3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
4 <title>complex128</title>
5 <link rel="stylesheet" href="../../../multiprecision.css" type="text/css">
6 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
7 <link rel="home" href="../../../index.html" title="Chapter 1. Boost.Multiprecision">
8 <link rel="up" href="../complex.html" title="Complex Number Types">
9 <link rel="prev" href="mpc_complex.html" title="mpc_complex">
10 <link rel="next" href="complex_adaptor.html" title="complex_adaptor">
12 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
13 <table cellpadding="2" width="100%"><tr>
14 <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
15 <td align="center"><a href="../../../../../../../index.html">Home</a></td>
16 <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
17 <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
18 <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
19 <td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
22 <div class="spirit-nav">
23 <a accesskey="p" href="mpc_complex.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../complex.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="complex_adaptor.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
26 <div class="titlepage"><div><div><h4 class="title">
27 <a name="boost_multiprecision.tut.complex.complex128"></a><a class="link" href="complex128.html" title="complex128">complex128</a>
28 </h4></div></div></div>
30 <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</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">></span></code>
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>
34 <span class="keyword">class</span> <span class="identifier">complex128_backend</span><span class="special">;</span>
36 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">complex128_backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">></span> <span class="identifier">complex128</span><span class="special">;</span>
38 <span class="special">}}</span> <span class="comment">// namespaces</span>
41 The <code class="computeroutput"><span class="identifier">complex128</span></code> number type
42 is a very thin wrapper around GCC's <code class="computeroutput"><a class="link" href="../floats/float128.html" title="float128">float128</a></code>
43 or Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data types
44 and provides a complex-number type that is a drop-in replacement for the
45 native C++ floating-point types, but with a 113 bit mantissa, and compatible
46 with FORTRAN's 128-bit QUAD real.
49 All the usual standard library functions are available, performance should
50 be equivalent to the underlying native types.
53 As well as the usual conversions from arithmetic and string types, instances
54 of <code class="computeroutput"><span class="identifier">float128</span></code> are copy constructible
55 and assignable from GCC's <code class="computeroutput"><a class="link" href="../floats/float128.html" title="float128">float128</a></code>
56 and Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code> data
60 Things you should know when using this type:
62 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
64 Default constructed <code class="computeroutput"><span class="identifier">complex128</span></code>s
68 This backend supports rvalue-references and is move-aware, making instantiations
69 of <code class="computeroutput"><span class="identifier">number</span></code> on this backend
73 It is not possible to round-trip objects of this type to and from a
74 string and get back exactly the same value when compiled with Intel's
75 C++ compiler and using <code class="computeroutput"><span class="identifier">_Quad</span></code>
76 as the underlying type: this is a current limitation of our code. Round
77 tripping when using <code class="computeroutput"><a class="link" href="../floats/float128.html" title="float128">float128</a></code>
78 as the underlying type is possible (both for GCC and Intel).
81 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>
82 being thrown if the string can not be interpreted as a valid floating-point
86 Division by zero results in an infinity being produced.
89 When using the Intel compiler, the underlying type defaults to <code class="computeroutput"><a class="link" href="../floats/float128.html" title="float128">float128</a></code>
90 if it's available and <code class="computeroutput"><span class="identifier">_Quad</span></code>
91 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>.
94 When the underlying type is Intel's <code class="computeroutput"><span class="identifier">_Quad</span></code>
95 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>.
99 <a name="boost_multiprecision.tut.complex.complex128.h0"></a>
100 <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
103 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span>
104 <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">complex</span><span class="special">></span>
105 <span class="preprocessor">#include</span> <span class="special"><</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">></span>
107 <span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Complex</span><span class="special">></span>
108 <span class="keyword">void</span> <span class="identifier">complex_number_examples</span><span class="special">()</span>
109 <span class="special">{</span>
110 <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>
111 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</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"><</span><span class="keyword">typename</span> <span class="identifier">Complex</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">);</span>
112 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">scientific</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">fixed</span><span class="special">;</span>
113 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Print a complex number: "</span> <span class="special"><<</span> <span class="identifier">z1</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
114 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Square it : "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
115 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Real part : "</span> <span class="special"><<</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
116 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Imaginary part : "</span> <span class="special"><<</span> <span class="identifier">z1</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" = "</span> <span class="special"><<</span> <span class="identifier">imag</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
117 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">;</span>
118 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Absolute value : "</span> <span class="special"><<</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
119 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Argument : "</span> <span class="special"><<</span> <span class="identifier">arg</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
120 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Norm : "</span> <span class="special"><<</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
121 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Complex conjugate : "</span> <span class="special"><<</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
122 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Projection onto Riemann sphere: "</span> <span class="special"><<</span> <span class="identifier">proj</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
123 <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>
124 <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>
125 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">polar</span><span class="special">;</span>
126 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Polar coordinates (phase = 0) : "</span> <span class="special"><<</span> <span class="identifier">polar</span><span class="special">(</span><span class="identifier">r</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
127 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Polar coordinates (phase !=0) : "</span> <span class="special"><<</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"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
129 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nElementary special functions:\n"</span><span class="special">;</span>
130 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">;</span>
131 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"exp(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
132 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span><span class="special">;</span>
133 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"log(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
134 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span><span class="special">;</span>
135 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"log10(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
136 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span>
137 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"pow(z1, z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
138 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">;</span>
139 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Take its square root : "</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">z1</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
140 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">;</span>
141 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"sin(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
142 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">;</span>
143 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"cos(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
144 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tan</span><span class="special">;</span>
145 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"tan(z1) = "</span> <span class="special"><<</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
146 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span><span class="special">;</span>
147 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"asin(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
148 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span><span class="special">;</span>
149 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"acos(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
150 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span><span class="special">;</span>
151 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"atan(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
152 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span><span class="special">;</span>
153 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"sinh(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
154 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span><span class="special">;</span>
155 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"cosh(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
156 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span><span class="special">;</span>
157 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"tanh(z1) = "</span> <span class="special"><<</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
158 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asinh</span><span class="special">;</span>
159 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"asinh(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
160 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">;</span>
161 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"acosh(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
162 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atanh</span><span class="special">;</span>
163 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"atanh(z1) = "</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="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
164 <span class="special">}</span>
166 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
167 <span class="special">{</span>
168 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"First, some operations we usually perform with std::complex:\n"</span><span class="special">;</span>
169 <span class="identifier">complex_number_examples</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">>>();</span>
170 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"\nNow the same operations performed using quad precision complex numbers:\n"</span><span class="special">;</span>
171 <span class="identifier">complex_number_examples</span><span class="special"><</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>
173 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
174 <span class="special">}</span>
177 Which results in the output:
179 <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>
180 <span class="identifier">Square</span> <span class="identifier">it</span> <span class="special">:</span> <span class="special">-</span><span class="number">1.000000000000000000000000000000000</span>
181 <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>
182 <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>
183 <span class="identifier">Absolute</span> <span class="identifier">value</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
184 <span class="identifier">Argument</span> <span class="special">:</span> <span class="number">1.570796326794896619231321691639751</span>
185 <span class="identifier">Norm</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span>
186 <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>
187 <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>
188 <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>
189 <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>
191 <span class="identifier">Elementary</span> <span class="identifier">special</span> <span class="identifier">functions</span><span class="special">:</span>
192 <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>
193 <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>
194 <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>
195 <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>
196 <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>
197 <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>
198 <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>
199 <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>
200 <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>
201 <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>
202 <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>
203 <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>
204 <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>
205 <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>
206 <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>
207 <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>
208 <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>
211 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
212 <td align="left"></td>
213 <td align="right"><div class="copyright-footer">Copyright © 2002-2019 John Maddock
214 and Christopher Kormanyos<p>
215 Distributed under the Boost Software License, Version 1.0. (See accompanying
216 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>)
221 <div class="spirit-nav">
222 <a accesskey="p" href="mpc_complex.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../complex.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="complex_adaptor.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>