Reversible logic has applications in low-power computing and quantum computing. However, there are few existing designs for reversible floating-point adders and none suitable for quantum computation. In this paper we propose a space-efficient reversible floating-point adder, suitable for binary quantum computation, improving the design of Nachtigal et al. Our work focuses on improving the reversible designs of the alignment unit and the normalization unit, which are the most expensive parts. By changing a few elements of the existing algorithm, including the circuit designs of the RLZC (reversible leading zero counter) and converter, we have reduced the cost about 68%. We also propose fault-tolerant designs for the circuits. The KQ for our fault-tolerant design is almost sixty times as expensive as for a 32-bit fixed-point addition. We note that the floating-point representation makes in-place, truly reversible arithmetic impossible, requiring us to retain both inputs, which limits the sustainability of its use for quantum computation.