ceph/src/boost/libs/multiprecision/doc/html/boost_multiprecision/tut/rounding.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Rounding Rules for Conversions</title>
   5 <link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css">
   6 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
   7 <link rel="home" href="../../index.html" title="Chapter&#160;1.&#160;Boost.Multiprecision">
   8 <link rel="up" href="../tut.html" title="Tutorial">
   9 <link rel="prev" href="import_export.html" title="Importing and Exporting Data to and from cpp_int and cpp_bin_float">
  10 <link rel="next" href="mixed.html" title="Mixed Precision Arithmetic">
  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="import_export.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="mixed.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_multiprecision.tut.rounding"></a><a class="link" href="rounding.html" title="Rounding Rules for Conversions">Rounding Rules for
  28       Conversions</a>
  29 </h3></div></div></div>
  30 <p>
  31         As a general rule, all conversions between unrelated types are performed
  32         using basic arithmetic operations, therefore conversions are either exact,
  33         or follow the same rounding rules as arithmetic for the type in question.
  34       </p>
  35 <p>
  36         The following table summarises the situation for conversions from native
  37         types:
  38       </p>
  39 <div class="informaltable"><table class="table">
  40 <colgroup>
  41 <col>
  42 <col>
  43 </colgroup>
  44 <thead><tr>
  45 <th>
  46                 <p>
  47                   Backend
  48                 </p>
  49               </th>
  50 <th>
  51                 <p>
  52                   Rounding Rules
  53                 </p>
  54               </th>
  55 </tr></thead>
  56 <tbody>
  57 <tr>
  58 <td>
  59                 <p>
  60                   <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
  61                 </p>
  62               </td>
  63 <td>
  64                 <p>
  65                   Conversions from integer types are exact if the target has sufficient
  66                   precision, otherwise they truncate to the first 2^MaxBits bits
  67                   (modulo arithmetic). Conversions from floating-point types are
  68                   truncating to the nearest integer.
  69                 </p>
  70               </td>
  71 </tr>
  72 <tr>
  73 <td>
  74                 <p>
  75                   <a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a>
  76                 </p>
  77               </td>
  78 <td>
  79                 <p>
  80                   Conversions are performed by the GMP library except for conversion
  81                   from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
  82                   which is truncating.
  83                 </p>
  84               </td>
  85 </tr>
  86 <tr>
  87 <td>
  88                 <p>
  89                   <a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a>
  90                 </p>
  91               </td>
  92 <td>
  93                 <p>
  94                   Conversions from floating-point types are truncating, all others
  95                   are performed by libtommath and are exact.
  96                 </p>
  97               </td>
  98 </tr>
  99 <tr>
 100 <td>
 101                 <p>
 102                   <a class="link" href="floats/gmp_float.html" title="gmp_float">gmp_float</a>
 103                 </p>
 104               </td>
 105 <td>
 106                 <p>
 107                   Conversions are performed by the GMP library except for conversion
 108                   from <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
 109                   which should be exact provided the target type has as much precision
 110                   as a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
 111                 </p>
 112               </td>
 113 </tr>
 114 <tr>
 115 <td>
 116                 <p>
 117                   <a class="link" href="floats/mpfr_float.html" title="mpfr_float">mpfr_float</a>
 118                 </p>
 119               </td>
 120 <td>
 121                 <p>
 122                   All conversions are performed by the underlying MPFR library.
 123                 </p>
 124               </td>
 125 </tr>
 126 <tr>
 127 <td>
 128                 <p>
 129                   <a class="link" href="floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a>
 130                 </p>
 131               </td>
 132 <td>
 133                 <p>
 134                   All conversions are performed using basic arithmetic operations
 135                   and are truncating.
 136                 </p>
 137               </td>
 138 </tr>
 139 <tr>
 140 <td>
 141                 <p>
 142                   <a class="link" href="rational/gmp_rational.html" title="gmp_rational">gmp_rational</a>
 143                 </p>
 144               </td>
 145 <td>
 146                 <p>
 147                   See <a class="link" href="ints/gmp_int.html" title="gmp_int">gmp_int</a>
 148                 </p>
 149               </td>
 150 </tr>
 151 <tr>
 152 <td>
 153                 <p>
 154                   <a class="link" href="rational/cpp_rational.html" title="cpp_rational">cpp_rational</a>
 155                 </p>
 156               </td>
 157 <td>
 158                 <p>
 159                   See <a class="link" href="ints/cpp_int.html" title="cpp_int">cpp_int</a>
 160                 </p>
 161               </td>
 162 </tr>
 163 <tr>
 164 <td>
 165                 <p>
 166                   <a class="link" href="rational/tommath_rational.html" title="tommath_rational">tommath_rational</a>
 167                 </p>
 168               </td>
 169 <td>
 170                 <p>
 171                   See <a class="link" href="ints/tom_int.html" title="tom_int">tom_int</a>
 172                 </p>
 173               </td>
 174 </tr>
 175 </tbody>
 176 </table></div>
 177 </div>
 178 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 179 <td align="left"></td>
 180 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2013 John Maddock and Christopher Kormanyos<p>
 181         Distributed under the Boost Software License, Version 1.0. (See accompanying
 182         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>)
 183       </p>
 184 </div></td>
 185 </tr></table>
 186 <hr>
 187 <div class="spirit-nav">
 188 <a accesskey="p" href="import_export.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="mixed.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
 189 </div>
 190 </body>
 191 </html>