Source code

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.Beta;
022import com.google.common.annotations.GwtCompatible;
023import com.google.errorprone.annotations.CanIgnoreReturnValue;
024import java.math.BigInteger;
025import java.util.Arrays;
026import java.util.Comparator;
027
028/**
029 * Static utility methods pertaining to {@code long} primitives that interpret values as
030 * <i>unsigned</i> (that is, any negative value {@code x} is treated as the positive value {@code
031 * 2^64 + x}). The methods for which signedness is not an issue are in {@link Longs}, as well as
032 * signed versions of methods for which signedness is an issue.
033 *
034 * <p>In addition, this class provides several static methods for converting a {@code long} to a
035 * {@code String} and a {@code String} to a {@code long} that treat the {@code long} as an unsigned
036 * number.
037 *
038 * <p>Users of these utilities must be <i>extremely careful</i> not to mix up signed and unsigned
039 * {@code long} values. When possible, it is recommended that the {@link UnsignedLong} wrapper class
040 * be used, at a small efficiency penalty, to enforce the distinction in the type system.
041 *
042 * <p>See the Guava User Guide article on <a
043 * href="https://github.com/google/guava/wiki/PrimitivesExplained#unsigned-support">unsigned
044 * primitive utilities</a>.
045 *
046 * @author Louis Wasserman
047 * @author Brian Milch
048 * @author Colin Evans
049 * @since 10.0
050 */
051@Beta
052@GwtCompatible
053@ElementTypesAreNonnullByDefault
054public final class UnsignedLongs {
055  private UnsignedLongs() {}
056
057  public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1
058
059  /**
060   * A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on
061   * longs, that is, {@code a <= b} as unsigned longs if and only if {@code flip(a) <= flip(b)} as
062   * signed longs.
063   */
064  private static long flip(long a) {
065    return a ^ Long.MIN_VALUE;
066  }
067
068  /**
069   * Compares the two specified {@code long} values, treating them as unsigned values between {@code
070   * 0} and {@code 2^64 - 1} inclusive.
071   *
072   * <p><b>Java 8 users:</b> use {@link Long#compareUnsigned(long, long)} instead.
073   *
074   * @param a the first unsigned {@code long} to compare
075   * @param b the second unsigned {@code long} to compare
076   * @return a negative value if {@code a} is less than {@code b}; a positive value if {@code a} is
077   *     greater than {@code b}; or zero if they are equal
078   */
079  public static int compare(long a, long b) {
080    return Longs.compare(flip(a), flip(b));
081  }
082
083  /**
084   * Returns the least value present in {@code array}, treating values as unsigned.
085   *
086   * @param array a <i>nonempty</i> array of unsigned {@code long} values
087   * @return the value present in {@code array} that is less than or equal to every other value in
088   *     the array according to {@link #compare}
089   * @throws IllegalArgumentException if {@code array} is empty
090   */
091  public static long min(long... array) {
092    checkArgument(array.length > 0);
093    long min = flip(array[0]);
094    for (int i = 1; i < array.length; i++) {
095      long next = flip(array[i]);
096      if (next < min) {
097        min = next;
098      }
099    }
100    return flip(min);
101  }
102
103  /**
104   * Returns the greatest value present in {@code array}, treating values as unsigned.
105   *
106   * @param array a <i>nonempty</i> array of unsigned {@code long} values
107   * @return the value present in {@code array} that is greater than or equal to every other value
108   *     in the array according to {@link #compare}
109   * @throws IllegalArgumentException if {@code array} is empty
110   */
111  public static long max(long... array) {
112    checkArgument(array.length > 0);
113    long max = flip(array[0]);
114    for (int i = 1; i < array.length; i++) {
115      long next = flip(array[i]);
116      if (next > max) {
117        max = next;
118      }
119    }
120    return flip(max);
121  }
122
123  /**
124   * Returns a string containing the supplied unsigned {@code long} values separated by {@code
125   * separator}. For example, {@code join("-", 1, 2, 3)} returns the string {@code "1-2-3"}.
126   *
127   * @param separator the text that should appear between consecutive values in the resulting string
128   *     (but not at the start or end)
129   * @param array an array of unsigned {@code long} values, possibly empty
130   */
131  public static String join(String separator, long... array) {
132    checkNotNull(separator);
133    if (array.length == 0) {
134      return "";
135    }
136
137    // For pre-sizing a builder, just get the right order of magnitude
138    StringBuilder builder = new StringBuilder(array.length * 5);
139    builder.append(toString(array[0]));
140    for (int i = 1; i < array.length; i++) {
141      builder.append(separator).append(toString(array[i]));
142    }
143    return builder.toString();
144  }
145
146  /**
147   * Returns a comparator that compares two arrays of unsigned {@code long} values <a
148   * href="http://en.wikipedia.org/wiki/Lexicographical_order">lexicographically</a>. That is, it
149   * compares, using {@link #compare(long, long)}), the first pair of values that follow any common
150   * prefix, or when one array is a prefix of the other, treats the shorter array as the lesser. For
151   * example, {@code [] < [1L] < [1L, 2L] < [2L] < [1L << 63]}.
152   *
153   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
154   * support only identity equality), but it is consistent with {@link Arrays#equals(long[],
155   * long[])}.
156   */
157  public static Comparator<long[]> lexicographicalComparator() {
158    return LexicographicalComparator.INSTANCE;
159  }
160
161  enum LexicographicalComparator implements Comparator<long[]> {
162    INSTANCE;
163
164    @Override
165    public int compare(long[] left, long[] right) {
166      int minLength = Math.min(left.length, right.length);
167      for (int i = 0; i < minLength; i++) {
168        if (left[i] != right[i]) {
169          return UnsignedLongs.compare(left[i], right[i]);
170        }
171      }
172      return left.length - right.length;
173    }
174
175    @Override
176    public String toString() {
177      return "UnsignedLongs.lexicographicalComparator()";
178    }
179  }
180
181  /**
182   * Sorts the array, treating its elements as unsigned 64-bit integers.
183   *
184   * @since 23.1
185   */
186  public static void sort(long[] array) {
187    checkNotNull(array);
188    sort(array, 0, array.length);
189  }
190
191  /**
192   * Sorts the array between {@code fromIndex} inclusive and {@code toIndex} exclusive, treating its
193   * elements as unsigned 64-bit integers.
194   *
195   * @since 23.1
196   */
197  public static void sort(long[] array, int fromIndex, int toIndex) {
198    checkNotNull(array);
199    checkPositionIndexes(fromIndex, toIndex, array.length);
200    for (int i = fromIndex; i < toIndex; i++) {
201      array[i] = flip(array[i]);
202    }
203    Arrays.sort(array, fromIndex, toIndex);
204    for (int i = fromIndex; i < toIndex; i++) {
205      array[i] = flip(array[i]);
206    }
207  }
208
209  /**
210   * Sorts the elements of {@code array} in descending order, interpreting them as unsigned 64-bit
211   * integers.
212   *
213   * @since 23.1
214   */
215  public static void sortDescending(long[] array) {
216    checkNotNull(array);
217    sortDescending(array, 0, array.length);
218  }
219
220  /**
221   * Sorts the elements of {@code array} between {@code fromIndex} inclusive and {@code toIndex}
222   * exclusive in descending order, interpreting them as unsigned 64-bit integers.
223   *
224   * @since 23.1
225   */
226  public static void sortDescending(long[] array, int fromIndex, int toIndex) {
227    checkNotNull(array);
228    checkPositionIndexes(fromIndex, toIndex, array.length);
229    for (int i = fromIndex; i < toIndex; i++) {
230      array[i] ^= Long.MAX_VALUE;
231    }
232    Arrays.sort(array, fromIndex, toIndex);
233    for (int i = fromIndex; i < toIndex; i++) {
234      array[i] ^= Long.MAX_VALUE;
235    }
236  }
237
238  /**
239   * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
240   * quantities.
241   *
242   * <p><b>Java 8 users:</b> use {@link Long#divideUnsigned(long, long)} instead.
243   *
244   * @param dividend the dividend (numerator)
245   * @param divisor the divisor (denominator)
246   * @throws ArithmeticException if divisor is 0
247   */
248  public static long divide(long dividend, long divisor) {
249    if (divisor < 0) { // i.e., divisor >= 2^63:
250      if (compare(dividend, divisor) < 0) {
251        return 0; // dividend < divisor
252      } else {
253        return 1; // dividend >= divisor
254      }
255    }
256
257    // Optimization - use signed division if dividend < 2^63
258    if (dividend >= 0) {
259      return dividend / divisor;
260    }
261
262    /*
263     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
264     * guaranteed to be either exact or one less than the correct value. This follows from fact that
265     * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
266     * trivial.
267     */
268    long quotient = ((dividend >>> 1) / divisor) << 1;
269    long rem = dividend - quotient * divisor;
270    return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
271  }
272
273  /**
274   * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
275   * quantities.
276   *
277   * <p><b>Java 8 users:</b> use {@link Long#remainderUnsigned(long, long)} instead.
278   *
279   * @param dividend the dividend (numerator)
280   * @param divisor the divisor (denominator)
281   * @throws ArithmeticException if divisor is 0
282   * @since 11.0
283   */
284  public static long remainder(long dividend, long divisor) {
285    if (divisor < 0) { // i.e., divisor >= 2^63:
286      if (compare(dividend, divisor) < 0) {
287        return dividend; // dividend < divisor
288      } else {
289        return dividend - divisor; // dividend >= divisor
290      }
291    }
292
293    // Optimization - use signed modulus if dividend < 2^63
294    if (dividend >= 0) {
295      return dividend % divisor;
296    }
297
298    /*
299     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
300     * guaranteed to be either exact or one less than the correct value. This follows from the fact
301     * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
302     * quite trivial.
303     */
304    long quotient = ((dividend >>> 1) / divisor) << 1;
305    long rem = dividend - quotient * divisor;
306    return rem - (compare(rem, divisor) >= 0 ? divisor : 0);
307  }
308
309  /**
310   * Returns the unsigned {@code long} value represented by the given decimal string.
311   *
312   * <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String)} instead.
313   *
314   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
315   *     value
316   * @throws NullPointerException if {@code string} is null (in contrast to {@link
317   *     Long#parseLong(String)})
318   */
319  @CanIgnoreReturnValue
320  public static long parseUnsignedLong(String string) {
321    return parseUnsignedLong(string, 10);
322  }
323
324  /**
325   * Returns the unsigned {@code long} value represented by a string with the given radix.
326   *
327   * <p><b>Java 8 users:</b> use {@link Long#parseUnsignedLong(String, int)} instead.
328   *
329   * @param string the string containing the unsigned {@code long} representation to be parsed.
330   * @param radix the radix to use while parsing {@code string}
331   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long} with
332   *     the given radix, or if {@code radix} is not between {@link Character#MIN_RADIX} and {@link
333   *     Character#MAX_RADIX}.
334   * @throws NullPointerException if {@code string} is null (in contrast to {@link
335   *     Long#parseLong(String)})
336   */
337  @CanIgnoreReturnValue
338  public static long parseUnsignedLong(String string, int radix) {
339    checkNotNull(string);
340    if (string.length() == 0) {
341      throw new NumberFormatException("empty string");
342    }
343    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
344      throw new NumberFormatException("illegal radix: " + radix);
345    }
346
347    int maxSafePos = ParseOverflowDetection.maxSafeDigits[radix] - 1;
348    long value = 0;
349    for (int pos = 0; pos < string.length(); pos++) {
350      int digit = Character.digit(string.charAt(pos), radix);
351      if (digit == -1) {
352        throw new NumberFormatException(string);
353      }
354      if (pos > maxSafePos && ParseOverflowDetection.overflowInParse(value, digit, radix)) {
355        throw new NumberFormatException("Too large for unsigned long: " + string);
356      }
357      value = (value * radix) + digit;
358    }
359
360    return value;
361  }
362
363  /**
364   * Returns the unsigned {@code long} value represented by the given string.
365   *
366   * <p>Accepts a decimal, hexadecimal, or octal number given by specifying the following prefix:
367   *
368   * <ul>
369   *   <li>{@code 0x}<i>HexDigits</i>
370   *   <li>{@code 0X}<i>HexDigits</i>
371   *   <li>{@code #}<i>HexDigits</i>
372   *   <li>{@code 0}<i>OctalDigits</i>
373   * </ul>
374   *
375   * @throws NumberFormatException if the string does not contain a valid unsigned {@code long}
376   *     value
377   * @since 13.0
378   */
379  @CanIgnoreReturnValue
380  public static long decode(String stringValue) {
381    ParseRequest request = ParseRequest.fromString(stringValue);
382
383    try {
384      return parseUnsignedLong(request.rawValue, request.radix);
385    } catch (NumberFormatException e) {
386      NumberFormatException decodeException =
387          new NumberFormatException("Error parsing value: " + stringValue);
388      decodeException.initCause(e);
389      throw decodeException;
390    }
391  }
392
393  /*
394   * We move the static constants into this class so ProGuard can inline UnsignedLongs entirely
395   * unless the user is actually calling a parse method.
396   */
397  private static final class ParseOverflowDetection {
398    private ParseOverflowDetection() {}
399
400    // calculated as 0xffffffffffffffff / radix
401    static final long[] maxValueDivs = new long[Character.MAX_RADIX + 1];
402    static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
403    static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];
404
405    static {
406      BigInteger overflow = new BigInteger("10000000000000000", 16);
407      for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
408        maxValueDivs[i] = divide(MAX_VALUE, i);
409        maxValueMods[i] = (int) remainder(MAX_VALUE, i);
410        maxSafeDigits[i] = overflow.toString(i).length() - 1;
411      }
412    }
413
414    /**
415     * Returns true if (current * radix) + digit is a number too large to be represented by an
416     * unsigned long. This is useful for detecting overflow while parsing a string representation of
417     * a number. Does not verify whether supplied radix is valid, passing an invalid radix will give
418     * undefined results or an ArrayIndexOutOfBoundsException.
419     */
420    static boolean overflowInParse(long current, int digit, int radix) {
421      if (current >= 0) {
422        if (current < maxValueDivs[radix]) {
423          return false;
424        }
425        if (current > maxValueDivs[radix]) {
426          return true;
427        }
428        // current == maxValueDivs[radix]
429        return (digit > maxValueMods[radix]);
430      }
431
432      // current < 0: high bit is set
433      return true;
434    }
435  }
436
437  /**
438   * Returns a string representation of x, where x is treated as unsigned.
439   *
440   * <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long)} instead.
441   */
442  public static String toString(long x) {
443    return toString(x, 10);
444  }
445
446  /**
447   * Returns a string representation of {@code x} for the given radix, where {@code x} is treated as
448   * unsigned.
449   *
450   * <p><b>Java 8 users:</b> use {@link Long#toUnsignedString(long, int)} instead.
451   *
452   * @param x the value to convert to a string.
453   * @param radix the radix to use while working with {@code x}
454   * @throws IllegalArgumentException if {@code radix} is not between {@link Character#MIN_RADIX}
455   *     and {@link Character#MAX_RADIX}.
456   */
457  public static String toString(long x, int radix) {
458    checkArgument(
459        radix >= Character.MIN_RADIX && radix <= Character.MAX_RADIX,
460        "radix (%s) must be between Character.MIN_RADIX and Character.MAX_RADIX",
461        radix);
462    if (x == 0) {
463      // Simply return "0"
464      return "0";
465    } else if (x > 0) {
466      return Long.toString(x, radix);
467    } else {
468      char[] buf = new char[64];
469      int i = buf.length;
470      if ((radix & (radix - 1)) == 0) {
471        // Radix is a power of two so we can avoid division.
472        int shift = Integer.numberOfTrailingZeros(radix);
473        int mask = radix - 1;
474        do {
475          buf[--i] = Character.forDigit(((int) x) & mask, radix);
476          x >>>= shift;
477        } while (x != 0);
478      } else {
479        // Separate off the last digit using unsigned division. That will leave
480        // a number that is nonnegative as a signed integer.
481        long quotient;
482        if ((radix & 1) == 0) {
483          // Fast path for the usual case where the radix is even.
484          quotient = (x >>> 1) / (radix >>> 1);
485        } else {
486          quotient = divide(x, radix);
487        }
488        long rem = x - quotient * radix;
489        buf[--i] = Character.forDigit((int) rem, radix);
490        x = quotient;
491        // Simple modulo/division approach
492        while (x > 0) {
493          buf[--i] = Character.forDigit((int) (x % radix), radix);
494          x /= radix;
495        }
496      }
497      // Generate string
498      return new String(buf, i, buf.length - i);
499    }
500  }
501}