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

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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.

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