    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}.
    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}.
    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 {@code long} arrays lexicographically. That is, it
    140       * compares, using {@link #compare(long, long)}), the first pair of values that follow any common
    141       * prefix, or when one array is a prefix of the other, treats the shorter array as the lesser.
    142       * For example, {@code [] < [1L] < [1L, 2L] < [2L]}. Values are treated as unsigned.
    143       *
    144       * <p>
    145       * The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
    146       * support only identity equality), but it is consistent with
    147       * {@link Arrays#equals(long[], long[])}.
    148       *
    149       * @see <a href="http://en.wikipedia.org/wiki/Lexicographical_order">Lexicographical order
    150       *      article at Wikipedia</a>
    151       */
    152      public static Comparator<long[]> lexicographicalComparator() {
    153        return LexicographicalComparator.INSTANCE;
    154      }
    155
    156      enum LexicographicalComparator implements Comparator<long[]> {
    157        INSTANCE;
    158
    159        @Override
    160        public int compare(long[] left, long[] right) {
    161          int minLength = Math.min(left.length, right.length);
    162          for (int i = 0; i < minLength; i++) {
    163            if (left[i] != right[i]) {
    164              return UnsignedLongs.compare(left[i], right[i]);
    165            }
    166          }
    167          return left.length - right.length;
    168        }
    169      }
    170
    171      /**
    172       * Returns dividend / divisor, where the dividend and divisor are treated as unsigned 64-bit
    173       * quantities.
    174       *
    175       * @param dividend the dividend (numerator)
    176       * @param divisor the divisor (denominator)
    177       * @throws ArithmeticException if divisor is 0
    178       */
    179      public static long divide(long dividend, long divisor) {
    180        if (divisor < 0) { // i.e., divisor >= 2^63:
    181          if (compare(dividend, divisor) < 0) {
    182            return 0; // dividend < divisor
    183          } else {
    184            return 1; // dividend >= divisor
    185          }
    186        }
    187
    188        // Optimization - use signed division if dividend < 2^63
    189        if (dividend >= 0) {
    190          return dividend / divisor;
    191        }
    192
    193        /*
    194         * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
    195         * guaranteed to be either exact or one less than the correct value. This follows from fact
    196         * that floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not
    197         * quite trivial.
    198         */
    199        long quotient = ((dividend >>> 1) / divisor) << 1;
    200        long rem = dividend - quotient * divisor;
    201        return quotient + (compare(rem, divisor) >= 0 ? 1 : 0);
    202      }
    203
    204      /**
    205       * Returns dividend % divisor, where the dividend and divisor are treated as unsigned 64-bit
    206       * quantities.
    207       *
    208       * @param dividend the dividend (numerator)
    209       * @param divisor the divisor (denominator)
    210       * @throws ArithmeticException if divisor is 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    }