static long flip(long a) {
059 return a ^ Long.MIN_VALUE;
060 }
061
062 /**
063 * Compares the two specified {@code long} values, treating them as unsigned values between
064 * {@code 0} and {@code 2^64 - 1} inclusive.
065 *
066 * @param a the first unsigned {@code long} to compare
067 * @param b the second unsigned {@code long} to compare
068 * @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
069 * greater than {@code b}; or zero if they are equal
070 */
071 public static int compare(long a, long b) {
072 return Longs.compare(flip(a), flip(b));
073 }
074
075 /**
076 * Returns the least value present in {@code array}, treating values as unsigned.
077 *
078 * @param array a <i>nonempty</i> array of unsigned {@code long} values
079 * @return the value present in {@code array} that is less than or equal to every other value in
080 * the array according to {@link #compare}
081 * @throws IllegalArgumentException if {@code array} is empty
082 */
083 public static long min(long... array) {
084 checkArgument(array.length > 0);
085 long min = flip(array[0]);
086 for (int i = 1; i < array.length; i++) {
087 long next = flip(array[i]);
088 if (next < min) {
089 min = next;
090 }
091 }
092 return flip(min);
093 }
094
095 /**
096 * Returns the greatest value present in {@code array}, treating values as unsigned.
097 *
098 * @param array a <i>nonempty</i> array of unsigned {@code long} values
099 * @return the value present in {@code array} that is greater than or equal to every other value
100 * in the array according to {@link #compare}
101 * @throws IllegalArgumentException if {@code array} is empty
102 */
103 public static long max(long... array) {
104 checkArgument(array.length > 0);
105 long max = flip(array[0]);
106 for (int i = 1; i < array.length; i++) {
107 long next = flip(array[i]);
108 if (next > max) {
109 max = next;
110 }
111 }
112 return flip(max);
113 }
114
115 /**
116 * Returns a string containing the supplied unsigned {@code long} values separated by
117 * {@code separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
118 *
119 * @param separator the text that should appear between consecutive values in the resulting
120 * string (but not at the start or end)
121 * @param array an array of unsigned {@code long} values, possibly empty
122 */
123 public static String join(String separator, long... array) {
124 checkNotNull(separator);
125 if (array.length == 0) {
126 return "";
127 }
128
129 // For pre-sizing a builder, just get the right order of magnitude
130 StringBuilder builder = new StringBuilder(array.length * 5);
131 builder.append(array[0]);
132 for (int i = 1; i < array.length; i++) {
133 builder.append(separator).append(toString(array[i]));
134 }
135 return builder.toString();
136 }
137
138 /**
139 * Returns a comparator that compares two arrays of unsigned {@code long} values
140 * lexicographically. That is, it compares, using {@link #compare(long, long)}), the first pair of
141 * values that follow any common prefix, or when one array is a prefix of the other, treats the
142 * shorter array as the lesser. For example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
143 *
144 * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
145 * support only identity equality), but it is consistent with
146 * {@link Arrays#equals(long[], long[])}.
147 *
148 * @see <a href="http://en.wikipedia.org/wiki/Lexicographical_order">Lexicographical order
149 * article at Wikipedia</a>
150 */
151 public static Comparator<long[]> lexicographicalComparator() {
152 return LexicographicalComparator.INSTANCE;
153 }
154
155 enum LexicographicalComparator implements Comparator<long[]> {
156 INSTANCE;
157
158 @Override
159 public int compare(long[] left, long[] right) {
160 int minLength = Math.min(left.length, right.length);
161 for (int i = 0; i < minLength; i++) {
162 if (left[i] != right[i]) {
163 return UnsignedLongs.compare(left[i], right[i]);
164 }
165 }
166 return left.length - right.length;
167 }
168 }
169
170 /**
171 * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
172 * quantities.
173 *
174 * @param dividend the dividend (numerator)
175 * @param divisor the divisor (denominator)
176 * @throws ArithmeticException if divisor is 0
177 */
178 public static long divide(long dividend, long divisor) {
179 if (divisor < 0) { // i.e., divisor >= 2^63:
180 if (compare(dividend, divisor) < 0) {
181 return 0; // dividend < divisor
182 } else {
183 return 1; // dividend >= divisor
184 }
185 }
186
187 // Optimization - use signed division if dividend < 2^63
188 if (dividend >= 0) {
189 return dividend / divisor;
190 }
191
192 /*
193 * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
194 * guaranteed to be either exact or one less than the correct value. This follows from fact
195 * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
196 * quite trivial.
197 */
198 long quotient = ((dividend >>> 1) / divisor) << 1;
199 long rem = dividend - quotient * divisor;
200 return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
201 }
202
203 /**
204 * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
205 * quantities.
206 *
207 * @param dividend the dividend (numerator)
208 * @param divisor the divisor (denominator)
209 * @throws ArithmeticException if divisor is 0
210 * @since 11.0
211 */
212 public static long remainder(long dividend, long divisor) {
213 if (divisor < 0) { // i.e., divisor >= 2^63:
214 if (compare(dividend, divisor) < 0) {
215 return dividend; // dividend < divisor
216 } else {
217 return dividend - divisor; // dividend >= divisor
218 }
219 }
220
221 // Optimization - use signed modulus if dividend < 2^63
222 if (dividend >= 0) {
223 return dividend % divisor;
224 }
225
226 /*
227 * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
228 * guaranteed to be either exact or one less than the correct value. This follows from fact
229 * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
230 * quite trivial.
231 */
232 long quotient = ((dividend >>> 1) / divisor) << 1;
233 long rem = dividend - quotient * divisor;
234 return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
235 }
236
237 /**
238 * Returns the unsigned {@code long} value represented by the given decimal string.
239 *
240 * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
241 * value
242 */
243 public static long parseUnsignedLong(String s) {
244 return parseUnsignedLong(s, 10);
245 }
246
247 /**
248 * Returns the unsigned {@code long} value represented by a string with the given radix.
249 *
250 * @param s the string containing the unsigned {@code long} representation to be parsed.
251 * @param radix the radix to use while parsing {@code s}
252 * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
253 * with the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX}
254 * and {@link Character#MAX_RADIX}.
255 */
256 public static long parseUnsignedLong(String s, int radix) {
257 checkNotNull(s);
258 if (s.length() == 0) {
259 throw new NumberFormatException("empty string");
260 }
261 if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
262 throw new NumberFormatException("illegal radix:" + radix);
263 }
264
265 int max_safe_pos = maxSafeDigits[radix] - 1;
266 long value = 0;
267 for (int pos = 0; pos < s.length(); pos++) {
268 int digit = Character.digit(s.charAt(pos), radix);
269 if (digit == -1) {
270 throw new NumberFormatException(s);
271 }
272 if (pos > max_safe_pos && overflowInParse(value, digit, radix)) {
273 throw new NumberFormatException("Too large for unsigned long: " + s);
274 }
275 value = (value * radix) + digit;
276 }
277
278 return value;
279 }
280
281 /**
282 * Returns true if (current * radix) + digit is a number too large to be represented by an
283 * unsigned long. This is useful for detecting overflow while parsing a string representation of
284 * a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
285 * undefined results or an ArrayIndexOutOfBoundsException.
286 */
287 private static boolean overflowInParse(long current, int digit, int radix) {
288 if (current >= 0) {
289 if (current < maxValueDivs[radix]) {
290 return false;
291 }
292 if (current > maxValueDivs[radix]) {
293 return true;
294 }
295 // current == maxValueDivs[radix]
296 return (digit > maxValueMods[radix]);
297 }
298
299 // current < 0: high bit is set
300 return true;
301 }
302
303 /**
304 * Returns a string representation of x, where x is treated as unsigned.
305 */
306 public static String toString(long x) {
307 return toString(x, 10);
308 }
309
310 /**
311 * Returns a string representation of {@code x} for the given radix, where {@code x} is treated
312 * as unsigned.
313 *
314 * @param x the value to convert to a string.
315 * @param radix the radix to use while working with {@code x}
316 * @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
317 * and {@link Character#MAX_RADIX}.
318 */
319 public static String toString(long x, int radix) {
320 checkArgument(radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
321 "radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX", radix);
322 if (x == 0) {
323 // Simply return "0"
324 return "0";
325 } else {
326 char[] buf = new char[64];
327 int i = buf.length;
328 if (x < 0) {
329 // Split x into high-order and low-order halves.
330 // Individual digits are generated from the bottom half into which
331 // bits are moved continously from the top half.
332 long top = x >>> 32;
333 long bot = (x & 0xffffffffl) + ((top % radix) << 32);
334 top /= radix;
335 while ((bot > 0) || (top > 0)) {
336 buf[--i] = Character.forDigit((int) (bot % radix), radix);
337 bot = (bot / radix) + ((top % radix) << 32);
338 top /= radix;
339 }
340 } else {
341 // Simple modulo/division approach
342 while (x > 0) {
343 buf[--i] = Character.forDigit((int) (x % radix), radix);
344 x /= radix;
345 }
346 }
347 // Generate string
348 return new String(buf, i, buf.length - i);
349 }
350 }
351
352 // calculated as 0xffffffffffffffff / radix
353 private static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
354 private static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
355 private static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];
356 static {
357 BigInteger overflow = new BigInteger("10000000000000000", 16);
358 for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
359 maxValueDivs[i] = divide(MAX_VALUE, i);
360 maxValueMods[i] = (int) remainder(MAX_VALUE, i);
361 maxSafeDigits[i] = overflow.toString(i).length() - 1;
362 }
363 }
364 }
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