1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Rounding Rules for Conversions</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="../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 © 2002-2020 John 181 Maddock and Christopher Kormanyos<p> 182 Distributed under the Boost Software License, Version 1.0. (See accompanying 183 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>) 184 </p> 185</div></td> 186</tr></table> 187<hr> 188<div class="spirit-nav"> 189<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> 190</div> 191</body> 192</html> 193
