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- <a name="complex"></a>
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- <a name="complex-1"></a>
- <h2 class="section">D.2 <code>complex</code></h2>
- <p>Complex numbers are represented according to the ISO C standard as
- <a name="index-complex-numbers"></a>
- arrays of two IEEE double precision floating point numbers of 8 bytes
- each, with the number representing the real part first.
- </p>
- <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>
- <p>One example is <code>library('complex','create')</code> which takes a pair
- of floating point numbers <code>(<var>x</var>,<var>y</var>)</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"><code>math</code></a> for information about constructing floating point
- numbers.
- </p>
- <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.
- </p>
- <dl compact="compact">
- <dt>• real valued unary operations</dt>
- <dd><table><tr><td> </td><td><pre class="example">
- creal cimag cabs carg
- </pre></td></tr></table>
- </dd>
- <dt>• complex valued unary operations</dt>
- <dd><table><tr><td> </td><td><pre class="example">
- ccos cexp clog conj csin csqrt
- ctan csinh ccosh ctanh casinh cacosh
- catanh casin cacos catan
- </pre></td></tr></table>
- </dd>
- <dt>• complex valued binary operations</dt>
- <dd><table><tr><td> </td><td><pre class="example">
- cpow vid bus mul add sub div
- </pre></td></tr></table>
- </dd>
- </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,
- </p>
- <table><tr><td> </td><td><pre class="example">library('complex','vid') (x,y)
- </pre></td></tr></table>
- <p>is equivalent to
- </p>
- <table><tr><td> </td><td><pre class="example">library('complex','div') (y,x)
- </pre></td></tr></table>
- <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.
- </p>
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