libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>cpp_dec_float</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&#160;1.&#160;Boost.Multiprecision">
   8 <link rel="up" href="../floats.html" title="floating-point Numbers">
   9 <link rel="prev" href="cpp_bin_float.html" title="cpp_bin_float">
  10 <link rel="next" href="gmp_float.html" title="gmp_float">
  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="cpp_bin_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.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="gmp_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section">
  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_multiprecision.tut.floats.cpp_dec_float"></a><a class="link" href="cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a>
  28 </h4></div></div></div>
  29 <p>
  30           <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
  31         </p>
  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>
  33
  34 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExponentType</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="keyword">class</span> <span class="identifier">Allocator</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">&gt;</span>
  35 <span class="keyword">class</span> <span class="identifier">cpp_dec_float</span><span class="special">;</span>
  36
  37 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">cpp_dec_float_50</span><span class="special">;</span>
  38 <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float</span><span class="special">&lt;</span><span class="number">100</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">cpp_dec_float_100</span><span class="special">;</span>
  39
  40 <span class="special">}}</span> <span class="comment">// namespaces</span>
  41 </pre>
  42 <p>
  43           The <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> back-end
  44           is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>:
  45           It acts as an entirely C++ (header only and dependency free) floating-point
  46           number type that is a drop-in replacement for the native C++ floating-point
  47           types, but with much greater precision.
  48         </p>
  49 <p>
  50           Type <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> can
  51           be used at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code>
  52           template parameter. The typedefs <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
  53           and <code class="computeroutput"><span class="identifier">cpp_dec_float_100</span></code> provide
  54           arithmetic types at 50 and 100 decimal digits precision respectively. Optionally,
  55           you can specify an integer type to use for the exponent, this defaults
  56           to a 32-bit integer type which is more than large enough for the vast majority
  57           of use cases, but larger types such as <code class="computeroutput"><span class="keyword">long</span>
  58           <span class="keyword">long</span></code> can also be specified if you
  59           need a truly huge exponent range. In any case the ExponentType must be
  60           a built in signed integer type at least 2 bytes and 16-bits wide.
  61         </p>
  62 <p>
  63           Normally <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>
  64           allocates no memory: all of the space required for its digits are allocated
  65           directly within the class. As a result care should be taken not to use
  66           the class with too high a digit count as stack space requirements can grow
  67           out of control. If that represents a problem then providing an allocator
  68           as the final template parameter causes <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>
  69           to dynamically allocate the memory it needs: this significantly reduces
  70           the size of <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>
  71           and increases the viable upper limit on the number of digits at the expense
  72           of performance. However, please bear in mind that arithmetic operations
  73           rapidly become <span class="emphasis"><em>very</em></span> expensive as the digit count grows:
  74           the current implementation really isn't optimized or designed for large
  75           digit counts.
  76         </p>
  77 <p>
  78           There is full standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
  79           support available for this type.
  80         </p>
  81 <p>
  82           Things you should know when using this type:
  83         </p>
  84 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  85 <li class="listitem">
  86               Default constructed <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>s
  87               have a value of zero.
  88             </li>
  89 <li class="listitem">
  90               The radix of this type is 10. As a result it can behave subtly differently
  91               from base-2 types.
  92             </li>
  93 <li class="listitem">
  94               The type has a number of internal guard digits over and above those
  95               specified in the template argument. Normally these should not be visible
  96               to the user.
  97             </li>
  98 <li class="listitem">
  99               The type supports both infinities and NaN's. An infinity is generated
 100               whenever the result would overflow, and a NaN is generated for any
 101               mathematically undefined operation.
 102             </li>
 103 <li class="listitem">
 104               There is a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> specialisation for
 105               this type.
 106             </li>
 107 <li class="listitem">
 108               Any <code class="computeroutput"><span class="identifier">number</span></code> instantiated
 109               on this type, is convertible to any other <code class="computeroutput"><span class="identifier">number</span></code>
 110               instantiated on this type - for example you can convert from <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float</span><span class="special">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="special">&gt;</span></code> to <code class="computeroutput"><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float</span><span class="special">&lt;</span><span class="identifier">SomeOtherValue</span><span class="special">&gt;</span> <span class="special">&gt;</span></code>.
 111               Narrowing conversions are truncating and <code class="computeroutput"><span class="keyword">explicit</span></code>.
 112             </li>
 113 <li class="listitem">
 114               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>
 115               being thrown if the string can not be interpreted as a valid floating-point
 116               number.
 117             </li>
 118 <li class="listitem">
 119               The actual precision of a <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>
 120               is always slightly higher than the number of digits specified in the
 121               template parameter, actually how much higher is an implementation detail
 122               but is always at least 8 decimal digits.
 123             </li>
 124 <li class="listitem">
 125               Operations involving <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>
 126               are always truncating. However, note that since their are guard digits
 127               in effect, in practice this has no real impact on accuracy for most
 128               use cases.
 129             </li>
 130 </ul></div>
 131 <h6>
 132 <a name="boost_multiprecision.tut.floats.cpp_dec_float.h0"></a>
 133           <span class="phrase"><a name="boost_multiprecision.tut.floats.cpp_dec_float.cpp_dec_float_example"></a></span><a class="link" href="cpp_dec_float.html#boost_multiprecision.tut.floats.cpp_dec_float.cpp_dec_float_example">cpp_dec_float
 134           example:</a>
 135         </h6>
 136 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_dec_float</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 137 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 138 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
 139
 140 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 141 <span class="special">{</span>
 142    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span>
 143
 144    <span class="comment">// Operations at fixed precision and full numeric_limits support:</span>
 145    <span class="identifier">cpp_dec_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 146    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_100</span><span class="special">&gt;::</span><span class="identifier">digits</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 147    <span class="comment">// Note that digits10 is the same as digits, since we're base 10! :</span>
 148    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">cpp_dec_float_100</span><span class="special">&gt;::</span><span class="identifier">digits10</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 149    <span class="comment">// We can use any C++ std lib function, lets print all the digits as well:</span>
 150    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</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">&lt;</span><span class="identifier">cpp_dec_float_100</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">)</span>
 151       <span class="special">&lt;&lt;</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span>
 152    <span class="comment">// We can also use any function from Boost.Math:</span>
 153    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 154    <span class="comment">// These even work when the argument is an expression template:</span>
 155    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 156    <span class="comment">// And since we have an extended exponent range we can generate some really large </span>
 157    <span class="comment">// numbers here (4.0238726007709377354370243e+2564):</span>
 158    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">cpp_dec_float_100</span><span class="special">(</span><span class="number">1000</span><span class="special">))</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 159    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 160 <span class="special">}</span>
 161 </pre>
 162 </div>
 163 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 164 <td align="left"></td>
 165 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 166       and Christopher Kormanyos<p>
 167         Distributed under the Boost Software License, Version 1.0. (See accompanying
 168         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>)
 169       </p>
 170 </div></td>
 171 </tr></table>
 172 <hr>
 173 <div class="spirit-nav">
 174 <a accesskey="p" href="cpp_bin_float.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../floats.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="gmp_float.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
 175 </div>
 176 </body>
 177 </html>