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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_multiprecision.tut.rational"></a><a class="link" href="rational.html" title="Rational Number Types">Rational Number Types</a>
  28 </h3></div></div></div>
  29 <div class="toc"><dl class="toc">
  30 <dt><span class="section"><a href="rational/cpp_rational.html">cpp_rational</a></span></dt>
  31 <dt><span class="section"><a href="rational/gmp_rational.html">gmp_rational</a></span></dt>
  32 <dt><span class="section"><a href="rational/tommath_rational.html">tommath_rational</a></span></dt>
  33 <dt><span class="section"><a href="rational/br.html">Use With Boost.Rational</a></span></dt>
  34 <dt><span class="section"><a href="rational/rational_adaptor.html">rational_adaptor</a></span></dt>
  35 </dl></div>
  36 <p>
  37         The following back-ends provide rational number arithmetic:
  38       </p>
  39 <div class="informaltable"><table class="table">
  40 <colgroup>
  41 <col>
  42 <col>
  43 <col>
  44 <col>
  45 <col>
  46 <col>
  47 </colgroup>
  48 <thead><tr>
  49 <th>
  50                 <p>
  51                   Backend Type
  52                 </p>
  53               </th>
  54 <th>
  55                 <p>
  56                   Header
  57                 </p>
  58               </th>
  59 <th>
  60                 <p>
  61                   Radix
  62                 </p>
  63               </th>
  64 <th>
  65                 <p>
  66                   Dependencies
  67                 </p>
  68               </th>
  69 <th>
  70                 <p>
  71                   Pros
  72                 </p>
  73               </th>
  74 <th>
  75                 <p>
  76                   Cons
  77                 </p>
  78               </th>
  79 </tr></thead>
  80 <tbody>
  81 <tr>
  82 <td>
  83                 <p>
  84                   <code class="computeroutput"><span class="identifier">cpp_rational</span></code>
  85                 </p>
  86               </td>
  87 <td>
  88                 <p>
  89                   boost/multiprecision/cpp_int.hpp
  90                 </p>
  91               </td>
  92 <td>
  93                 <p>
  94                   2
  95                 </p>
  96               </td>
  97 <td>
  98                 <p>
  99                   None
 100                 </p>
 101               </td>
 102 <td>
 103                 <p>
 104                   An all C++ Boost-licensed implementation.
 105                 </p>
 106               </td>
 107 <td>
 108                 <p>
 109                   Slower than <a href="http://gmplib.org" target="_top">GMP</a>.
 110                 </p>
 111               </td>
 112 </tr>
 113 <tr>
 114 <td>
 115                 <p>
 116                   <code class="computeroutput"><span class="identifier">gmp_rational</span></code>
 117                 </p>
 118               </td>
 119 <td>
 120                 <p>
 121                   boost/multiprecision/gmp.hpp
 122                 </p>
 123               </td>
 124 <td>
 125                 <p>
 126                   2
 127                 </p>
 128               </td>
 129 <td>
 130                 <p>
 131                   <a href="http://gmplib.org" target="_top">GMP</a>
 132                 </p>
 133               </td>
 134 <td>
 135                 <p>
 136                   Very fast and efficient back-end.
 137                 </p>
 138               </td>
 139 <td>
 140                 <p>
 141                   Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
 142                   library.
 143                 </p>
 144               </td>
 145 </tr>
 146 <tr>
 147 <td>
 148                 <p>
 149                   <code class="computeroutput"><span class="identifier">tommath_rational</span></code>
 150                 </p>
 151               </td>
 152 <td>
 153                 <p>
 154                   boost/multiprecision/tommath.hpp
 155                 </p>
 156               </td>
 157 <td>
 158                 <p>
 159                   2
 160                 </p>
 161               </td>
 162 <td>
 163                 <p>
 164                   <a href="http://libtom.net" target="_top">libtommath</a>
 165                 </p>
 166               </td>
 167 <td>
 168                 <p>
 169                   All C/C++ implementation that's Boost Software Licence compatible.
 170                 </p>
 171               </td>
 172 <td>
 173                 <p>
 174                   Slower than <a href="http://gmplib.org" target="_top">GMP</a>.
 175                 </p>
 176               </td>
 177 </tr>
 178 <tr>
 179 <td>
 180                 <p>
 181                   <code class="computeroutput"><span class="identifier">rational_adaptor</span></code>
 182                 </p>
 183               </td>
 184 <td>
 185                 <p>
 186                   boost/multiprecision/rational_adaptor.hpp
 187                 </p>
 188               </td>
 189 <td>
 190                 <p>
 191                   N/A
 192                 </p>
 193               </td>
 194 <td>
 195                 <p>
 196                   none
 197                 </p>
 198               </td>
 199 <td>
 200                 <p>
 201                   All C++ adaptor that allows any integer back-end type to be used
 202                   as a rational type.
 203                 </p>
 204               </td>
 205 <td>
 206                 <p>
 207                   Requires an underlying integer back-end type.
 208                 </p>
 209               </td>
 210 </tr>
 211 <tr>
 212 <td>
 213                 <p>
 214                   <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>
 215                 </p>
 216               </td>
 217 <td>
 218                 <p>
 219                   boost/rational.hpp
 220                 </p>
 221               </td>
 222 <td>
 223                 <p>
 224                   N/A
 225                 </p>
 226               </td>
 227 <td>
 228                 <p>
 229                   None
 230                 </p>
 231               </td>
 232 <td>
 233                 <p>
 234                   A C++ rational number type that can used with any <code class="computeroutput"><span class="identifier">number</span></code> integer type.
 235                 </p>
 236               </td>
 237 <td>
 238                 <p>
 239                   The expression templates used by <code class="computeroutput"><span class="identifier">number</span></code>
 240                   end up being "hidden" inside <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>:
 241                   performance may well suffer as a result.
 242                 </p>
 243               </td>
 244 </tr>
 245 </tbody>
 246 </table></div>
 247 </div>
 248 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 249 <td align="left"></td>
 250 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 251       and Christopher Kormanyos<p>
 252         Distributed under the Boost Software License, Version 1.0. (See accompanying
 253         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>)
 254       </p>
 255 </div></td>
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