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<div class="titlepage"><div><div><h4 class="title">
<a name="boost_multiprecision.tut.complex.complex128"></a><a class="link" href="complex128.html" title="complex128">complex128</a>
</h4></div></div></div>
<p>
<code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">complex128</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
<span class="keyword">class</span> <span class="identifier">complex128_backend</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">complex128_backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">&gt;</span> <span class="identifier">complex128</span><span class="special">;</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
The <code class="computeroutput"><span class="identifier">complex128</span></code> number type
is a very thin wrapper around GCC's <code class="computeroutput"><span class="identifier">__float128</span></code>
or Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data types
and provides a complex-number type that is a drop-in replacement for the
native C++ floating-point types, but with a 113 bit mantissa, and compatible
with FORTRAN's 128-bit QUAD real.
</p>
<p>
All the usual standard library functions are available, performance should
be equivalent to the underlying native types.
</p>
<p>
As well as the usual conversions from arithmetic and string types, instances
of <code class="computeroutput"><span class="identifier">float128</span></code> are copy constructible
and assignable from GCC's <code class="computeroutput"><span class="identifier">__float128</span></code>
and Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data
types.
</p>
<p>
Things you should know when using this type:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Default constructed <code class="computeroutput"><span class="identifier">complex128</span></code>s
have the value zero.
</li>
<li class="listitem">
This backend supports rvalue-references and is move-aware, making instantiations
of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
move aware.
</li>
<li class="listitem">
It is not possible to round-trip objects of this type to and from a
string and get back exactly the same value when compiled with Intel's
C++ compiler and using <code class="computeroutput"><span class="identifier">_Quad</span></code>
as the underlying type: this is a current limitation of our code. Round
tripping when using <code class="computeroutput"><span class="identifier">__float128</span></code>
as the underlying type is possible (both for GCC and Intel).
</li>
<li class="listitem">
Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
being thrown if the string can not be interpreted as a valid floating-point
number.
</li>
<li class="listitem">
Division by zero results in an infinity being produced.
</li>
<li class="listitem">
When using the Intel compiler, the underlying type defaults to <code class="computeroutput"><span class="identifier">__float128</span></code> if it's available and
<code class="computeroutput"><span class="identifier">_Quad</span></code> if not. You can
override the default by defining either <code class="computeroutput"><span class="identifier">BOOST_MP_USE_FLOAT128</span></code>
or <code class="computeroutput"><span class="identifier">BOOST_MP_USE_QUAD</span></code>.
</li>
<li class="listitem">
When the underlying type is Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code>
type, the code must be compiled with the compiler option <code class="computeroutput"><span class="special">-</span><span class="identifier">Qoption</span><span class="special">,</span><span class="identifier">cpp</span><span class="special">,--</span><span class="identifier">extended_float_type</span></code>.
</li>
</ul></div>
<h6>
<a name="boost_multiprecision.tut.complex.complex128.h0"></a>
<span class="phrase"><a name="boost_multiprecision.tut.complex.complex128.complex128_example"></a></span><a class="link" href="complex128.html#boost_multiprecision.tut.complex.complex128.complex128_example">complex128
example:</a>
</h6>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">complex128</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Complex</span><span class="special">&gt;</span>
<span class="keyword">void</span> <span class="identifier">complex_number_examples</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">Complex</span> <span class="identifier">z1</span><span class="special">{</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Print a complex number: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Square it : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">*</span><span class="identifier">z1</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Real part : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Imaginary part : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">imag</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Absolute value : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Argument : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">arg</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Norm : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Complex conjugate : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Projection onto Riemann sphere: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">proj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
<span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">theta</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">polar</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Polar coordinates (phase = 0) : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Polar coordinates (phase !=0) : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">theta</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nElementary special functions:\n"</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"exp(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"log(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"log10(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">log10</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pow(z1, z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">z1</span><span class="special">,</span> <span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Take its square root : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sin(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cos(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tan</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"tan(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"asin(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">asin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"acos(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">acos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"atan(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">atan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sinh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cosh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"tanh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asinh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"asinh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">asinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"acosh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">acosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atanh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"atanh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">atanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"First, some operations we usually perform with std::complex:\n"</span><span class="special">;</span>
<span class="identifier">complex_number_examples</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&gt;();</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nNow the same operations performed using quad precision complex numbers:\n"</span><span class="special">;</span>
<span class="identifier">complex_number_examples</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">complex128</span><span class="special">&gt;();</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
Which results in the output:
</p>
<pre class="programlisting"><span class="identifier">Print</span> <span class="identifier">a</span> <span class="identifier">complex</span> <span class="identifier">number</span><span class="special">:</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Square</span> <span class="identifier">it</span> <span class="special">:</span> <span class="special">-</span><span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Real</span> <span class="identifier">part</span> <span class="special">:</span> <span class="number">0.000000000000000000000000000000000</span> <span class="special">=</span> <span class="number">0.000000000000000000000000000000000</span>
<span class="identifier">Imaginary</span> <span class="identifier">part</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span> <span class="special">=</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Absolute</span> <span class="identifier">value</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Argument</span> <span class="special">:</span> <span class="number">1.570796326794896619231321691639751</span>
<span class="identifier">Norm</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Complex</span> <span class="identifier">conjugate</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,-</span><span class="number">1.000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Projection</span> <span class="identifier">onto</span> <span class="identifier">Riemann</span> <span class="identifier">sphere</span><span class="special">:</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Polar</span> <span class="identifier">coordinates</span> <span class="special">(</span><span class="identifier">phase</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Polar</span> <span class="identifier">coordinates</span> <span class="special">(</span><span class="identifier">phase</span> <span class="special">!=</span><span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.696706709347165389063740022772449</span><span class="special">,</span><span class="number">0.717356090899522792567167815703377</span><span class="special">)</span>
<span class="identifier">Elementary</span> <span class="identifier">special</span> <span class="identifier">functions</span><span class="special">:</span>
<span class="identifier">exp</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.540302305868139717400936607442977</span><span class="special">,</span><span class="number">0.841470984807896506652502321630299</span><span class="special">)</span>
<span class="identifier">log</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.570796326794896619231321691639751</span><span class="special">)</span>
<span class="identifier">log10</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.682188176920920673742891812715678</span><span class="special">)</span>
<span class="identifier">pow</span><span class="special">(</span><span class="identifier">z1</span><span class="special">,</span> <span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.207879576350761908546955619834979</span>
<span class="identifier">Take</span> <span class="identifier">its</span> <span class="identifier">square</span> <span class="identifier">root</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.707106781186547524400844362104849</span><span class="special">,</span><span class="number">0.707106781186547524400844362104849</span><span class="special">)</span>
<span class="identifier">sin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.175201193643801456882381850595601</span><span class="special">)</span>
<span class="identifier">cos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">1.543080634815243778477905620757061</span>
<span class="identifier">tan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.761594155955764888119458282604794</span><span class="special">)</span>
<span class="identifier">asin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.881373587019543025232609324979792</span><span class="special">)</span>
<span class="identifier">acos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">1.570796326794896619231321691639751</span><span class="special">,-</span><span class="number">0.881373587019543025232609324979792</span><span class="special">)</span>
<span class="identifier">atan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="identifier">inf</span><span class="special">)</span>
<span class="identifier">sinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.841470984807896506652502321630299</span><span class="special">)</span>
<span class="identifier">cosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.540302305868139717400936607442977</span>
<span class="identifier">tanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.557407724654902230506974807458360</span><span class="special">)</span>
<span class="identifier">asinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.570796326794896619231321691639751</span><span class="special">)</span>
<span class="identifier">acosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.881373587019543025232609324979792</span><span class="special">,</span><span class="number">1.570796326794896619231321691639751</span><span class="special">)</span>
<span class="identifier">atanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.785398163397448309615660845819876</span><span class="special">)</span>
</pre>
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<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">complex_adaptor</span><span class="special">;</span>
<span class="special">}}</span>
</pre>
<p>
Class template <code class="computeroutput"><span class="identifier">complex_adaptor</span></code>
is designed to sit inbetween class <code class="computeroutput"><span class="identifier">number</span></code>
and an actual floating point backend, in order to create a new complex
number type.
</p>
<p>
It is the means by which we implement <a class="link" href="cpp_complex.html" title="cpp_complex">cpp_complex</a>
and <a class="link" href="complex128.html" title="complex128">complex128</a>.
</p>
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<p>
<code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_complex</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_type</span> <span class="identifier">DigitBase</span> <span class="special">=</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Exponent</span> <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">Exponent</span> <span class="identifier">MinExponent</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">Exponent</span> <span class="identifier">MaxExponent</span> <span class="special">=</span> <span class="number">0</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="identifier">cpp_complex_backend</span> <span class="special">=</span> <span class="identifier">complex_adaptor</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float</span><span class="special">&lt;</span><span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">DigitBase</span><span class="special">,</span> <span class="identifier">Allocator</span><span class="special">,</span> <span class="identifier">Exponent</span><span class="special">,</span> <span class="identifier">MinExponent</span><span class="special">,</span> <span class="identifier">MaxExponent</span><span class="special">&gt;</span> <span class="special">&gt;;</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_type</span> <span class="identifier">DigitBase</span> <span class="special">=</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Exponent</span> <span class="special">=</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">Exponent</span> <span class="identifier">MinExponent</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">Exponent</span> <span class="identifier">MaxExponent</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span> <span class="special">=</span> <span class="identifier">et_off</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="identifier">cpp_complex</span> <span class="special">=</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">complex_adaptor</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float</span><span class="special">&lt;</span><span class="identifier">Digits</span><span class="special">,</span> <span class="identifier">DigitBase</span><span class="special">,</span> <span class="identifier">Allocator</span><span class="special">,</span> <span class="identifier">Exponent</span><span class="special">,</span> <span class="identifier">MinExponent</span><span class="special">,</span> <span class="identifier">MaxExponent</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">ExpressionTemplates</span><span class="special">&gt;;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_50</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">100</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_100</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">24</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">126</span><span class="special">,</span> <span class="number">127</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_single</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">53</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">1022</span><span class="special">,</span> <span class="number">1023</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_double</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">64</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_extended</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">113</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">,</span> <span class="special">-</span><span class="number">16382</span><span class="special">,</span> <span class="number">16383</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_quad</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">237</span><span class="special">,</span> <span class="identifier">backends</span><span class="special">::</span><span class="identifier">digit_base_2</span><span class="special">,</span> <span class="keyword">void</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">int32_t</span><span class="special">,</span> <span class="special">-</span><span class="number">262142</span><span class="special">,</span> <span class="number">262143</span><span class="special">&gt;</span> <span class="identifier">cpp_complex_oct</span><span class="special">;</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
The <code class="computeroutput"><span class="identifier">cpp_complex_backend</span></code>
back-end is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>:
It acts as an entirely C++ (header only and dependency free) complex number
type that is a drop-in replacement for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>,
but with much greater precision.
</p>
<p>
The template alias <code class="computeroutput"><span class="identifier">cpp_complex</span></code>
avoids the need to use class <code class="computeroutput"><span class="identifier">number</span></code>
directly.
</p>
<p>
Type <code class="computeroutput"><span class="identifier">cpp_complex</span></code> can be
used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits</span></code>
template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_complex_50</span></code>
and <code class="computeroutput"><span class="identifier">cpp_complex_100</span></code> provide
complex number types at 50 and 100 decimal digits precision respectively.
</p>
<p>
Optionally, you can specify whether the precision is specified in decimal
digits or binary bits - for example to declare a <code class="computeroutput"><span class="identifier">cpp_complex</span></code>
with exactly the same precision as <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span></code> one would use <code class="computeroutput"><span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">53</span><span class="special">,</span>
<span class="identifier">digit_base_2</span><span class="special">&gt;</span></code>.
The typedefs <code class="computeroutput"><span class="identifier">cpp_complex_single</span></code>,
<code class="computeroutput"><span class="identifier">cpp_complex_double</span></code>, <code class="computeroutput"><span class="identifier">cpp_complex_quad</span></code>, <code class="computeroutput"><span class="identifier">cpp_complex_oct</span></code>
and <code class="computeroutput"><span class="identifier">cpp_complex_double_extended</span></code>
provide software analogues of the IEEE single, double, quad and octuple
float data types, plus the Intel-extended-double type respectively. Note
that while these types are functionally equivalent to the native IEEE types,
but they do not have the same size or bit-layout as true IEEE compatible
types.
</p>
<p>
Normally <code class="computeroutput"><span class="identifier">cpp_complex</span></code> allocates
no memory: all of the space required for its digits are allocated directly
within the class. As a result care should be taken not to use the class
with too high a digit count as stack space requirements can grow out of
control. If that represents a problem then providing an allocator as a
template parameter causes <code class="computeroutput"><span class="identifier">cpp_complex</span></code>
to dynamically allocate the memory it needs: this significantly reduces
the size of <code class="computeroutput"><span class="identifier">cpp_complex</span></code>
and increases the viable upper limit on the number of digits at the expense
of performance. However, please bear in mind that arithmetic operations
rapidly become <span class="emphasis"><em>very</em></span> expensive as the digit count grows:
the current implementation really isn't optimized or designed for large
digit counts. Note that since the actual type of the objects allocated
is completely opaque, the suggestion would be to use an allocator with
<code class="computeroutput"><span class="keyword">char</span></code> <code class="computeroutput"><span class="identifier">value_type</span></code>,
for example: <code class="computeroutput"><span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">1000</span><span class="special">,</span> <span class="identifier">digit_base_10</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">allocator</span><span class="special">&lt;</span><span class="keyword">char</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>.
</p>
<p>
The next template parameters determine the type and range of the exponent:
parameter <code class="computeroutput"><span class="identifier">Exponent</span></code> can
be any signed integer type, but note that <code class="computeroutput"><span class="identifier">MinExponent</span></code>
and <code class="computeroutput"><span class="identifier">MaxExponent</span></code> can not
go right up to the limits of the <code class="computeroutput"><span class="identifier">Exponent</span></code>
type as there has to be a little extra headroom for internal calculations.
You will get a compile time error if this is the case. In addition if MinExponent
or MaxExponent are zero, then the library will choose suitable values that
are as large as possible given the constraints of the type and need for
extra headroom for internal calculations.
</p>
<p>
Finally, as with class <code class="computeroutput"><span class="identifier">number</span></code>,
the final template parameter determines whether expression templates are
turn on or not. Since by default this type allocates no memory, expression
template support is off by default. However, you should probably turn it
on if you specify an allocator.
</p>
<p>
There is full standard library support available for this type, comparable
with what <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code> provides.
</p>
<p>
Things you should know when using this type:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Default constructed <code class="computeroutput"><span class="identifier">cpp_complex</span></code>s
have a value of zero.
</li>
<li class="listitem">
The radix of this type is 2, even when the precision is specified as
decimal digits.
</li>
<li class="listitem">
The type supports both infinities and NaNs. An infinity is generated
whenever the result would overflow, and a NaN is generated for any
mathematically undefined operation.
</li>
<li class="listitem">
There is no <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> specialisation for
this type: this is the same behaviour as <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>.
If you need <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> support you need to
look at <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">my_complex_number_type</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">&gt;</span></code>.
</li>
<li class="listitem">
Any <code class="computeroutput"><span class="identifier">number</span></code> instantiated
on this type, is convertible to any other <code class="computeroutput"><span class="identifier">number</span></code>
instantiated on this type - for example you can convert from <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_complex</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="special">&gt;</span></code> to <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float</span><span class="special">&lt;</span><span class="identifier">SomeOtherValue</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>.
Narrowing conversions round to nearest and are <code class="computeroutput"><span class="keyword">explicit</span></code>.
</li>
<li class="listitem">
Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
being thrown if the string can not be interpreted as a valid complex
number.
</li>
</ul></div>
<h6>
<a name="boost_multiprecision.tut.complex.cpp_complex.h0"></a>
<span class="phrase"><a name="boost_multiprecision.tut.complex.cpp_complex.example"></a></span><a class="link" href="cpp_complex.html#boost_multiprecision.tut.complex.cpp_complex.example">example:</a>
</h6>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_complex</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Complex</span><span class="special">&gt;</span>
<span class="keyword">void</span> <span class="identifier">complex_number_examples</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">Complex</span> <span class="identifier">z1</span><span class="special">{</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Print a complex number: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Square it : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">*</span><span class="identifier">z1</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Real part : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Imaginary part : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">imag</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Absolute value : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Argument : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">arg</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Norm : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Complex conjugate : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Projection onto Riemann sphere: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">proj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
<span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">theta</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">polar</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Polar coordinates (phase = 0) : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Polar coordinates (phase !=0) : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">theta</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nElementary special functions:\n"</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"exp(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"log(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"log10(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">log10</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pow(z1, z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">z1</span><span class="special">,</span> <span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Take its square root : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sin(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cos(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tan</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"tan(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"asin(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">asin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"acos(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">acos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"atan(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">atan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sinh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cosh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"tanh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asinh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"asinh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">asinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"acosh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">acosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atanh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"atanh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">atanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"First, some operations we usually perform with std::complex:\n"</span><span class="special">;</span>
<span class="identifier">complex_number_examples</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&gt;();</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nNow the same operations performed using quad precision complex numbers:\n"</span><span class="special">;</span>
<span class="identifier">complex_number_examples</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_complex_quad</span><span class="special">&gt;();</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
Which produces the output (for the multiprecision type):
</p>
<pre class="programlisting"><span class="identifier">Print</span> <span class="identifier">a</span> <span class="identifier">complex</span> <span class="identifier">number</span><span class="special">:</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Square</span> <span class="identifier">it</span> <span class="special">:</span> <span class="special">-</span><span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Real</span> <span class="identifier">part</span> <span class="special">:</span> <span class="number">0.000000000000000000000000000000000</span> <span class="special">=</span> <span class="number">0.000000000000000000000000000000000</span>
<span class="identifier">Imaginary</span> <span class="identifier">part</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span> <span class="special">=</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Absolute</span> <span class="identifier">value</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Argument</span> <span class="special">:</span> <span class="number">1.570796326794896619231321691639751</span>
<span class="identifier">Norm</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Complex</span> <span class="identifier">conjugate</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,-</span><span class="number">1.000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Projection</span> <span class="identifier">onto</span> <span class="identifier">Riemann</span> <span class="identifier">sphere</span><span class="special">:</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Polar</span> <span class="identifier">coordinates</span> <span class="special">(</span><span class="identifier">phase</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
<span class="identifier">Polar</span> <span class="identifier">coordinates</span> <span class="special">(</span><span class="identifier">phase</span> <span class="special">!=</span><span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.696706709347165389063740022772448</span><span class="special">,</span><span class="number">0.717356090899522792567167815703377</span><span class="special">)</span>
<span class="identifier">Elementary</span> <span class="identifier">special</span> <span class="identifier">functions</span><span class="special">:</span>
<span class="identifier">exp</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.540302305868139717400936607442977</span><span class="special">,</span><span class="number">0.841470984807896506652502321630299</span><span class="special">)</span>
<span class="identifier">log</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.570796326794896619231321691639751</span><span class="special">)</span>
<span class="identifier">log10</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.682188176920920673742891812715678</span><span class="special">)</span>
<span class="identifier">pow</span><span class="special">(</span><span class="identifier">z1</span><span class="special">,</span> <span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.207879576350761908546955619834979</span>
<span class="identifier">Take</span> <span class="identifier">its</span> <span class="identifier">square</span> <span class="identifier">root</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.707106781186547524400844362104849</span><span class="special">,</span><span class="number">0.707106781186547524400844362104849</span><span class="special">)</span>
<span class="identifier">sin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.175201193643801456882381850595601</span><span class="special">)</span>
<span class="identifier">cos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">1.543080634815243778477905620757062</span>
<span class="identifier">tan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.761594155955764888119458282604794</span><span class="special">)</span>
<span class="identifier">asin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.881373587019543025232609324979793</span><span class="special">)</span>
<span class="identifier">acos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">1.570796326794896619231321691639751</span><span class="special">,-</span><span class="number">0.881373587019543025232609324979793</span><span class="special">)</span>
<span class="identifier">atan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="identifier">inf</span><span class="special">)</span>
<span class="identifier">sinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.841470984807896506652502321630299</span><span class="special">)</span>
<span class="identifier">cosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.540302305868139717400936607442977</span>
<span class="identifier">tanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.557407724654902230506974807458360</span><span class="special">)</span>
<span class="identifier">asinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.570796326794896619231321691639751</span><span class="special">)</span>
<span class="identifier">acosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.881373587019543025232609324979792</span><span class="special">,</span><span class="number">1.570796326794896619231321691639751</span><span class="special">)</span>
<span class="identifier">atanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.785398163397448309615660845819876</span><span class="special">)</span>
</pre>
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<a name="boost_multiprecision.tut.complex.mpc_complex"></a><a class="link" href="mpc_complex.html" title="mpc_complex">mpc_complex</a>
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<p>
<code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpc</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">mpc_complex_backend</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpc_complex_backend</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mpc_complex_50</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpc_complex_backend</span><span class="special">&lt;</span><span class="number">100</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mpc_complex_100</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpc_complex_backend</span><span class="special">&lt;</span><span class="number">500</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mpc_complex_500</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpc_complex_backend</span><span class="special">&lt;</span><span class="number">1000</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mpc_complex_1000</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpc_complex_backend</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">mpc_complex</span><span class="special">;</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
The <code class="computeroutput"><span class="identifier">mpc_complex_backend</span></code>
type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>:
It acts as a thin wrapper around the <a href="http://www.multiprecision.org" target="_top">MPC</a>
<code class="computeroutput"><span class="identifier">mpc_t</span></code> to provide an real-number
type that is a drop-in replacement for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>,
but with much greater precision.
</p>
<p>
Type <code class="computeroutput"><span class="identifier">mpc_complex_backend</span></code>
can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code>
template parameter, or at variable precision by setting the template argument
to zero. The typedefs mpc_complex_50, mpc_complex_100, mpc_complex_500,
mpc_complex_1000 provide complex types at 50, 100, 500 and 1000 decimal
digits precision respectively. The typedef mpc_complex provides a variable
precision type whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s member functions.
</p>
<p>
The <code class="computeroutput"><span class="identifier">mpc</span></code> backend should
allow use of the same syntax as the C++ standard library complex type.
When using this backend, remember to link with the flags <code class="computeroutput"><span class="special">-</span><span class="identifier">lmpc</span> <span class="special">-</span><span class="identifier">lmpfr</span> <span class="special">-</span><span class="identifier">lgmp</span></code>.
</p>
<p>
As well as the usual conversions from arithmetic and string types, instances
of <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpc_complex_backend</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span></code> are copy constructible and assignable
from:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
The <a href="http://gmplib.org" target="_top">GMP</a> native types <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>,
<code class="computeroutput"><span class="identifier">mpq_t</span></code>.
</li>
<li class="listitem">
The <a href="http://www.mpfr.org" target="_top">MPFR</a> native type <code class="computeroutput"><span class="identifier">mpfr_t</span></code>.
</li>
<li class="listitem">
The <a href="http://www.multiprecision.org" target="_top">MPC</a> native type
<code class="computeroutput"><span class="identifier">mpc_t</span></code>.
</li>
<li class="listitem">
The <code class="computeroutput"><span class="identifier">number</span></code> wrappers
around those types: <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">M</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>,
<code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpf_float</span><span class="special">&lt;</span><span class="identifier">M</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_int</span><span class="special">&gt;</span></code>, <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">gmp_rational</span><span class="special">&gt;</span></code>.
</li>
</ul></div>
<p>
It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpc_t</span></code>
via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code>
member function of <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>.
</p>
<p>
Things you should know when using this type:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
A default constructed <code class="computeroutput"><span class="identifier">mpc_complex_backend</span></code>
is set to zero (<span class="emphasis"><em>Note that this is <span class="bold"><strong>not</strong></span>
the default <a href="http://www.multiprecision.org" target="_top">MPC</a>
behavior</em></span>).
</li>
<li class="listitem">
All operations use round to nearest.
</li>
<li class="listitem">
No changes are made to <a href="http://www.multiprecision.org" target="_top">MPC</a>,
<a href="http://gmplib.org" target="_top">GMP</a> or <a href="http://www.mpfr.org" target="_top">MPFR</a>
global settings, so this type can coexist with existing <a href="http://www.multiprecision.org" target="_top">MPC</a>,
<a href="http://www.mpfr.org" target="_top">MPFR</a> or <a href="http://gmplib.org" target="_top">GMP</a>
code.
</li>
<li class="listitem">
The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a>
in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that
is the preferred option on Win32.
</li>
<li class="listitem">
This backend supports rvalue-references and is move-aware, making instantiations
of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
move aware.
</li>
<li class="listitem">
Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>
being thrown if the string can not be interpreted as a valid complex
number.
</li>
<li class="listitem">
Division by zero results in a complex-infinity.
</li>
<li class="listitem">
Unlike <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>, you can not use <code class="computeroutput"><span class="keyword">reinterpret_cast</span></code> to treat this type
as an array of the underlying floating point type.
</li>
<li class="listitem">
Unlike <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>, there are no literals for
imaginary values.
</li>
<li class="listitem">
When using the variable precision type <code class="computeroutput"><span class="identifier">mpc_complex</span></code>,
then copy construction and assignment <span class="emphasis"><em>copies the precision
of the source variable</em></span>. Likewise move construction and assignment.
</li>
<li class="listitem">
When constructing the variable precision type <code class="computeroutput"><span class="identifier">mpc_complex</span></code>
you can specify two arguments to the constructor - the first is the
value to assign to the variable, the second is an unsigned integer
specifying the precision in decimal places. The <code class="computeroutput"><span class="identifier">assign</span></code>
member function similarly has a 2-argument overload taking the value
to assign and the precision. You can use this to preserve the precision
of the target variable using the somewhat arcane: <code class="computeroutput"><span class="identifier">a</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">precision</span><span class="special">())</span></code>, which assigns <code class="computeroutput"><span class="identifier">b</span></code>
to <code class="computeroutput"><span class="identifier">a</span></code> but preserves
the precision of <code class="computeroutput"><span class="identifier">a</span></code>.
</li>
</ul></div>
<h6>
<a name="boost_multiprecision.tut.complex.mpc_complex.h0"></a>
<span class="phrase"><a name="boost_multiprecision.tut.complex.mpc_complex.mpc_example"></a></span><a class="link" href="mpc_complex.html#boost_multiprecision.tut.complex.mpc_complex.mpc_example"> MPC example:</a>
</h6>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">mpc</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Complex</span><span class="special">&gt;</span>
<span class="keyword">void</span> <span class="identifier">complex_number_examples</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">Complex</span> <span class="identifier">z1</span><span class="special">{</span><span class="number">0</span><span class="special">,</span> <span class="number">1</span><span class="special">};</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Print a complex number: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Square it : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">*</span><span class="identifier">z1</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Real part : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Imaginary part : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">imag</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Absolute value : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Argument : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">arg</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Norm : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Complex conjugate : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Projection onto Riemann sphere: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">proj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
<span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">theta</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">polar</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Polar coordinates (phase = 0) : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Polar coordinates (phase !=0) : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">theta</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nElementary special functions:\n"</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"exp(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"log(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"log10(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">log10</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"pow(z1, z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">z1</span><span class="special">,</span> <span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Take its square root : "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sin(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cos(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tan</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"tan(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"asin(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">asin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"acos(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">acos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"atan(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">atan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sinh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"cosh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"tanh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asinh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"asinh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">asinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"acosh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">acosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atanh</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"atanh(z1) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">atanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"First, some operations we usually perform with std::complex:\n"</span><span class="special">;</span>
<span class="identifier">complex_number_examples</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&gt;();</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\nNow the same operations performed using the MPC backend:\n"</span><span class="special">;</span>
<span class="identifier">complex_number_examples</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">mpc_complex_50</span><span class="special">&gt;();</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
Which produces the output (for the multiprecision type):
</p>
<pre class="programlisting"><span class="identifier">Print</span> <span class="identifier">a</span> <span class="identifier">complex</span> <span class="identifier">number</span><span class="special">:</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.00000000000000000000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Square</span> <span class="identifier">it</span> <span class="special">:</span> <span class="special">-</span><span class="number">1.00000000000000000000000000000000000000000000000000</span>
<span class="identifier">Real</span> <span class="identifier">part</span> <span class="special">:</span> <span class="number">0.00000000000000000000000000000000000000000000000000</span> <span class="special">=</span> <span class="number">0.00000000000000000000000000000000000000000000000000</span>
<span class="identifier">Imaginary</span> <span class="identifier">part</span> <span class="special">:</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span> <span class="special">=</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span>
<span class="identifier">Absolute</span> <span class="identifier">value</span> <span class="special">:</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span>
<span class="identifier">Argument</span> <span class="special">:</span> <span class="number">1.57079632679489661923132169163975144209858469968755</span>
<span class="identifier">Norm</span> <span class="special">:</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span>
<span class="identifier">Complex</span> <span class="identifier">conjugate</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,-</span><span class="number">1.00000000000000000000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Projection</span> <span class="identifier">onto</span> <span class="identifier">Riemann</span> <span class="identifier">sphere</span><span class="special">:</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.00000000000000000000000000000000000000000000000000</span><span class="special">)</span>
<span class="identifier">Polar</span> <span class="identifier">coordinates</span> <span class="special">(</span><span class="identifier">phase</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span>
<span class="identifier">Polar</span> <span class="identifier">coordinates</span> <span class="special">(</span><span class="identifier">phase</span> <span class="special">!=</span><span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.69670670934716538906374002277244853473117519431538</span><span class="special">,</span><span class="number">0.71735609089952279256716781570337728075604730751255</span><span class="special">)</span>
<span class="identifier">Elementary</span> <span class="identifier">special</span> <span class="identifier">functions</span><span class="special">:</span>
<span class="identifier">exp</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.54030230586813971740093660744297660373231042061792</span><span class="special">,</span><span class="number">0.84147098480789650665250232163029899962256306079837</span><span class="special">)</span>
<span class="identifier">log</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.57079632679489661923132169163975144209858469968755</span><span class="special">)</span>
<span class="identifier">log10</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.68218817692092067374289181271567788510506374186196</span><span class="special">)</span>
<span class="identifier">pow</span><span class="special">(</span><span class="identifier">z1</span><span class="special">,</span> <span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.20787957635076190854695561983497877003387784163177</span>
<span class="identifier">Take</span> <span class="identifier">its</span> <span class="identifier">square</span> <span class="identifier">root</span> <span class="special">:</span> <span class="special">(</span><span class="number">0.70710678118654752440084436210484903928483593768847</span><span class="special">,</span><span class="number">0.70710678118654752440084436210484903928483593768847</span><span class="special">)</span>
<span class="identifier">sin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.17520119364380145688238185059560081515571798133410</span><span class="special">)</span>
<span class="identifier">cos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">1.54308063481524377847790562075706168260152911236587</span>
<span class="identifier">tan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.76159415595576488811945828260479359041276859725794</span><span class="special">)</span>
<span class="identifier">asin</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.88137358701954302523260932497979230902816032826163</span><span class="special">)</span>
<span class="identifier">acos</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">1.57079632679489661923132169163975144209858469968755</span><span class="special">,-</span><span class="number">0.88137358701954302523260932497979230902816032826163</span><span class="special">)</span>
<span class="identifier">atan</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="identifier">inf</span><span class="special">)</span>
<span class="identifier">sinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.84147098480789650665250232163029899962256306079837</span><span class="special">)</span>
<span class="identifier">cosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.54030230586813971740093660744297660373231042061792</span>
<span class="identifier">tanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.55740772465490223050697480745836017308725077238152</span><span class="special">)</span>
<span class="identifier">asinh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">1.57079632679489661923132169163975144209858469968755</span><span class="special">)</span>
<span class="identifier">acosh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.88137358701954302523260932497979230902816032826163</span><span class="special">,</span><span class="number">1.57079632679489661923132169163975144209858469968755</span><span class="special">)</span>
<span class="identifier">atanh</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special">=</span> <span class="special">(</span><span class="number">0.00000000000000000000000000000000000000000000000000</span><span class="special">,</span><span class="number">0.78539816339744830961566084581987572104929234984378</span><span class="special">)</span>
</pre>
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