Essentially there are two different sets of floating point instructions on x86 and x86-64: - the x87 instructions, which descend from the original 8087 coprocessor (and have 80-bit registers), and - the SSE instructions, which descend from the Pentium MMX feature set, are faster, support SIMD operations, and can be fully pipelined.

The x87 instructions are basically for legacy compatibility, or if you manually use long doubles on some platforms.

The idea behind extended precision registers was good in theory, but ultimately caused too much hassle in practice.