1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Constructing and Interconverting Between Number Types</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. 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In particular: 33 </p> 34<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 35<li class="listitem"> 36<p class="simpara"> 37 Any number type can be constructed (or assigned) from any <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 38 (built-in)</a> arithmetic type, as long as the conversion isn't lossy 39 (for example float to int conversion): 40 </p> 41<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="number">0.5</span><span class="special">);</span> <span class="comment">// OK construction from double</span> 42<span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">450</span><span class="special">);</span> <span class="comment">// OK constructs from signed int</span> 43<span class="identifier">cpp_int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, lossy conversion.</span> 44</pre> 45</li> 46<li class="listitem"> 47<p class="simpara"> 48 A number can be explicitly constructed from an arithmetic type, even 49 when the conversion is lossy: 50 </p> 51<pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK explicit conversion</span> 52<span class="identifier">i</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">>(</span><span class="number">3.14</span><span class="special">)</span> <span class="comment">// OK explicit conversion</span> 53<span class="identifier">i</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// OK, explicit assign and avoid a temporary from the cast above</span> 54<span class="identifier">i</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no implicit assignment operator for lossy conversion.</span> 55<span class="identifier">cpp_int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no implicit constructor for lossy conversion.</span> 56</pre> 57</li> 58<li class="listitem"> 59<p class="simpara"> 60 A <code class="computeroutput"><span class="identifier">number</span></code> can be converted 61 to any <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 62 (built-in)</a> type, via the <code class="computeroutput"><span class="identifier">convert_to</span></code> 63 member function: 64 </p> 65<pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> 66<span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">.</span><span class="identifier">convert_to</span><span class="special"><</span><span class="keyword">int</span><span class="special">>();</span> <span class="comment">// sets i to 2</span> 67</pre> 68</li> 69<li class="listitem"> 70 Conversions to rational numbers from floating-point ones are always allowed, 71 and are exact and implicit as long as the rational number uses an unbounded 72 integer type. Please be aware that constructing a rational number from 73 an extended precision floating-point type with a large exponent range 74 can effectively run the system out of memory, as in the extreme case 75 <span class="emphasis"><em>2<sup>max_exponent</sup> / CHAR_BITS</em></span> bytes of storage may be 76 required. This does not represent a problem for <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 77 (built-in)</a> floating-point types however, as the exponent range 78 for these is rather limited. 79 </li> 80<li class="listitem"> 81 Conversions to floating-point numbers from rational ones are rounded 82 to nearest (less than 0.5 <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place" target="_top">Unit 83 in the last place (ULP)</a> error) as long as the floating-point 84 number is binary, and the integer type used by the rational number is 85 unbounded. 86 </li> 87</ul></div> 88<p> 89 Additional conversions may be supported by particular backends. 90 </p> 91<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 92<li class="listitem"> 93<p class="simpara"> 94 A <code class="computeroutput"><span class="identifier">number</span></code> can be converted 95 to any <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 96 (built-in)</a> type, via an explicit conversion operator: this functionality 97 is only available on compilers supporting C++11's explicit conversion 98 syntax. 99 </p> 100<pre class="programlisting"><span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> 101<span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">;</span> <span class="comment">// Error, implicit conversion not allowed.</span> 102<span class="keyword">int</span> <span class="identifier">j</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="keyword">int</span><span class="special">>(</span><span class="identifier">z</span><span class="special">);</span> <span class="comment">// OK explicit conversion.</span> 103</pre> 104</li> 105<li class="listitem"> 106<p class="simpara"> 107 Any number type can be <span class="emphasis"><em>explicitly</em></span> constructed (or 108 assigned) from a <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code> 109 or a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code>: 110 </p> 111<pre class="programlisting"><span class="comment">// pi to 50 places from a string:</span> 112<span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">);</span> 113<span class="comment">// Integer type will automatically detect "0x" and "0" prefixes and parse the string accordingly:</span> 114<span class="identifier">cpp_int</span> <span class="identifier">i</span><span class="special">(</span><span class="string">"0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000"</span><span class="special">);</span> 115<span class="comment">// Invalid input always results in a std::runtime_error being thrown:</span> 116<span class="identifier">i</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_int</span><span class="special">>(</span><span class="string">"3.14"</span><span class="special">);</span> 117<span class="comment">// implicit conversions from strings are not allowed:</span> 118<span class="identifier">i</span> <span class="special">=</span> <span class="string">"23"</span><span class="special">;</span> <span class="comment">// Error, no assignment operator for implicit conversion from string</span> 119<span class="comment">// assign member function, avoids having to create a temporary via a static_cast:</span> 120<span class="identifier">i</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="string">"23"</span><span class="special">);</span> <span class="comment">// OK</span> 121</pre> 122</li> 123<li class="listitem"> 124<p class="simpara"> 125 Any number type will interoperate with the <a href="https://en.cppreference.com/w/cpp/language/types" target="_top">fundamental 126 (built-in)</a> types in arithmetic expressions as long as the conversions 127 are not lossy: 128 </p> 129<pre class="programlisting"><span class="comment">// pi to 50 places from a string:</span> 130<span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span> <span class="special">=</span> <span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">;</span> 131<span class="comment">// Multiply by 2 - using an integer literal here is usually more efficient</span> 132<span class="comment">// than constructing a temporary:</span> 133<span class="identifier">df</span> <span class="special">*=</span> <span class="number">2</span><span class="special">;</span> 134 135<span class="comment">// You can't mix integer types with floats though:</span> 136<span class="identifier">cpp_int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> 137<span class="identifier">i</span> <span class="special">*=</span> <span class="number">3.14</span><span class="special">;</span> <span class="comment">// Error, no *= operator will be found.</span> 138</pre> 139</li> 140<li class="listitem"> 141<p class="simpara"> 142 Any number type can be streamed to and from the C++ iostreams: 143 </p> 144<pre class="programlisting"><span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span> <span class="special">=</span> <span class="string">"3.14159265358979323846264338327950288419716939937510"</span><span class="special">;</span> 145<span class="comment">// Now print at full precision:</span> 146<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="identifier">cpp_dec_float_50</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">)</span> 147 <span class="special"><<</span> <span class="identifier">df</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> 148<span class="identifier">cpp_int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> 149<span class="identifier">i</span> <span class="special"><<=</span> <span class="number">256</span><span class="special">;</span> 150<span class="comment">// Now print in hex format with prefix:</span> 151<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">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span> <span class="special"><<</span> <span class="identifier">i</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 152</pre> 153</li> 154<li class="listitem"> 155<p class="simpara"> 156 Interconversions between number types of the same family are allowed 157 and are implicit conversions if no loss of precision is involved, and 158 explicit if it is: 159 </p> 160<pre class="programlisting"><span class="identifier">int128_t</span> <span class="identifier">i128</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> 161<span class="identifier">int266_t</span> <span class="identifier">i256</span> <span class="special">=</span> <span class="identifier">i128</span><span class="special">;</span> <span class="comment">// OK implicit widening conversion</span> 162<span class="identifier">i128_t</span> <span class="special">=</span> <span class="identifier">i256</span><span class="special">;</span> <span class="comment">// Error, no assignment operator found, narrowing conversion is explicit.</span> 163<span class="identifier">i128_t</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">int128_t</span><span class="special">>(</span><span class="identifier">i256</span><span class="special">);</span> <span class="comment">// OK, explicit narrowing conversion.</span> 164 165<span class="identifier">mpz_int</span> <span class="identifier">z</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> 166<span class="identifier">mpf_float</span> <span class="identifier">f</span> <span class="special">=</span> <span class="identifier">z</span><span class="special">;</span> <span class="comment">// OK, GMP handles this conversion natively, and it's not lossy and therefore implicit.</span> 167 168<span class="identifier">mpf_float_50</span> <span class="identifier">f50</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> 169<span class="identifier">f</span> <span class="special">=</span> <span class="identifier">f50</span><span class="special">;</span> <span class="comment">// OK, conversion from fixed to variable precision, f will have 50 digits precision.</span> 170<span class="identifier">f50</span> <span class="special">=</span> <span class="identifier">f</span><span class="special">;</span> <span class="comment">// Error, conversion from variable to fixed precision is potentially lossy, explicit cast required.</span> 171</pre> 172</li> 173<li class="listitem"> 174<p class="simpara"> 175 Some interconversions between number types are completely generic, and 176 are always available, albeit the conversions are always <span class="emphasis"><em>explicit</em></span>: 177 </p> 178<pre class="programlisting"><span class="identifier">cpp_int</span> <span class="identifier">cppi</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> 179<span class="comment">// We can always convert between numbers of the same category -</span> 180<span class="comment">// int to int, rational to rational, or float to float, so this is OK</span> 181<span class="comment">// as long as we use an explicit conversion:</span> 182<span class="identifier">mpz_int</span> <span class="identifier">z</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> 183<span class="comment">// We can always promote from int to rational, int to float, or rational to float:</span> 184<span class="identifier">cpp_rational</span> <span class="identifier">cppr</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> <span class="comment">// OK, int to rational</span> 185<span class="identifier">cpp_dec_float_50</span> <span class="identifier">df</span><span class="special">(</span><span class="identifier">cppi</span><span class="special">);</span> <span class="comment">// OK, int to float</span> 186<span class="identifier">df</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">cpp_dec_float_50</span><span class="special">>(</span><span class="identifier">cppr</span><span class="special">);</span> <span class="comment">// OK, explicit rational to float conversion</span> 187<span class="comment">// However narrowing and/or implicit conversions always fail:</span> 188<span class="identifier">cppi</span> <span class="special">=</span> <span class="identifier">df</span><span class="special">;</span> <span class="comment">// Compiler error, conversion not allowed</span> 189</pre> 190</li> 191<li class="listitem"> 192<p class="simpara"> 193 Other interconversions may be allowed as special cases, whenever the 194 backend allows it: 195 </p> 196<pre class="programlisting"><span class="identifier">mpf_t</span> <span class="identifier">m</span><span class="special">;</span> <span class="comment">// Native GMP type.</span> 197<span class="identifier">mpf_init_set_ui</span><span class="special">(</span><span class="identifier">m</span><span class="special">,</span> <span class="number">0</span><span class="special">);</span> <span class="comment">// set to a value;</span> 198<span class="identifier">mpf_float</span> <span class="identifier">i</span><span class="special">(</span><span class="identifier">m</span><span class="special">);</span> <span class="comment">// copies the value of the native type.</span> 199</pre> 200</li> 201</ul></div> 202<p> 203 More information on what additional types a backend supports conversions 204 from are given in the tutorial for each backend. The converting constructor 205 will be implicit if the backend's converting constructor is also implicit, 206 and explicit if the backends converting constructor is also explicit. 207 </p> 208</div> 209<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 210<td align="left"></td> 211<td align="right"><div class="copyright-footer">Copyright © 2002-2020 John 212 Maddock and Christopher Kormanyos<p> 213 Distributed under the Boost Software License, Version 1.0. (See accompanying 214 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>) 215 </p> 216</div></td> 217</tr></table> 218<hr> 219<div class="spirit-nav"> 220<a accesskey="p" href="misc/visualizers.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="random.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 221</div> 222</body> 223</html> 224
