1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>cpp_complex</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="../complex.html" title="Complex Number Types"> 10<link rel="next" href="mpc_complex.html" title="mpc_complex"> 11</head> 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> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="../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="mpc_complex.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h4 class="title"> 27<a name="boost_multiprecision.tut.complex.cpp_complex"></a><a class="link" href="cpp_complex.html" title="cpp_complex">cpp_complex</a> 28</h4></div></div></div> 29<p> 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">cpp_complex</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></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"><</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">></span> 35 <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"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</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">></span> <span class="special">>;</span> 36 37 <span class="keyword">template</span> <span class="special"><</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">></span> 38 <span class="keyword">using</span> <span class="identifier">cpp_complex</span> <span class="special">=</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">complex_adaptor</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</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">></span> <span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>;</span> 39 40 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="identifier">cpp_complex_50</span><span class="special">;</span> 41 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="identifier">cpp_complex_100</span><span class="special">;</span> 42 43 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</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">boost</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">></span> <span class="identifier">cpp_complex_single</span><span class="special">;</span> 44 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</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">boost</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">></span> <span class="identifier">cpp_complex_double</span><span class="special">;</span> 45 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</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">boost</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">></span> <span class="identifier">cpp_complex_extended</span><span class="special">;</span> 46 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</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">boost</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">></span> <span class="identifier">cpp_complex_quad</span><span class="special">;</span> 47 <span class="keyword">typedef</span> <span class="identifier">cpp_complex</span><span class="special"><</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">boost</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">></span> <span class="identifier">cpp_complex_oct</span><span class="special">;</span> 48 49 50<span class="special">}}</span> <span class="comment">// namespaces</span> 51</pre> 52<p> 53 The <code class="computeroutput"><span class="identifier">cpp_complex_backend</span></code> 54 back-end is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>: 55 It acts as an entirely C++ (header only and dependency free) complex number 56 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>, 57 but with much greater precision. 58 </p> 59<p> 60 The template alias <code class="computeroutput"><span class="identifier">cpp_complex</span></code> 61 avoids the need to use class <code class="computeroutput"><span class="identifier">number</span></code> 62 directly. 63 </p> 64<p> 65 Type <code class="computeroutput"><span class="identifier">cpp_complex</span></code> can be 66 used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits</span></code> 67 template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_complex_50</span></code> 68 and <code class="computeroutput"><span class="identifier">cpp_complex_100</span></code> provide 69 complex number types at 50 and 100 decimal digits precision respectively. 70 </p> 71<p> 72 Optionally, you can specify whether the precision is specified in decimal 73 digits or binary bits - for example to declare a <code class="computeroutput"><span class="identifier">cpp_complex</span></code> 74 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"><</span><span class="keyword">double</span><span class="special">></span></code> one would use <code class="computeroutput"><span class="identifier">cpp_complex</span><span class="special"><</span><span class="number">53</span><span class="special">,</span> 75 <span class="identifier">digit_base_2</span><span class="special">></span></code>. 76 The typedefs <code class="computeroutput"><span class="identifier">cpp_complex_single</span></code>, 77 <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> 78 and <code class="computeroutput"><span class="identifier">cpp_complex_double_extended</span></code> 79 provide software analogues of the IEEE single, double, quad and octuple 80 float data types, plus the Intel-extended-double type respectively. Note 81 that while these types are functionally equivalent to the native IEEE types, 82 but they do not have the same size or bit-layout as true IEEE compatible 83 types. 84 </p> 85<p> 86 Normally <code class="computeroutput"><span class="identifier">cpp_complex</span></code> allocates 87 no memory: all of the space required for its digits are allocated directly 88 within the class. As a result care should be taken not to use the class 89 with too high a digit count as stack space requirements can grow out of 90 control. If that represents a problem then providing an allocator as a 91 template parameter causes <code class="computeroutput"><span class="identifier">cpp_complex</span></code> 92 to dynamically allocate the memory it needs: this significantly reduces 93 the size of <code class="computeroutput"><span class="identifier">cpp_complex</span></code> 94 and increases the viable upper limit on the number of digits at the expense 95 of performance. However, please bear in mind that arithmetic operations 96 rapidly become <span class="emphasis"><em>very</em></span> expensive as the digit count grows: 97 the current implementation really isn't optimized or designed for large 98 digit counts. Note that since the actual type of the objects allocated 99 is completely opaque, the suggestion would be to use an allocator with 100 <code class="computeroutput"><span class="keyword">char</span></code> <code class="computeroutput"><span class="identifier">value_type</span></code>, 101 for example: <code class="computeroutput"><span class="identifier">cpp_complex</span><span class="special"><</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"><</span><span class="keyword">char</span><span class="special">></span> <span class="special">></span></code>. 102 </p> 103<p> 104 The next template parameters determine the type and range of the exponent: 105 parameter <code class="computeroutput"><span class="identifier">Exponent</span></code> can 106 be any signed integer type, but note that <code class="computeroutput"><span class="identifier">MinExponent</span></code> 107 and <code class="computeroutput"><span class="identifier">MaxExponent</span></code> can not 108 go right up to the limits of the <code class="computeroutput"><span class="identifier">Exponent</span></code> 109 type as there has to be a little extra headroom for internal calculations. 110 You will get a compile time error if this is the case. In addition if MinExponent 111 or MaxExponent are zero, then the library will choose suitable values that 112 are as large as possible given the constraints of the type and need for 113 extra headroom for internal calculations. 114 </p> 115<p> 116 Finally, as with class <code class="computeroutput"><span class="identifier">number</span></code>, 117 the final template parameter determines whether expression templates are 118 turn on or not. Since by default this type allocates no memory, expression 119 template support is off by default. However, you should probably turn it 120 on if you specify an allocator. 121 </p> 122<p> 123 There is full standard library support available for this type, comparable 124 with what <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code> provides. 125 </p> 126<p> 127 Things you should know when using this type: 128 </p> 129<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 130<li class="listitem"> 131 Default constructed <code class="computeroutput"><span class="identifier">cpp_complex</span></code>s 132 have a value of zero. 133 </li> 134<li class="listitem"> 135 The radix of this type is 2, even when the precision is specified as 136 decimal digits. 137 </li> 138<li class="listitem"> 139 The type supports both infinities and NaNs. An infinity is generated 140 whenever the result would overflow, and a NaN is generated for any 141 mathematically undefined operation. 142 </li> 143<li class="listitem"> 144 There is no <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> specialisation for 145 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>. 146 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 147 look at <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">my_complex_number_type</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">></span></code>. 148 </li> 149<li class="listitem"> 150 Any <code class="computeroutput"><span class="identifier">number</span></code> instantiated 151 on this type, is convertible to any other <code class="computeroutput"><span class="identifier">number</span></code> 152 instantiated on this type - for example you can convert from <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_complex</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span></code> to <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">cpp_bin_float</span><span class="special"><</span><span class="identifier">SomeOtherValue</span><span class="special">></span> <span class="special">></span></code>. 153 Narrowing conversions round to nearest and are <code class="computeroutput"><span class="keyword">explicit</span></code>. 154 </li> 155<li class="listitem"> 156 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> 157 being thrown if the string can not be interpreted as a valid complex 158 number. 159 </li> 160</ul></div> 161<h6> 162<a name="boost_multiprecision.tut.complex.cpp_complex.h0"></a> 163 <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> 164 </h6> 165<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 166<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">complex</span><span class="special">></span> 167<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">cpp_complex</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 168 169<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">Complex</span><span class="special">></span> 170<span class="keyword">void</span> <span class="identifier">complex_number_examples</span><span class="special">()</span> 171<span class="special">{</span> 172 <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> 173 <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> 174 <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> 175 <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> 176 <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> 177 <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> 178 <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> 179 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">abs</span><span class="special">;</span> 180 <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> 181 <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> 182 <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> 183 <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> 184 <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> 185 <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> 186 <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> 187 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">polar</span><span class="special">;</span> 188 <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> 189 <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> 190 191 <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> 192 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">;</span> 193 <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> 194 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span><span class="special">;</span> 195 <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> 196 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span><span class="special">;</span> 197 <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> 198 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">;</span> 199 <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> 200 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">;</span> 201 <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> 202 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">;</span> 203 <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> 204 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">;</span> 205 <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> 206 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tan</span><span class="special">;</span> 207 <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> 208 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span><span class="special">;</span> 209 <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> 210 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span><span class="special">;</span> 211 <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> 212 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span><span class="special">;</span> 213 <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> 214 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span><span class="special">;</span> 215 <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> 216 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span><span class="special">;</span> 217 <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> 218 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span><span class="special">;</span> 219 <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> 220 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">asinh</span><span class="special">;</span> 221 <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> 222 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">acosh</span><span class="special">;</span> 223 <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> 224 <span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">atanh</span><span class="special">;</span> 225 <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> 226<span class="special">}</span> 227 228<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> 229<span class="special">{</span> 230 <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> 231 <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> 232 <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> 233 <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">cpp_complex_quad</span><span class="special">>();</span> 234 235 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> 236<span class="special">}</span> 237</pre> 238<p> 239 Which produces the output (for the multiprecision type): 240 </p> 241<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> 242<span class="identifier">Square</span> <span class="identifier">it</span> <span class="special">:</span> <span class="special">-</span><span class="number">1.000000000000000000000000000000000</span> 243<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> 244<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> 245<span class="identifier">Absolute</span> <span class="identifier">value</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span> 246<span class="identifier">Argument</span> <span class="special">:</span> <span class="number">1.570796326794896619231321691639751</span> 247<span class="identifier">Norm</span> <span class="special">:</span> <span class="number">1.000000000000000000000000000000000</span> 248<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> 249<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> 250<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> 251<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> 252 253<span class="identifier">Elementary</span> <span class="identifier">special</span> <span class="identifier">functions</span><span class="special">:</span> 254<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> 255<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> 256<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> 257<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> 258<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> 259<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> 260<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> 261<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> 262<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> 263<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> 264<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> 265<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> 266<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> 267<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> 268<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> 269<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> 270<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> 271</pre> 272</div> 273<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 274<td align="left"></td> 275<td align="right"><div class="copyright-footer">Copyright © 2002-2020 John 276 Maddock and Christopher Kormanyos<p> 277 Distributed under the Boost Software License, Version 1.0. (See accompanying 278 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>) 279 </p> 280</div></td> 281</tr></table> 282<hr> 283<div class="spirit-nav"> 284<a accesskey="p" href="../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="mpc_complex.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 285</div> 286</body> 287</html> 288
