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   4 <title>Logging floating point type numbers</title>
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  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_test.test_output.test_tools_support_for_logging.log_floating_points"></a><a class="link" href="log_floating_points.html" title="Logging floating point type numbers">Logging
  28         floating point type numbers</a>
  29 </h4></div></div></div>
  30 <p>
  31           It may appear that floating-point numbers are displayed by the <span class="emphasis"><em>Unit
  32           Test Framework</em></span> with an excessive number of decimal digits. However
  33           the number of digits shown is chosen to avoid apparently nonsensical displays
  34           like <code class="computeroutput"><span class="special">[</span><span class="number">1.00000</span>
  35           <span class="special">!=</span> <span class="number">1.00000</span><span class="special">]</span></code> when comparing exactly unity against a
  36           value which is increased by just one least significant binary digit using
  37           the default precision for float of just 6 decimal digits, given by <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">digits10</span></code>. The function used for the number
  38           of decimal digits displayed is that proposed for a future C++ Standard,
  39           <a href="http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2005/n1822.pdf" target="_top">A
  40           Proposal to add a max significant decimal digits value</a>, to be called
  41           <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">::</span><span class="identifier">max_digits10</span><span class="special">();</span></code>.
  42           For 32-bit floats, 9 decimal digits are needed to ensure a single bit change
  43           produces a different decimal digit string.
  44         </p>
  45 <p>
  46           So a much more helpful display using 9 decimal digits is thus: <code class="computeroutput"><span class="special">[</span><span class="number">1.00000000</span> <span class="special">!=</span> <span class="number">1.00000012</span><span class="special">]</span></code> showing that the two values are in fact
  47           different.
  48         </p>
  49 <p>
  50           For <span class="bold"><strong>IEEE754</strong></span> 32-bit float values - 9 decimal
  51           digits are shown. For 64-bit <span class="bold"><strong>IEEE754</strong></span> double
  52           - 17 decimal digits. For <span class="bold"><strong>IEEE754</strong></span> extended
  53           long double using 80-bit - 21 decimal digits. For <span class="bold"><strong>IEEE754</strong></span>
  54           quadruple long double 128-bit, and SPARC extended long double 128-bit -
  55           36 decimal digits. For floating-point types, a convenient formula to calculate
  56           <code class="computeroutput"><span class="identifier">max_digits10</span></code> is: <code class="computeroutput"><span class="number">2</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">FPT</span><span class="special">&gt;::</span><span class="identifier">digits</span>
  57           <span class="special">*</span> <span class="number">3010</span><span class="special">/</span><span class="number">10000</span></code>;
  58         </p>
  59 <div class="note"><table border="0" summary="Note">
  60 <tr>
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  62 <th align="left">Note</th>
  63 </tr>
  64 <tr><td align="left" valign="top"><p>
  65             Note that a user defined floating point type UDFPT must define <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">UDFPT</span><span class="special">&gt;::</span><span class="identifier">is_specialized</span> <span class="special">=</span>
  66             <span class="keyword">true</span></code> and provide an appropriate
  67             value for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">UDFPT</span><span class="special">&gt;::</span><span class="identifier">digits</span></code>, the number of bits used for
  68             the significand or mantissa. For example, for the SPARC extended long
  69             double 128, 113 bits are used for the significand (one of which is implicit).
  70           </p></td></tr>
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