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Logging floating point type numbers

It may appear that floating-point numbers are displayed by the Unit Test Framework 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, 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

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).