CORDIC ALGORITHM WITH DIGITS SKIPPING

1. CORDIC algorithm using circular coordinates Technique for consecutive zeros skipping • Elementary angles: On rotation mode, a vector is rotated through an angle b. Using n bits precision: • After n/3 iterations, only the angles aj fulfilling dj=1 are subtracted to achieve the convergence. • If the technique is used after n/2 iterations, the scale factor remains constant. • Equation of a microrotation: dn/2 Zn/2 = ···000101001011··· Zn/2+1= ···000001001011··· Zn/2+2= ···000001001011··· Zn/2+3= ···000000001011··· Zn/2+4= ···000000001011··· Zn/2+5= ···000000001011··· • Scale Factor: For regular operations, the scale factor is a constant. C Zi SH INC LDz LDx, Ldy 0 x 0 CLK CLK CLK 1 0 CLK4 CLK4 0 0 1 1 CLK CLK 0 CLK Hardware added to the classical CORDIC architecture • The number of consecutive zeros skipped is limited for hardware reduction purposes. To skip m consecutive zeros, a clock m times faster is required. • The Rz register adds the left-shift capacity. • A small register to store the current iteration is added . C Pi Zi+3 Zi+1 Zi+2 Pi SH INC LDz LDx, Ldy si 0 x x x x 0 0 CLK CLK CLK sign(z) 1 0 0 0 x 0 CLK4 CLK4 0 0 x 1 0 0 1 0 0 CLK4 CLK4 0 0 x 1 0 1 x x 0 CLK CLK 0 CLK 0 1 0 0 1 1 1 CLK CLK 0 CLK 0 1 1 1 1 x 1 CLK4 CLK4 0 0 x 1 1 1 0 1 1 CLK4 CLK4 0 0 x 1 1 1 0 0 0 CLK CLK 0 CLK 1 1 1 0 x x 1 CLK CLK 0 CLK 1 Technique for consecutive ones skipping 0.0111110··· 0.1000010··· • 1’s skipping is performed using Booth recoding on-the-fly. • The Booth recoding changes the consecutive ones into zeros, plus a suitable positive and negative one. • The control unit is a little more complex. CORDIC ALGORITHM WITH DIGITS SKIPPING Javier Hormigo, Julio Villalba and Emilio L. Zapata Dept. Computer Architecture. University of Malaga (SPAIN) • Reduction in number of iterations. • Very low hardware cost. • Average nearly 25% for 0 skipping. • Additional 5% adding 1 skipping.