Prof. Kantabutra published a new circuit design for computing transcendental functions. This design is a nontrivial modification of the CORDIC method. The new design involves using very fast iterations using low-precision circuits. These iterations accumulate errors, which are very quickly corrected to full accuracy only periodically. The result is an ultra-fast, high-precision circuit at near low-precision speed. For example, a 64-bit circuit would perform 8 iterations at 9-10 bits of precisions in one or two clock cycles using a combinational array, and would then make a correction in about a clock cycle. After 8 repetitions of the same operations, the computation would be complete with full accuracy.
V. Kantabutra, "On Hardware for Computing Exponential and Trigonometric Functions," IEEE Transactions on Computers, March, 1996.