Low Latency Time CORDIC Algorithms

　　　　　因CORDIC演算法是一種迭代的運算，在整個運算中需要做適切的正規化處理，以使 向量長度保持恆定，雖然可以簡單地重複某些迭代運算來取代正規化，但是乃需額外的迭代 過程。在此提出一種修正的旋轉系統 CORDIC 演算法，使正規化運算子的運算步驟併入一般 的迭代運算過程而未增加時間。 只需 n 個迭代運算步驟，n 是內部暫存器的位元數。正因 為正規化運算子與一般迭代運算是並行處理，若採用快速的加法器，則修正的 CORDIC 演算 法所花的時間最快約是傳統演算法的 75 ％。 這種方法亦可良好地應用在拋物線系統的 CORDIC 演算法中。
　　　　　As the CORDIC (COordinate Rotation DIgital Computer) algorithm is a rotation-extension iterative operation, it needs to perform scaling operations before or after all the rotations in the Circular and Hyperbolic coordinate systems. It may repeat some iterations to replace the scaling operations. However, they need extra iterations to complete the CORDIC rotation algorithm. A modified CORDIC algorithm that performs exact scaling is proposed in this work. In the proposed scheme, the scaling factor iterations that normally follow the main iterations are incorporated as an extra term into the main CORDIC iterations. The iterative rotations and scaling operations can be combined in a circular coordinate system, and completed in n iterations, where n is the number of bits in the internal register. As scaling iterations can be processed in parallel with rotation iterations, the overall time required by the modified algorithm is estimated about 75% of that required by the conventional one, if fast adders are adopted.