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
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;
022
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
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 * <p>See the Guava User Guide article on <a href=
042 * "http://code.google.com/p/guava-libraries/wiki/PrimitivesExplained#Unsigned_support">
043 * unsigned 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)}
060   * as 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
124   *        string (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
144   * lexicographically. That is, it compares, using {@link #compare(long, long)}), the first pair of
145   * values that follow any common prefix, or when one array is a prefix of the other, treats the
146   * shorter array as the lesser. For example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
147   *
148   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
149   * support only identity equality), but it is consistent with
150   * {@link Arrays#equals(long[], long[])}.
151   *
152   * @see <a href="http://en.wikipedia.org/wiki/Lexicographical_order">Lexicographical order
153   *      article at Wikipedia</a>
154   */
155  public static Comparator<long[]> lexicographicalComparator() {
156    return LexicographicalComparator.INSTANCE;
157  }
158
159  enum LexicographicalComparator implements Comparator<long[]> {
160    INSTANCE;
161
162    @Override
163    public int compare(long[] left, long[] right) {
164      int minLength = Math.min(left.length, right.length);
165      for (int i = 0; i < minLength; i++) {
166        if (left[i] != right[i]) {
167          return UnsignedLongs.compare(left[i], right[i]);
168        }
169      }
170      return left.length - right.length;
171    }
172  }
173
174  /**
175   * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
176   * quantities.
177   *
178   * @param dividend the dividend (numerator)
179   * @param divisor the divisor (denominator)
180   * @throws ArithmeticException if divisor is 0
181   */
182  public static long divide(long dividend, long divisor) {
183    if (divisor < 0) { // i.e., divisor >= 2^63:
184      if (compare(dividend, divisor) < 0) {
185        return 0; // dividend < divisor
186      } else {
187        return 1; // dividend >= divisor
188      }
189    }
190
191    // Optimization - use signed division if dividend < 2^63
192    if (dividend >= 0) {
193      return dividend / divisor;
194    }
195
196    /*
197     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
198     * guaranteed to be either exact or one less than the correct value. This follows from fact
199     * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
200     * quite trivial.
201     */
202    long quotient = ((dividend >>> 1) / divisor) << 1;
203    long rem = dividend - quotient * divisor;
204    return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
205  }
206
207  /**
208   * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
209   * quantities.
210   *
211   * @param dividend the dividend (numerator)
212   * @param divisor the divisor (denominator)
213   * @throws ArithmeticException if divisor is 0
214   * @since 11.0
215   */
216  public static long remainder(long dividend, long divisor) {
217    if (divisor < 0) { // i.e., divisor >= 2^63:
218      if (compare(dividend, divisor) < 0) {
219        return dividend; // dividend < divisor
220      } else {
221        return dividend - divisor; // dividend >= divisor
222      }
223    }
224
225    // Optimization - use signed modulus if dividend < 2^63
226    if (dividend >= 0) {
227      return dividend % divisor;
228    }
229
230    /*
231     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
232     * guaranteed to be either exact or one less than the correct value. This follows from fact
233     * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
234     * quite trivial.
235     */
236    long quotient = ((dividend >>> 1) / divisor) << 1;
237    long rem = dividend - quotient * divisor;
238    return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
239  }
240
241  /**
242   * Returns the unsigned {@code long} value represented by the given decimal string.
243   *
244   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
245   *         value
246   * @throws NullPointerException if {@code s} is null 
247   *         (in contrast to {@link Long#parseLong(String)})
248   */
249  public static long parseUnsignedLong(String s) {
250    return parseUnsignedLong(s, 10);
251  }
252
253  /**
254   * Returns the unsigned {@code long} value represented by the given string.
255   *
256   * Accepts a decimal, hexadecimal, or octal number given by specifying the following prefix:
257   *
258   * <ul>
259   * <li>{@code 0x}<i>HexDigits</i>
260   * <li>{@code 0X}<i>HexDigits</i>
261   * <li>{@code #}<i>HexDigits</i>
262   * <li>{@code 0}<i>OctalDigits</i>
263   * </ul>
264   *
265   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
266   *         value
267   * @since 13.0
268   */
269  public static long decode(String stringValue) {
270    ParseRequest request = ParseRequest.fromString(stringValue);
271
272    try {
273      return parseUnsignedLong(request.rawValue, request.radix);
274    } catch (NumberFormatException e) {
275      NumberFormatException decodeException =
276          new NumberFormatException("Error parsing value: " + stringValue);
277      decodeException.initCause(e);
278      throw decodeException;
279    }
280  }
281
282  /**
283   * Returns the unsigned {@code long} value represented by a string with the given radix.
284   *
285   * @param s the string containing the unsigned {@code long} representation to be parsed.
286   * @param radix the radix to use while parsing {@code s}
287   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
288   *         with the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX}
289   *         and {@link Character#MAX_RADIX}.
290   * @throws NullPointerException if {@code s} is null 
291   *         (in contrast to {@link Long#parseLong(String)})
292   */
293  public static long parseUnsignedLong(String s, int radix) {
294    checkNotNull(s);
295    if (s.length() == 0) {
296      throw new NumberFormatException("empty string");
297    }
298    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
299      throw new NumberFormatException("illegal radix: " + radix);
300    }
301
302    int max_safe_pos = maxSafeDigits[radix] - 1;
303    long value = 0;
304    for (int pos = 0; pos < s.length(); pos++) {
305      int digit = Character.digit(s.charAt(pos), radix);
306      if (digit == -1) {
307        throw new NumberFormatException(s);
308      }
309      if (pos > max_safe_pos && overflowInParse(value, digit, radix)) {
310        throw new NumberFormatException("Too large for unsigned long: " + s);
311      }
312      value = (value * radix) + digit;
313    }
314
315    return value;
316  }
317
318  /**
319   * Returns true if (current * radix) + digit is a number too large to be represented by an
320   * unsigned long. This is useful for detecting overflow while parsing a string representation of
321   * a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
322   * undefined results or an ArrayIndexOutOfBoundsException.
323   */
324  private static boolean overflowInParse(long current, int digit, int radix) {
325    if (current >= 0) {
326      if (current < maxValueDivs[radix]) {
327        return false;
328      }
329      if (current > maxValueDivs[radix]) {
330        return true;
331      }
332      // current == maxValueDivs[radix]
333      return (digit > maxValueMods[radix]);
334    }
335
336    // current < 0: high bit is set
337    return true;
338  }
339
340  /**
341   * Returns a string representation of x, where x is treated as unsigned.
342   */
343  public static String toString(long x) {
344    return toString(x, 10);
345  }
346
347  /**
348   * Returns a string representation of {@code x} for the given radix, where {@code x} is treated
349   * as unsigned.
350   *
351   * @param x the value to convert to a string.
352   * @param radix the radix to use while working with {@code x}
353   * @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
354   *         and {@link Character#MAX_RADIX}.
355   */
356  public static String toString(long x, int radix) {
357    checkArgument(radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
358        "radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX", radix);
359    if (x == 0) {
360      // Simply return "0"
361      return "0";
362    } else {
363      char[] buf = new char[64];
364      int i = buf.length;
365      if (x < 0) {
366        // Separate off the last digit using unsigned division. That will leave
367        // a number that is nonnegative as a signed integer.
368        long quotient = divide(x, radix);
369        long rem = x - quotient * radix;
370        buf[--i] = Character.forDigit((int) rem, radix);
371        x = quotient;
372      }
373      // Simple modulo/division approach
374      while (x > 0) {
375        buf[--i] = Character.forDigit((int) (x % radix), radix);
376        x /= radix;
377      }
378      // Generate string
379      return new String(buf, i, buf.length - i);
380    }
381  }
382
383  // calculated as 0xffffffffffffffff / radix
384  private static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
385  private static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
386  private static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];
387  static {
388    BigInteger overflow = new BigInteger("10000000000000000", 16);
389    for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
390      maxValueDivs[i] = divide(MAX_VALUE, i);
391      maxValueMods[i] = (int) remainder(MAX_VALUE, i);
392      maxSafeDigits[i] = overflow.toString(i).length() - 1;
393    }
394  }
395}