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   9    <title>libstdc++-v3 HOWTO:  Chapter 26</title>
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  14 <h1 CLASS="centered"><a name="top">Chapter 26:  Numerics</a></h1>
  15
  16 <p>Chapter 26 deals with building block abstractions to aid in
  17    numerical computing:
  18    <ul>
  19      <li>Template data structures such as <code>valarray&lt;&gt;</code>
  20          and <code>complex&lt;&gt;</code>.
  21      <li>Template numerical functions such as <code>accumulate</code>;
  22          <code>inner_product</code>; <code>partial_sum</code> and
  23          <code>adjacent_difference</code>.
  24    </ul>
  25    All of the Standard C math functions are of course included in C++,
  26    and overloaded versions for <code>long</code>, <code>float</code>, and
  27    <code>long double</code> have been added for all of them.
  28 </p>
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  31 <hr>
  32 <h1>Contents</h1>
  33 <ul>
  34    <li><a href="#1">Complex Number Processing</a>
  35    <li><a href="#2">Array Processing</a>
  36    <li><a href="#3">Numerical Functions</a>
  37    <li><a href="#4">C99</a>
  38 </ul>
  39
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  43
  44 <h2><a name="1">Complex Number Processing</a></h2>
  45    <p>Using <code>complex&lt;&gt;</code> becomes even more comple- er, sorry,
  46       <em>complicated</em>, with the not-quite-gratuitously-incompatible
  47       addition of complex types to the C language.  David Tribble has
  48       compiled a list of C++98 and C99 conflict points; his description of
  49       C's new type versus those of C++ and how to get them playing together
  50       nicely is
  51 <a href="http://home.flash.net/~dtribble/text/cdiffs.htm#C99.complex">here</a>.
  52    </p>
  53    <p><code>complex&lt;&gt;</code> is intended to be instantiated with a
  54       floating-point type.  As long as you meet that and some other basic
  55       requirements, then the resulting instantiation has all of the usual
  56       math operators defined, as well as definitions of <code>op&lt;&lt;</code>
  57       and <code>op&gt;&gt;</code> that work with iostreams: <code>op&lt;&lt;</code>
  58       prints <code>(u,v)</code> and <code>op&gt;&gt;</code> can read <code>u</code>,
  59       <code>(u)</code>, and <code>(u,v)</code>.
  60    </p>
  61    <p>Return <a href="#top">to top of page</a> or
  62       <a href="../faq/index.html">to the FAQ</a>.
  63    </p>
  64
  65 <hr>
  66 <h2><a name="2">Array Processing</a></h2>
  67    <p>One of the major reasons why FORTRAN can chew through numbers so well
  68       is that it is defined to be free of pointer aliasing, an assumption
  69       that C89 is not allowed to make, and neither is C++.  C99 adds a new
  70       keyword, <code>restrict</code>, to apply to individual pointers.  The C++
  71       solution is contained in the library rather than the language
  72       (although many vendors can be expected to add this to their compilers
  73       as an extension).
  74    </p>
  75    <p>That library solution is a set of two classes, five template classes,
  76       and &quot;a whole bunch&quot; of functions.  The classes are required
  77       to be free of pointer aliasing, so compilers can optimize the
  78       daylights out of them the same way that they have been for FORTRAN.
  79       They are collectively called <code>valarray</code>, although strictly
  80       speaking this is only one of the five template classes, and they are
  81       designed to be familiar to people who have worked with the BLAS
  82       libraries before.
  83    </p>
  84    <p>Some more stuff should go here once somebody has time to write it.
  85    </p>
  86    <p>Return <a href="#top">to top of page</a> or
  87       <a href="../faq/index.html">to the FAQ</a>.
  88    </p>
  89
  90 <hr>
  91 <h2><a name="3">Numerical Functions</a></h2>
  92    <p>There are four generalized functions in the &lt;numeric&gt; header
  93       that follow the same conventions as those in &lt;algorithm&gt;.  Each
  94       of them is overloaded:  one signature for common default operations,
  95       and a second for fully general operations.  Their names are
  96       self-explanatory to anyone who works with numerics on a regular basis:
  97       <ul>
  98         <li><code>accumulate</code>
  99         <li><code>inner_product</code>
 100         <li><code>partial_sum</code>
 101         <li><code>adjacent_difference</code>
 102       </ul>
 103    </p>
 104    <p>Here is a simple example of the two forms of <code>accumulate</code>.
 105       <PRE>
 106    int   ar[50];
 107    int   someval = somefunction();
 108
 109    // ...initialize members of ar to something...
 110
 111    int  sum       = std::accumulate(ar,ar+50,0);
 112    int  sum_stuff = std::accumulate(ar,ar+50,someval);
 113    int  product   = std::accumulate(ar,ar+50,1,std::multiplies&lt;int&gt;());
 114       </PRE>
 115       The first call adds all the members of the array, using zero as an
 116       initial value for <code>sum</code>.  The second does the same, but uses
 117       <code>someval</code> as the starting value (thus, <code>sum_stuff == sum +
 118       someval</code>).  The final call uses the second of the two signatures,
 119       and multiplies all the members of the array; here we must obviously
 120       use 1 as a starting value instead of 0.
 121    </p>
 122    <p>The other three functions have similar dual-signature forms.
 123    </p>
 124    <p>Return <a href="#top">to top of page</a> or
 125       <a href="../faq/index.html">to the FAQ</a>.
 126    </p>
 127
 128 <hr>
 129 <h2><a name="4">C99</a></h2>
 130    <p>In addition to the other topics on this page, we'll note here some
 131       of the C99 features that appear in libstdc++-v3.
 132    </p>
 133    <p>The C99 features depend on the <code>--enable-c99</code> configure flag.
 134       This flag is already on by default, but it can be disabled by the
 135       user.  Also, the configuration machinery will disable it if the
 136       neccessary support for C99 (e.g., header files) cannot be found.
 137    </p>
 138    <p>As of GCC 3.0, C99 support includes classification functions
 139       such as <code>isnormal</code>, <code>isgreater</code>, <code>isnan</code>, etc.
 140       The functions used for 'long long' support such as <code>strtoll</code>
 141       are supported, as is the <code>lldiv_t</code> typedef.  Also supported
 142       are the wide character functions using 'long long', like
 143       <code>wcstoll</code>.
 144    </p>
 145    <p>Return <a href="#top">to top of page</a> or
 146       <a href="../faq/index.html">to the FAQ</a>.
 147    </p>
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