Does the C++ standard specify anything on the representation of floating point numbers?

Question

For types T for which std::is_floating_point<T>::value is true, does the C++ standard specify anything on the way that T should be implemented?

For example, does T has even to follow a sign/mantissa/exponent representation? Or can it be completely arbitrary?

Answer 1

From N3337:

[basic.fundamental/8]: There are three floating point types: float, double, and long double. The type double provides at least as much precision as float, and the type long double provides at least as much precision as double. The set of values of the type float is a subset of the set of values of the type double; the set of values of the type double is a subset of the set of values of the type long double. The value representation of floating-point types is implementation-defined. Integral and floating types are collectively called arithmetic types. Specializations of the standard template std::numeric_limits (18.3) shall specify the maximum and minimum values of each arithmetic type for an implementation.

If you want to check if your implementation uses IEEE-754, you can use std::numeric_limits::is_iec559:

static_assert(std::numeric_limits<double>::is_iec559,
              "This code requires IEEE-754 doubles");

There are a number of other helper traits in this area, such as has_infinity, quiet_NaN and more.

Answer 2

The C standard has an "annex" (in C11 it's Annex F) which lays out what it means for an implementation of C to be compliant with IEC 60559, the successor standard to IEEE 754. An implementation that conforms to Annex F must have IEEE-representation floating point numbers. However, implementing this annex is optional; the core standard specifically avoids saying anything about the representation of floating point numbers.

I do not know whether there is an equivalent annex for C++. It doesn't appear in N3337, but that might just mean it's distributed separately. The existence of std::numeric_limits<floating-type>::is_iec559 indicates that the C++ committee at least thought about this, but perhaps not in as much detail as the C committee did. (It is and has always been a damned shame that the C++ standard is not expressed as a set of edits to the C standard.)