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[ceph.git] / ceph / src / boost / libs / test / doc / test_output / logging_floating_point.qbk

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 / Copyright (c) 2003 Boost.Test contributors 
 /
 / Distributed under the Boost Software License, Version 1.0. (See accompanying
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[section:log_floating_points Logging floating point type numbers]

It may appear that floating-point numbers are displayed by the __UTF__ with an excessive number of decimal digits.
However the number of digits shown is chosen to avoid apparently nonsensical displays like `[1.00000 != 1.00000]`
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
 `std::numeric_limits<float>::digits10`. The function used for the number of decimal
digits displayed is that proposed for a future C++ Standard,
[@http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2005/n1822.pdf A Proposal to add a max
significant decimal digits value], to be called `std::numeric_limits::max_digits10();`.
For 32-bit floats, 9 decimal digits are needed to ensure a single bit change produces a different decimal digit
string.

So a much more helpful display using 9 decimal digits is thus:
`[1.00000000 != 1.00000012]` showing that the two values are in fact different.


For __IEEE754__ 32-bit float values - 9 decimal digits are shown. For 64-bit __IEEE754__ double - 17 decimal digits. For
__IEEE754__ extended long double using 80-bit - 21 decimal digits. For __IEEE754__ 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 + std::numeric_limits<FPT>::digits * 3010/10000`;

[note
     Note that a user defined floating point type UDFPT must define
     `std::numeric_limits<UDFPT>::is_specialized = true` and provide an appropriate value
     for `std::numeric_limits<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).
]
[endsect] [/section:log_floating_points]