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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>
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>
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">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>
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>
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>
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>
50 <span class="special">}}</span> <span class="comment">// namespaces</span>
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.
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>
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.
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
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>.
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.
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.
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.
127 Things you should know when using this type:
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.
134 <li class="listitem">
135 The radix of this type is 2, even when the precision is specified as
138 <li class="listitem">
139 The type supports both infinities and NaN's. An infinity is generated
140 whenever the result would overflow, and a NaN is generated for any
141 mathematically undefined operation.
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>.
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>.
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
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>
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>
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>
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>
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>
235 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
236 <span class="special">}</span>
239 Which produces the output (for the multiprecision type):
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>
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>
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 © 2002-2019 John Maddock
276 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>)
283 <div class="spirit-nav">
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