CORDIC Architectures: A Survey

Table 2

Comparison of various rotational CORDIC architectures, (SD: signed digit, CS: carry save).

Method (year)	Radix, $\rho$	Arithmetic	Latency $(t_{\text{FA}})$		Iterative	Iterative	Scale factor
			Nonpipelined	Pipelined	$X/Y$ path	$Z$-path	$K$
Nonredundant (1959) [3]	$2$	2's compliment	$n^2$	$n^2$	$\surd$	$\surd$	Constant
Redundant (1987) [42]	$2$	CS	$n{t}_{\text{stage}}$	$n{t}_{\text{stage}}$	$\surd$	$\surd$	Variable
Double-rotation/	$2$	SD	$1.5n{t}_{\text{stage}}$	$1.5n{t}_{\text{stage}}$	$\surd$	$\surd$	Constant
Correcting (1991) [51]
Low latency (1992) [55]	$2$	CS	$(n+{\log \hspace{0.17em}}_{3}n-1)t_{\text{stage}}$	$((9n-3)/8)t_{\text{stage}}$	$\surd$	$\surd$	Constant
Branching (1993) [52]	$2$	SD	$n{t}_{\text{stage}}$	$n{t}_{\text{stage}}$	$\surd$	$\surd$	Constant
DCORDIC (1996) [56]	$2$	SD/CS	—	$(n{t}_{\text{stage}}+n+1)$	$\surd$	$\surd$	Constant
Radix-4 (1993) [58]	$4$	SD	—	$(3n/4+1)t_{\text{stage}}$	$\surd$	$\surd$	Variable
Radix2-4 (1996) [59]	$2\text{–}4$	CS	—	$(3n/4+1)t_{\text{stage}}$	$\surd$	$\surd$	Constant
Radix-4 (1997) [43]	$4$	CS	—	$(2n/3+1)t_{\text{stage}}$	$\surd$	$n/6$	Variable
PCORDIC (2002) [61]	$2$	SD	$(1.7n+1.25+{\log \hspace{0.17em}}_{2}n)$	—	$\surd$	$\times$	Constant
Flat CORDIC (2002) [63]	$2$	SD	34 for 16-bit, 50 for 32-bit	—	combinational	$\times$	Constant
Para-CORDIC (2004) [64]	$2$	CS	$(2(s(n)+n/2-l+2)+\lceil {\log \hspace{0.17em}}_{1.5}n+2\rceil )$	—	$\surd$	$\times$	Constant
Semi-flat (2006) [65]	$2$	SD	33 for 16-bit	—	$\lambda /$combinational	$\lambda$	Constant
Nonredundant low-latency (2008) [49]	$2$	2's compliment	—	$(n/2+2)t_{\text{adder}}$ + $t_{\text{multiplier}}$	$(n/2+1)/$multiplier	$n/3$	Constant