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xml:id="std.numerics" xreflabel="Numerics">
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<keyword>ISO C++</keyword>
<!-- Sect1 01 : Complex -->
<section xml:id="std.numerics.complex" xreflabel="complex"><info><title>Complex</title></info>
<?dbhtml filename="complex.html"?>
<section xml:id="numerics.complex.processing" xreflabel="complex Processing"><info><title>complex Processing</title></info>
<para>Using <code>complex&lt;&gt;</code> becomes even more comple- er, sorry,
<emphasis>complicated</emphasis>, with the not-quite-gratuitously-incompatible
addition of complex types to the C language. David Tribble has
compiled a list of C++98 and C99 conflict points; his description of
C's new type versus those of C++ and how to get them playing together
nicely is
<link xmlns:xlink="" xlink:href="">here</link>.
<para><code>complex&lt;&gt;</code> is intended to be instantiated with a
floating-point type. As long as you meet that and some other basic
requirements, then the resulting instantiation has all of the usual
math operators defined, as well as definitions of <code>op&lt;&lt;</code>
and <code>op&gt;&gt;</code> that work with iostreams: <code>op&lt;&lt;</code>
prints <code>(u,v)</code> and <code>op&gt;&gt;</code> can read <code>u</code>,
<code>(u)</code>, and <code>(u,v)</code>.
<para>As an extension to C++11 and for increased compatibility with C,
<code>&lt;complex.h&gt;</code> includes both <code>&lt;complex&gt;</code>
and the C99 <code>&lt;complex.h&gt;</code> (if the C library provides
<!-- Sect1 02 : Generalized Operations -->
<section xml:id="std.numerics.generalized_ops" xreflabel="Generalized Ops"><info><title>Generalized Operations</title></info>
<?dbhtml filename="generalized_numeric_operations.html"?>
<para>There are four generalized functions in the &lt;numeric&gt; header
that follow the same conventions as those in &lt;algorithm&gt;. Each
of them is overloaded: one signature for common default operations,
and a second for fully general operations. Their names are
self-explanatory to anyone who works with numerics on a regular basis:
<para>Here is a simple example of the two forms of <code>accumulate</code>.
int ar[50];
int someval = somefunction();
// ...initialize members of ar to something...
int sum = std::accumulate(ar,ar+50,0);
int sum_stuff = std::accumulate(ar,ar+50,someval);
int product = std::accumulate(ar,ar+50,1,std::multiplies&lt;int&gt;());
<para>The first call adds all the members of the array, using zero as an
initial value for <code>sum</code>. The second does the same, but uses
<code>someval</code> as the starting value (thus, <code>sum_stuff == sum +
someval</code>). The final call uses the second of the two signatures,
and multiplies all the members of the array; here we must obviously
use 1 as a starting value instead of 0.
<para>The other three functions have similar dual-signature forms.
<!-- Sect1 03 : Interacting with C -->
<section xml:id="std.numerics.c" xreflabel="Interacting with C"><info><title>Interacting with C</title></info>
<?dbhtml filename="numerics_and_c.html"?>
<section xml:id="numerics.c.array" xreflabel="Numerics vs. Arrays"><info><title>Numerics vs. Arrays</title></info>
<para>One of the major reasons why FORTRAN can chew through numbers so well
is that it is defined to be free of pointer aliasing, an assumption
that C89 is not allowed to make, and neither is C++98. C99 adds a new
keyword, <code>restrict</code>, to apply to individual pointers. The
C++ solution is contained in the library rather than the language
(although many vendors can be expected to add this to their compilers
as an extension).
<para>That library solution is a set of two classes, five template classes,
and "a whole bunch" of functions. The classes are required
to be free of pointer aliasing, so compilers can optimize the
daylights out of them the same way that they have been for FORTRAN.
They are collectively called <code>valarray</code>, although strictly
speaking this is only one of the five template classes, and they are
designed to be familiar to people who have worked with the BLAS
libraries before.
<section xml:id="numerics.c.c99" xreflabel="C99"><info><title>C99</title></info>
<para>In addition to the other topics on this page, we'll note here some
of the C99 features that appear in libstdc++.
<para>The C99 features depend on the <code>--enable-c99</code> configure flag.
This flag is already on by default, but it can be disabled by the
user. Also, the configuration machinery will disable it if the
necessary support for C99 (e.g., header files) cannot be found.
<para>As of GCC 3.0, C99 support includes classification functions
such as <code>isnormal</code>, <code>isgreater</code>,
<code>isnan</code>, etc.
The functions used for 'long long' support such as <code>strtoll</code>
are supported, as is the <code>lldiv_t</code> typedef. Also supported
are the wide character functions using 'long long', like