/**
    * Licensed to the Apache Software Foundation (ASF) under one
    * or more contributor license agreements.  See the NOTICE file
    * distributed with this work for additional information
    * regarding copyright ownership.  The ASF licenses this file
    * to you under the Apache License, Version 2.0 (the
    * "License"); you may not use this file except in compliance
    * with the License.  You may obtain a copy of the License at
    *
   *     http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.hadoop.hbase.util;
  
  import static org.apache.hadoop.hbase.util.Order.ASCENDING;
  import static org.apache.hadoop.hbase.util.Order.DESCENDING;
  
  import java.math.BigDecimal;
  import java.math.BigInteger;
  import java.math.MathContext;
  import java.math.RoundingMode;
  import java.nio.charset.Charset;
  
  import org.apache.hadoop.hbase.classification.InterfaceAudience;
  import org.apache.hadoop.hbase.classification.InterfaceStability;
  
  /**
   * Utility class that handles ordered byte arrays. That is, unlike
   * {@link Bytes}, these methods produce byte arrays which maintain the sort
   * order of the original values.
   * <h3>Encoding Format summary</h3>
   * <p>
   * Each value is encoded as one or more bytes. The first byte of the encoding,
   * its meaning, and a terse description of the bytes that follow is given by
   * the following table:
   * </p>
   * <table summary="Encodings">
   * <tr><th>Content Type</th><th>Encoding</th></tr>
   * <tr><td>NULL</td><td>0x05</td></tr>
   * <tr><td>negative infinity</td><td>0x07</td></tr>
   * <tr><td>negative large</td><td>0x08, ~E, ~M</td></tr>
   * <tr><td>negative medium</td><td>0x13-E, ~M</td></tr>
   * <tr><td>negative small</td><td>0x14, -E, ~M</td></tr>
   * <tr><td>zero</td><td>0x15</td></tr>
   * <tr><td>positive small</td><td>0x16, ~-E, M</td></tr>
   * <tr><td>positive medium</td><td>0x17+E, M</td></tr>
   * <tr><td>positive large</td><td>0x22, E, M</td></tr>
   * <tr><td>positive infinity</td><td>0x23</td></tr>
   * <tr><td>NaN</td><td>0x25</td></tr>
   * <tr><td>fixed-length 32-bit integer</td><td>0x27, I</td></tr>
   * <tr><td>fixed-length 64-bit integer</td><td>0x28, I</td></tr>
   * <tr><td>fixed-length 8-bit integer</td><td>0x29</td></tr>
   * <tr><td>fixed-length 16-bit integer</td><td>0x2a</td></tr>
   * <tr><td>fixed-length 32-bit float</td><td>0x30, F</td></tr>
   * <tr><td>fixed-length 64-bit float</td><td>0x31, F</td></tr>
   * <tr><td>TEXT</td><td>0x33, T</td></tr>
   * <tr><td>variable length BLOB</td><td>0x35, B</td></tr>
   * <tr><td>byte-for-byte BLOB</td><td>0x36, X</td></tr>
   * </table>
   *
   * <h3>Null Encoding</h3>
   * <p>
   * Each value that is a NULL encodes as a single byte of 0x05. Since every
   * other value encoding begins with a byte greater than 0x05, this forces NULL
   * values to sort first.
   * </p>
   * <h3>Text Encoding</h3>
   * <p>
   * Each text value begins with a single byte of 0x33 and ends with a single
   * byte of 0x00. There are zero or more intervening bytes that encode the text
   * value. The intervening bytes are chosen so that the encoding will sort in
   * the desired collating order. The intervening bytes may not contain a 0x00
   * character; the only 0x00 byte allowed in a text encoding is the final byte.
   * </p>
   * <p>
   * The text encoding ends in 0x00 in order to ensure that when there are two
   * strings where one is a prefix of the other that the shorter string will
   * sort first.
   * </p>
   * <h3>Binary Encoding</h3>
   * <p>
   * There are two encoding strategies for binary fields, referred to as
   * "BlobVar" and "BlobCopy". BlobVar is less efficient in both space and
   * encoding time. It has no limitations on the range of encoded values.
   * BlobCopy is a byte-for-byte copy of the input data followed by a
   * termination byte. It is extremely fast to encode and decode. It carries the
   * restriction of not allowing a 0x00 value in the input byte[] as this value
   * is used as the termination byte.
   * </p>
   * <h4>BlobVar</h4>
   * <p>
   * "BlobVar" encodes the input byte[] in a manner similar to a variable length
   * integer encoding. As with the other {@code OrderedBytes} encodings,
   * the first encoded byte is used to indicate what kind of value follows. This
  * header byte is 0x37 for BlobVar encoded values. As with the traditional
  * varint encoding, the most significant bit of each subsequent encoded
  * {@code byte} is used as a continuation marker. The 7 remaining bits
  * contain the 7 most significant bits of the first unencoded byte. The next
  * encoded byte starts with a continuation marker in the MSB. The least
  * significant bit from the first unencoded byte follows, and the remaining 6
  * bits contain the 6 MSBs of the second unencoded byte. The encoding
  * continues, encoding 7 bytes on to 8 encoded bytes. The MSB of the final
  * encoded byte contains a termination marker rather than a continuation
  * marker, and any remaining bits from the final input byte. Any trailing bits
  * in the final encoded byte are zeros.
  * </p>
  * <h4>BlobCopy</h4>
  * <p>
  * "BlobCopy" is a simple byte-for-byte copy of the input data. It uses 0x38
  * as the header byte, and is terminated by 0x00 in the DESCENDING case. This
  * alternative encoding is faster and more space-efficient, but it cannot
  * accept values containing a 0x00 byte in DESCENDING order.
  * </p>
  * <h3>Variable-length Numeric Encoding</h3>
  * <p>
  * Numeric values must be coded so as to sort in numeric order. We assume that
  * numeric values can be both integer and floating point values. Clients must
  * be careful to use inspection methods for encoded values (such as
  * {@link #isNumericInfinite(PositionedByteRange)} and
  * {@link #isNumericNaN(PositionedByteRange)} to protect against decoding
  * values into object which do not support these numeric concepts (such as
  * {@link Long} and {@link BigDecimal}).
  * </p>
  * <p>
  * Simplest cases first: If the numeric value is a NaN, then the encoding is a
  * single byte of 0x25. This causes NaN values to sort after every other
  * numeric value.
  * </p>
  * <p>
  * If the numeric value is a negative infinity then the encoding is a single
  * byte of 0x07. Since every other numeric value except NaN has a larger
  * initial byte, this encoding ensures that negative infinity will sort prior
  * to every other numeric value other than NaN.
  * </p>
  * <p>
  * If the numeric value is a positive infinity then the encoding is a single
  * byte of 0x23. Every other numeric value encoding begins with a smaller
  * byte, ensuring that positive infinity always sorts last among numeric
  * values. 0x23 is also smaller than 0x33, the initial byte of a text value,
  * ensuring that every numeric value sorts before every text value.
  * </p>
  * <p>
  * If the numeric value is exactly zero then it is encoded as a single byte of
  * 0x15. Finite negative values will have initial bytes of 0x08 through 0x14
  * and finite positive values will have initial bytes of 0x16 through 0x22.
  * </p>
  * <p>
  * For all numeric values, we compute a mantissa M and an exponent E. The
  * mantissa is a base-100 representation of the value. The exponent E
  * determines where to put the decimal point.
  * </p>
  * <p>
  * Each centimal digit of the mantissa is stored in a byte. If the value of
  * the centimal digit is X (hence X&ge;0 and X&le;99) then the byte value will
  * be 2*X+1 for every byte of the mantissa, except for the last byte which
  * will be 2*X+0. The mantissa must be the minimum number of bytes necessary
  * to represent the value; trailing X==0 digits are omitted. This means that
  * the mantissa will never contain a byte with the value 0x00.
  * </p>
  * <p>
  * If we assume all digits of the mantissa occur to the right of the decimal
  * point, then the exponent E is the power of one hundred by which one must
  * multiply the mantissa to recover the original value.
  * </p>
  * <p>
  * Values are classified as large, medium, or small according to the value of
  * E. If E is 11 or more, the value is large. For E between 0 and 10, the
  * value is medium. For E less than zero, the value is small.
  * </p>
  * <p>
  * Large positive values are encoded as a single byte 0x22 followed by E as a
  * varint and then M. Medium positive values are a single byte of 0x17+E
  * followed by M. Small positive values are encoded as a single byte 0x16
  * followed by the ones-complement of the varint for -E followed by M.
  * </p>
  * <p>
  * Small negative values are encoded as a single byte 0x14 followed by -E as a
  * varint and then the ones-complement of M. Medium negative values are
  * encoded as a byte 0x13-E followed by the ones-complement of M. Large
  * negative values consist of the single byte 0x08 followed by the
  * ones-complement of the varint encoding of E followed by the ones-complement
  * of M.
  * </p>
  * <h3>Fixed-length Integer Encoding</h3>
  * <p>
  * All 4-byte integers are serialized to a 5-byte, fixed-width, sortable byte
  * format. All 8-byte integers are serialized to the equivelant 9-byte format.
  * Serialization is performed by writing a header byte, inverting the integer
  * sign bit and writing the resulting bytes to the byte array in big endian
  * order.
  * </p>
  * <h3>Fixed-length Floating Point Encoding</h3>
  * <p>
  * 32-bit and 64-bit floating point numbers are encoded to a 5-byte and 9-byte
  * encoding format, respectively. The format is identical, save for the
  * precision respected in each step of the operation.
  * <p>
  * This format ensures the following total ordering of floating point values:
  * Float.NEGATIVE_INFINITY &lt; -Float.MAX_VALUE &lt; ... &lt;
  * -Float.MIN_VALUE &lt; -0.0 &lt; +0.0; &lt; Float.MIN_VALUE &lt; ... &lt;
  * Float.MAX_VALUE &lt; Float.POSITIVE_INFINITY &lt; Float.NaN
  * </p>
  * <p>
  * Floating point numbers are encoded as specified in IEEE 754. A 32-bit
  * single precision float consists of a sign bit, 8-bit unsigned exponent
  * encoded in offset-127 notation, and a 23-bit significand. The format is
  * described further in the <a
  * href="http://en.wikipedia.org/wiki/Single_precision"> Single Precision
  * Floating Point Wikipedia page</a>
  * </p>
  * <p>
  * The value of a normal float is -1 <sup>sign bit</sup> &times;
  * 2<sup>exponent - 127</sup> &times; 1.significand
  * </p>
  * <p>
  * The IEE754 floating point format already preserves sort ordering for
  * positive floating point numbers when the raw bytes are compared in most
  * significant byte order. This is discussed further at <a href=
  * "http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm">
  * http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm</a>
  * </p>
  * <p>
  * Thus, we need only ensure that negative numbers sort in the the exact
  * opposite order as positive numbers (so that say, negative infinity is less
  * than negative 1), and that all negative numbers compare less than any
  * positive number. To accomplish this, we invert the sign bit of all floating
  * point numbers, and we also invert the exponent and significand bits if the
  * floating point number was negative.
  * </p>
  * <p>
  * More specifically, we first store the floating point bits into a 32-bit int
  * {@code j} using {@link Float#floatToIntBits}. This method collapses
  * all NaNs into a single, canonical NaN value but otherwise leaves the bits
  * unchanged. We then compute
  * </p>
  *
  * <pre>
  * j &circ;= (j &gt;&gt; (Integer.SIZE - 1)) | Integer.MIN_SIZE
  * </pre>
  * <p>
  * which inverts the sign bit and XOR's all other bits with the sign bit
  * itself. Comparing the raw bytes of {@code j} in most significant byte
  * order is equivalent to performing a single precision floating point
  * comparison on the underlying bits (ignoring NaN comparisons, as NaNs don't
  * compare equal to anything when performing floating point comparisons).
  * </p>
  * <p>
  * The resulting integer is then converted into a byte array by serializing
  * the integer one byte at a time in most significant byte order. The
  * serialized integer is prefixed by a single header byte. All serialized
  * values are 5 bytes in length.
  * </p>
  * <p>
  * {@code OrderedBytes} encodings are heavily influenced by the
  * <a href="http://sqlite.org/src4/doc/trunk/www/key_encoding.wiki">SQLite4 Key
  * Encoding</a>. Slight deviations are make in the interest of order
  * correctness and user extensibility. Fixed-width {@code Long} and
  * {@link Double} encodings are based on implementations from the now defunct
  * Orderly library.
  * </p>
  */
 @InterfaceAudience.Public
 @InterfaceStability.Evolving
 public class OrderedBytes {
 
   /*
    * These constants define header bytes used to identify encoded values. Note
    * that the values here are not exhaustive as the Numeric format encodes
    * portions of its value within the header byte. The values listed here are
    * directly applied to persisted data -- DO NOT modify the values specified
    * here. Instead, gaps are placed intentionally between values so that new
    * implementations can be inserted into the total ordering enforced here.
    */
   private static final byte NULL = 0x05;
   // room for 1 expansion type
   private static final byte NEG_INF = 0x07;
   private static final byte NEG_LARGE = 0x08;
   private static final byte NEG_MED_MIN = 0x09;
   private static final byte NEG_MED_MAX = 0x13;
   private static final byte NEG_SMALL = 0x14;
   private static final byte ZERO = 0x15;
   private static final byte POS_SMALL = 0x16;
   private static final byte POS_MED_MIN = 0x17;
   private static final byte POS_MED_MAX = 0x21;
   private static final byte POS_LARGE = 0x22;
   private static final byte POS_INF = 0x23;
   // room for 2 expansion type
   private static final byte NAN = 0x26;
   // room for 2 expansion types
   private static final byte FIXED_INT8 = 0x29;
   private static final byte FIXED_INT16 = 0x2a;
   private static final byte FIXED_INT32 = 0x2b;
   private static final byte FIXED_INT64 = 0x2c;
   // room for 3 expansion types
   private static final byte FIXED_FLOAT32 = 0x30;
   private static final byte FIXED_FLOAT64 = 0x31;
   // room for 2 expansion type
   private static final byte TEXT = 0x34;
   // room for 2 expansion type
   private static final byte BLOB_VAR = 0x37;
   private static final byte BLOB_COPY = 0x38;
 
   /*
    * The following constant values are used by encoding implementations
    */
 
   public static final Charset UTF8 = Charset.forName("UTF-8");
   private static final byte TERM = 0x00;
   private static final BigDecimal E8 = BigDecimal.valueOf(1e8);
   private static final BigDecimal E32 = BigDecimal.valueOf(1e32);
   private static final BigDecimal EN2 = BigDecimal.valueOf(1e-2);
   private static final BigDecimal EN10 = BigDecimal.valueOf(1e-10);
 
   /**
    * Max precision guaranteed to fit into a {@code long}.
    */
   public static final int MAX_PRECISION = 31;
 
   /**
    * The context used to normalize {@link BigDecimal} values.
    */
   public static final MathContext DEFAULT_MATH_CONTEXT =
       new MathContext(MAX_PRECISION, RoundingMode.HALF_UP);
 
   /**
    * Creates the standard exception when the encoded header byte is unexpected for the decoding
    * context.
    * @param header value used in error message.
    */
   private static IllegalArgumentException unexpectedHeader(byte header) {
     throw new IllegalArgumentException("unexpected value in first byte: 0x"
         + Long.toHexString(header));
   }
 
   /**
    * Perform unsigned comparison between two long values. Conforms to the same interface as
    * {@link Comparator#compare(Object, Object)}.
    */
   private static int unsignedCmp(long x1, long x2) {
     int cmp;
     if ((cmp = (x1 < x2 ? -1 : (x1 == x2 ? 0 : 1))) == 0) return 0;
     // invert the result when either value is negative
     if ((x1 < 0) != (x2 < 0)) return -cmp;
     return cmp;
   }
 
   /**
    * Write a 32-bit unsigned integer to {@code dst} as 4 big-endian bytes.
    * @return number of bytes written.
    */
   private static int putUint32(PositionedByteRange dst, int val) {
     dst.put((byte) (val >>> 24))
        .put((byte) (val >>> 16))
        .put((byte) (val >>> 8))
        .put((byte) val);
     return 4;
   }
 
   /**
    * Encode an unsigned 64-bit unsigned integer {@code val} into {@code dst}.
    * @param dst The destination to which encoded bytes are written.
    * @param val The value to write.
    * @param comp Compliment the encoded value when {@code comp} is true.
    * @return number of bytes written.
    */
   @InterfaceAudience.Private
   static int putVaruint64(PositionedByteRange dst, long val, boolean comp) {
     int w, y, len = 0;
     final int offset = dst.getOffset(), start = dst.getPosition();
     byte[] a = dst.getBytes();
     Order ord = comp ? DESCENDING : ASCENDING;
     if (-1 == unsignedCmp(val, 241L)) {
       dst.put((byte) val);
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     if (-1 == unsignedCmp(val, 2288L)) {
       y = (int) (val - 240);
       dst.put((byte) (y / 256 + 241))
          .put((byte) (y % 256));
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     if (-1 == unsignedCmp(val, 67824L)) {
       y = (int) (val - 2288);
       dst.put((byte) 249)
          .put((byte) (y / 256))
          .put((byte) (y % 256));
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     y = (int) val;
     w = (int) (val >>> 32);
     if (w == 0) {
       if (-1 == unsignedCmp(y, 16777216L)) {
         dst.put((byte) 250)
            .put((byte) (y >>> 16))
            .put((byte) (y >>> 8))
            .put((byte) y);
         len = dst.getPosition() - start;
         ord.apply(a, offset + start, len);
         return len;
       }
       dst.put((byte) 251);
       putUint32(dst, y);
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     if (-1 == unsignedCmp(w, 256L)) {
       dst.put((byte) 252)
          .put((byte) w);
       putUint32(dst, y);
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     if (-1 == unsignedCmp(w, 65536L)) {
       dst.put((byte) 253)
          .put((byte) (w >>> 8))
          .put((byte) w);
       putUint32(dst, y);
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     if (-1 == unsignedCmp(w, 16777216L)) {
       dst.put((byte) 254)
          .put((byte) (w >>> 16))
          .put((byte) (w >>> 8))
          .put((byte) w);
       putUint32(dst, y);
       len = dst.getPosition() - start;
       ord.apply(a, offset + start, len);
       return len;
     }
     dst.put((byte) 255);
     putUint32(dst, w);
     putUint32(dst, y);
     len = dst.getPosition() - start;
     ord.apply(a, offset + start, len);
     return len;
   }
 
   /**
    * Inspect {@code src} for an encoded varuint64 for its length in bytes.
    * Preserves the state of {@code src}.
    * @param src source buffer
    * @param comp if true, parse the compliment of the value.
    * @return the number of bytes consumed by this value.
    */
   @InterfaceAudience.Private
   static int lengthVaruint64(PositionedByteRange src, boolean comp) {
     int a0 = (comp ? DESCENDING : ASCENDING).apply(src.peek()) & 0xff;
     if (a0 <= 240) return 1;
     if (a0 <= 248) return 2;
     if (a0 == 249) return 3;
     if (a0 == 250) return 4;
     if (a0 == 251) return 5;
     if (a0 == 252) return 6;
     if (a0 == 253) return 7;
     if (a0 == 254) return 8;
     if (a0 == 255) return 9;
     throw unexpectedHeader(src.peek());
   }
 
   /**
    * Skip {@code src} over the encoded varuint64.
    * @param src source buffer
    * @param cmp if true, parse the compliment of the value.
    * @return the number of bytes skipped.
    */
   @InterfaceAudience.Private
   static int skipVaruint64(PositionedByteRange src, boolean cmp) {
     final int len = lengthVaruint64(src, cmp);
     src.setPosition(src.getPosition() + len);
     return len;
   }
 
   /**
    * Decode a sequence of bytes in {@code src} as a varuint64. Compliment the
    * encoded value when {@code comp} is true.
    * @return the decoded value.
    */
   @InterfaceAudience.Private
   static long getVaruint64(PositionedByteRange src, boolean comp) {
     assert src.getRemaining() >= lengthVaruint64(src, comp);
     final long ret;
     Order ord = comp ? DESCENDING : ASCENDING;
     byte x = src.get();
     final int a0 = ord.apply(x) & 0xff, a1, a2, a3, a4, a5, a6, a7, a8;
     if (-1 == unsignedCmp(a0, 241)) {
       return a0;
     }
     x = src.get();
     a1 = ord.apply(x) & 0xff;
     if (-1 == unsignedCmp(a0, 249)) {
       return (a0 - 241L) * 256 + a1 + 240;
     }
     x = src.get();
     a2 = ord.apply(x) & 0xff;
     if (a0 == 249) {
       return 2288L + 256 * a1 + a2;
     }
     x = src.get();
     a3 = ord.apply(x) & 0xff;
     if (a0 == 250) {
       return ((long) a1 << 16L) | (a2 << 8) | a3;
     }
     x = src.get();
     a4 = ord.apply(x) & 0xff;
     ret = (((long) a1) << 24) | (a2 << 16) | (a3 << 8) | a4;
     if (a0 == 251) {
       return ret;
     }
     x = src.get();
     a5 = ord.apply(x) & 0xff;
     if (a0 == 252) {
       return (ret << 8) | a5;
     }
     x = src.get();
     a6 = ord.apply(x) & 0xff;
     if (a0 == 253) {
       return (ret << 16) | (a5 << 8) | a6;
     }
     x = src.get();
     a7 = ord.apply(x) & 0xff;
     if (a0 == 254) {
       return (ret << 24) | (a5 << 16) | (a6 << 8) | a7;
     }
     x = src.get();
     a8 = ord.apply(x) & 0xff;
     return (ret << 32) | (((long) a5) << 24) | (a6 << 16) | (a7 << 8) | a8;
   }
 
   /**
    * Strip all trailing zeros to ensure that no digit will be zero and round
    * using our default context to ensure precision doesn't exceed max allowed.
    * From Phoenix's {@code NumberUtil}.
    * @return new {@link BigDecimal} instance
    */
   @InterfaceAudience.Private
   static BigDecimal normalize(BigDecimal val) {
     return null == val ? null : val.stripTrailingZeros().round(DEFAULT_MATH_CONTEXT);
   }
 
   /**
    * Read significand digits from {@code src} according to the magnitude
    * of {@code e}.
    * @param src The source from which to read encoded digits.
    * @param e The magnitude of the first digit read.
    * @param comp Treat encoded bytes as compliments when {@code comp} is true.
    * @return The decoded value.
    * @throws IllegalArgumentException when read exceeds the remaining length
    *     of {@code src}.
    */
   private static BigDecimal decodeSignificand(PositionedByteRange src, int e, boolean comp) {
     // TODO: can this be made faster?
     byte[] a = src.getBytes();
     final int start = src.getPosition(), offset = src.getOffset(), remaining = src.getRemaining();
     Order ord = comp ? DESCENDING : ASCENDING;
     BigDecimal m = BigDecimal.ZERO;
     e--;
     for (int i = 0;; i++) {
       if (i > remaining) {
         // we've exceeded this range's window
         src.setPosition(start);
         throw new IllegalArgumentException(
             "Read exceeds range before termination byte found. offset: " + offset + " position: "
                 + (start + i));
       }
       // base-100 digits are encoded as val * 2 + 1 except for the termination digit.
       m = m.add( // m +=
         new BigDecimal(BigInteger.ONE, e * -2).multiply( // 100 ^ p * [decoded digit]
           BigDecimal.valueOf((ord.apply(a[offset + start + i]) & 0xff) / 2)));
       e--;
       // detect termination digit
       if ((ord.apply(a[offset + start + i]) & 1) == 0) {
         src.setPosition(start + i + 1);
         break;
       }
     }
     return normalize(m);
   }
 
   /**
    * Skip {@code src} over the significand bytes.
    * @param src The source from which to read encoded digits.
    * @param comp Treat encoded bytes as compliments when {@code comp} is true.
    * @return the number of bytes skipped.
    */
   private static int skipSignificand(PositionedByteRange src, boolean comp) {
     byte[] a = src.getBytes();
     final int offset = src.getOffset(), start = src.getPosition();
     int i = src.getPosition();
     while (((comp ? DESCENDING : ASCENDING).apply(a[offset + i++]) & 1) != 0)
       ;
     src.setPosition(i);
     return i - start;
   }
 
   /**
    * <p>
    * Encode the small magnitude floating point number {@code val} using the
    * key encoding. The caller guarantees that 1.0 > abs(val) > 0.0.
    * </p>
    * <p>
    * A floating point value is encoded as an integer exponent {@code E} and a
    * mantissa {@code M}. The original value is equal to {@code (M * 100^E)}.
    * {@code E} is set to the smallest value possible without making {@code M}
    * greater than or equal to 1.0.
    * </p>
    * <p>
    * For this routine, {@code E} will always be zero or negative, since the
    * original value is less than one. The encoding written by this routine is
    * the ones-complement of the varint of the negative of {@code E} followed
    * by the mantissa:
    * <pre>
    *   Encoding:   ~-E  M
    * </pre>
    * </p>
    * @param dst The destination to which encoded digits are written.
    * @param val The value to encode.
    * @return the number of bytes written.
    */
   private static int encodeNumericSmall(PositionedByteRange dst, BigDecimal val) {
     // TODO: this can be done faster?
     // assert 1.0 > abs(val) > 0.0
     BigDecimal abs = val.abs();
     assert BigDecimal.ZERO.compareTo(abs) < 0 && BigDecimal.ONE.compareTo(abs) > 0;
     byte[] a = dst.getBytes();
     boolean isNeg = val.signum() == -1;
     final int offset = dst.getOffset(), start = dst.getPosition();
     int e = 0, d, startM;
 
     if (isNeg) { /* Small negative number: 0x14, -E, ~M */
       dst.put(NEG_SMALL);
     } else { /* Small positive number: 0x16, ~-E, M */
       dst.put(POS_SMALL);
     }
 
     // normalize abs(val) to determine E
     while (abs.compareTo(EN10) < 0) { abs = abs.movePointRight(8); e += 4; }
     while (abs.compareTo(EN2) < 0) { abs = abs.movePointRight(2); e++; }
 
     putVaruint64(dst, e, !isNeg); // encode appropriate E value.
 
     // encode M by peeling off centimal digits, encoding x as 2x+1
     startM = dst.getPosition();
     // TODO: 18 is an arbitrary encoding limit. Reevaluate once we have a better handling of
     // numeric scale.
     for (int i = 0; i < 18 && abs.compareTo(BigDecimal.ZERO) != 0; i++) {
       abs = abs.movePointRight(2);
       d = abs.intValue();
       dst.put((byte) ((2 * d + 1) & 0xff));
       abs = abs.subtract(BigDecimal.valueOf(d));
     }
     // terminal digit should be 2x
     a[offset + dst.getPosition() - 1] = (byte) (a[offset + dst.getPosition() - 1] & 0xfe);
     if (isNeg) {
       // negative values encoded as ~M
       DESCENDING.apply(a, offset + startM, dst.getPosition() - startM);
     }
     return dst.getPosition() - start;
   }
 
   /**
    * Encode the large magnitude floating point number {@code val} using
    * the key encoding. The caller guarantees that {@code val} will be
    * finite and abs(val) >= 1.0.
    * <p>
    * A floating point value is encoded as an integer exponent {@code E}
    * and a mantissa {@code M}. The original value is equal to
    * {@code (M * 100^E)}. {@code E} is set to the smallest value
    * possible without making {@code M} greater than or equal to 1.0.
    * </p>
    * <p>
    * Each centimal digit of the mantissa is stored in a byte. If the value of
    * the centimal digit is {@code X} (hence {@code X>=0} and
    * {@code X<=99}) then the byte value will be {@code 2*X+1} for
    * every byte of the mantissa, except for the last byte which will be
    * {@code 2*X+0}. The mantissa must be the minimum number of bytes
    * necessary to represent the value; trailing {@code X==0} digits are
    * omitted. This means that the mantissa will never contain a byte with the
    * value {@code 0x00}.
    * </p>
    * <p>
    * If {@code E > 10}, then this routine writes of {@code E} as a
    * varint followed by the mantissa as described above. Otherwise, if
    * {@code E <= 10}, this routine only writes the mantissa and leaves
    * the {@code E} value to be encoded as part of the opening byte of the
    * field by the calling function.
    *
    * <pre>
    *   Encoding:  M       (if E<=10)
    *              E M     (if E>10)
    * </pre>
    * </p>
    * @param dst The destination to which encoded digits are written.
    * @param val The value to encode.
    * @return the number of bytes written.
    */
   private static int encodeNumericLarge(PositionedByteRange dst, BigDecimal val) {
     // TODO: this can be done faster
     BigDecimal abs = val.abs();
     byte[] a = dst.getBytes();
     boolean isNeg = val.signum() == -1;
     final int start = dst.getPosition(), offset = dst.getOffset();
     int e = 0, d, startM;
 
     if (isNeg) { /* Large negative number: 0x08, ~E, ~M */
       dst.put(NEG_LARGE);
     } else { /* Large positive number: 0x22, E, M */
       dst.put(POS_LARGE);
     }
 
     // normalize abs(val) to determine E
     while (abs.compareTo(E32) >= 0 && e <= 350) { abs = abs.movePointLeft(32); e +=16; }
     while (abs.compareTo(E8) >= 0 && e <= 350) { abs = abs.movePointLeft(8); e+= 4; }
     while (abs.compareTo(BigDecimal.ONE) >= 0 && e <= 350) { abs = abs.movePointLeft(2); e++; }
 
     // encode appropriate header byte and/or E value.
     if (e > 10) { /* large number, write out {~,}E */
       putVaruint64(dst, e, isNeg);
     } else {
       if (isNeg) { /* Medium negative number: 0x13-E, ~M */
         dst.put(start, (byte) (NEG_MED_MAX - e));
       } else { /* Medium positive number: 0x17+E, M */
         dst.put(start, (byte) (POS_MED_MIN + e));
       }
     }
 
     // encode M by peeling off centimal digits, encoding x as 2x+1
     startM = dst.getPosition();
     // TODO: 18 is an arbitrary encoding limit. Reevaluate once we have a better handling of
     // numeric scale.
     for (int i = 0; i < 18 && abs.compareTo(BigDecimal.ZERO) != 0; i++) {
       abs = abs.movePointRight(2);
       d = abs.intValue();
       dst.put((byte) (2 * d + 1));
       abs = abs.subtract(BigDecimal.valueOf(d));
     }
     // terminal digit should be 2x
     a[offset + dst.getPosition() - 1] = (byte) (a[offset + dst.getPosition() - 1] & 0xfe);
     if (isNeg) {
       // negative values encoded as ~M
       DESCENDING.apply(a, offset + startM, dst.getPosition() - startM);
     }
     return dst.getPosition() - start;
   }
 
   /**
    * Encode a numerical value using the variable-length encoding.
    * @param dst The destination to which encoded digits are written.
    * @param val The value to encode.
    * @param ord The {@link Order} to respect while encoding {@code val}.
    * @return the number of bytes written.
    */
   public static int encodeNumeric(PositionedByteRange dst, long val, Order ord) {
     return encodeNumeric(dst, BigDecimal.valueOf(val), ord);
   }
 
   /**
    * Encode a numerical value using the variable-length encoding.
    * @param dst The destination to which encoded digits are written.
    * @param val The value to encode.
    * @param ord The {@link Order} to respect while encoding {@code val}.
    * @return the number of bytes written.
    */
   public static int encodeNumeric(PositionedByteRange dst, double val, Order ord) {
     if (val == 0.0) {
       dst.put(ord.apply(ZERO));
       return 1;
     }
     if (Double.isNaN(val)) {
       dst.put(ord.apply(NAN));
       return 1;
     }
     if (val == Double.NEGATIVE_INFINITY) {
       dst.put(ord.apply(NEG_INF));
       return 1;
     }
     if (val == Double.POSITIVE_INFINITY) {
       dst.put(ord.apply(POS_INF));
       return 1;
     }
     return encodeNumeric(dst, BigDecimal.valueOf(val), ord);
   }
 
   /**
    * Encode a numerical value using the variable-length encoding.
    * @param dst The destination to which encoded digits are written.
    * @param val The value to encode.
    * @param ord The {@link Order} to respect while encoding {@code val}.
    * @return the number of bytes written.
    */
   public static int encodeNumeric(PositionedByteRange dst, BigDecimal val, Order ord) {
     final int len, offset = dst.getOffset(), start = dst.getPosition();
     if (null == val) {
       return encodeNull(dst, ord);
     } else if (BigDecimal.ZERO.compareTo(val) == 0) {
       dst.put(ord.apply(ZERO));
       return 1;
     }
     BigDecimal abs = val.abs();
     if (BigDecimal.ONE.compareTo(abs) <= 0) { // abs(v) >= 1.0
       len = encodeNumericLarge(dst, normalize(val));
     } else { // 1.0 > abs(v) >= 0.0
       len = encodeNumericSmall(dst, normalize(val));
     }
     ord.apply(dst.getBytes(), offset + start, len);
     return len;
   }
 
   /**
    * Decode a {@link BigDecimal} from {@code src}. Assumes {@code src} encodes
    * a value in Numeric encoding and is within the valid range of
    * {@link BigDecimal} values. {@link BigDecimal} does not support {@code NaN}
    * or {@code Infinte} values.
    * @see #decodeNumericAsDouble(PositionedByteRange)
    */
   private static BigDecimal decodeNumericValue(PositionedByteRange src) {
     final int e;
     byte header = src.get();
     boolean dsc = -1 == Integer.signum(header);
     header = dsc ? DESCENDING.apply(header) : header;
 
     if (header == NULL) return null;
     if (header == NEG_LARGE) { /* Large negative number: 0x08, ~E, ~M */
       e = (int) getVaruint64(src, !dsc);
       return decodeSignificand(src, e, !dsc).negate();
     }
     if (header >= NEG_MED_MIN && header <= NEG_MED_MAX) {
       /* Medium negative number: 0x13-E, ~M */
       e = NEG_MED_MAX - header;
       return decodeSignificand(src, e, !dsc).negate();
     }
     if (header == NEG_SMALL) { /* Small negative number: 0x14, -E, ~M */
       e = (int) -getVaruint64(src, dsc);
       return decodeSignificand(src, e, !dsc).negate();
     }
     if (header == ZERO) {
       return BigDecimal.ZERO;
     }
     if (header == POS_SMALL) { /* Small positive number: 0x16, ~-E, M */
       e = (int) -getVaruint64(src, !dsc);
       return decodeSignificand(src, e, dsc);
     }
     if (header >= POS_MED_MIN && header <= POS_MED_MAX) {
       /* Medium positive number: 0x17+E, M */
       e = header - POS_MED_MIN;
       return decodeSignificand(src, e, dsc);
     }
     if (header == POS_LARGE) { /* Large positive number: 0x22, E, M */
       e = (int) getVaruint64(src, dsc);
       return decodeSignificand(src, e, dsc);
     }
     throw unexpectedHeader(header);
   }
 
   /**
    * Decode a primitive {@code double} value from the Numeric encoding. Numeric
    * encoding is based on {@link BigDecimal}; in the event the encoded value is
    * larger than can be represented in a {@code double}, this method performs
    * an implicit narrowing conversion as described in
    * {@link BigDecimal#doubleValue()}.
    * @throws NullPointerException when the encoded value is {@code NULL}.
    * @throws IllegalArgumentException when the encoded value is not a Numeric.
    * @see #encodeNumeric(PositionedByteRange, double, Order)
    * @see BigDecimal#doubleValue()
    */
   public static double decodeNumericAsDouble(PositionedByteRange src) {
     // TODO: should an encoded NULL value throw unexpectedHeader() instead?
     if (isNull(src)) {
       throw new NullPointerException("A null value cannot be decoded to a double.");
     }
     if (isNumericNaN(src)) {
       src.get();
       return Double.NaN;
     }
     if (isNumericZero(src)) {
       src.get();
       return Double.valueOf(0.0);
     }
 
     byte header = -1 == Integer.signum(src.peek()) ? DESCENDING.apply(src.peek()) : src.peek();
 
     if (header == NEG_INF) {
       src.get();
       return Double.NEGATIVE_INFINITY;
     } else if (header == POS_INF) {
       src.get();
       return Double.POSITIVE_INFINITY;
     } else {
       return decodeNumericValue(src).doubleValue();
     }
   }
 
   /**
    * Decode a primitive {@code long} value from the Numeric encoding. Numeric
    * encoding is based on {@link BigDecimal}; in the event the encoded value is
    * larger than can be represented in a {@code long}, this method performs an
    * implicit narrowing conversion as described in
    * {@link BigDecimal#doubleValue()}.
    * @throws NullPointerException when the encoded value is {@code NULL}.
    * @throws IllegalArgumentException when the encoded value is not a Numeric.
    * @see #encodeNumeric(PositionedByteRange, long, Order)
    * @see BigDecimal#longValue()
    */
   public static long decodeNumericAsLong(PositionedByteRange src) {
     // TODO: should an encoded NULL value throw unexpectedHeader() instead?
     if (isNull(src)) throw new NullPointerException();
     if (!isNumeric(src)) throw unexpectedHeader(src.peek());
     if (isNumericNaN(src)) throw unexpectedHeader(src.peek());
     if (isNumericInfinite(src)) throw unexpectedHeader(src.peek());
 
     if (isNumericZero(src)) {
       src.get();
       return Long.valueOf(0);
     }
     return decodeNumericValue(src).longValue();
   }
 
   /**
    * Decode a {@link BigDecimal} value from the variable-length encoding.
    * @throws IllegalArgumentException when the encoded value is not a Numeric.
    * @see #encodeNumeric(PositionedByteRange, BigDecimal, Order)
    */
   public static BigDecimal decodeNumericAsBigDecimal(PositionedByteRange src) {
     if (isNull(src)) {
       src.get();
       return null;
     }
     if (!isNumeric(src)) throw unexpectedHeader(src.peek());
     if (isNumericNaN(src)) throw unexpectedHeader(src.peek());
     if (isNumericInfinite(src)) throw unexpectedHeader(src.peek());
     return decodeNumericValue(src);
   }
 
   /**
    * Encode a String value. String encoding is 0x00-terminated and so it does
    * not support {@code \u0000} codepoints in the value.
    * @param dst The destination to which the encoded value is written.
    * @param val The value to encode.
    * @param ord The {@link Order} to respect while encoding {@code val}.
    * @return the number of bytes written.
    * @throws IllegalArgumentException when {@code val} contains a {@code \u0000}.
    */
   public static int encodeString(PositionedByteRange dst, String val, Order ord) {
     if (null == val) {
       return encodeNull(dst, ord);
     }
     if (val.contains("\u0000"))
       throw new IllegalArgumentException("Cannot encode String values containing '\\u0000'");
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(TEXT);
     // TODO: is there no way to decode into dst directly?
     dst.put(val.getBytes(UTF8));
     dst.put(TERM);
     ord.apply(dst.getBytes(), offset + start, dst.getPosition() - start);
     return dst.getPosition() - start;
   }
 
   /**
    * Decode a String value.
    */
   public static String decodeString(PositionedByteRange src) {
     final byte header = src.get();
     if (header == NULL || header == DESCENDING.apply(NULL))
       return null;
     assert header == TEXT || header == DESCENDING.apply(TEXT);
     Order ord = header == TEXT ? ASCENDING : DESCENDING;
     byte[] a = src.getBytes();
     final int offset = src.getOffset(), start = src.getPosition();
     final byte terminator = ord.apply(TERM);
     int rawStartPos = offset + start, rawTermPos = rawStartPos;
     for (; a[rawTermPos] != terminator; rawTermPos++)
       ;
     src.setPosition(rawTermPos - offset + 1); // advance position to TERM + 1
     if (DESCENDING == ord) {
       // make a copy so that we don't disturb encoded value with ord.
       byte[] copy = new byte[rawTermPos - rawStartPos];
       System.arraycopy(a, rawStartPos, copy, 0, copy.length);
       ord.apply(copy);
       return new String(copy, UTF8);
     } else {
       return new String(a, rawStartPos, rawTermPos - rawStartPos, UTF8);
     }
   }
 
   /**
    * Calculate the expected BlobVar encoded length based on unencoded length.
    */
   public static int blobVarEncodedLength(int len) {
     if (0 == len)
       return 2; // 1-byte header + 1-byte terminator
     else
       return (int)
           Math.ceil(
             (len * 8) // 8-bits per input byte
             / 7.0)    // 7-bits of input data per encoded byte, rounded up
           + 1;        // + 1-byte header
   }
 
   /**
    * Calculate the expected BlobVar decoded length based on encoded length.
    */
   @InterfaceAudience.Private
   static int blobVarDecodedLength(int len) {
     return
         ((len
           - 1) // 1-byte header
           * 7) // 7-bits of payload per encoded byte
           / 8; // 8-bits per byte
   }
 
   /**
    * Encode a Blob value using a modified varint encoding scheme.
    * <p>
    * This format encodes a byte[] value such that no limitations on the input
    * value are imposed. The first byte encodes the encoding scheme that
    * follows, {@link #BLOB_VAR}. Each encoded byte thereafter consists of a
    * header bit followed by 7 bits of payload. A header bit of '1' indicates
    * continuation of the encoding. A header bit of '0' indicates this byte
    * contains the last of the payload. An empty input value is encoded as the
    * header byte immediately followed by a termination byte {@code 0x00}. This
    * is not ambiguous with the encoded value of {@code []}, which results in
    * {@code [0x80, 0x00]}.
    * </p>
    * @return the number of bytes written.
    */
   public static int encodeBlobVar(PositionedByteRange dst, byte[] val, int voff, int vlen,
       Order ord) {
     if (null == val) {
       return encodeNull(dst, ord);
     }
     // Empty value is null-terminated. All other values are encoded as 7-bits per byte.
     assert dst.getRemaining() >= blobVarEncodedLength(vlen) : "buffer overflow expected.";
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(BLOB_VAR);
     if (0 == vlen) {
       dst.put(TERM);
     } else {
       byte s = 1, t = 0;
       for (int i = voff; i < vlen; i++) {
         dst.put((byte) (0x80 | t | ((val[i] & 0xff) >>> s)));
         if (s < 7) {
           t = (byte) (val[i] << (7 - s));
           s++;
         } else {
           dst.put((byte) (0x80 | val[i]));
           s = 1;
           t = 0;
         }
       }
       if (s > 1) {
         dst.put((byte) (0x7f & t));
       } else {
         dst.getBytes()[offset + dst.getPosition() - 1] =
           (byte) (dst.getBytes()[offset + dst.getPosition() - 1] & 0x7f);
       }
     }
     ord.apply(dst.getBytes(), offset + start, dst.getPosition() - start);
     return dst.getPosition() - start;
   }
 
   /**
    * Encode a blob value using a modified varint encoding scheme.
    * @return the number of bytes written.
    * @see #encodeBlobVar(PositionedByteRange, byte[], int, int, Order)
    */
   public static int encodeBlobVar(PositionedByteRange dst, byte[] val, Order ord) {
     return encodeBlobVar(dst, val, 0, null != val ? val.length : 0, ord);
   }
 
   /**
    * Decode a blob value that was encoded using BlobVar encoding.
    */
   public static byte[] decodeBlobVar(PositionedByteRange src) {
     final byte header = src.get();
     if (header == NULL || header == DESCENDING.apply(NULL)) {
       return null;
     }
     assert header == BLOB_VAR || header == DESCENDING.apply(BLOB_VAR);
     Order ord = BLOB_VAR == header ? ASCENDING : DESCENDING;
     if (src.peek() == ord.apply(TERM)) {
       // skip empty input buffer.
       src.get();
       return new byte[0];
     }
     final int offset = src.getOffset(), start = src.getPosition();
     int end;
     byte[] a = src.getBytes();
     for (end = start; (byte) (ord.apply(a[offset + end]) & 0x80) != TERM; end++)
       ;
     end++; // increment end to 1-past last byte
     // create ret buffer using length of encoded data + 1 (header byte)
     PositionedByteRange ret = new SimplePositionedMutableByteRange(blobVarDecodedLength(end - start
         + 1));
     int s = 6;
     byte t = (byte) ((ord.apply(a[offset + start]) << 1) & 0xff);
     for (int i = start + 1; i < end; i++) {
       if (s == 7) {
         ret.put((byte) (t | (ord.apply(a[offset + i]) & 0x7f)));
         i++;
                // explicitly reset t -- clean up overflow buffer after decoding
                // a full cycle and retain assertion condition below. This happens
         t = 0; // when the LSB in the last encoded byte is 1. (HBASE-9893)
       } else {
         ret.put((byte) (t | ((ord.apply(a[offset + i]) & 0x7f) >>> s)));
       }
       if (i == end) break;
       t = (byte) ((ord.apply(a[offset + i]) << (8 - s)) & 0xff);
       s = s == 1 ? 7 : s - 1;
     }
     src.setPosition(end);
     assert t == 0 : "Unexpected bits remaining after decoding blob.";
     assert ret.getPosition() == ret.getLength() : "Allocated unnecessarily large return buffer.";
     return ret.getBytes();
   }
 
   /**
    * Encode a Blob value as a byte-for-byte copy. BlobCopy encoding in
    * DESCENDING order is NULL terminated so as to preserve proper sorting of
    * {@code []} and so it does not support {@code 0x00} in the value.
    * @return the number of bytes written.
    * @throws IllegalArgumentException when {@code ord} is DESCENDING and
    *    {@code val} contains a {@code 0x00} byte.
    */
   public static int encodeBlobCopy(PositionedByteRange dst, byte[] val, int voff, int vlen,
       Order ord) {
     if (null == val) {
       encodeNull(dst, ord);
       if (ASCENDING == ord) return 1;
       else {
         // DESCENDING ordered BlobCopy requires a termination bit to preserve
         // sort-order semantics of null values.
         dst.put(ord.apply(TERM));
         return 2;
       }
     }
     // Blobs as final entry in a compound key are written unencoded.
     assert dst.getRemaining() >= vlen + (ASCENDING == ord ? 1 : 2);
     if (DESCENDING == ord) {
       for (int i = 0; i < vlen; i++) {
         if (TERM == val[voff + i]) {
           throw new IllegalArgumentException("0x00 bytes not permitted in value.");
         }
       }
     }
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(BLOB_COPY);
     dst.put(val, voff, vlen);
     // DESCENDING ordered BlobCopy requires a termination bit to preserve
     // sort-order semantics of null values.
     if (DESCENDING == ord) dst.put(TERM);
     ord.apply(dst.getBytes(), offset + start, dst.getPosition() - start);
     return dst.getPosition() - start;
   }
 
   /**
    * Encode a Blob value as a byte-for-byte copy. BlobCopy encoding in
    * DESCENDING order is NULL terminated so as to preserve proper sorting of
    * {@code []} and so it does not support {@code 0x00} in the value.
    * @return the number of bytes written.
    * @throws IllegalArgumentException when {@code ord} is DESCENDING and
    *    {@code val} contains a {@code 0x00} byte.
    * @see #encodeBlobCopy(PositionedByteRange, byte[], int, int, Order)
    */
   public static int encodeBlobCopy(PositionedByteRange dst, byte[] val, Order ord) {
     return encodeBlobCopy(dst, val, 0, null != val ? val.length : 0, ord);
   }
 
   /**
    * Decode a Blob value, byte-for-byte copy.
    * @see #encodeBlobCopy(PositionedByteRange, byte[], int, int, Order)
    */
   public static byte[] decodeBlobCopy(PositionedByteRange src) {
     byte header = src.get();
     if (header == NULL || header == DESCENDING.apply(NULL)) {
       return null;
     }
     assert header == BLOB_COPY || header == DESCENDING.apply(BLOB_COPY);
     Order ord = header == BLOB_COPY ? ASCENDING : DESCENDING;
     final int length = src.getRemaining() - (ASCENDING == ord ? 0 : 1);
     byte[] ret = new byte[length];
     src.get(ret);
     ord.apply(ret, 0, ret.length);
     // DESCENDING ordered BlobCopy requires a termination bit to preserve
     // sort-order semantics of null values.
     if (DESCENDING == ord) src.get();
     return ret;
   }
 
   /**
    * Encode a null value.
    * @param dst The destination to which encoded digits are written.
    * @param ord The {@link Order} to respect while encoding {@code val}.
    * @return the number of bytes written.
    */
   public static int encodeNull(PositionedByteRange dst, Order ord) {
     dst.put(ord.apply(NULL));
     return 1;
   }
 
   /**
    * Encode an {@code int8} value using the fixed-length encoding.
    * @return the number of bytes written.
    * @see #encodeInt64(PositionedByteRange, long, Order)
    * @see #decodeInt8(PositionedByteRange)
    */
   public static int encodeInt8(PositionedByteRange dst, byte val, Order ord) {
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(FIXED_INT8)
        .put((byte) (val ^ 0x80));
     ord.apply(dst.getBytes(), offset + start, 2);
     return 2;
   }
 
   /**
    * Decode an {@code int8} value.
    * @see #encodeInt8(PositionedByteRange, byte, Order)
    */
   public static byte decodeInt8(PositionedByteRange src) {
     final byte header = src.get();
     assert header == FIXED_INT8 || header == DESCENDING.apply(FIXED_INT8);
     Order ord = header == FIXED_INT8 ? ASCENDING : DESCENDING;
     return (byte)((ord.apply(src.get()) ^ 0x80) & 0xff);
   }
 
   /**
    * Encode an {@code int16} value using the fixed-length encoding.
    * @return the number of bytes written.
    * @see #encodeInt64(PositionedByteRange, long, Order)
    * @see #decodeInt16(PositionedByteRange)
    */
   public static int encodeInt16(PositionedByteRange dst, short val, Order ord) {
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(FIXED_INT16)
        .put((byte) ((val >> 8) ^ 0x80))
        .put((byte) val);
     ord.apply(dst.getBytes(), offset + start, 3);
     return 3;
   }
 
   /**
    * Decode an {@code int16} value.
    * @see #encodeInt16(PositionedByteRange, short, Order)
    */
   public static short decodeInt16(PositionedByteRange src) {
     final byte header = src.get();
     assert header == FIXED_INT16 || header == DESCENDING.apply(FIXED_INT16);
     Order ord = header == FIXED_INT16 ? ASCENDING : DESCENDING;
     short val = (short) ((ord.apply(src.get()) ^ 0x80) & 0xff);
     val = (short) ((val << 8) + (ord.apply(src.get()) & 0xff));
     return val;
   }
 
   /**
    * Encode an {@code int32} value using the fixed-length encoding.
    * @return the number of bytes written.
    * @see #encodeInt64(PositionedByteRange, long, Order)
    * @see #decodeInt32(PositionedByteRange)
    */
   public static int encodeInt32(PositionedByteRange dst, int val, Order ord) {
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(FIXED_INT32)
         .put((byte) ((val >> 24) ^ 0x80))
         .put((byte) (val >> 16))
         .put((byte) (val >> 8))
         .put((byte) val);
     ord.apply(dst.getBytes(), offset + start, 5);
     return 5;
   }
 
   /**
    * Decode an {@code int32} value.
    * @see #encodeInt32(PositionedByteRange, int, Order)
    */
   public static int decodeInt32(PositionedByteRange src) {
     final byte header = src.get();
     assert header == FIXED_INT32 || header == DESCENDING.apply(FIXED_INT32);
     Order ord = header == FIXED_INT32 ? ASCENDING : DESCENDING;
     int val = (ord.apply(src.get()) ^ 0x80) & 0xff;
     for (int i = 1; i < 4; i++) {
       val = (val << 8) + (ord.apply(src.get()) & 0xff);
     }
     return val;
   }
 
   /**
    * Encode an {@code int64} value using the fixed-length encoding.
    * <p>
    * This format ensures that all longs sort in their natural order, as they
    * would sort when using signed long comparison.
    * </p>
    * <p>
    * All Longs are serialized to an 8-byte, fixed-width sortable byte format.
    * Serialization is performed by inverting the integer sign bit and writing
    * the resulting bytes to the byte array in big endian order. The encoded
    * value is prefixed by the {@link #FIXED_INT64} header byte. This encoding
    * is designed to handle java language primitives and so Null values are NOT
    * supported by this implementation.
    * </p>
    * <p>
    * For example:
    * </p>
    * <pre>
    * Input:   0x0000000000000005 (5)
    * Result:  0x288000000000000005
    *
    * Input:   0xfffffffffffffffb (-4)
    * Result:  0x280000000000000004
    *
    * Input:   0x7fffffffffffffff (Long.MAX_VALUE)
    * Result:  0x28ffffffffffffffff
    *
    * Input:   0x8000000000000000 (Long.MIN_VALUE)
    * Result:  0x287fffffffffffffff
    * </pre>
    * <p>
    * This encoding format, and much of this documentation string, is based on
    * Orderly's {@code FixedIntWritableRowKey}.
    * </p>
    * @return the number of bytes written.
    * @see #decodeInt64(PositionedByteRange)
    */
   public static int encodeInt64(PositionedByteRange dst, long val, Order ord) {
     final int offset = dst.getOffset(), start = dst.getPosition();
     dst.put(FIXED_INT64)
        .put((byte) ((val >> 56) ^ 0x80))
        .put((byte) (val >> 48))
        .put((byte) (val >> 40))
        .put((byte) (val >> 32))
        .put((byte) (val >> 24))
        .put((byte) (val >> 16))
        .put((byte) (val >> 8))
        .put((byte) val);
     ord.apply(dst.getBytes(), offset + start, 9);
     return 9;
   }
 
   /**
    * Decode an {@code int64} value.
    * @see #encodeInt64(PositionedByteRange, long, Order)
    */
   public static long decodeInt64(PositionedByteRange src) {
     final byte header = src.get();
     assert header == FIXED_INT64 || header == DESCENDING.apply(FIXED_INT64);
     Order ord = header == FIXED_INT64 ? ASCENDING : DESCENDING;
     long val = (ord.apply(src.get()) ^ 0x80) & 0xff;
     for (int i = 1; i < 8; i++) {
       val = (val << 8) + (ord.apply(src.get()) & 0xff);
     }
     return val;
   }
 
   /**
    * Encode a 32-bit floating point value using the fixed-length encoding.
    * Encoding format is described at length in
    * {@link #encodeFloat64(PositionedByteRange, double, Order)}.
    * @return the number of bytes written.
    * @see #decodeFloat32(PositionedByteRange)
    * @see #encodeFloat64(PositionedByteRange, double, Order)
    */
   public static int encodeFloat32(PositionedByteRange dst, float val, Order ord) {
     final int offset = dst.getOffset(), start = dst.getPosition();
     int i = Float.floatToIntBits(val);
     i ^= ((i >> (Integer.SIZE - 1)) | Integer.MIN_VALUE);
     dst.put(FIXED_FLOAT32)
         .put((byte) (i >> 24))
         .put((byte) (i >> 16))
         .put((byte) (i >> 8))
         .put((byte) i);
     ord.apply(dst.getBytes(), offset + start, 5);
     return 5;
   }
 
   /**
    * Decode a 32-bit floating point value using the fixed-length encoding.
    * @see #encodeFloat32(PositionedByteRange, float, Order)
    */
   public static float decodeFloat32(PositionedByteRange src) {
     final byte header = src.get();
     assert header == FIXED_FLOAT32 || header == DESCENDING.apply(FIXED_FLOAT32);
     Order ord = header == FIXED_FLOAT32 ? ASCENDING : DESCENDING;
     int val = ord.apply(src.get()) & 0xff;
     for (int i = 1; i < 4; i++) {
       val = (val << 8) + (ord.apply(src.get()) & 0xff);
     }
     val ^= (~val >> (Integer.SIZE - 1)) | Integer.MIN_VALUE;
     return Float.intBitsToFloat(val);
   }
 
   /**
    * Encode a 64-bit floating point value using the fixed-length encoding.
    * <p>
    * This format ensures the following total ordering of floating point
    * values: Double.NEGATIVE_INFINITY &lt; -Double.MAX_VALUE &lt; ... &lt;
    * -Double.MIN_VALUE &lt; -0.0 &lt; +0.0; &lt; Double.MIN_VALUE &lt; ...
    * &lt; Double.MAX_VALUE &lt; Double.POSITIVE_INFINITY &lt; Double.NaN
    * </p>
    * <p>
    * Floating point numbers are encoded as specified in IEEE 754. A 64-bit
    * double precision float consists of a sign bit, 11-bit unsigned exponent
    * encoded in offset-1023 notation, and a 52-bit significand. The format is
    * described further in the <a
    * href="http://en.wikipedia.org/wiki/Double_precision"> Double Precision
    * Floating Point Wikipedia page</a> </p>
    * <p>
    * The value of a normal float is -1 <sup>sign bit</sup> &times;
    * 2<sup>exponent - 1023</sup> &times; 1.significand
    * </p>
    * <p>
    * The IEE754 floating point format already preserves sort ordering for
    * positive floating point numbers when the raw bytes are compared in most
    * significant byte order. This is discussed further at <a href=
    * "http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm"
    * > http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.
    * htm</a>
    * </p>
    * <p>
    * Thus, we need only ensure that negative numbers sort in the the exact
    * opposite order as positive numbers (so that say, negative infinity is
    * less than negative 1), and that all negative numbers compare less than
    * any positive number. To accomplish this, we invert the sign bit of all
    * floating point numbers, and we also invert the exponent and significand
    * bits if the floating point number was negative.
    * </p>
    * <p>
    * More specifically, we first store the floating point bits into a 64-bit
    * long {@code l} using {@link Double#doubleToLongBits}. This method
    * collapses all NaNs into a single, canonical NaN value but otherwise
    * leaves the bits unchanged. We then compute
    * </p>
    * <pre>
    * l &circ;= (l &gt;&gt; (Long.SIZE - 1)) | Long.MIN_SIZE
    * </pre>
    * <p>
    * which inverts the sign bit and XOR's all other bits with the sign bit
    * itself. Comparing the raw bytes of {@code l} in most significant
    * byte order is equivalent to performing a double precision floating point
    * comparison on the underlying bits (ignoring NaN comparisons, as NaNs
    * don't compare equal to anything when performing floating point
    * comparisons).
    * </p>
    * <p>
    * The resulting long integer is then converted into a byte array by
    * serializing the long one byte at a time in most significant byte order.
    * The serialized integer is prefixed by a single header byte. All
    * serialized values are 9 bytes in length.
    * </p>
    * <p>
    * This encoding format, and much of this highly detailed documentation
    * string, is based on Orderly's {@code DoubleWritableRowKey}.
    * </p>
    * @return the number of bytes written.
    * @see #decodeFloat64(PositionedByteRange)
    */
   public static int encodeFloat64(PositionedByteRange dst, double val, Order ord) {
     final int offset = dst.getOffset(), start = dst.getPosition();
     long lng = Double.doubleToLongBits(val);
     lng ^= ((lng >> (Long.SIZE - 1)) | Long.MIN_VALUE);
     dst.put(FIXED_FLOAT64)
         .put((byte) (lng >> 56))
         .put((byte) (lng >> 48))
         .put((byte) (lng >> 40))
         .put((byte) (lng >> 32))
         .put((byte) (lng >> 24))
         .put((byte) (lng >> 16))
         .put((byte) (lng >> 8))
         .put((byte) lng);
     ord.apply(dst.getBytes(), offset + start, 9);
     return 9;
   }
 
   /**
    * Decode a 64-bit floating point value using the fixed-length encoding.
    * @see #encodeFloat64(PositionedByteRange, double, Order)
    */
   public static double decodeFloat64(PositionedByteRange src) {
     final byte header = src.get();
     assert header == FIXED_FLOAT64 || header == DESCENDING.apply(FIXED_FLOAT64);
     Order ord = header == FIXED_FLOAT64 ? ASCENDING : DESCENDING;
     long val = ord.apply(src.get()) & 0xff;
     for (int i = 1; i < 8; i++) {
       val = (val << 8) + (ord.apply(src.get()) & 0xff);
     }
     val ^= (~val >> (Long.SIZE - 1)) | Long.MIN_VALUE;
     return Double.longBitsToDouble(val);
   }
 
   /**
    * Returns true when {@code src} appears to be positioned an encoded value,
    * false otherwise.
    */
   public static boolean isEncodedValue(PositionedByteRange src) {
     return isNull(src) || isNumeric(src) || isFixedInt8(src) || isFixedInt16(src)
         || isFixedInt32(src) || isFixedInt64(src)
         || isFixedFloat32(src) || isFixedFloat64(src) || isText(src) || isBlobCopy(src)
         || isBlobVar(src);
   }
 
   /**
    * Return true when the next encoded value in {@code src} is null, false
    * otherwise.
    */
   public static boolean isNull(PositionedByteRange src) {
     return NULL ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses Numeric
    * encoding, false otherwise. {@code NaN}, {@code +/-Inf} are valid Numeric
    * values.
    */
   public static boolean isNumeric(PositionedByteRange src) {
     byte x = (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
     return x >= NEG_INF && x <= NAN;
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses Numeric
    * encoding and is {@code Infinite}, false otherwise.
    */
   public static boolean isNumericInfinite(PositionedByteRange src) {
     byte x = (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
     return NEG_INF == x || POS_INF == x;
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses Numeric
    * encoding and is {@code NaN}, false otherwise.
    */
   public static boolean isNumericNaN(PositionedByteRange src) {
     return NAN == (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses Numeric
    * encoding and is {@code 0}, false otherwise.
    */
   public static boolean isNumericZero(PositionedByteRange src) {
     return ZERO ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses fixed-width
    * Int8 encoding, false otherwise.
    */
   public static boolean isFixedInt8(PositionedByteRange src) {
     return FIXED_INT8 ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses fixed-width
    * Int16 encoding, false otherwise.
    */
   public static boolean isFixedInt16(PositionedByteRange src) {
     return FIXED_INT16 ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses fixed-width
    * Int32 encoding, false otherwise.
    */
   public static boolean isFixedInt32(PositionedByteRange src) {
     return FIXED_INT32 ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses fixed-width
    * Int64 encoding, false otherwise.
    */
   public static boolean isFixedInt64(PositionedByteRange src) {
     return FIXED_INT64 ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses fixed-width
    * Float32 encoding, false otherwise.
    */
   public static boolean isFixedFloat32(PositionedByteRange src) {
     return FIXED_FLOAT32 ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses fixed-width
    * Float64 encoding, false otherwise.
    */
   public static boolean isFixedFloat64(PositionedByteRange src) {
     return FIXED_FLOAT64 ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses Text encoding,
    * false otherwise.
    */
   public static boolean isText(PositionedByteRange src) {
     return TEXT ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses BlobVar
    * encoding, false otherwise.
    */
   public static boolean isBlobVar(PositionedByteRange src) {
     return BLOB_VAR ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Return true when the next encoded value in {@code src} uses BlobCopy
    * encoding, false otherwise.
    */
   public static boolean isBlobCopy(PositionedByteRange src) {
     return BLOB_COPY ==
         (-1 == Integer.signum(src.peek()) ? DESCENDING : ASCENDING).apply(src.peek());
   }
 
   /**
    * Skip {@code buff}'s position forward over one encoded value.
    * @return number of bytes skipped.
    */
   public static int skip(PositionedByteRange src) {
     final int start = src.getPosition();
     byte header = src.get();
     Order ord = (-1 == Integer.signum(header)) ? DESCENDING : ASCENDING;
     header = ord.apply(header);
 
     switch (header) {
       case NULL:
       case NEG_INF:
         return 1;
       case NEG_LARGE: /* Large negative number: 0x08, ~E, ~M */
         skipVaruint64(src, DESCENDING != ord);
         skipSignificand(src, DESCENDING != ord);
         return src.getPosition() - start;
       case NEG_MED_MIN: /* Medium negative number: 0x13-E, ~M */
       case NEG_MED_MIN + 0x01:
       case NEG_MED_MIN + 0x02:
       case NEG_MED_MIN + 0x03:
       case NEG_MED_MIN + 0x04:
       case NEG_MED_MIN + 0x05:
       case NEG_MED_MIN + 0x06:
       case NEG_MED_MIN + 0x07:
       case NEG_MED_MIN + 0x08:
       case NEG_MED_MIN + 0x09:
       case NEG_MED_MAX:
         skipSignificand(src, DESCENDING != ord);
         return src.getPosition() - start;
       case NEG_SMALL: /* Small negative number: 0x14, -E, ~M */
         skipVaruint64(src, DESCENDING == ord);
         skipSignificand(src, DESCENDING != ord);
         return src.getPosition() - start;
       case ZERO:
         return 1;
       case POS_SMALL: /* Small positive number: 0x16, ~-E, M */
         skipVaruint64(src, DESCENDING != ord);
         skipSignificand(src, DESCENDING == ord);
         return src.getPosition() - start;
       case POS_MED_MIN: /* Medium positive number: 0x17+E, M */
       case POS_MED_MIN + 0x01:
       case POS_MED_MIN + 0x02:
       case POS_MED_MIN + 0x03:
       case POS_MED_MIN + 0x04:
       case POS_MED_MIN + 0x05:
       case POS_MED_MIN + 0x06:
       case POS_MED_MIN + 0x07:
       case POS_MED_MIN + 0x08:
       case POS_MED_MIN + 0x09:
       case POS_MED_MAX:
         skipSignificand(src, DESCENDING == ord);
         return src.getPosition() - start;
       case POS_LARGE: /* Large positive number: 0x22, E, M */
         skipVaruint64(src, DESCENDING == ord);
         skipSignificand(src, DESCENDING == ord);
         return src.getPosition() - start;
       case POS_INF:
         return 1;
       case NAN:
         return 1;
       case FIXED_INT8:
         src.setPosition(src.getPosition() + 1);
         return src.getPosition() - start;
       case FIXED_INT16:
         src.setPosition(src.getPosition() + 2);
         return src.getPosition() - start;
       case FIXED_INT32:
         src.setPosition(src.getPosition() + 4);
         return src.getPosition() - start;
       case FIXED_INT64:
         src.setPosition(src.getPosition() + 8);
         return src.getPosition() - start;
       case FIXED_FLOAT32:
         src.setPosition(src.getPosition() + 4);
         return src.getPosition() - start;
       case FIXED_FLOAT64:
         src.setPosition(src.getPosition() + 8);
         return src.getPosition() - start;
       case TEXT:
         // for null-terminated values, skip to the end.
         do {
           header = ord.apply(src.get());
         } while (header != TERM);
         return src.getPosition() - start;
       case BLOB_VAR:
         // read until we find a 0 in the MSB
         do {
           header = ord.apply(src.get());
         } while ((byte) (header & 0x80) != TERM);
         return src.getPosition() - start;
       case BLOB_COPY:
         if (Order.DESCENDING == ord) {
           // if descending, read to termination byte.
           do {
             header = ord.apply(src.get());
           } while (header != TERM);
           return src.getPosition() - start;
         } else {
           // otherwise, just skip to the end.
           src.setPosition(src.getLength());
           return src.getPosition() - start;
         }
       default:
         throw unexpectedHeader(header);
     }
   }
 
   /**
    * Return the number of encoded entries remaining in {@code buff}. The
    * state of {@code buff} is not modified through use of this method.
    */
   public static int length(PositionedByteRange buff) {
     PositionedByteRange b =
         new SimplePositionedMutableByteRange(buff.getBytes(), buff.getOffset(), buff.getLength());
     b.setPosition(buff.getPosition());
     int cnt = 0;
     for (; isEncodedValue(b); skip(b), cnt++)
       ;
     return cnt;
   }
 }