Programmatically determining max value of a signed integer type

This related question is about determining the max value of a signed type at compile-time:

C question: off_t (and other signed integer types) minimum and maximum values

However, I've since realized that determining the max value of a signed type (e.g. time_t or off_t) at runtime seems to be a very difficult task.

The closest thing to a solution I can think of is:

uintmax_t x = (uintmax_t)1<>=1;

This avoids any looping as long as type has no padding bits, but if type does have padding bits, the cast invokes implementation-defined behavior, which could be a signal or a nonsensical implementation-defined conversion (e.g. stripping the sign bit).

I'm beginning to think the problem is unsolvable, which is a bit unsettling and would be a defect in the C standard, in my opinion. Any ideas for proving me wrong?