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 License
010 * is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
011 * or implied. See the License for the specific language governing permissions and limitations under
012 * the License.
013 */
014
015package com.google.common.primitives;
016
017import static com.google.common.base.Preconditions.checkArgument;
018import static com.google.common.base.Preconditions.checkNotNull;
019
020import com.google.common.annotations.Beta;
021import com.google.common.annotations.GwtCompatible;
022import com.google.errorprone.annotations.CanIgnoreReturnValue;
023import java.math.BigInteger;
024import java.util.Arrays;
025import java.util.Comparator;
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 well
031 * 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 class
039 * be used, at a small efficiency penalty, to enforce the distinction in the type system.
040 *
041 * <p>See the Guava User Guide article on
042 * <a href="https://github.com/google/guava/wiki/PrimitivesExplained#unsigned-support">unsigned
043 * primitive utilities</a>.
044 *
045 * @author Louis Wasserman
046 * @author Brian Milch
047 * @author Colin Evans
048 * @since 10.0
049 */
050@Beta
051@GwtCompatible
052public final class UnsignedLongs {
053  private UnsignedLongs() {}
054
055  public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1
056
057  /**
058   * A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on
059   * longs, that is, {@code a <= b} as unsigned longs if and only if {@code flip(a) <= flip(b)} as
060   * signed longs.
061   */
062  private static long flip(long a) {
063    return a ^ Long.MIN_VALUE;
064  }
065
066  /**
067   * Compares the two specified {@code long} values, treating them as unsigned values between
068   * {@code 0} and {@code 2^64 - 1} inclusive.
069   *
070   * @param a the first unsigned {@code long} to compare
071   * @param b the second unsigned {@code long} to compare
072   * @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
073   *     greater than {@code b}; or zero if they are equal
074   */
075  public static int compare(long a, long b) {
076    return Longs.compare(flip(a), flip(b));
077  }
078
079  /**
080   * Returns the least value present in {@code array}, treating values as unsigned.
081   *
082   * @param array a <i>nonempty</i> array of unsigned {@code long} values
083   * @return the value present in {@code array} that is less than or equal to every other value in
084   *     the array according to {@link #compare}
085   * @throws IllegalArgumentException if {@code array} is empty
086   */
087  public static long min(long... array) {
088    checkArgument(array.length > 0);
089    long min = flip(array[0]);
090    for (int i = 1; i < array.length; i++) {
091      long next = flip(array[i]);
092      if (next < min) {
093        min = next;
094      }
095    }
096    return flip(min);
097  }
098
099  /**
100   * Returns the greatest value present in {@code array}, treating values as unsigned.
101   *
102   * @param array a <i>nonempty</i> array of unsigned {@code long} values
103   * @return the value present in {@code array} that is greater than or equal to every other value
104   *     in the array according to {@link #compare}
105   * @throws IllegalArgumentException if {@code array} is empty
106   */
107  public static long max(long... array) {
108    checkArgument(array.length > 0);
109    long max = flip(array[0]);
110    for (int i = 1; i < array.length; i++) {
111      long next = flip(array[i]);
112      if (next > max) {
113        max = next;
114      }
115    }
116    return flip(max);
117  }
118
119  /**
120   * Returns a string containing the supplied unsigned {@code long} values separated by
121   * {@code separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
122   *
123   * @param separator the text that should appear between consecutive values in the resulting string
124   *     (but not at the start or end)
125   * @param array an array of unsigned {@code long} values, possibly empty
126   */
127  public static String join(String separator, long... array) {
128    checkNotNull(separator);
129    if (array.length == 0) {
130      return "";
131    }
132
133    // For pre-sizing a builder, just get the right order of magnitude
134    StringBuilder builder = new StringBuilder(array.length * 5);
135    builder.append(toString(array[0]));
136    for (int i = 1; i < array.length; i++) {
137      builder.append(separator).append(toString(array[i]));
138    }
139    return builder.toString();
140  }
141
142  /**
143   * Returns a comparator that compares two arrays of unsigned {@code long} values <a
144   * href="http://en.wikipedia.org/wiki/Lexicographical_order">lexicographically</a>. That is, it
145   * compares, using {@link #compare(long, long)}), the first pair of values that follow any common
146   * prefix, or when one array is a prefix of the other, treats the shorter array as the lesser. For
147   * example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
148   *
149   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
150   * support only identity equality), but it is consistent with
151   * {@link Arrays#equals(long[], long[])}.
152   */
153  public static Comparator<long[]> lexicographicalComparator() {
154    return LexicographicalComparator.INSTANCE;
155  }
156
157  enum LexicographicalComparator implements Comparator<long[]> {
158    INSTANCE;
159
160    @Override
161    public int compare(long[] left, long[] right) {
162      int minLength = Math.min(left.length, right.length);
163      for (int i = 0; i < minLength; i++) {
164        if (left[i] != right[i]) {
165          return UnsignedLongs.compare(left[i], right[i]);
166        }
167      }
168      return left.length - right.length;
169    }
170
171    @Override
172    public String toString() {
173      return "UnsignedLongs.lexicographicalComparator()";
174    }
175  }
176
177  /**
178   * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
179   * quantities.
180   *
181   * @param dividend the dividend (numerator)
182   * @param divisor the divisor (denominator)
183   * @throws ArithmeticException if divisor is 0
184   */
185  public static long divide(long dividend, long divisor) {
186    if (divisor < 0) { // i.e., divisor >= 2^63:
187      if (compare(dividend, divisor) < 0) {
188        return 0; // dividend < divisor
189      } else {
190        return 1; // dividend >= divisor
191      }
192    }
193
194    // Optimization - use signed division if dividend < 2^63
195    if (dividend >= 0) {
196      return dividend / divisor;
197    }
198
199    /*
200     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
201     * guaranteed to be either exact or one less than the correct value. This follows from fact that
202     * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
203     * trivial.
204     */
205    long quotient = ((dividend >>> 1) / divisor) << 1;
206    long rem = dividend - quotient * divisor;
207    return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
208  }
209
210  /**
211   * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
212   * quantities.
213   *
214   * @param dividend the dividend (numerator)
215   * @param divisor the divisor (denominator)
216   * @throws ArithmeticException if divisor is 0
217   * @since 11.0
218   */
219  public static long remainder(long dividend, long divisor) {
220    if (divisor < 0) { // i.e., divisor >= 2^63:
221      if (compare(dividend, divisor) < 0) {
222        return dividend; // dividend < divisor
223      } else {
224        return dividend - divisor; // dividend >= divisor
225      }
226    }
227
228    // Optimization - use signed modulus if dividend < 2^63
229    if (dividend >= 0) {
230      return dividend % divisor;
231    }
232
233    /*
234     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
235     * guaranteed to be either exact or one less than the correct value. This follows from the fact
236     * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
237     * quite trivial.
238     */
239    long quotient = ((dividend >>> 1) / divisor) << 1;
240    long rem = dividend - quotient * divisor;
241    return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
242  }
243
244  /**
245   * Returns the unsigned {@code long} value represented by the given decimal string.
246   *
247   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
248   *     value
249   * @throws NullPointerException if {@code string} is null (in contrast to
250   *     {@link Long#parseLong(String)})
251   */
252  @CanIgnoreReturnValue
253  public static long parseUnsignedLong(String string) {
254    return parseUnsignedLong(string, 10);
255  }
256
257  /**
258   * Returns the unsigned {@code long} value represented by the given string.
259   *
260   * Accepts a decimal, hexadecimal, or octal number given by specifying the following prefix:
261   *
262   * <ul>
263   * <li>{@code 0x}<i>HexDigits</i>
264   * <li>{@code 0X}<i>HexDigits</i>
265   * <li>{@code #}<i>HexDigits</i>
266   * <li>{@code 0}<i>OctalDigits</i>
267   * </ul>
268   *
269   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
270   *     value
271   * @since 13.0
272   */
273  @CanIgnoreReturnValue
274  public static long decode(String stringValue) {
275    ParseRequest request = ParseRequest.fromString(stringValue);
276
277    try {
278      return parseUnsignedLong(request.rawValue, request.radix);
279    } catch (NumberFormatException e) {
280      NumberFormatException decodeException =
281          new NumberFormatException("Error parsing value: " + stringValue);
282      decodeException.initCause(e);
283      throw decodeException;
284    }
285  }
286
287  /**
288   * Returns the unsigned {@code long} value represented by a string with the given radix.
289   *
290   * @param string the string containing the unsigned {@code long} representation to be parsed.
291   * @param radix the radix to use while parsing {@code string}
292   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long} with
293   *     the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX} and
294   *     {@link Character#MAX_RADIX}.
295   * @throws NullPointerException if {@code string} is null (in contrast to
296   *     {@link Long#parseLong(String)})
297   */
298  @CanIgnoreReturnValue
299  public static long parseUnsignedLong(String string, int radix) {
300    checkNotNull(string);
301    if (string.length() == 0) {
302      throw new NumberFormatException("empty string");
303    }
304    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
305      throw new NumberFormatException("illegal radix: " + radix);
306    }
307
308    int maxSafePos = maxSafeDigits[radix] - 1;
309    long value = 0;
310    for (int pos = 0; pos < string.length(); pos++) {
311      int digit = Character.digit(string.charAt(pos), radix);
312      if (digit == -1) {
313        throw new NumberFormatException(string);
314      }
315      if (pos > maxSafePos && overflowInParse(value, digit, radix)) {
316        throw new NumberFormatException("Too large for unsigned long: " + string);
317      }
318      value = (value * radix) + digit;
319    }
320
321    return value;
322  }
323
324  /**
325   * Returns true if (current * radix) + digit is a number too large to be represented by an
326   * unsigned long. This is useful for detecting overflow while parsing a string representation of a
327   * number. Does not verify whether supplied radix is valid, passing an invalid radix will give
328   * undefined results or an ArrayIndexOutOfBoundsException.
329   */
330  private static boolean overflowInParse(long current, int digit, int radix) {
331    if (current >= 0) {
332      if (current < maxValueDivs[radix]) {
333        return false;
334      }
335      if (current > maxValueDivs[radix]) {
336        return true;
337      }
338      // current == maxValueDivs[radix]
339      return (digit > maxValueMods[radix]);
340    }
341
342    // current < 0: high bit is set
343    return true;
344  }
345
346  /**
347   * Returns a string representation of x, where x is treated as unsigned.
348   */
349  public static String toString(long x) {
350    return toString(x, 10);
351  }
352
353  /**
354   * Returns a string representation of {@code x} for the given radix, where {@code x} is treated as
355   * unsigned.
356   *
357   * @param x the value to convert to a string.
358   * @param radix the radix to use while working with {@code x}
359   * @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
360   *     and {@link Character#MAX_RADIX}.
361   */
362  public static String toString(long x, int radix) {
363    checkArgument(
364        radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
365        "radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX",
366        radix);
367    if (x == 0) {
368      // Simply return "0"
369      return "0";
370    } else if (x > 0) {
371      return Long.toString(x, radix);
372    } else {
373      char[] buf = new char[64];
374      int i = buf.length;
375      if ((radix & (radix - 1)) == 0) {
376        // Radix is a power of two so we can avoid division.
377        int shift = Integer.numberOfTrailingZeros(radix);
378        int mask = radix - 1;
379        do {
380          buf[--i] = Character.forDigit(((int) x) & mask, radix);
381          x >>>= shift;
382        } while (x != 0);
383      } else {
384        // Separate off the last digit using unsigned division. That will leave
385        // a number that is nonnegative as a signed integer.
386        long quotient;
387        if ((radix & 1) == 0) {
388          // Fast path for the usual case where the radix is even.
389          quotient = (x >>> 1) / (radix >>> 1);
390        } else {
391          quotient = divide(x, radix);
392        }
393        long rem = x - quotient * radix;
394        buf[--i] = Character.forDigit((int) rem, radix);
395        x = quotient;
396        // Simple modulo/division approach
397        while (x > 0) {
398          buf[--i] = Character.forDigit((int) (x % radix), radix);
399          x /= radix;
400        }
401      }
402      // Generate string
403      return new String(buf, i, buf.length - i);
404    }
405  }
406
407  // calculated as 0xffffffffffffffff / radix
408  private static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
409  private static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
410  private static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];
411
412  static {
413    BigInteger overflow = new BigInteger("10000000000000000", 16);
414    for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
415      maxValueDivs[i] = divide(MAX_VALUE, i);
416      maxValueMods[i] = (int) remainder(MAX_VALUE, i);
417      maxSafeDigits[i] = overflow.toString(i).length() - 1;
418    }
419  }
420}