Multi-angle Constant Multiplier Givens Rotation Algorithm

This paper presents a new algorithm for implementing exact Givens rotation for use in QR matrix decomposition. The algorithm is based on constant multipliers to perform multiple angle rotations in parallel, reducing latency and gate count, and is called multi-angle constant multiplier. Complexity and optimal angle division sequences have been studied for up to 20 bits of precision. Bit-exact software implementation of the algorithm was used in QR decomposition of 4 × 4 matrices with 16 bits of precision, and its numerical stability was extensively tested. QR decomposition was implemented in Xilinx Virtex 6, where pipelining strategies for latency-operating frequency trade-offs have been considered.