libs/multiprecision/doc/html/boost_multiprecision/tut/input_output.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Input Output</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="../tut.html" title="Tutorial">
   9 <link rel="prev" href="limits/how_to_tell.html" title="How to Determine the Kind of a Number From std::numeric_limits">
  10 <link rel="next" href="hash.html" title="Hash Function Support">
  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="limits/how_to_tell.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="hash.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.input_output"></a><a class="link" href="input_output.html" title="Input Output">Input Output</a>
  28 </h3></div></div></div>
  29 <h5>
  30 <a name="boost_multiprecision.tut.input_output.h0"></a>
  31         <span class="phrase"><a name="boost_multiprecision.tut.input_output.loopback_testing"></a></span><a class="link" href="input_output.html#boost_multiprecision.tut.input_output.loopback_testing">Loopback
  32         testing</a>
  33       </h5>
  34 <p>
  35         <span class="emphasis"><em>Loopback</em></span> or <span class="emphasis"><em>round-tripping</em></span> refers
  36         to writing out a value as a decimal digit string using <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">iostream</span></code>,
  37         usually to a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span></code>, and then reading the string
  38         back in to another value, and confirming that the two values are identical.
  39         A trivial example using <code class="computeroutput"><span class="keyword">float</span></code>
  40         is:
  41       </p>
  42 <pre class="programlisting"><span class="keyword">float</span> <span class="identifier">write</span><span class="special">;</span> <span class="comment">// Value to round-trip.</span>
  43 <span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span>  <span class="comment">// Read and write std::stringstream.</span>
  44 <span class="identifier">ss</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">T</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">);</span>  <span class="comment">// Ensure all potentially significant bits are output.</span>
  45 <span class="identifier">ss</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">fmtflags</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">scientific</span><span class="special">));</span> <span class="comment">// Use scientific format.</span>
  46 <span class="identifier">ss</span> <span class="special">&lt;&lt;</span> <span class="identifier">write</span><span class="special">;</span> <span class="comment">// Output to string.</span>
  47 <span class="keyword">float</span> <span class="identifier">read</span><span class="special">;</span>  <span class="comment">// Expected.</span>
  48 <span class="identifier">ss</span> <span class="special">&gt;&gt;</span> <span class="identifier">read</span><span class="special">;</span> <span class="comment">// Read decimal digits string from stringstream.</span>
  49 <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">write</span><span class="special">,</span> <span class="identifier">read</span><span class="special">);</span> <span class="comment">// Should be the same.</span>
  50 </pre>
  51 <p>
  52         and this can be run in a loop for all possible values of a 32-bit float.
  53         For other floating-point types <code class="computeroutput"><span class="identifier">T</span></code>,
  54         including built-in <code class="computeroutput"><span class="keyword">double</span></code>, it
  55         takes far too long to test all values, so a reasonable test strategy is to
  56         use a large number of random values.
  57       </p>
  58 <pre class="programlisting"><span class="identifier">T</span> <span class="identifier">write</span><span class="special">;</span>
  59 <span class="identifier">std</span><span class="special">::</span><span class="identifier">stringstream</span> <span class="identifier">ss</span><span class="special">;</span>
  60 <span class="identifier">ss</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">T</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">);</span>  <span class="comment">// Ensure all potentially significant bits are output.</span>
  61 <span class="identifier">ss</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span> <span class="comment">// Changed from default iostream format flags if desired.</span>
  62 <span class="identifier">ss</span> <span class="special">&lt;&lt;</span> <span class="identifier">write</span><span class="special">;</span> <span class="comment">// Output to stringstream.</span>
  63
  64 <span class="identifier">T</span> <span class="identifier">read</span><span class="special">;</span>
  65 <span class="identifier">ss</span> <span class="special">&gt;&gt;</span> <span class="identifier">read</span><span class="special">;</span> <span class="comment">// Get read using operator&gt;&gt; from stringstream.</span>
  66 <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">read</span><span class="special">,</span> <span class="identifier">write</span><span class="special">);</span>
  67
  68 <span class="identifier">read</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">ss</span><span class="special">.</span><span class="identifier">str</span><span class="special">());</span> <span class="comment">// Get read by converting from decimal digits string representation of write.</span>
  69 <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">read</span><span class="special">,</span> <span class="identifier">write</span><span class="special">);</span>
  70
  71 <span class="identifier">read</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">write</span><span class="special">.</span><span class="identifier">str</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">f</span><span class="special">));</span>  <span class="comment">// Get read using format specified when written.</span>
  72 <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="identifier">read</span><span class="special">,</span> <span class="identifier">write</span><span class="special">);</span>
  73 </pre>
  74 <p>
  75         The test at <a href="../../../../test/test_cpp_bin_float_io.cpp" target="_top">test_cpp_bin_float_io.cpp</a>
  76         allows any floating-point type to be <span class="emphasis"><em>round_tripped</em></span> using
  77         a wide range of fairly random values. It also includes tests compared a collection
  78         of <a href="../../../../test/string_data.ipp" target="_top">stringdata</a> test cases
  79         in a file.
  80       </p>
  81 <h5>
  82 <a name="boost_multiprecision.tut.input_output.h1"></a>
  83         <span class="phrase"><a name="boost_multiprecision.tut.input_output.comparing_with_output_using_buil"></a></span><a class="link" href="input_output.html#boost_multiprecision.tut.input_output.comparing_with_output_using_buil">Comparing
  84         with output using Built-in types</a>
  85       </h5>
  86 <p>
  87         One can make some comparisons with the output of
  88       </p>
  89 <pre class="programlisting"><span class="special">&lt;</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">cpp_bin_float</span><span class="special">&lt;</span><span class="number">53</span><span class="special">,</span> <span class="identifier">digit_count_2</span><span class="special">&gt;</span> <span class="special">&gt;</span>
  90 </pre>
  91 <p>
  92         which has the same number of significant bits (53) as 64-bit double precision
  93         floating-point.
  94       </p>
  95 <p>
  96         However, although most outputs are identical, there are differences on some
  97         platforms caused by the implementation-dependent behaviours allowed by the
  98         C99 specification <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf" target="_top">C99
  99         ISO/IEC 9899:TC2</a>, incorporated by C++.
 100       </p>
 101 <div class="blockquote"><blockquote class="blockquote"><p>
 102           <span class="emphasis"><em>"For e, E, f, F, g, and G conversions, if the number of
 103           significant decimal digits is at most DECIMAL_DIG, then the result should
 104           be correctly rounded. If the number of significant decimal digits is more
 105           than DECIMAL_DIG but the source value is exactly representable with DECIMAL_DIG
 106           digits, then the result should be an exact representation with trailing
 107           zeros. Otherwise, the source value is bounded by two adjacent decimal strings
 108           L &lt; U, both having DECIMAL_DIG significant digits; the value of the
 109           resultant decimal string D should satisfy L&lt;= D &lt;= U, with the extra
 110           stipulation that the error should have a correct sign for the current rounding
 111           direction."</em></span>
 112         </p></blockquote></div>
 113 <p>
 114         So not only is correct rounding for the full number of digits not required,
 115         but even if the <span class="bold"><strong>optional</strong></span> recommended practice
 116         is followed, then the value of these last few digits is unspecified as long
 117         as the value is within certain bounds.
 118       </p>
 119 <div class="note"><table border="0" summary="Note">
 120 <tr>
 121 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
 122 <th align="left">Note</th>
 123 </tr>
 124 <tr><td align="left" valign="top"><p>
 125           Do not expect the output from different platforms to be <span class="bold"><strong>identical</strong></span>,
 126           but <code class="computeroutput"><span class="identifier">cpp_dec_float</span></code>, <code class="computeroutput"><span class="identifier">cpp_bin_float</span></code> (and other backends) outputs
 127           should be correctly rounded to the number of digits requested by the set
 128           precision and format.
 129         </p></td></tr>
 130 </table></div>
 131 <h5>
 132 <a name="boost_multiprecision.tut.input_output.h2"></a>
 133         <span class="phrase"><a name="boost_multiprecision.tut.input_output.macro_boost_mp_min_exponent_digi"></a></span><a class="link" href="input_output.html#boost_multiprecision.tut.input_output.macro_boost_mp_min_exponent_digi">Macro
 134         BOOST_MP_MIN_EXPONENT_DIGITS</a>
 135       </h5>
 136 <p>
 137         <a href="http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf" target="_top">C99
 138         Standard</a> for format specifiers, 7.19.6 Formatted input/output functions
 139         requires:
 140       </p>
 141 <p>
 142         "The exponent always contains at least two digits, and only as many
 143         more digits as necessary to represent the exponent."
 144       </p>
 145 <p>
 146         So to conform to the C99 standard (incorporated by C++)
 147       </p>
 148 <pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MP_MIN_EXPONENT_DIGITS</span> <span class="number">2</span>
 149 </pre>
 150 <p>
 151         Confusingly, Microsoft (and MinGW) do not conform to this standard and provide
 152         <span class="bold"><strong>at least three digits</strong></span>, for example <code class="computeroutput"><span class="number">1e+001</span></code>. So if you want the output to match
 153         that from built-in floating-point types on compilers that use Microsofts
 154         runtime then use:
 155       </p>
 156 <pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MP_MIN_EXPONENT_DIGITS</span> <span class="number">3</span>
 157 </pre>
 158 <p>
 159         Also useful to get the minimum exponent field width is
 160       </p>
 161 <pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">BOOST_MP_MIN_EXPONENT_DIGITS</span> <span class="number">1</span>
 162 </pre>
 163 <p>
 164         producing a compact output like <code class="computeroutput"><span class="number">2e+4</span></code>,
 165         useful when conserving space is important.
 166       </p>
 167 <p>
 168         Larger values are also supported, for example, value 4 for <code class="computeroutput"><span class="number">2e+0004</span></code> which may be useful to ensure that
 169         columns line up.
 170       </p>
 171 </div>
 172 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 173 <td align="left"></td>
 174 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 175       and Christopher Kormanyos<p>
 176         Distributed under the Boost Software License, Version 1.0. (See accompanying
 177         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>)
 178       </p>
 179 </div></td>
 180 </tr></table>
 181 <hr>
 182 <div class="spirit-nav">
 183 <a accesskey="p" href="limits/how_to_tell.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="hash.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
 184 </div>
 185 </body>
 186 </html>