Implementation Defined behavior means the standards authors provided a list of possible behaviors, and compiler authors must pick one and document which they picked.
Unspecified behavior is more what you're thinking of, though in that case the standard still provides a list of possibilities that compiler authors have to pick from, they just don't have to document it or always make the same choice for every program.
There's no allowed subset of behavior where compiler authors are free to pick whatever they want and document it (but must do so). IMO there should be, most "Undefined Behavior" could be specified and documented, even where that choice would be "the compiler assumes such situations are unreachable and optimizes based on that assumption" like much of current UB. At least it'd be explicit!
> Implementation Defined behavior means the standards authors provided a list of possible behaviors
The standard definitely does not require implementations to pick from a list of possible behaviors. All the standard requires is that the implementation document the behavior.
For example, the behavior on integer demotion is implementation-defined and there's no list of possible behaviors:
> When an integer is demoted to a signed integer with smaller size, or an unsigned integer is converted to its corresponding signed integer, if the value cannot be represented the result is implementation-defined.
> Unspecified behavior is more what you're thinking of, though in that case the standard still provides a list of possibilities that compiler authors have to pick from
That contradicts the standard's definition of unspecified behavior. For example, from the C89 draft (emphasis added) [0]:
> Unspecified behavior --- behavior, for a correct program construct and correct data, for which the Standard imposes no requirements.
