Cordic approximation algorithm

Start Learning Cordic algorithm now

Learn the blog:

(1) http://blog.csdn.net/liyuanbhu/article/details/8458769 trigonometric calculation, Cordic algorithm Introduction

(1) A good explanation of the idea of the CORDIC algorithm. Coordinate rotation formula. Derivation http://www.cnblogs.com/ywxgod/archive/2010/08/06/1793609.html

Clockwise rotation: X ' = Xcos (θ) + ysin (θ), y ' =-xsin (θ) + ycos (θ);

Counterclockwise Rotation: X ' = Xcos (θ)-ysin (θ), y ' = xsin (θ) + ycos (θ);

Once you know this, determine (x, y) polar coordinates ρ= sqrt (x2+y2), θ= arctan (y/x). The solution of θ is a requirement super function. In blog post is to find the hair by two points. Where the approximation of the indicator is y = 0; I estimate that the cordic algorithm is a similar approximation.

This two-point search is really an image.

The implementation of the FPGA is as follows: only 5-level pipelining is used. Its angular accuracy is 26-7.

1 //*****************************************************************************************2 //3 //function:achieve The coordinate rotation digital computers 54 //5 //6 //Corn 2014.11.157 //8 //9 //*****************************************************************************************Ten  One ModuleCordic_module ( A inputCLK, Rst_n, -  - input        signed[7:0] x0, y0, the  - Output    Reg    signed[7:0] R, Syta -  - ); +  - parameterWIDTH =8; +  A  at Reg    signed[WIDTH-1:0] X0_r, X1_r, X2_r, X3_r, X4_r; - Reg    signed[WIDTH-1:0] Y0_r, Y1_r, Y2_r, Y3_r, Y4_r; - Reg    signed[WIDTH-1:0] Syta0_r, Syta1_r, Syta2_r, Syta3_r, Syta4_r; -  -  -  always@(PosedgeClassor NegedgeRst_n)begin in     if(!rst_n)begin -Syta0_r <=0; to     End +     Else    begin -     //First stage---------------------------------------------------------- the         if(X0 >=0)begin        //In the first sector or forth sector *X0_r <=x0; $Y0_r <=y0;Panax NotoginsengSyta0_r <=0; -         End the         Else    if(Y0 >=0)begin    //In the second sector +X0_r <=y0; AY0_r <=-x0; theSyta0_r <= -; +         End -         Else    begin                    //In the third sector $X0_r <=-y0; $Y0_r <=x0; -Syta0_r <=- -; -         End the     //Second Stage arctan (1)------------------------------------------------------- -         if(Y0_r >=0)beginWuyiX1_r <= X0_r +Y0_r; theY1_r <= Y0_r-X0_r; -Syta1_r <= Syta0_r + $; Wu         End -         Else    begin AboutX1_r <= X0_r-Y0_r; $Y1_r <= Y0_r +X0_r; -Syta1_r <= Syta0_r- $; -         End -     //Third Stage arctan (2)--------------------------------------------------------- A         if(Y1_r >=0)begin +X2_r <= X1_r + y1_r/2; theY2_r <= Y1_r-x1_r/2; -Syta2_r <= Syta1_r + -; $         End the         Else    begin theX2_r <= X1_r-y1_r/2; theY2_r <= Y1_r + x1_r/2; theSyta2_r <= Syta1_r- -; -         End in     //Forth Stage arctan (4)--------------------------------------------------------- the         if(Y2_r >=0)begin theX3_r <= X2_r + y2_r/4; AboutY3_r <= y2_r-x2_r/4; theSyta3_r <= Syta2_r + -; the         End the         Else    begin +X3_r <= x2_r-y2_r/4; -Y3_r <= Y2_r + x2_r/4; theSyta3_r <= Syta2_r- -;Bayi         End the     //Fiveth Stage arctan (8)--------------------------------------------------------- the         if(Y3_r >=0)begin -X4_r <= X3_r + y3_r/8; -Y4_r <= Y3_r-x3_r/8; theSyta4_r <= Syta3_r +7; the         End the         Else    begin theX4_r <= X3_r-y3_r/8; -Y4_r <= Y3_r + x3_r/8; theSyta4_r <= Syta3_r-7; the         End the     94     //Output theR <=X4_r; theSyta <=Syta4_r; the     End98  About  - 101 End    // always102 //103 104  the 106 Endmodule

Simulation results:

Three groups of data were used: (-41, 55), (4,-4), (3, 3)

Results of using the computer: (68.6,-53), (5.6,-45) (4.2, 45)

Simulation results: (112,-126), (9,-40), (6, 50) where (-126) 180 = 54

Conclusion: The RADIUS has increased, the angle has a certain error range of 27-7. There is a certain error in the angle. If you want to increase the precision, increase the number of iterations.

Cordic approximation algorithm