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 <div class="subTitle">org.apache.hadoop.hbase.util</div>
 <h2 title="Class OrderedBytes" class="title">Class OrderedBytes</h2>
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 <pre>@InterfaceAudience.Public
 public class <a href="../../../../../src-html/org/apache/hadoop/hbase/util/OrderedBytes.html#line.297">OrderedBytes</a>
 extends <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
 <div class="block">Utility class that handles ordered byte arrays. That is, unlike <a href="../../../../../org/apache/hadoop/hbase/util/Bytes.html" title="class in org.apache.hadoop.hbase.util"><code>Bytes</code></a>, 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</code> 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</code> 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 <a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#isNumericInfinite-org.apache.hadoop.hbase.util.PositionedByteRange-"><code>isNumericInfinite(PositionedByteRange)</code></a> and
  <a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#isNumericNaN-org.apache.hadoop.hbase.util.PositionedByteRange-"><code>isNumericNaN(PositionedByteRange)</code></a> to protect against decoding values into object which
  do not support these numeric concepts (such as <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Long.html?is-external=true" title="class or interface in java.lang"><code>Long</code></a> and <a href="https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html?is-external=true" title="class or interface in java.math"><code>BigDecimal</code></a>).
  </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</code> using
  <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Float.html?is-external=true#floatToIntBits-float-" title="class or interface in java.lang"><code>Float.floatToIntBits(float)</code></a>. 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</code> 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</code> 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</code> and <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang"><code>Double</code></a> encodings are based on implementations from the now defunct
  Orderly library.
  </p></div>
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 <h3>Field Summary</h3>
 <table class="memberSummary" border="0" cellpadding="3" cellspacing="0" summary="Field Summary table, listing fields, and an explanation">
 <caption><span>Fields</span><span class="tabEnd">&nbsp;</span></caption>
 <tr>
 <th class="colFirst" scope="col">Modifier and Type</th>
 <th class="colLast" scope="col">Field and Description</th>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#BLOB_COPY">BLOB_COPY</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#BLOB_VAR">BLOB_VAR</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>static <a href="https://docs.oracle.com/javase/8/docs/api/java/math/MathContext.html?is-external=true" title="class or interface in java.math">MathContext</a></code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#DEFAULT_MATH_CONTEXT">DEFAULT_MATH_CONTEXT</a></span></code>
 <div class="block">The context used to normalize <a href="https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html?is-external=true" title="class or interface in java.math"><code>BigDecimal</code></a> values.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#FIXED_FLOAT32">FIXED_FLOAT32</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#FIXED_FLOAT64">FIXED_FLOAT64</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#FIXED_INT16">FIXED_INT16</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#FIXED_INT32">FIXED_INT32</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#FIXED_INT64">FIXED_INT64</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#FIXED_INT8">FIXED_INT8</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>static int</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#MAX_PRECISION">MAX_PRECISION</a></span></code>
 <div class="block">Max precision guaranteed to fit into a <code>long</code>.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NAN">NAN</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NEG_INF">NEG_INF</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NEG_LARGE">NEG_LARGE</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NEG_MED_MAX">NEG_MED_MAX</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NEG_MED_MIN">NEG_MED_MIN</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NEG_SMALL">NEG_SMALL</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#NULL">NULL</a></span></code>&nbsp;</td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#POS_INF">POS_INF</a></span></code>&nbsp;</td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>private static byte</code></td>
 <td class="colLast"><code><span class="memberNameLink"><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#POS_LARGE">POS_LARGE</a></span></code>&nbsp;</td>
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  digits are omitted. This means that the mantissa will never contain a byte with the value
  <code>0x00</code>.
  </p>
  <p>
  If <code>E &gt; 10</code>, then this routine writes of <code>E</code> as a varint followed by the mantissa
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  leaves the <code>E</code> value to be encoded as part of the opening byte of the field by the
  calling function.

  <pre>
    Encoding:  M       (if E&lt;=10)
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 <div class="block">Encode a numerical value using the variable-length encoding. If the number of significant
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  not support <code>NaN</code> or <code>Infinte</code> values.</div>
 <dl>
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 <dd><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#decodeNumericAsDouble-org.apache.hadoop.hbase.util.PositionedByteRange-"><code>decodeNumericAsDouble(PositionedByteRange)</code></a></dd>
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  <a href="https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html?is-external=true" title="class or interface in java.math"><code>BigDecimal</code></a>; in the event the encoded value is larger than can be represented in a
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  <a href="https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html?is-external=true#doubleValue--" title="class or interface in java.math"><code>BigDecimal.doubleValue()</code></a>.</div>
 <dl>
 <dt><span class="throwsLabel">Throws:</span></dt>
 <dd><code><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - when the encoded value is <code>NULL</code>.</dd>
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 <dd><a href="../../../../../org/apache/hadoop/hbase/util/OrderedBytes.html#encodeNumeric-org.apache.hadoop.hbase.util.PositionedByteRange-double-org.apache.hadoop.hbase.util.Order-"><code>encodeNumeric(PositionedByteRange, double, Order)</code></a>,
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 <div class="block">Decode a primitive <code>long</code> value from the Numeric encoding. Numeric encoding is based on
  <a href="https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html?is-external=true" title="class or interface in java.math"><code>BigDecimal</code></a>; in the event the encoded value is larger than can be represented in a
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  <a href="https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html?is-external=true#doubleValue--" title="class or interface in java.math"><code>BigDecimal.doubleValue()</code></a>.</div>
 <dl>
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 <dd><code><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/NullPointerException.html?is-external=true" title="class or interface in java.lang">NullPointerException</a></code> - when the encoded value is <code>NULL</code>.</dd>
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 <div class="block">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>[]</code> and so it does not support
  <code>0x00</code> in the value.</div>
 <dl>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>the number of bytes written.</dd>
 <dt><span class="throwsLabel">Throws:</span></dt>
 <dd><code><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - when <code>ord</code> is DESCENDING and <code>val</code> contains a
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 <div class="block">Encode a Blob value as a byte-for-byte copy. BlobCopy encoding in DESCENDING order is NULL
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 <dl>
 <dt><span class="returnLabel">Returns:</span></dt>
 <dd>the number of bytes written.</dd>
 <dt><span class="throwsLabel">Throws:</span></dt>
 <dd><code><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - when <code>ord</code> is DESCENDING and <code>val</code> contains a
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