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| </a><b>Logging floating point type numbers</b> |
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| <a name="utf.user-guide.test-output.log.FPT"></a>Logging floating point type numbers</h6></div></div></div> |
| <p class="first-line-indented"> |
| It may appear that floating-point numbers are displayed by the <acronym class="acronym">UTF</acronym> with an excessive number of decimal digits. |
| However the number of digits shown is chosen to avoid apparently nonsensical displays like <code class="computeroutput">[1.00000 != 1.00000]</code> |
| when comparing exactly unity against a value which is increased by just one least significant binary digit using |
| the default precision for float of just 6 decimal digits, given by |
| <code class="computeroutput">std::numeric_limits</code><float>::digits10. The function used for the number of decimal |
| digits displayed is that proposed for a future C++ Standard, |
| <a href="http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2005/n1822.pdf" target="_top">A Proposal to add a max |
| significant decimal digits value</a>, to be called <code class="computeroutput">std::numeric_limits</code>::max_digits10();. |
| For 32-bit floats, 9 decimal digits are needed to ensure a single bit change produces a different decimal digit |
| string. |
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| So a much more helpful display using 9 decimal digits is thus: |
| <code class="computeroutput">[1.00000000 != 1.00000012]</code> showing that the two values are in fact different. |
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| For <acronym class="acronym">IEEE754</acronym> 32-bit float values - 9 decimal digits are shown. For 64-bit <acronym class="acronym">IEEE754</acronym> double - 17 decimal digits. For |
| <acronym class="acronym">IEEE754</acronym> extended long double using 80-bit - 21 decimal digits. For <acronym class="acronym">IEEE754</acronym> quadruple long double 128-bit, and Sparc |
| extended long double 128-bit - 36 decimal digits. For floating-point types, a convenient formula to calculate |
| max_digits10 is: 2 + <code class="computeroutput">std::numeric_limits</code><FPT>::digits * 3010/10000; |
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| Note that a user defined floating point type UDFPT must define |
| <code class="computeroutput">std::numeric_limits</code><UDFPT>::is_specialized = true and provide an appropriate value |
| for <code class="computeroutput">std::numeric_limits</code><UDFPT>::digits, the number of bits used for the significand |
| or mantissa. For example, for the Sparc extended long double 128, 113 bits are used for the significand (one of |
| which is implicit). |
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