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<chapter>
  <header>
    <copyright>
      <year>2003</year><year>2009</year>
      <holder>Ericsson AB. All Rights Reserved.</holder>
    </copyright>
    <legalnotice>
      The contents of this file are subject to the Erlang Public License,
      Version 1.1, (the "License"); you may not use this file except in
      compliance with the License. You should have received a copy of the
      Erlang Public License along with this software. If not, it can be
      retrieved online at http://www.erlang.org/.
    
      Software distributed under the License is distributed on an "AS IS"
      basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
      the License for the specific language governing rights and limitations
      under the License.
    
    </legalnotice>

    <title>Bit Syntax</title>
    <prepared></prepared>
    <docno></docno>
    <date></date>
    <rev></rev>
    <file>bit_syntax.xml</file>
  </header>

  <section>
    <title>Introduction</title>
    <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 be able to, from a high level, construct a binary,</p>
    <code type="none"><![CDATA[
Bin = <<E1, E2, ... En>>]]></code>
    <p>in which case all elements must be bound, or to match a binary,</p>
    <code type="none"><![CDATA[
<<E1, E2, ... En>> = Bin ]]></code>
    <p>where <c>Bin</c> is bound, and where the elements are bound or
      unbound, as in any match.</p>
    <p>In R12B, a Bin need not 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 doesn't 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 etc.</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>yields binaries of size 3; <c>binary_to_list(Bin11)</c>
        evaluates to <c>[1, 17, 42]</c>, and
        <c>binary_to_list(Bin12)</c> evaluates to <c>[97, 98, 99]</c>.</p>
      <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>yields a binary of size 4, and <c>binary_to_list(Bin2)</c>
        evaluates to <c>[1, 17, 00, 42]</c> too. Here we used a
        <em>size expression</em> for the variable <c>C</c> in order to
        specify a 16-bits segment of <c>Bin2</c>.</p>
      <p><em>Example 3: </em>A Bin can also be used for matching: if
        <c>D</c>, <c>E</c>, and <c>F</c> are unbound variables, and
        <c>Bin2</c> is bound as in the former example,</p>
      <code type="none"><![CDATA[
<<D:16, E, F/binary>> = Bin2]]></code>
      <p>yields <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, where <c>Dgram</c> is bound to the consecutive
        bytes of an IP datagram of IP protocol version 4, and where we
        want 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> should
        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, and its length -
        measured in the number of 32-bit words - is given in
        the segment corresponding to <c>HLen</c>, the minimum value of
        which is 5. It is the segment corresponding to <c>Opts</c>
        that is variable: if <c>HLen</c> is equal to 5, <c>Opts</c>
        will be an empty binary.</p>
      <p>The tail variables <c>RestDgram</c> and <c>Data</c> bind to
        binaries, as all tail variables do. Both may bind to empty
        binaries.</p>
      <p>If the first 4-bits segment of <c>Dgram</c> is not equal to
        4, or if <c>HLen</c> is less than 5, or if the size of
        <c>Dgram</c> is less than <c>4*HLen</c>, the match of
        <c>Dgram</c> fails.</p>
    </section>
  </section>

  <section>
    <title>A Lexical Note</title>
    <p>Note 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>Both the <c>Size</c> and the <c>TypeSpecifier</c> or both may be
      omitted; thus the following variations are allowed:</p>
    <p><c>Value</c></p>
    <p><c>Value:Size</c></p>
    <p><c>Value/TypeSpecifierList</c></p>
    <p>Default values will be used for missing specifications.
      The default values are described in the section
      <seealso marker="#Defaults">Defaults</seealso>.</p>
    <p>Used in binary construction, the <c>Value</c> part is any
      expression. Used in binary matching, the <c>Value</c> part must
      be a literal or variable. You can read more about
      the <c>Value</c> part in the section about constructing
      binaries and matching binaries.</p>
    <p>The <c>Size</c> part of the segment multiplied by the unit in
      the <c>TypeSpecifierList</c> (described below) 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 type can be <c>integer</c>, <c>float</c>, or
      <c>binary</c>.</item>
      <tag>Signedness</tag>
      <item>The signedness specification can be either <c>signed</c>
       or <c>unsigned</c>. Note 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 will be 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 will be multiplied by
       the <c>Size</c> specifier to give the effective size of
       the segment. In R12B, the unit size specifies the alignment
       for binary segments without size (examples will follow).</item>
    </taglist>
    <p>Example:</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 instance, 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 very 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>
    <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 (i.e. only whole bytes).
      Example:</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 will be generated if <c>Bin</c> would
    consist of (for instance) 17 bits.</p>

    <p>On the other hand, the variable <c>Bitstring</c> may consist of
    any number of bits, for instance 0, 1, 8, 11, 17, 42, and so on,
    because the default <c>unit</c> for bitstrings is 1.</p>

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

    <p>The following example</p>
    <code type="none"><![CDATA[
<<X:1,Y:6>>]]></code>
    <p>will successfully construct a bitstring of 7 bits.
      (Provided that all of X and Y are integers.)</p>
    <p>As noted 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 variable. The following gives a compiler syntax error:</p>
    <code type="none"><![CDATA[
<<X+1:8>>]]></code>
    <p>This expression must be rewritten to</p>
    <code type="none"><![CDATA[
<<(X+1):8>>]]></code>
    <p>in order to be accepted by the compiler.</p>

    <section>
      <title>Including Literal Strings</title>
      <p>As syntactic sugar, an literal string may be written instead
        of a element.</p>
      <code type="none"><![CDATA[
<<"hello">>]]></code>
      <p>which is syntactic sugar for</p>
      <code type="none"><![CDATA[
<<$h,$e,$l,$l,$o>>]]></code>
    </section>
  </section>

  <section>
    <title>Matching Binaries</title>
    <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 in every place patterns are allowed,
      also inside other patterns. Binary patterns cannot be nested.</p>
    <p>The pattern '<c><![CDATA[<<>>]]></c>' matches a zero length binary.</p>
    <p>Each segment in a binary can consist of zero or more bits.</p>
    <p>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).</p>
    <p>A segment of type <c>bitstring</c> has no restrictions on the size.</p>
    <p>As noted 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 floating point literal. Expressions are not
      allowed.</p>
    <p><c>Size</c> must be an integer literal, or a previously bound
      variable. Note that 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 like this:</p>
    <code type="none"><![CDATA[
foo(N, Bin) ->
   <<X:N,T/binary>> = Bin,
   {X,T}.]]></code>

    <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 is no restriction on the number of bits in the tail.</p>
    </section>
  </section>

  <section>
    <title>Appending to a Binary</title>
    <p>In R12B, the following function for creating a binary out of
    a list of triples of integers is now efficient:</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>>);   % inefficient before R12B
triples_to_bin([], Acc) -> 
    Acc.]]></code>
    <p>In previous releases, this function was highly inefficient, because
    the binary constructed so far (<c>Acc</c>) was copied in each recursion step.
    That is no longer the case. See the Efficiency Guide for more information.</p>
  </section>
</chapter>

