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  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_multiprecision.tut.complex.mpc_complex"></a><a class="link" href="mpc_complex.html" title="mpc_complex">mpc_complex</a>
  28 </h4></div></div></div>
  29 <p>
  30           <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>
  31         </p>
  32 <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>
  33
  34 <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>
  35 <span class="keyword">class</span> <span class="identifier">mpc_complex_backend</span><span class="special">;</span>
  36
  37 <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>
  38 <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>
  39 <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>
  40 <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>
  41 <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>
  42
  43 <span class="special">}}</span> <span class="comment">// namespaces</span>
  44 </pre>
  45 <p>
  46           The <code class="computeroutput"><span class="identifier">mpc_complex_backend</span></code>
  47           type is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>:
  48           It acts as a thin wrapper around the <a href="http://www.multiprecision.org" target="_top">MPC</a>
  49           <code class="computeroutput"><span class="identifier">mpc_t</span></code> to provide an real-number
  50           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>,
  51           but with much greater precision.
  52         </p>
  53 <p>
  54           Type <code class="computeroutput"><span class="identifier">mpc_complex_backend</span></code>
  55           can be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code>
  56           template parameter, or at variable precision by setting the template argument
  57           to zero. The typedefs mpc_complex_50, mpc_complex_100, mpc_complex_500,
  58           mpc_complex_1000 provide complex types at 50, 100, 500 and 1000 decimal
  59           digits precision respectively. The typedef mpc_complex provides a variable
  60           precision type whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s member functions.
  61         </p>
  62 <p>
  63           The <code class="computeroutput"><span class="identifier">mpc</span></code> backend should
  64           allow use of the same syntax as the C++ standard library complex type.
  65           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>.
  66         </p>
  67 <p>
  68           As well as the usual conversions from arithmetic and string types, instances
  69           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
  70           from:
  71         </p>
  72 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  73 <li class="listitem">
  74               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>,
  75               <code class="computeroutput"><span class="identifier">mpq_t</span></code>.
  76             </li>
  77 <li class="listitem">
  78               The <a href="http://www.mpfr.org" target="_top">MPFR</a> native type <code class="computeroutput"><span class="identifier">mpfr_t</span></code>.
  79             </li>
  80 <li class="listitem">
  81               The <a href="http://www.multiprecision.org" target="_top">MPC</a> native type
  82               <code class="computeroutput"><span class="identifier">mpc_t</span></code>.
  83             </li>
  84 <li class="listitem">
  85               The <code class="computeroutput"><span class="identifier">number</span></code> wrappers
  86               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>,
  87               <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>.
  88             </li>
  89 </ul></div>
  90 <p>
  91           It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpc_t</span></code>
  92           via the data() member function of <code class="computeroutput"><span class="identifier">mpfr_float_backend</span></code>.
  93         </p>
  94 <p>
  95           Things you should know when using this type:
  96         </p>
  97 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  98 <li class="listitem">
  99               A default constructed <code class="computeroutput"><span class="identifier">mpc_complex_backend</span></code>
 100               is set to zero (<span class="emphasis"><em>Note that this is <span class="bold"><strong>not</strong></span>
 101               the default <a href="http://www.multiprecision.org" target="_top">MPC</a>
 102               behavior</em></span>).
 103             </li>
 104 <li class="listitem">
 105               All operations use round to nearest.
 106             </li>
 107 <li class="listitem">
 108               No changes are made to <a href="http://www.multiprecision.org" target="_top">MPC</a>,
 109               <a href="http://gmplib.org" target="_top">GMP</a> or <a href="http://www.mpfr.org" target="_top">MPFR</a>
 110               global settings, so this type can coexist with existing <a href="http://www.multiprecision.org" target="_top">MPC</a>,
 111               <a href="http://www.mpfr.org" target="_top">MPFR</a> or <a href="http://gmplib.org" target="_top">GMP</a>
 112               code.
 113             </li>
 114 <li class="listitem">
 115               The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a>
 116               in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that
 117               is the preferred option on Win32.
 118             </li>
 119 <li class="listitem">
 120               This backend supports rvalue-references and is move-aware, making instantiations
 121               of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
 122               move aware.
 123             </li>
 124 <li class="listitem">
 125               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>
 126               being thrown if the string can not be interpreted as a valid complex
 127               number.
 128             </li>
 129 <li class="listitem">
 130               Division by zero results in a complex-infinity.
 131             </li>
 132 <li class="listitem">
 133               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
 134               as an array of the underlying floating point type.
 135             </li>
 136 <li class="listitem">
 137               Unlike <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>, there are no literals for
 138               imaginary values.
 139             </li>
 140 <li class="listitem">
 141               When using the variable precision type <code class="computeroutput"><span class="identifier">mpc_complex</span></code>,
 142               then copy construction and assignment <span class="emphasis"><em>copies the precision
 143               of the source variable</em></span>. Likewise move construction and assignment.
 144             </li>
 145 <li class="listitem">
 146               When constructing the variable precision type <code class="computeroutput"><span class="identifier">mpc_complex</span></code>
 147               you can specify two arguments to the constructor - the first is the
 148               value to assign to the variable, the second is an unsigned integer
 149               specifying the precision in decimal places. The <code class="computeroutput"><span class="identifier">assign</span></code>
 150               member function similarly has a 2-argument overload taking the value
 151               to assign and the precision. You can use this to preserve the precision
 152               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>
 153               to <code class="computeroutput"><span class="identifier">a</span></code> but preserves
 154               the precision of <code class="computeroutput"><span class="identifier">a</span></code>.
 155             </li>
 156 </ul></div>
 157 <h6>
 158 <a name="boost_multiprecision.tut.complex.mpc_complex.h0"></a>
 159           <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>
 160         </h6>
 161 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
 162 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&gt;</span>
 163 <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>
 164
 165 <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>
 166 <span class="keyword">void</span> <span class="identifier">complex_number_examples</span><span class="special">()</span>
 167 <span class="special">{</span>
 168     <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>
 169     <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>
 170     <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>
 171     <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>
 172     <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>
 173     <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>
 174     <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>
 175     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">;</span>
 176     <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>
 177     <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>
 178     <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>
 179     <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>
 180     <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>
 181     <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>
 182     <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>
 183     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">polar</span><span class="special">;</span>
 184     <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>
 185     <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>
 186
 187     <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>
 188     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">;</span>
 189     <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>
 190     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span><span class="special">;</span>
 191     <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>
 192     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span><span class="special">;</span>
 193     <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>
 194     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span>
 195     <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>
 196     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">;</span>
 197     <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>
 198     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">;</span>
 199     <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>
 200     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">;</span>
 201     <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>
 202     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tan</span><span class="special">;</span>
 203     <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>
 204     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span><span class="special">;</span>
 205     <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>
 206     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span><span class="special">;</span>
 207     <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>
 208     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span><span class="special">;</span>
 209     <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>
 210     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span><span class="special">;</span>
 211     <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>
 212     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span><span class="special">;</span>
 213     <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>
 214     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span><span class="special">;</span>
 215     <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>
 216     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asinh</span><span class="special">;</span>
 217     <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>
 218     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">;</span>
 219     <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>
 220     <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atanh</span><span class="special">;</span>
 221     <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>
 222 <span class="special">}</span>
 223
 224 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 225 <span class="special">{</span>
 226     <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>
 227     <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>
 228     <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>
 229     <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>
 230
 231     <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 232 <span class="special">}</span>
 233 </pre>
 234 <p>
 235           Which produces the output (for the multiprecision type):
 236         </p>
 237 <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>
 238 <span class="identifier">Square</span> <span class="identifier">it</span>             <span class="special">:</span> <span class="special">-</span><span class="number">1.00000000000000000000000000000000000000000000000000</span>
 239 <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>
 240 <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>
 241 <span class="identifier">Absolute</span> <span class="identifier">value</span>        <span class="special">:</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span>
 242 <span class="identifier">Argument</span>              <span class="special">:</span> <span class="number">1.57079632679489661923132169163975144209858469968755</span>
 243 <span class="identifier">Norm</span>                  <span class="special">:</span> <span class="number">1.00000000000000000000000000000000000000000000000000</span>
 244 <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>
 245 <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>
 246 <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>
 247 <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>
 248
 249 <span class="identifier">Elementary</span> <span class="identifier">special</span> <span class="identifier">functions</span><span class="special">:</span>
 250 <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>
 251 <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>
 252 <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>
 253 <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>
 254 <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>
 255 <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>
 256 <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>
 257 <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>
 258 <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>
 259 <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>
 260 <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>
 261 <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>
 262 <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>
 263 <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>
 264 <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>
 265 <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>
 266 <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>
 267 </pre>
 268 </div>
 269 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 270 <td align="left"></td>
 271 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 272       and Christopher Kormanyos<p>
 273         Distributed under the Boost Software License, Version 1.0. (See accompanying
 274         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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