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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.high_precision.using_test"></a><a class="link" href="using_test.html" title="Using without expression templates for Boost.Test and others">Using without
  28       expression templates for Boost.Test and others</a>
  29 </h3></div></div></div>
  30 <p>
  31         As noted in the <a href="../../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>
  32         documentation, certain program constructs will not compile when using expression
  33         templates. One example that many users may encounter is Boost.Test (1.54
  34         and earlier) when using macro BOOST_CHECK_CLOSE and BOOST_CHECK_CLOSE_FRACTION.
  35       </p>
  36 <p>
  37         If, for example, you wish to use any multiprecision type like <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> in place of <code class="computeroutput"><span class="keyword">double</span></code> to give more precision, you will need
  38         to override the default <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">et_on</span></code>
  39         with <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">et_off</span></code>.
  40       </p>
  41 <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>
  42 </pre>
  43 <p>
  44         To define a 50 decimal digit type using <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>,
  45         you must pass two template parameters to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number</span></code>.
  46       </p>
  47 <p>
  48         It may be more legible to use a two-staged type definition such as this:
  49       </p>
  50 <pre class="programlisting"><span class="keyword">typedef</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">&lt;</span><span class="number">50</span><span class="special">&gt;</span> <span class="identifier">mp_backend</span><span class="special">;</span>
  51 <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mp_backend</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">et_off</span><span class="special">&gt;</span> <span class="identifier">cpp_dec_float_50_noet</span><span class="special">;</span>
  52 </pre>
  53 <p>
  54         Here, we first define <code class="computeroutput"><span class="identifier">mp_backend</span></code>
  55         as <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code> with 50
  56         digits. The second step passes this backend to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number</span></code>
  57         with <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">et_off</span></code>, an enumerated type.
  58       </p>
  59 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number</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">&lt;</span><span class="number">50</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">et_off</span><span class="special">&gt;</span>
  60 <span class="identifier">cpp_dec_float_50_noet</span><span class="special">;</span>
  61 </pre>
  62 <p>
  63         You can reduce typing with a <code class="computeroutput"><span class="keyword">using</span></code>
  64         directive <code class="computeroutput"><span class="keyword">using</span> <span class="keyword">namespace</span>
  65         <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span></code>
  66         if desired, as shown below.
  67       </p>
  68 <pre class="programlisting"><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>
  69 </pre>
  70 <p>
  71         Now <code class="computeroutput"><span class="identifier">cpp_dec_float_50_noet</span></code>
  72         or <code class="computeroutput"><span class="identifier">cpp_dec_float_50_et</span></code> can
  73         be used as a direct replacement for built-in types like <code class="computeroutput"><span class="keyword">double</span></code>
  74         etc.
  75       </p>
  76 <pre class="programlisting"><span class="identifier">BOOST_AUTO_TEST_CASE</span><span class="special">(</span><span class="identifier">cpp_float_test_check_close_noet</span><span class="special">)</span>
  77 <span class="special">{</span> <span class="comment">// No expression templates/</span>
  78   <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="identifier">et_off</span><span class="special">&gt;</span> <span class="identifier">cpp_dec_float_50_noet</span><span class="special">;</span>
  79
  80   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</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_50_noet</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span> <span class="comment">// All significant digits.</span>
  81   <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">showpoint</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">// Show trailing zeros.</span>
  82
  83   <span class="identifier">cpp_dec_float_50_noet</span> <span class="identifier">a</span> <span class="special">(</span><span class="string">"1.0"</span><span class="special">);</span>
  84   <span class="identifier">cpp_dec_float_50_noet</span> <span class="identifier">b</span> <span class="special">(</span><span class="string">"1.0"</span><span class="special">);</span>
  85   <span class="identifier">b</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_50_noet</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">();</span> <span class="comment">// Increment least significant decimal digit.</span>
  86
  87   <span class="identifier">cpp_dec_float_50_noet</span> <span class="identifier">eps</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_50_noet</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">();</span>
  88
  89   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span><span class="string">"a = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">a</span> <span class="special">&lt;&lt;</span> <span class="string">",\nb = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">b</span> <span class="special">&lt;&lt;</span> <span class="string">",\neps = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">eps</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>
  90
  91   <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">eps</span> <span class="special">*</span> <span class="number">100</span><span class="special">);</span> <span class="comment">// Expected to pass (because tolerance is as percent).</span>
  92   <span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">eps</span><span class="special">);</span> <span class="comment">// Expected to pass (because tolerance is as fraction).</span>
  93
  94
  95
  96 <span class="special">}</span> <span class="comment">// BOOST_AUTO_TEST_CASE(cpp_float_test_check_close)</span>
  97
  98 <span class="identifier">BOOST_AUTO_TEST_CASE</span><span class="special">(</span><span class="identifier">cpp_float_test_check_close_et</span><span class="special">)</span>
  99 <span class="special">{</span> <span class="comment">// Using expression templates.</span>
 100   <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="identifier">et_on</span><span class="special">&gt;</span> <span class="identifier">cpp_dec_float_50_et</span><span class="special">;</span>
 101
 102   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</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_50_et</span><span class="special">&gt;::</span><span class="identifier">digits10</span><span class="special">);</span> <span class="comment">// All significant digits.</span>
 103   <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">showpoint</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">// Show trailing zeros.</span>
 104
 105   <span class="identifier">cpp_dec_float_50_et</span> <span class="identifier">a</span><span class="special">(</span><span class="string">"1.0"</span><span class="special">);</span>
 106   <span class="identifier">cpp_dec_float_50_et</span> <span class="identifier">b</span><span class="special">(</span><span class="string">"1.0"</span><span class="special">);</span>
 107   <span class="identifier">b</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_50_et</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">();</span> <span class="comment">// Increment least significant decimal digit.</span>
 108
 109   <span class="identifier">cpp_dec_float_50_et</span> <span class="identifier">eps</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_50_et</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">();</span>
 110
 111   <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"a = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">a</span> <span class="special">&lt;&lt;</span> <span class="string">",\nb = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">b</span> <span class="special">&lt;&lt;</span> <span class="string">",\neps = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">eps</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>
 112
 113   <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">eps</span> <span class="special">*</span> <span class="number">100</span><span class="special">);</span> <span class="comment">// Expected to pass (because tolerance is as percent).</span>
 114   <span class="identifier">BOOST_CHECK_CLOSE_FRACTION</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">eps</span><span class="special">);</span> <span class="comment">// Expected to pass (because tolerance is as fraction).</span>
 115 </pre>
 116 <p>
 117         Using <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> with
 118         the default expression template use switched on, the compiler error message
 119         for `BOOST_CHECK_CLOSE_FRACTION(a, b, eps); would be:
 120       </p>
 121 <pre class="programlisting"><span class="comment">// failure floating_point_comparison.hpp(59): error C2440: 'static_cast' :</span>
 122 <span class="comment">// cannot convert from 'int' to 'boost::multiprecision::detail::expression&lt;tag,Arg1,Arg2,Arg3,Arg4&gt;'</span>
 123 </pre>
 124 <p>
 125         A full example code is at <a href="../../../../example/test_cpp_float_close_fraction.cpp" target="_top">test_cpp_float_close_fraction.cpp</a>
 126       </p>
 127 </div>
 128 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 129 <td align="left"></td>
 130 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 131       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 132       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 133       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 134       Daryle Walker and Xiaogang Zhang<p>
 135         Distributed under the Boost Software License, Version 1.0. (See accompanying
 136         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>)
 137       </p>
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