You can save/load 80-bit values to memory with the regular x87 instructions, it's just called "extended precision". And the accelerated "save FPU state" instructions save the full 80-bit state. Otherwise it would be pretty nutty.
Where you can get unpredictable (though still repeatable) behaviour is when your compiler spills into 64-bit memory slots, and does it a little differently with each little modification to the code.
Where you can get unpredictable (though still repeatable) behaviour is when your compiler spills into 64-bit memory slots, and does it a little differently with each little modification to the code.