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<chapter>
  <header>
    <copyright>
      <year>2003</year><year>2020</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
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      Licensed under the Apache License, Version 2.0 (the "License");
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    <title>Bit Syntax</title>
    <prepared></prepared>
    <docno></docno>
    <date></date>
    <rev></rev>
    <file>bit_syntax.xml</file>
  </header>

  <section>
    <title>Introduction</title>
    <p>The complete specification for the bit syntax appears in the
    <seeguide marker="system/reference_manual:expressions#bit_syntax">Reference Manual</seeguide>.</p>
    <p>In Erlang, a Bin is used for constructing binaries and matching
      binary patterns. A Bin is written with the following syntax:</p>
    <code type="none"><![CDATA[
      <<E1, E2, ... En>>]]></code>
    <p>A Bin is a low-level sequence of bits or bytes.
    The purpose of a Bin is to enable construction of binaries:</p>
    <code type="none"><![CDATA[
Bin = <<E1, E2, ... En>>]]></code>
    <p>All elements must be bound. Or match a binary:</p>
    <code type="none"><![CDATA[
<<E1, E2, ... En>> = Bin ]]></code>
    <p>Here, <c>Bin</c> is bound and the elements are bound or
      unbound, as in any match.</p>
    <p>A Bin does not need to consist of a whole number of bytes.</p>

    <p>A <em>bitstring</em> is a sequence of zero or more bits, where
    the number of bits does not need to be divisible by 8. If the number
    of bits is divisible by 8, the bitstring is also a binary.</p>
    <p>Each element specifies a certain <em>segment</em> of the bitstring.
      A segment is a set of contiguous bits of the binary (not
      necessarily on a byte boundary). The first element specifies
      the initial segment, the second element specifies the following
      segment, and so on.</p>
    <p>The following examples illustrate how binaries are constructed,
      or matched, and how elements and tails are specified.</p>

    <section>
      <title>Examples</title>
      <p><em>Example 1:</em> A binary can be constructed from a set of
        constants or a string literal:</p>
      <code type="none"><![CDATA[
Bin11 = <<1, 17, 42>>,
Bin12 = <<"abc">>]]></code>
      <p>This gives two binaries of size 3, with the following evaluations:</p>
	<list type="bulleted">
       <item><c>binary_to_list(Bin11)</c> evaluates to <c>[1, 17, 42]</c>.</item>
       <item><c>binary_to_list(Bin12)</c> evaluates to <c>[97, 98, 99]</c>.</item>
     </list>
      <p><em>Example 2:</em>Similarly, a binary can be constructed
        from a set of bound variables:</p>
      <code type="none"><![CDATA[
A = 1, B = 17, C = 42,
Bin2 = <<A, B, C:16>>]]></code>
      <p>This gives a binary of size 4.
      Here, a <em>size expression</em> is used for the variable <c>C</c> to
        specify a 16-bits segment of <c>Bin2</c>.</p>
	<p><c>binary_to_list(Bin2)</c> evaluates to <c>[1, 17, 00, 42]</c>.</p>
      <p><em>Example 3:</em> A Bin can also be used for matching.
        <c>D</c>, <c>E</c>, and <c>F</c> are unbound variables, and
        <c>Bin2</c> is bound, as in Example 2:</p>
      <code type="none"><![CDATA[
<<D:16, E, F/binary>> = Bin2]]></code>
      <p>This gives <c>D = 273</c>, <c>E = 00</c>, and F binds to a binary
        of size 1: <c>binary_to_list(F) = [42]</c>.</p>
      <p><em>Example 4:</em> The following is a more elaborate example
        of matching. Here, <c>Dgram</c> is bound to the consecutive
        bytes of an IP datagram of IP protocol version 4. The ambition is
      to extract the header and the data of the datagram:</p>
      <code type="none"><![CDATA[
-define(IP_VERSION, 4).
-define(IP_MIN_HDR_LEN, 5).

DgramSize = byte_size(Dgram),
case Dgram of 
    <<?IP_VERSION:4, HLen:4, SrvcType:8, TotLen:16, 
      ID:16, Flgs:3, FragOff:13,
      TTL:8, Proto:8, HdrChkSum:16,
      SrcIP:32,
      DestIP:32, RestDgram/binary>> when HLen>=5, 4*HLen=<DgramSize ->
        OptsLen = 4*(HLen - ?IP_MIN_HDR_LEN),
        <<Opts:OptsLen/binary,Data/binary>> = RestDgram,
    ...
end.]]></code>
      <p>Here, the segment corresponding to the <c>Opts</c> variable
        has a <em>type modifier</em>, specifying that <c>Opts</c> is to
        bind to a binary. All other variables have the default type
        equal to unsigned integer.</p>
      <p>An IP datagram header is of variable length. This length is
        measured in the number of 32-bit words and is given in
        the segment corresponding to <c>HLen</c>. The minimum value of
        <c>HLen</c> is 5. It is the segment corresponding to <c>Opts</c>
        that is variable, so if <c>HLen</c> is equal to 5, <c>Opts</c>
        becomes an empty binary.</p>
      <p>The tail variables <c>RestDgram</c> and <c>Data</c> bind to
        binaries, as all tail variables do. Both can bind to empty
        binaries.</p>
	<p>The match of <c>Dgram</c> fails if one of the following occurs:</p>
	<list type="bulleted">
       <item>The first 4-bits segment of <c>Dgram</c> is not equal to 4.</item>
       <item><c>HLen</c> is less than 5.</item>
       <item>The size of <c>Dgram</c> is less than <c>4*HLen</c>.</item>
     </list>
    </section>
  </section>

  <section>
    <title>Lexical Note</title>
    <p>Notice that "<c><![CDATA[B=<<1>>]]></c>" will be interpreted as
      "<c><![CDATA[B =< <1>>]]></c>", which is a syntax error.
      The correct way to write the expression is:
      <c><![CDATA[B = <<1>>]]></c>.</p>
  </section>

  <section>
    <title>Segments</title>
    <p>Each segment has the following general syntax:</p>
    <p><c>Value:Size/TypeSpecifierList</c></p>
    <p>The <c>Size</c> or the <c>TypeSpecifier</c>, or both, can be
      omitted. Thus, the following variants are allowed:</p>
      <list type="bulleted">
       <item><c>Value</c></item>
       <item><c>Value:Size</c></item>
       <item><c>Value/TypeSpecifierList</c></item>
     </list>
    <p>Default values are used when specifications are missing.
      The default values are described in
      <seeguide marker="#Defaults">Defaults</seeguide>.</p>
    <p>The <c>Value</c> part is any expression, when used in binary construction.
      Used in binary matching, the <c>Value</c> part must
      be a literal or a variable. For more information about
      the <c>Value</c> part, see
      <seeguide marker="#Constructing Binaries and Bitstrings">Constructing Binaries and Bitstrings</seeguide>
      and
      <seeguide marker="#Matching Binaries">Matching Binaries</seeguide>.</p>
    <p>The <c>Size</c> part of the segment multiplied by the unit in
      <c>TypeSpecifierList</c> (described later) gives the number
      of bits for the segment. In construction, <c>Size</c> is any
      expression that evaluates to an integer. In matching,
      <c>Size</c> must be a constant expression or a variable.</p>
    <p>The <c>TypeSpecifierList</c> is a list of type specifiers
      separated by hyphens.</p>
    <taglist>
      <tag>Type</tag>
      <item>The most commonly used types are <c>integer</c>, <c>float</c>, and <c>binary</c>.
      See <seeguide marker="system/reference_manual:expressions#bit_syntax">Bit Syntax Expressions in the Reference Manual</seeguide> for a complete description.
</item>
      <tag>Signedness</tag>
      <item>The signedness specification can be either <c>signed</c>
       or <c>unsigned</c>. Notice that signedness only matters for
       matching.</item>
      <tag>Endianness</tag>
      <item>The endianness specification can be either <c>big</c>,
      <c>little</c>, or <c>native</c>. Native-endian means that
       the endian is resolved at load time, to be either
       big-endian or little-endian, depending on what is "native"
       for the CPU that the Erlang machine is run on.</item>
      <tag>Unit</tag>
      <item>The unit size is given as <c>unit:IntegerLiteral</c>.
       The allowed range is 1-256. It is multiplied by
       the <c>Size</c> specifier to give the effective size of
       the segment. The unit size specifies the alignment
       for binary segments without size.</item>
    </taglist>
    <p><em>Example:</em></p>
    <code type="none">
X:4/little-signed-integer-unit:8</code>
    <p>This element has a total size of 4*8 = 32 bits, and it contains
      a signed integer in little-endian order.</p>
  </section>

  <section>
    <title>Defaults</title>
    <p><marker id="Defaults"></marker>The default type for
     a segment is integer. The default
      type does not depend on the value, even if the value is a
      literal. For example, the default type in <c><![CDATA[<<3.14>>]]></c> is
      integer, not float.</p>
    <p>The default <c>Size</c> depends on the type. For integer it is
      8. For float it is 64. For binary it is all of the binary. In
      matching, this default value is only valid for the last
      element. All other binary elements in matching must have a size
      specification.</p>
    <p>The default unit depends on the the type. For <c>integer</c>,
      <c>float</c>, and <c>bitstring</c> it is 1. For binary it is 8.</p>
    <p>The default signedness is <c>unsigned</c>.</p>
    <p>The default endianness is <c>big</c>.</p>
  </section>

  <section>
    <title>Constructing Binaries and Bitstrings</title>
    <marker id="Constructing Binaries and Bitstrings"></marker>
    <p>This section describes the rules for constructing binaries using
      the bit syntax. Unlike when constructing lists or tuples,
      the construction of a binary can fail with a <c>badarg</c>
      exception.</p>
    <p>There can be zero or more segments in a binary to be
      constructed. The expression <c><![CDATA[<<>>]]></c> constructs a zero
      length binary.</p>
    <p>Each segment in a binary can consist of zero or more bits.
      There are no alignment rules for individual segments of type
      <c>integer</c> and <c>float</c>. For binaries and bitstrings
      without size, the unit specifies the alignment. Since the default
      alignment for the <c>binary</c> type is 8, the size of a binary
      segment must be a multiple of 8 bits, that is, only whole bytes.</p>
      <p><em>Example:</em></p>
    <code type="none"><![CDATA[
<<Bin/binary,Bitstring/bitstring>>]]></code>
    <p>The variable <c>Bin</c> must contain a whole number of bytes,
    because the <c>binary</c> type defaults to <c>unit:8</c>.
    A <c>badarg</c> exception is generated if <c>Bin</c>
    consist of, for example, 17 bits.</p>

    <p>The <c>Bitstring</c> variable can consist of
    any number of bits, for example, 0, 1, 8, 11, 17, 42, and so on.
    This is because the default <c>unit</c> for bitstrings is 1.</p>

    <p>For clarity, it is recommended not to change the unit
    size for binaries. Instead, use <c>binary</c> when you need byte alignment
    and <c>bitstring</c> when you need bit alignment.</p>

    <p>The following example successfully constructs a bitstring of 7 bits,
      provided that all of X and Y are integers:</p>
    <code type="none"><![CDATA[
<<X:1,Y:6>>]]></code>
    <p>As mentioned earlier, segments have the following general syntax:</p>
    <p><c>Value:Size/TypeSpecifierList</c></p>
    <p>When constructing binaries, <c>Value</c> and <c>Size</c> can be
      any Erlang expression. However, for syntactical reasons, both
      <c>Value</c> and <c>Size</c> must be enclosed in parenthesis if
      the expression consists of anything more than a single literal
      or a variable. The following gives a compiler syntax error:</p>
    <code type="none"><![CDATA[
<<X+1:8>>]]></code>
    <p>This expression must be rewritten into the following,
    to be accepted by the compiler:</p>
    <code type="none"><![CDATA[
<<(X+1):8>>]]></code>

    <section>
      <title>Including Literal Strings</title>
      <p>A literal string can be written instead of an element:</p>
      <code type="none"><![CDATA[
<<"hello">>]]></code>
      <p>This is syntactic sugar for the following:</p>
      <code type="none"><![CDATA[
<<$h,$e,$l,$l,$o>>]]></code>
    </section>
  </section>

  <section>
    <title>Matching Binaries</title>
    <marker id="Matching Binaries"></marker>
    <p>This section describes the rules for matching binaries, using
      the bit syntax.</p>
    <p>There can be zero or more segments in a binary pattern.
      A binary pattern can occur wherever patterns are allowed,
      including inside other patterns. Binary patterns cannot be nested.
      The pattern <c><![CDATA[<<>>]]></c> matches a zero length binary.</p>
    <p>Each segment in a binary can consist of zero or more bits.
       A segment of type <c>binary</c> must have a size evenly divisible by 8
    (or divisible by the unit size, if the unit size has been changed).
    A segment of type <c>bitstring</c> has no restrictions on the size.
    A segment of type <c>float</c> must have size 64 or 32.</p>
    <p>As mentioned earlier, segments have the following general syntax:</p>
    <p><c>Value:Size/TypeSpecifierList</c></p>
    <p>When matching <c>Value</c>, value must be either a variable or
      an integer, or a floating point literal. Expressions are not
      allowed.</p>
      <p><c>Size</c> must be a
      <seeguide marker="system/reference_manual:expressions#guard_expressions">guard expression</seeguide>, which can use literals and previously bound variables.
      The following is not allowed:</p>
    <code type="none"><![CDATA[
foo(N, <<X:N,T/binary>>) ->
   {X,T}.]]></code>
    <p>The two occurrences of <c>N</c> are not related. The compiler
      will complain that the <c>N</c> in the size field is unbound.</p>
    <p>The correct way to write this example is as follows:</p>
    <code type="none"><![CDATA[
foo(N, Bin) ->
   <<X:N,T/binary>> = Bin,
   {X,T}.]]></code>
    <note><p>Before OTP 23, <c>Size</c> was restricted to be an
    integer or a variable bound to an integer.</p></note>

    <section>
      <title>Binding and Using a Size Variable</title>
      <p>There is one exception to the rule that a variable that is
      as size must be previously bound. It is possible to match and
      bind a variable, and use it as a size within the the same
      binary pattern. For example:</p>

    <code type="none"><![CDATA[
bar(<<Sz:8,Payload:Sz/binary-unit:8,Rest/binary>>) ->
   {Payload,Rest}.]]></code>

    <p>Here <c>Sz</c> is bound to the value in the first byte of
    the binary. <c>Sz</c> is then used at the number of bytes
    to match out as a binary.</p>

    <p>Starting in OTP 23, the size can be a guard expression:</p>
    <code type="none"><![CDATA[
bar(<<Sz:8,Payload:((Sz-1)*8)/binary,Rest/binary>>) ->
   {Payload,Rest}.]]></code>

    <p>Here <c>Sz</c> is the combined size of the header and the
    payload, so we will need to subtract one byte to get the size
    of the payload.</p>
    </section>

    <section>
      <title>Getting the Rest of the Binary or Bitstring</title>
      <p>To match out the rest of a binary, specify a binary field
        without size:</p>
      <code type="none"><![CDATA[
foo(<<A:8,Rest/binary>>) ->]]></code>
      <p>The size of the tail must be evenly divisible by 8.</p>

      <p>To match out the rest of a bitstring, specify a field
        without size:</p>
      <code type="none"><![CDATA[
foo(<<A:8,Rest/bitstring>>) ->]]></code>
      <p>There are no restrictions on the number of bits in the tail.</p>
    </section>
  </section>

  <section>
    <title>Appending to a Binary</title>
    <p>Appending to a binary in an efficient way can be done as follows:</p>
    <code type="none"><![CDATA[
triples_to_bin(T) ->
    triples_to_bin(T, <<>>).

triples_to_bin([{X,Y,Z} | T], Acc) ->
    triples_to_bin(T, <<Acc/binary,X:32,Y:32,Z:32>>);
triples_to_bin([], Acc) -> 
    Acc.]]></code>
  </section>
</chapter>

