NaN comparison rule in C/C++

Question

Doing some optimziation on a piece of code, the correctness of the code depending on how the compiler handle NaNs.

I read the IEEE-754 rules on NaN, which states:

Answer 1

C/C++ does not require specific floating-point representation and does not require that any comparison against NaN is false.

In C++ you can check if all floating-point types fulfill IEEE 754 using std::numeric_limits::is_iec559:

static constexpr bool is_iec559;

⁵⁶ True if and only if the type adheres to IEC 559 standard.²¹⁷

⁵⁷ Meaningful for all floating point types.

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217) International Electrotechnical Commission standard 559 is the same as IEEE 754.

For other floating-point representations comparison against NaN may or may not behave the same way.

In fact, even representing NaN itself is not required. See std::numeric_limits<T>::has_quiet_NaN, std::numeric_limits<T>::has_signaling_NaN.

Answer 2

The == and != operators appear to not be constrained to the IEEE 754 behavior for NaNs, as pointed out in @AlexD's answer already.

However, the <math.h> comparison macros are required to follow NaN rules equivalent to IEEE 754's. The following from the C11 draft N1580 under 7.12.14 Comparison Macros states that the <math.h> comparison macros are required to ensure that, if either or both of x, y are NaNs then:

• isunordered(x, y) is true

• isgreater(x, y), isgreaterequal(x, y), isless(x, y), islessequal(x, y) are all false

The relational and equality operators support the usual mathematical relationships between numeric values. For any ordered pair of numeric values exactly one of the relationships - less, greater, and equal - is true. Relational operators may raise the "invalid" floating-point exception when argument values are NaNs. For a NaN and a numeric value, or for two NaNs, just the unordered relationship is true.

The C++ standard simply defers to the C one on <math.h> matters:

The classification/comparison functions behave the same as the C macros with the corresponding names defined in 7.12.3, Classification macros, and 7.12.14, Comparison macros in the C Standard.