We present circuit implementations for computing exponentials and logarithms suitable for rapid single-flux-quantum (RSFQ) logic. We propose hardware algorithms based on the sequential table-lookup (STL) method using the radix-2 signed-digit representation that achieve high-throughput, digit-serial calculations. The circuits are implemented by processing elements formed in systolic-array-like, regularly-aligned pipeline structures. The processing elements are composed of adders, shifters, and readouts of precomputed constants. The iterative calculations are fully overlapped, and throughputs approach the maximum throughput of serial processing. The circuit size for calculating significand parts is estimated to be approximately 5-10 times larger than that of a bit-serial floating-point adder or multiplier.