1. A method for performing failsafe, hardware-independent floating-point arithmetic in an automation system during runtime of a computer program in real time, the method comprising: establishing, in an arithmetic unit, a first result in a first calculation in floating-point notation using standard floating-point arithmetic based on a plurality of items of starting data comprising floating-point numbers; converting, in the arithmetic unit, the plurality of items of starting data in floating-point notation into a floating-point interval notation; and executing, in the arithmetic unit, a second calculation, which is analogous to the first calculation, based on the plurality of items of starting data converted into the floating-point interval notation, the second calculation establishing a result interval; wherein the first result of the first calculation is checked for erroneous calculation based on the result interval established by the second calculation.