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