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;
019import static com.google.common.base.Preconditions.checkPositionIndexes;
020
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 {@code
030 * 2^64 + x}). The methods for which signedness is not an issue are in {@link Longs}, as well as
031 * 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 <a
042 * 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@GwtCompatible
051@ElementTypesAreNonnullByDefault
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 {@code
068   * 0} and {@code 2^64 - 1} inclusive.
069   *
070   * <p><b>Java 8 users:</b> use {@link Long#compareUnsigned(long, long)} instead.
071   *
072   * @param a the first unsigned {@code long} to compare
073   * @param b the second unsigned {@code long} to compare
074   * @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
075   *     greater than {@code b}; or zero if they are equal
076   */
077  public static int compare(long a, long b) {
078    return Longs.compare(flip(a), flip(b));
079  }
080
081  /**
082   * Returns the least value present in {@code array}, treating values as unsigned.
083   *
084   * @param array a <i>nonempty</i> array of unsigned {@code long} values
085   * @return the value present in {@code array} that is less than or equal to every other value in
086   *     the array according to {@link #compare}
087   * @throws IllegalArgumentException if {@code array} is empty
088   */
089  public static long min(long... array) {
090    checkArgument(array.length > 0);
091    long min = flip(array[0]);
092    for (int i = 1; i < array.length; i++) {
093      long next = flip(array[i]);
094      if (next < min) {
095        min = next;
096      }
097    }
098    return flip(min);
099  }
100
101  /**
102   * Returns the greatest value present in {@code array}, treating values as unsigned.
103   *
104   * @param array a <i>nonempty</i> array of unsigned {@code long} values
105   * @return the value present in {@code array} that is greater than or equal to every other value
106   *     in the array according to {@link #compare}
107   * @throws IllegalArgumentException if {@code array} is empty
108   */
109  public static long max(long... array) {
110    checkArgument(array.length > 0);
111    long max = flip(array[0]);
112    for (int i = 1; i < array.length; i++) {
113      long next = flip(array[i]);
114      if (next > max) {
115        max = next;
116      }
117    }
118    return flip(max);
119  }
120
121  /**
122   * Returns a string containing the supplied unsigned {@code long} values separated by {@code
123   * separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
124   *
125   * @param separator the text that should appear between consecutive values in the resulting string
126   *     (but not at the start or end)
127   * @param array an array of unsigned {@code long} values, possibly empty
128   */
129  public static String join(String separator, long... array) {
130    checkNotNull(separator);
131    if (array.length == 0) {
132      return "";
133    }
134
135    // For pre-sizing a builder, just get the right order of magnitude
136    StringBuilder builder = new StringBuilder(array.length * 5);
137    builder.append(toString(array[0]));
138    for (int i = 1; i < array.length; i++) {
139      builder.append(separator).append(toString(array[i]));
140    }
141    return builder.toString();
142  }
143
144  /**
145   * Returns a comparator that compares two arrays of unsigned {@code long} values <a
146   * href="http://en.wikipedia.org/wiki/Lexicographical_order">lexicographically</a>. That is, it
147   * compares, using {@link #compare(long, long)}), the first pair of values that follow any common
148   * prefix, or when one array is a prefix of the other, treats the shorter array as the lesser. For
149   * example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
150   *
151   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
152   * support only identity equality), but it is consistent with {@link Arrays#equals(long[],
153   * long[])}.
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    @Override
174    public String toString() {
175      return "UnsignedLongs.lexicographicalComparator()";
176    }
177  }
178
179  /**
180   * Sorts the array, treating its elements as unsigned 64-bit integers.
181   *
182   * @since 23.1
183   */
184  public static void sort(long[] array) {
185    checkNotNull(array);
186    sort(array, 0, array.length);
187  }
188
189  /**
190   * Sorts the array between {@code fromIndex} inclusive and {@code toIndex} exclusive, treating its
191   * elements as unsigned 64-bit integers.
192   *
193   * @since 23.1
194   */
195  public static void sort(long[] array, int fromIndex, int toIndex) {
196    checkNotNull(array);
197    checkPositionIndexes(fromIndex, toIndex, array.length);
198    for (int i = fromIndex; i < toIndex; i++) {
199      array[i] = flip(array[i]);
200    }
201    Arrays.sort(array, fromIndex, toIndex);
202    for (int i = fromIndex; i < toIndex; i++) {
203      array[i] = flip(array[i]);
204    }
205  }
206
207  /**
208   * Sorts the elements of {@code array} in descending order, interpreting them as unsigned 64-bit
209   * integers.
210   *
211   * @since 23.1
212   */
213  public static void sortDescending(long[] array) {
214    checkNotNull(array);
215    sortDescending(array, 0, array.length);
216  }
217
218  /**
219   * Sorts the elements of {@code array} between {@code fromIndex} inclusive and {@code toIndex}
220   * exclusive in descending order, interpreting them as unsigned 64-bit integers.
221   *
222   * @since 23.1
223   */
224  public static void sortDescending(long[] array, int fromIndex, int toIndex) {
225    checkNotNull(array);
226    checkPositionIndexes(fromIndex, toIndex, array.length);
227    for (int i = fromIndex; i < toIndex; i++) {
228      array[i] ^= Long.MAX_VALUE;
229    }
230    Arrays.sort(array, fromIndex, toIndex);
231    for (int i = fromIndex; i < toIndex; i++) {
232      array[i] ^= Long.MAX_VALUE;
233    }
234  }
235
236  /**
237   * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
238   * quantities.
239   *
240   * <p><b>Java 8 users:</b> use {@link Long#divideUnsigned(long, long)} instead.
241   *
242   * @param dividend the dividend (numerator)
243   * @param divisor the divisor (denominator)
244   * @throws ArithmeticException if divisor is 0
245   */
246  public static long divide(long dividend, long divisor) {
247    if (divisor < 0) { // i.e., divisor >= 2^63:
248      if (compare(dividend, divisor) < 0) {
249        return 0; // dividend < divisor
250      } else {
251        return 1; // dividend >= divisor
252      }
253    }
254
255    // Optimization - use signed division if dividend < 2^63
256    if (dividend >= 0) {
257      return dividend / divisor;
258    }
259
260    /*
261     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
262     * guaranteed to be either exact or one less than the correct value. This follows from fact that
263     * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
264     * trivial.
265     */
266    long quotient = ((dividend >>> 1) / divisor) << 1;
267    long rem = dividend - quotient * divisor;
268    return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
269  }
270
271  /**
272   * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
273   * quantities.
274   *
275   * <p><b>Java 8 users:</b> use {@link Long#remainderUnsigned(long, long)} instead.
276   *
277   * @param dividend the dividend (numerator)
278   * @param divisor the divisor (denominator)
279   * @throws ArithmeticException if divisor is 0
280   * @since 11.0
281   */
282  public static long remainder(long dividend, long divisor) {
283    if (divisor < 0) { // i.e., divisor >= 2^63:
284      if (compare(dividend, divisor) < 0) {
285        return dividend; // dividend < divisor
286      } else {
287        return dividend - divisor; // dividend >= divisor
288      }
289    }
290
291    // Optimization - use signed modulus if dividend < 2^63
292    if (dividend >= 0) {
293      return dividend % divisor;
294    }
295
296    /*
297     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
298     * guaranteed to be either exact or one less than the correct value. This follows from the fact
299     * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
300     * quite trivial.
301     */
302    long quotient = ((dividend >>> 1) / divisor) << 1;
303    long rem = dividend - quotient * divisor;
304    return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
305  }
306
307  /**
308   * Returns the unsigned {@code long} value represented by the given decimal string.
309   *
310   * <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String)} instead.
311   *
312   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
313   *     value
314   * @throws NullPointerException if {@code string} is null (in contrast to {@link
315   *     Long#parseLong(String)})
316   */
317  @CanIgnoreReturnValue
318  public static long parseUnsignedLong(String string) {
319    return parseUnsignedLong(string, 10);
320  }
321
322  /**
323   * Returns the unsigned {@code long} value represented by a string with the given radix.
324   *
325   * <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String, int)} instead.
326   *
327   * @param string the string containing the unsigned {@code long} representation to be parsed.
328   * @param radix the radix to use while parsing {@code string}
329   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long} with
330   *     the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX} and {@link
331   *     Character#MAX_RADIX}.
332   * @throws NullPointerException if {@code string} is null (in contrast to {@link
333   *     Long#parseLong(String)})
334   */
335  @CanIgnoreReturnValue
336  public static long parseUnsignedLong(String string, int radix) {
337    checkNotNull(string);
338    if (string.length() == 0) {
339      throw new NumberFormatException("empty string");
340    }
341    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
342      throw new NumberFormatException("illegal radix: " + radix);
343    }
344
345    int maxSafePos = ParseOverflowDetection.maxSafeDigits[radix] - 1;
346    long value = 0;
347    for (int pos = 0; pos < string.length(); pos++) {
348      int digit = Character.digit(string.charAt(pos), radix);
349      if (digit == -1) {
350        throw new NumberFormatException(string);
351      }
352      if (pos > maxSafePos && ParseOverflowDetection.overflowInParse(value, digit, radix)) {
353        throw new NumberFormatException("Too large for unsigned long: " + string);
354      }
355      value = (value * radix) + digit;
356    }
357
358    return value;
359  }
360
361  /**
362   * Returns the unsigned {@code long} value represented by the given string.
363   *
364   * <p>Accepts a decimal, hexadecimal, or octal number given by specifying the following prefix:
365   *
366   * <ul>
367   *   <li>{@code 0x}<i>HexDigits</i>
368   *   <li>{@code 0X}<i>HexDigits</i>
369   *   <li>{@code #}<i>HexDigits</i>
370   *   <li>{@code 0}<i>OctalDigits</i>
371   * </ul>
372   *
373   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
374   *     value
375   * @since 13.0
376   */
377  @CanIgnoreReturnValue
378  public static long decode(String stringValue) {
379    ParseRequest request = ParseRequest.fromString(stringValue);
380
381    try {
382      return parseUnsignedLong(request.rawValue, request.radix);
383    } catch (NumberFormatException e) {
384      NumberFormatException decodeException =
385          new NumberFormatException("Error parsing value: " + stringValue);
386      decodeException.initCause(e);
387      throw decodeException;
388    }
389  }
390
391  /*
392   * We move the static constants into this class so ProGuard can inline UnsignedLongs entirely
393   * unless the user is actually calling a parse method.
394   */
395  private static final class ParseOverflowDetection {
396    private ParseOverflowDetection() {}
397
398    // calculated as 0xffffffffffffffff / radix
399    static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
400    static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
401    static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];
402
403    static {
404      BigInteger overflow = new BigInteger("10000000000000000", 16);
405      for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
406        maxValueDivs[i] = divide(MAX_VALUE, i);
407        maxValueMods[i] = (int) remainder(MAX_VALUE, i);
408        maxSafeDigits[i] = overflow.toString(i).length() - 1;
409      }
410    }
411
412    /**
413     * Returns true if (current * radix) + digit is a number too large to be represented by an
414     * unsigned long. This is useful for detecting overflow while parsing a string representation of
415     * a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
416     * undefined results or an ArrayIndexOutOfBoundsException.
417     */
418    static boolean overflowInParse(long current, int digit, int radix) {
419      if (current >= 0) {
420        if (current < maxValueDivs[radix]) {
421          return false;
422        }
423        if (current > maxValueDivs[radix]) {
424          return true;
425        }
426        // current == maxValueDivs[radix]
427        return (digit > maxValueMods[radix]);
428      }
429
430      // current < 0: high bit is set
431      return true;
432    }
433  }
434
435  /**
436   * Returns a string representation of x, where x is treated as unsigned.
437   *
438   * <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long)} instead.
439   */
440  public static String toString(long x) {
441    return toString(x, 10);
442  }
443
444  /**
445   * Returns a string representation of {@code x} for the given radix, where {@code x} is treated as
446   * unsigned.
447   *
448   * <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long, int)} instead.
449   *
450   * @param x the value to convert to a string.
451   * @param radix the radix to use while working with {@code x}
452   * @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
453   *     and {@link Character#MAX_RADIX}.
454   */
455  public static String toString(long x, int radix) {
456    checkArgument(
457        radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
458        "radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX",
459        radix);
460    if (x == 0) {
461      // Simply return "0"
462      return "0";
463    } else if (x > 0) {
464      return Long.toString(x, radix);
465    } else {
466      char[] buf = new char[64];
467      int i = buf.length;
468      if ((radix & (radix - 1)) == 0) {
469        // Radix is a power of two so we can avoid division.
470        int shift = Integer.numberOfTrailingZeros(radix);
471        int mask = radix - 1;
472        do {
473          buf[--i] = Character.forDigit(((int) x) & mask, radix);
474          x >>>= shift;
475        } while (x != 0);
476      } else {
477        // Separate off the last digit using unsigned division. That will leave
478        // a number that is nonnegative as a signed integer.
479        long quotient;
480        if ((radix & 1) == 0) {
481          // Fast path for the usual case where the radix is even.
482          quotient = (x >>> 1) / (radix >>> 1);
483        } else {
484          quotient = divide(x, radix);
485        }
486        long rem = x - quotient * radix;
487        buf[--i] = Character.forDigit((int) rem, radix);
488        x = quotient;
489        // Simple modulo/division approach
490        while (x > 0) {
491          buf[--i] = Character.forDigit((int) (x % radix), radix);
492          x /= radix;
493        }
494      }
495      // Generate string
496      return new String(buf, i, buf.length - i);
497    }
498  }
499}