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<chapter>
  <header>
    <copyright>
      <year>2001</year><year>2022</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>Functions</title>
    <prepared>Bjorn Gustavsson</prepared>
    <docno></docno>
    <date>2007-11-22</date>
    <rev></rev>
    <file>functions.xml</file>
  </header>

  <section>
    <title>Pattern Matching</title>
    <p>Pattern matching in function head as well as in <c>case</c> and
    <c>receive</c> clauses are optimized by the compiler. With a few
    exceptions, there is nothing to gain by rearranging clauses.</p>

    <p>One exception is pattern matching of binaries. The compiler
    does not rearrange clauses that match binaries. Placing the
    clause that matches against the empty binary <em>last</em> is usually
    slightly faster than placing it <em>first</em>.</p>

    <p>The following is a rather unnatural example to show another
    exception:</p>

    <p><em>DO NOT</em></p>
    <code type="erl">
atom_map1(one) -> 1;
atom_map1(two) -> 2;
atom_map1(three) -> 3;
atom_map1(Int) when is_integer(Int) -> Int;
atom_map1(four) -> 4;
atom_map1(five) -> 5;
atom_map1(six) -> 6.</code>

     <p>The problem is the clause with the variable <c>Int</c>.
     As a variable can match anything, including the atoms
     <c>four</c>, <c>five</c>, and <c>six</c>, which the following clauses
     also match, the compiler must generate suboptimal code that
     executes as follows:</p>

     <list type="bulleted">
     <item>First, the input value is compared to <c>one</c>, <c>two</c>, and
     <c>three</c> (using a single instruction that does a binary search;
     thus, quite efficient even if there are many values) to select which
     one of the first three clauses to execute (if any).</item>

     <item>If none of the first three clauses match, the fourth clause
     match as a variable always matches.</item>

     <item>If the guard test <c>is_integer(Int)</c> succeeds, the fourth
     clause is executed.</item>

     <item>If the guard test fails, the input value is compared to
     <c>four</c>, <c>five</c>, and <c>six</c>, and the appropriate clause
     is selected. (There is a <c>function_clause</c> exception if none of
     the values matched.)</item>
     </list>

     <p>Rewriting to either:</p>

     <p><em>DO</em></p>
     <code type="erl"><![CDATA[
atom_map2(one) -> 1;
atom_map2(two) -> 2;
atom_map2(three) -> 3;
atom_map2(four) -> 4;
atom_map2(five) -> 5;
atom_map2(six) -> 6;
atom_map2(Int) when is_integer(Int) -> Int.]]></code>

     <p>or:</p>

     <p><em>DO</em></p>
     <code type="erl"><![CDATA[
atom_map3(Int) when is_integer(Int) -> Int;
atom_map3(one) -> 1;
atom_map3(two) -> 2;
atom_map3(three) -> 3;
atom_map3(four) -> 4;
atom_map3(five) -> 5;
atom_map3(six) -> 6.]]></code>

     <p>gives slightly more efficient matching code.</p>

     <p>Another example:</p>

     <p><em>DO NOT</em></p>
     <code type="erl"><![CDATA[
map_pairs1(_Map, [], Ys) ->
    Ys;
map_pairs1(_Map, Xs, [] ) ->
    Xs;
map_pairs1(Map, [X|Xs], [Y|Ys]) ->
    [Map(X, Y)|map_pairs1(Map, Xs, Ys)].]]></code>

     <p>The first argument is <em>not</em> a problem. It is variable, but it
     is a variable in all clauses. The problem is the variable in the second
     argument, <c>Xs</c>, in the middle clause. Because the variable can
     match anything, the compiler is not allowed to rearrange the clauses,
     but must generate code that matches them in the order written.</p>

     <p>If the function is rewritten as follows, the compiler is free to
     rearrange the clauses:</p>

     <p><em>DO</em></p>
     <code type="erl"><![CDATA[
map_pairs2(_Map, [], Ys) ->
    Ys;
map_pairs2(_Map, [_|_]=Xs, [] ) ->
    Xs;
map_pairs2(Map, [X|Xs], [Y|Ys]) ->
    [Map(X, Y)|map_pairs2(Map, Xs, Ys)].]]></code>

    <p>The compiler will generate code similar to this:</p>

    <p><em>DO NOT (already done by the compiler)</em></p>
    <code type="erl"><![CDATA[
explicit_map_pairs(Map, Xs0, Ys0) ->
    case Xs0 of
	[X|Xs] ->
	    case Ys0 of
		[Y|Ys] ->
		    [Map(X, Y)|explicit_map_pairs(Map, Xs, Ys)];
		[] ->
		    Xs0
	    end;
	[] ->
	    Ys0
    end.]]></code>
      
    <p>This is slightly faster for probably the most common case
    that the input lists are not empty or very short.
    (Another advantage is that Dialyzer can deduce a better type
    for the <c>Xs</c> variable.)</p>
  </section>

  <section>
    <title>Function Calls</title>

    <p>This is a rough hierarchy of the performance of the
    different types of function calls:</p>

    <list type="bulleted">
    <item>Calls to local or external functions (<c>foo()</c>, <c>m:foo()</c>)
    are the fastest calls.</item>

    <item>Calling or applying a fun (<c>Fun()</c>, <c>apply(Fun, [])</c>)
    is just a little slower than external calls.</item>

    <item>Applying an exported function (<c>Mod:Name()</c>,
    <c>apply(Mod, Name, [])</c>) where the number of arguments is known
    at compile time is next.</item>

    <item>Applying an exported function (<c>apply(Mod, Name, Args)</c>)
    where the number of arguments is not known at compile time is the
    least efficient.</item>
    </list>

    <section>
       <title>Notes and Implementation Details</title>

       <p>Calling and applying a fun does not involve any hash-table lookup.
       A fun contains an (indirect) pointer to the function that implements
       the fun.</p>

       <p><c>apply/3</c> must look up the code for the function to execute
       in a hash table. It is therefore always slower than a
       direct call or a fun call.</p>

       <p>Caching callback functions into funs may be more efficient
       in the long run than apply calls for frequently-used callbacks.</p>

    </section>
  </section>

  <section>
    <title>Memory Usage in Recursion</title>
    <p>When writing recursive functions, it is preferable to make them
      tail-recursive so that they can execute in constant memory space:</p>

    <p><em>DO</em></p>
    <code type="none">
list_length(List) ->
    list_length(List, 0).

list_length([], AccLen) -> 
    AccLen; % Base case

list_length([_|Tail], AccLen) ->
    list_length(Tail, AccLen + 1). % Tail-recursive</code>

    <p><em>DO NOT</em></p>

    <code type="none">
list_length([]) ->
    0. % Base case
list_length([_ | Tail]) ->
    list_length(Tail) + 1. % Not tail-recursive</code>
  </section>
</chapter>

