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<h3 class="section">D.2 <code>complex</code></h3>

<p>Complex numbers are represented according to the ISO C standard as
<a name="index-complex-numbers-711"></a>arrays of two IEEE double precision floating point numbers of 8 bytes
each, with the number representing the real part first.

   <p>A small selection of operations on complex numbers is available by
function calls of the form <code>library('complex',f)</code>. These
functions are implemented by the host system's C library.

   <p>One example is <code>library('complex','create')</code> which takes a pair
of floating point numbers <code>(</code><var>x</var><code>,</code><var>y</var><code>)</code> to a complex number
whose real part is <var>x</var> and whose imaginary part is <var>y</var>. 
See <a href="math.html#math">math</a> for information about constructing floating point
numbers.

   <p>Other than that, the <code>complex</code> library functions <code>f</code> fall
into three main groups, which are the real valued unary operations,
the complex valued unary operations, and the complex valued binary
operations. All of these operations are designated by their standard C
names as documented elsewhere, such as the GNU <code>libc</code> reference
manual, except as noted.

     <dl>
<dt>&bull; real valued unary operations<dd>
     <pre class="example">          
          creal  cimag  cabs  carg
</pre>
     <br><dt>&bull; complex valued unary operations<dd>
     <pre class="example">          
          ccos   cexp    clog   conj   csin    csqrt
          ctan   csinh   ccosh  ctanh  casinh  cacosh
          catanh casin   cacos  catan
</pre>
     <br><dt>&bull; complex valued binary operations<dd>
     <pre class="example">          
          cpow  vid  bus  mul  add  sub  div
</pre>
     </dl>

   <p>The last four correspond to the C language operators <code>*</code>,
<code>+</code>, <code>-</code>, and <code>/</code> for complex numbers.  The functions
named <code>vid</code> and <code>bus</code> are similar to <code>div</code> and
<code>sub</code>, respectively, but with the operands interchanged. That is,

<pre class="example">     library('complex','vid') (x,y)
</pre>
   <p class="noindent">is equivalent to

<pre class="example">     library('complex','div') (y,x)
</pre>
   <p>All functions in this library taking complex numbers as input may also
operate on real numbers, and binary operators can have either or both
operands real. For real operands, a value of zero is inferred as the
imaginary part. The result type of the function is the same
regardless.

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