In C++, is exactly one of <, == and > guaranteed to be true on floats?

Question

In C++, do I have a guarantee that, for any given float a and float b, one and only one of a < b, a == b and a > b is true?

If this differs between compilers and platforms, I am interested in Visual C++ on x86.

Answer 1

No.

It's enough for either a or b to be NaN for each of a < b, a == b and a > b to be false.

If both a and b are non-NaN then exactly one of a < b, a == b or a > b has to be true.

In complement, this answer tells you how you can get a NaN value in C++ (there are several NaN values, that can be distinguished by inspecting their representations; they are all different from each other because NaN is never equal to anything,) and how you can test whether a value is a NaN (an idiomatic test to see if a variable x is a NaN is x != x, and indeed std::isnan() is often implemented this way, but some programmers who will have to read your code may be confused by it).

And then, if a and b are the results of previous computations, there is the problem of excess precision. See this article for a discussion in C. The C99 standard solved the problem by making rules explicit for where excess precision could and could not occur, but despite C++ more or less inheriting these rules by deferring to the C standard for the definition of FLT_EVAL_METHOD in cfloat, in practice C compilers take the rules more seriously than C++ compilers. For instance GCC implements the rules for C when compiling with -std=c99, and in this context you can rely on the property to hold, but as of this writing GCC does not implement these rules when used as a C++ compiler.