All the floating-point arithmetic that is natively supported these days is the 32- and 64-bit kind in SSE instruction sets and its extensions. The fact that something is "available" doesn't mean much in terms of actual support. As far as I know, long double means 128-bit floats in modern clang/gcc, and they are done in software.
Long doubles are typically 80-bit x87 "extended precision" doubles as far as I've seen. (Except on windows :-P ). It's part of the reason why LLVM has the 80 bit float type.
They are definitely still supported in modern Intel processors. That said, there can be some confusion because they end up being padded to 16 bytes for alignment reasons, so take 128 bits of memory, but they are still only 10 byte types.
They are a distinct type from the "quad" precision float128 type, which is software emulated as you mentioned.
All that being said, you are right that most of the time float math ends up in SSE style instructions, but as soon as you add long doubles to the mix, the compiler will emit x87 style float instructions to gain the extra precision.
