CORDIC算法原理详解及其Verilog实现
2024-04-28 08:59:00
CORDIC算法原理详解及其Verilog实现
本文的verilog代码
链接：https://pan.baidu.com/s/1GGbRjxO5CxoIODQAg1l6Lw
提取码：jo0h
*本文的Verilog代码均没有考虑象限问题，MATLAB代码有考虑。
*本文参考博客
[1]https://blog.csdn.net/qq_39210023/article/details/77456031
[2]https://blog.csdn.net/longxuekun1992/article/details/52435024
文章目录
- CORDIC 简介
- 算法实现
- 1.已知坐标(x,y)，求其向量对应的相角θ（反正切）和模值
- 1.1 MATLAB代码
- 1.2 Verilog代码
- 1.3 testbench A
- 2.已知角度θ，求正弦sinθ和余弦cosθ
- 2.1 MATLAB代码
- 2.2 Verilog代码
- 2.3 Testbench B
CORDIC 简介
CORDIC（Coordinate Rotation Digital Computer）坐标旋转数字计算机，是数学与计算机技术交叉产生的一种机器算法，用于解决计算机的数学计算问题。发展到现在，CORDIC算法及其扩展算法大致有三种计算模式：圆周旋转模式、线性旋转模式和双曲线旋转模式，分别用来实现不同的数学运算。本文介绍圆周旋转模式下的CORDIC算法原理及实现过程，另两种模式将分期介绍。
简单来讲，CORDIC利用近似逼近的思想，将计算机中三角函数、开根号、求对数等复杂运算，转化为简单的加减和移位操作。
1）算法描述
如图，XY平面中一点( x 1 , y 1 ) 经圆周旋转θ角度，得到点( x 2 , y 2 ) 。经简单的三角函数关系，可得到：
通过提出因数cosθ，可得：
如果不考虑cosθ，得到“伪旋转”方程：
伪旋转仅实现了正确的角度旋转，但向量模值变为原来的1/cosθ。
2）CORDIC方法
注意!上式已经仅剩加减和移位运算。
可以确定的是，任意旋转角度θ，都可以由上表中的大小不同θi进行多次旋转得到。CORDIC正是利用这一点，将θ角度的旋转分解为从大到小、逐次逼近真实旋转角度的一组旋转，而这些旋转的实现又都可以由加减和移位运算来完成。θi可以预先制成表格，供计算机查找使用。
算法实现
1.已知坐标(x,y)，求其向量对应的相角θ（反正切）和模值
思想:把原向量逐次向X正轴进行伪旋转逼近，整个过程的累计旋转角度即为θ，而旋转后的x坐标补偿模值增益K后即为原向量模值。
每次迭代的方程为：
模值总增益K为：
其中d决定旋转方向为逆时针还是顺时针，z为角度累加值。
注意！查找表中所有θi的总和约为99度，因此能实现计算的角度在-99~99度之间。实际算法实现时，我们可预先判断坐标象限，人为将其转化为第一象限内的计算，并在事后补偿为真实值。
1.1 MATLAB代码
%% ***********************************************************************************
% 已知坐标，用cordic算法计算相角和幅值。基本公式如下：
% x(k+1) = x(k) - d(k)*y(k)*2^(-k)
% y(k+1) = y(k) + d(k)*x(k)*2^(-k)
% z(k) = z(k) - d(k)*actan(2^(-k))
%% ***********************************************************************************clear;close all;clc;
% 初始化----------------------------------------
N = 16; %迭代次数
tan_table = 2.^-(0 : N-1);
angle_LUT = atan(tan_table);K = 1;
for k = 0 : N-1K = K*(1/sqrt(1 + 2^(-2*k)));
endx = 3;
y = sqrt(3);
angle_accumulate = 0;% cordic算法计算-------------------------------
if (x==0 && y==0) radian_out = 0;amplitude_out = 0;
else % 先做象限判断，得到相位补偿值if (x > 0)phase_shift = 0;elseif (y < 0)phase_shift = -pi;elsephase_shift = pi;endfor k = 0 : N-1 % 迭代开始x_temp = x;if (y < 0) % d(k)=1，逆时针旋转x = x_temp - y*2^(-k);y = y + x_temp*2^(-k);angle_accumulate = angle_accumulate - angle_LUT(k+1);else % d(k)=-1，顺时针旋转x = x_temp + y*2^(-k);y = y - x_temp*2^(-k);angle_accumulate = angle_accumulate + angle_LUT(k+1);end radian_out = angle_accumulate + phase_shift; %弧度输出endamplitude_out = x*K; %幅值输出
endangle_out = radian_out*180/pi; %相角输出</span>1.2 Verilog代码
采用16级流水的Verilog (未考虑象限问题)
//*********************************************************
//功能1：已知角度θ，求正弦sinθ和余弦cosθ//思想:若向量模值为1，则其x坐标就是余弦值，y坐标就是正弦值。
//利用这一点，从(K,0)处迭代旋转至θ处的单位矢量即可。
//*********************************************************module cordic_A(
input clk,
input rst_n,
input [8:0] angle,
input start,output reg signed[31:0] Sin,
output reg signed[31:0] Cos,
output finished);parameter angle_0 = 32'd2949120; //45度*2^16
parameter angle_1 = 32'd1740992; //26.5651度*2^16
parameter angle_2 = 32'd919872; //14.0362度*2^16
parameter angle_3 = 32'd466944; //7.1250度*2^16
parameter angle_4 = 32'd234368; //3.5763度*2^16
parameter angle_5 = 32'd117312; //1.7899度*2^16
parameter angle_6 = 32'd58688; //0.8952度*2^16
parameter angle_7 = 32'd29312; //0.4476度*2^16
parameter angle_8 = 32'd14656; //0.2238度*2^16
parameter angle_9 = 32'd7360; //0.1119度*2^16
parameter angle_10 = 32'd3648; //0.0560度*2^16
parameter angle_11 = 32'd1856; //0.0280度*2^16
parameter angle_12 = 32'd896; //0.0140度*2^16
parameter angle_13 = 32'd448; //0.0070度*2^16
parameter angle_14 = 32'd256; //0.0035度*2^16
parameter angle_15 = 32'd128; //0.0018度*2^16parameter pipeline = 16;
parameter K = 32'h09b74; //0.607253*2^16,// reg signed [31:0] Sin;
// reg signed [31:0] Cos;reg signed [31:0] x0 =0,y0 =0,z0 =0;
reg signed [31:0] x1 =0,y1 =0,z1 =0;
reg signed [31:0] x2 =0,y2 =0,z2 =0;
reg signed [31:0] x3 =0,y3 =0,z3 =0;
reg signed [31:0] x4 =0,y4 =0,z4 =0;
reg signed [31:0] x5 =0,y5 =0,z5 =0;
reg signed [31:0] x6 =0,y6 =0,z6 =0;
reg signed [31:0] x7 =0,y7 =0,z7 =0;
reg signed [31:0] x8 =0,y8 =0,z8 =0;
reg signed [31:0] x9 =0,y9 =0,z9 =0;
reg signed [31:0] x10=0,y10=0,z10=0;
reg signed [31:0] x11=0,y11=0,z11=0;
reg signed [31:0] x12=0,y12=0,z12=0;
reg signed [31:0] x13=0,y13=0,z13=0;
reg signed [31:0] x14=0,y14=0,z14=0;
reg signed [31:0] x15=0,y15=0,z15=0;
reg signed [31:0] x16=0,y16=0,z16=0;reg [4:0] count;always@(posedge clk or negedge rst_n)beginif(!rst_n)count <= 'b0;else if(start)beginif(count != 5'd18)count <= count + 1'b1;else count <= count;end
endassign finished = (count == 5'd18)?1'b1:1'b0;always@(posedge clk or negedge rst_n)beginif(!rst_n)beginx0 <= 'b0;y0 <= 'b0;z0 <= 'b0;endelse beginx0 <= K;y0 <= 32'd0;z0 <= angle << 16;end
end always@(posedge clk or negedge rst_n)begin//第一次迭代if(!rst_n)beginx1 <= 'b0;y1 <= 'b0;z1 <= 'b0;endelse if(z0[31]) beginx1 <= x0 + y0;y1 <= y0 - x0;z1 <= z0 + angle_0;endelse beginx1 <= x0 - y0;y1 <= y0 + x0;z1 <= z0 - angle_0; end
end always@(posedge clk or negedge rst_n)begin//第二次迭代if(!rst_n)beginx2 <= 'b0;y2 <= 'b0;z2 <= 'b0;endelse if(z1[31]) beginx2 <= x1 + (y1>>>1);y2 <= y1 - (x1>>>1);z2 <= z1 + angle_1;endelse beginx2 <= x1 - (y1>>>1);y2 <= y1 + (x1>>>1);z2 <= z1 - angle_1; end
end always@(posedge clk or negedge rst_n)begin//第3次迭代if(!rst_n)beginx3 <= 'b0;y3 <= 'b0;z3 <= 'b0;endelse if(z2[31]) beginx3 <= x2 + (y2>>>2);y3 <= y2 - (x2>>>2);z3 <= z2 + angle_2;endelse beginx3 <= x2 - (y2>>>2);y3 <= y2 + (x2>>>2);z3 <= z2 - angle_2; end
end always@(posedge clk or negedge rst_n)begin//第4次迭代if(!rst_n)beginx4 <= 'b0;y4 <= 'b0;z4 <= 'b0;endelse if(z3[31]) beginx4 <= x3 + (y3>>>3);y4 <= y3 - (x3>>>3);z4 <= z3 + angle_3;endelse beginx4 <= x3 - (y3>>>3);y4 <= y3 + (x3>>>3);z4 <= z3 - angle_3; end
end always@(posedge clk or negedge rst_n)begin//第5次迭代if(!rst_n)beginx5 <= 'b0;y5 <= 'b0;z5 <= 'b0;endelse if(z4[31]) beginx5 <= x4 + (y4>>>4);y5 <= y4 - (x4>>>4);z5 <= z4 + angle_4;endelse beginx5 <= x4 - (y4>>>4);y5 <= y4 + (x4>>>4);z5 <= z4 - angle_4; end
end always@(posedge clk or negedge rst_n)begin//第6次迭代if(!rst_n)beginx6 <= 'b0;y6 <= 'b0;z6 <= 'b0;endelse if(z5[31]) beginx6 <= x5 + (y5>>>5);y6 <= y5 - (x5>>>5);z6 <= z5 + angle_5;endelse beginx6 <= x5 - (y5>>>5);y6 <= y5 + (x5>>>5);z6 <= z5 - angle_5; end
end always@(posedge clk or negedge rst_n)begin//第7次迭代if(!rst_n)beginx7 <= 'b0;y7 <= 'b0;z7 <= 'b0;endelse if(z6[31]) beginx7 <= x6 + (y6>>>6);y7 <= y6 - (x6>>>6);z7 <= z6 + angle_6;endelse beginx7 <= x6 - (y6>>>6);y7 <= y6 + (x6>>>6);z7 <= z6 - angle_6; end
end always@(posedge clk or negedge rst_n)begin//第8次迭代if(!rst_n)beginx8 <= 'b0;y8 <= 'b0;z8 <= 'b0;endelse if(z7[31]) beginx8 <= x7 + (y7>>>7);y8 <= y7 - (x7>>>7);z8 <= z7 + angle_7;endelse beginx8 <= x7 - (y7>>>7);y8 <= y7 + (x7>>>7);z8 <= z7 - angle_7; end
end always@(posedge clk or negedge rst_n)begin//第9次迭代if(!rst_n)beginx9 <= 'b0;y9 <= 'b0;z9 <= 'b0;endelse if(z8[31]) beginx9 <= x8 + (y8>>>8);y9 <= y8 - (x8>>>8);z9 <= z8 + angle_8;endelse beginx9 <= x8 - (y8>>>8);y9 <= y8 + (x8>>>8);z9 <= z8 - angle_8; end
end always@(posedge clk or negedge rst_n)begin//第10次迭代if(!rst_n)beginx10 <= 'b0;y10 <= 'b0;z10 <= 'b0;endelse if(z9[31]) beginx10 <= x9 + (y9>>>9);y10 <= y9 - (x9>>>9);z10 <= z9 + angle_9;endelse beginx10 <= x9 - (y9>>>9);y10 <= y9 + (x9>>>9);z10 <= z9 - angle_9; end
end always@(posedge clk or negedge rst_n)begin//第11次迭代if(!rst_n)beginx11 <= 'b0;y11 <= 'b0;z11 <= 'b0;endelse if(z10[31]) beginx11 <= x10 + (y10>>>10);y11 <= y10 - (x10>>>10);z11 <= z10 + angle_10;endelse beginx11 <= x10 - (y10>>>10);y11 <= y10 + (x10>>>10);z11 <= z10 - angle_10; end
end always@(posedge clk or negedge rst_n)begin//第12次迭代if(!rst_n)beginx12 <= 'b0;y12 <= 'b0;z12 <= 'b0;endelse if(z11[31]) beginx12 <= x11 + (y11>>>11);y12 <= y11 - (x11>>>11);z12 <= z11 + angle_11;endelse beginx12 <= x11 - (y11>>>11);y12 <= y11 + (x11>>>11);z12 <= z11 - angle_11; end
end always@(posedge clk or negedge rst_n)begin//第13次迭代if(!rst_n)beginx13 <= 'b0;y13 <= 'b0;z13 <= 'b0;endelse if(z12[31]) beginx13 <= x12 + (y12>>>12);y13 <= y12 - (x12>>>12);z13 <= z12 + angle_12;endelse beginx13 <= x12 - (y12>>>12);y13 <= y12 + (x12>>>12);z13 <= z12 - angle_12; end
end always@(posedge clk or negedge rst_n)begin//第14次迭代if(!rst_n)beginx14 <= 'b0;y14 <= 'b0;z14 <= 'b0;endelse if(z13[31]) beginx14 <= x13 + (y13>>>13);y14 <= y13 - (x13>>>13);z14 <= z13 + angle_13;endelse beginx14 <= x13 - (y13>>>13);y14 <= y13 + (x13>>>13);z14 <= z13 - angle_13; end
end always@(posedge clk or negedge rst_n)begin//第15次迭代if(!rst_n)beginx15 <= 'b0;y15 <= 'b0;z15 <= 'b0;endelse if(z14[31]) beginx15 <= x14 + (y14>>>14);y15 <= y14 - (x14>>>14);z15 <= z14 + angle_14;endelse beginx15 <= x14 - (y14>>>14);y15 <= y14 + (x14>>>14);z15 <= z14 - angle_14; end
end always@(posedge clk or negedge rst_n)begin//第16次迭代if(!rst_n)beginx16 <= 'b0;y16 <= 'b0;z16 <= 'b0;endelse if(z15[31]) beginx16 <= x15 + (y15>>>15);y16 <= y15 - (x15>>>15);z16 <= z15 + angle_15;endelse beginx16 <= x15 - (y15>>>15);y16 <= y15 + (x15>>>15);z16 <= z15 - angle_15; end
end always@(posedge clk or negedge rst_n)beginif(!rst_n)beginCos <= 'b0;Sin <= 'b0;endelse beginSin = y16;Cos = x16;end
end endmodule1.3 testbench A
输入连续5个时钟上升沿输入60°，30°，45°，90°，30°，看是否能够连续输出相应结果。
`timescale 1ns/1psmodule cordic_Atb();parameter PERIOD = 10;
reg clk;
reg rst_n;
reg [8:0]angle;
reg start;wire [31:0] Sin;
wire [31:0] Cos;
wire finished;initial beginclk = 0;rst_n = 0;start = 0;angle = 'b0;#100 rst_n =1;#10 @(posedge clk) start = 1'b1;angle = 9'd60;#10 @(posedge clk) angle = 9'd30;#10 @(posedge clk) angle = 9'd45;#10 @(posedge clk) angle = 9'd90;#10 @(posedge clk) angle = 9'd30;#100000 $stop;
endalways #(PERIOD/2) clk = ~clk;cordic_A inst1(.clk(clk),.rst_n(rst_n),.angle(angle),.start(start),.Sin(Sin),.Cos(Cos),.finished(finished));endmodule由于硬件实现将数据整体左移16位，从而换区更高精度，因此得到的结果需要向右移16位，进行还原。还原后我们发现跟预期的值相等。
2.已知角度θ，求正弦sinθ和余弦cosθ
思想:若向量模值为1，则其x坐标就是余弦值，y坐标就是正弦值。利用这一点，从(K,0)处迭代旋转至θ处的单位矢量即可。
迭代方程及K的计算同第一小节。同时也要注意预先对象限的判断和补偿。
2.1 MATLAB代码
%% ***********************************************************************************
% 已知相角theta，计算其正弦和余弦值。基本公式如下：
% x(k+1) = x(k) - d(k)*y(k)*2^(-k)
% y(k+1) = y(k) + d(k)*x(k)*2^(-k)
% z(k) = z(k) - d(k)*actan(2^(-k))
%% ***********************************************************************************
clear;close all;clc;% 初始化----------------------------------------
N = 16; %迭代次数
tan_table = 2.^-(0 : N-1);
angle_LUT = atan(tan_table);K = 1;
for k = 0 : N-1K = K*(1/sqrt(1 + 2^(-2*k)));
endtheta = -90;
x = 1;
y = 0;
phase_accumulate = theta/180*pi; %转化为弧度% cordic算法计算-------------------------------
if (phase_accumulate > pi/2) % 先做象限判断，得到相位补偿值phase_accumulate = phase_accumulate - pi;sign_x = -1;sign_y = -1;
elseif (phase_accumulate < -pi/2)phase_accumulate = phase_accumulate + pi;sign_x = -1;sign_y = -1;
elsesign_x = 1;sign_y = 1;
endfor k = 0 : N-1 % 迭代开始x_temp = x;if (phase_accumulate > 0) % d(k)=1，逆时针旋转x = x_temp - y*2^(-k);y = y + x_temp*2^(-k);phase_accumulate = phase_accumulate - angle_LUT(k+1);else % d(k)=-1，顺时针旋转x = x_temp + y*2^(-k);y = y - x_temp*2^(-k);phase_accumulate = phase_accumulate + angle_LUT(k+1);end
endcos_out = sign_x*x*K; %余弦输出
sin_out = sign_y*y*K; %正弦输出</span>2.2 Verilog代码
16级流水的Verilog代码如下：
//*********************************************************
//已知坐标(x,y)，求其向量对应的相角θ（反正切）和模值//思想:把原向量逐次向X正轴进行伪旋转逼近.
//整个过程的累计旋转角度即为θ，
//而旋转后的x坐标补偿模值增益K后即为原向量模值。
//*********************************************************module cordic_B(
input clk,
input rst_n,
input signed [31:0] x,
input signed [31:0] y,
input start,
output reg signed[31:0] angle,
output reg signed[31:0] mozhi,
output finished
);parameter angle_0 = 32'd2949120; //45度*2^16
parameter angle_1 = 32'd1740992; //26.5651度*2^16
parameter angle_2 = 32'd919872; //14.0362度*2^16
parameter angle_3 = 32'd466944; //7.1250度*2^16
parameter angle_4 = 32'd234368; //3.5763度*2^16
parameter angle_5 = 32'd117312; //1.7899度*2^16
parameter angle_6 = 32'd58688; //0.8952度*2^16
parameter angle_7 = 32'd29312; //0.4476度*2^16
parameter angle_8 = 32'd14656; //0.2238度*2^16
parameter angle_9 = 32'd7360; //0.1119度*2^16
parameter angle_10 = 32'd3648; //0.0560度*2^16
parameter angle_11 = 32'd1856; //0.0280度*2^16
parameter angle_12 = 32'd896; //0.0140度*2^16
parameter angle_13 = 32'd448; //0.0070度*2^16
parameter angle_14 = 32'd256; //0.0035度*2^16
parameter angle_15 = 32'd128; //0.0018度*2^16parameter pipeline = 16;
parameter K = 32'h09b74; //0.607253*2^16,// reg signed [31:0] Sin;
// reg signed [31:0] Cos;reg signed [31:0] x0 =0,y0 =0,z0 =0;
reg signed [31:0] x1 =0,y1 =0,z1 =0;
reg signed [31:0] x2 =0,y2 =0,z2 =0;
reg signed [31:0] x3 =0,y3 =0,z3 =0;
reg signed [31:0] x4 =0,y4 =0,z4 =0;
reg signed [31:0] x5 =0,y5 =0,z5 =0;
reg signed [31:0] x6 =0,y6 =0,z6 =0;
reg signed [31:0] x7 =0,y7 =0,z7 =0;
reg signed [31:0] x8 =0,y8 =0,z8 =0;
reg signed [31:0] x9 =0,y9 =0,z9 =0;
reg signed [31:0] x10=0,y10=0,z10=0;
reg signed [31:0] x11=0,y11=0,z11=0;
reg signed [31:0] x12=0,y12=0,z12=0;
reg signed [31:0] x13=0,y13=0,z13=0;
reg signed [31:0] x14=0,y14=0,z14=0;
reg signed [31:0] x15=0,y15=0,z15=0;
reg signed [31:0] x16=0,y16=0,z16=0;reg [4:0] count;always@(posedge clk or negedge rst_n)beginif(!rst_n)count <= 'b0;else if(start)beginif(count != 5'd18)count <= count + 1'b1;else count <= count;end
endassign finished = (count == 5'd18)?1'b1:1'b0;always@(posedge clk or negedge rst_n)beginif(!rst_n)beginx0 <= 'b0;y0 <= 'b0;z0 <= 'b0;endelse beginx0 <= x<<<16;y0 <= y<<<16;z0 <= 'b0;end
end always@(posedge clk or negedge rst_n)begin//第一次迭代if(!rst_n)beginx1 <= 'b0;y1 <= 'b0;z1 <= 'b0;endelse if(!y0[31]) begin //和A不同的是，每次判断y坐标的正负，从而决定是顺时针还是逆时针旋转。x1 <= x0 + y0;y1 <= y0 - x0;z1 <= z0 + angle_0;endelse beginx1 <= x0 - y0;y1 <= y0 + x0;z1 <= z0 - angle_0; end
end always@(posedge clk or negedge rst_n)begin//第二次迭代if(!rst_n)beginx2 <= 'b0;y2 <= 'b0;z2 <= 'b0;endelse if(!y1[31]) beginx2 <= x1 + (y1>>>1);y2 <= y1 - (x1>>>1);z2 <= z1 + angle_1;endelse beginx2 <= x1 - (y1>>>1);y2 <= y1 + (x1>>>1);z2 <= z1 - angle_1; end
end always@(posedge clk or negedge rst_n)begin//第3次迭代if(!rst_n)beginx3 <= 'b0;y3 <= 'b0;z3 <= 'b0;endelse if(!y2[31]) beginx3 <= x2 + (y2>>>2);y3 <= y2 - (x2>>>2);z3 <= z2 + angle_2;endelse beginx3 <= x2 - (y2>>>2);y3 <= y2 + (x2>>>2);z3 <= z2 - angle_2; end
end always@(posedge clk or negedge rst_n)begin//第4次迭代if(!rst_n)beginx4 <= 'b0;y4 <= 'b0;z4 <= 'b0;endelse if(!y3[31]) beginx4 <= x3 + (y3>>>3);y4 <= y3 - (x3>>>3);z4 <= z3 + angle_3;endelse beginx4 <= x3 - (y3>>>3);y4 <= y3 + (x3>>>3);z4 <= z3 - angle_3; end
end always@(posedge clk or negedge rst_n)begin//第5次迭代if(!rst_n)beginx5 <= 'b0;y5 <= 'b0;z5 <= 'b0;endelse if(!y4[31]) beginx5 <= x4 + (y4>>>4);y5 <= y4 - (x4>>>4);z5 <= z4 + angle_4;endelse beginx5 <= x4 - (y4>>>4);y5 <= y4 + (x4>>>4);z5 <= z4 - angle_4; end
end always@(posedge clk or negedge rst_n)begin//第6次迭代if(!rst_n)beginx6 <= 'b0;y6 <= 'b0;z6 <= 'b0;endelse if(!y5[31]) beginx6 <= x5 + (y5>>>5);y6 <= y5 - (x5>>>5);z6 <= z5 + angle_5;endelse beginx6 <= x5 - (y5>>>5);y6 <= y5 + (x5>>>5);z6 <= z5 - angle_5; end
end always@(posedge clk or negedge rst_n)begin//第7次迭代if(!rst_n)beginx7 <= 'b0;y7 <= 'b0;z7 <= 'b0;endelse if(!y6[31]) beginx7 <= x6 + (y6>>>6);y7 <= y6 - (x6>>>6);z7 <= z6 + angle_6;endelse beginx7 <= x6 - (y6>>>6);y7 <= y6 + (x6>>>6);z7 <= z6 - angle_6; end
end always@(posedge clk or negedge rst_n)begin//第8次迭代if(!rst_n)beginx8 <= 'b0;y8 <= 'b0;z8 <= 'b0;endelse if(!y7[31]) beginx8 <= x7 + (y7>>>7);y8 <= y7 - (x7>>>7);z8 <= z7 + angle_7;endelse beginx8 <= x7 - (y7>>>7);y8 <= y7 + (x7>>>7);z8 <= z7 - angle_7; end
end always@(posedge clk or negedge rst_n)begin//第9次迭代if(!rst_n)beginx9 <= 'b0;y9 <= 'b0;z9 <= 'b0;endelse if(!y8[31]) beginx9 <= x8 + (y8>>>8);y9 <= y8 - (x8>>>8);z9 <= z8 + angle_8;endelse beginx9 <= x8 - (y8>>>8);y9 <= y8 + (x8>>>8);z9 <= z8 - angle_8; end
end always@(posedge clk or negedge rst_n)begin//第10次迭代if(!rst_n)beginx10 <= 'b0;y10 <= 'b0;z10 <= 'b0;endelse if(!y9[31]) beginx10 <= x9 + (y9>>>9);y10 <= y9 - (x9>>>9);z10 <= z9 + angle_9;endelse beginx10 <= x9 - (y9>>>9);y10 <= y9 + (x9>>>9);z10 <= z9 - angle_9; end
end always@(posedge clk or negedge rst_n)begin//第11次迭代if(!rst_n)beginx11 <= 'b0;y11 <= 'b0;z11 <= 'b0;endelse if(!y10[31]) beginx11 <= x10 + (y10>>>10);y11 <= y10 - (x10>>>10);z11 <= z10 + angle_10;endelse beginx11 <= x10 - (y10>>>10);y11 <= y10 + (x10>>>10);z11 <= z10 - angle_10; end
end always@(posedge clk or negedge rst_n)begin//第12次迭代if(!rst_n)beginx12 <= 'b0;y12 <= 'b0;z12 <= 'b0;endelse if(!y11[31]) beginx12 <= x11 + (y11>>>11);y12 <= y11 - (x11>>>11);z12 <= z11 + angle_11;endelse beginx12 <= x11 - (y11>>>11);y12 <= y11 + (x11>>>11);z12 <= z11 - angle_11; end
end always@(posedge clk or negedge rst_n)begin//第13次迭代if(!rst_n)beginx13 <= 'b0;y13 <= 'b0;z13 <= 'b0;endelse if(!y12[31]) beginx13 <= x12 + (y12>>>12);y13 <= y12 - (x12>>>12);z13 <= z12 + angle_12;endelse beginx13 <= x12 - (y12>>>12);y13 <= y12 + (x12>>>12);z13 <= z12 - angle_12; end
end always@(posedge clk or negedge rst_n)begin//第14次迭代if(!rst_n)beginx14 <= 'b0;y14 <= 'b0;z14 <= 'b0;endelse if(!y13[31]) beginx14 <= x13 + (y13>>>13);y14 <= y13 - (x13>>>13);z14 <= z13 + angle_13;endelse beginx14 <= x13 - (y13>>>13);y14 <= y13 + (x13>>>13);z14 <= z13 - angle_13; end
end always@(posedge clk or negedge rst_n)begin//第15次迭代if(!rst_n)beginx15 <= 'b0;y15 <= 'b0;z15 <= 'b0;endelse if(!y14[31]) beginx15 <= x14 + (y14>>>14);y15 <= y14 - (x14>>>14);z15 <= z14 + angle_14;endelse beginx15 <= x14 - (y14>>>14);y15 <= y14 + (x14>>>14);z15 <= z14 - angle_14; end
end always@(posedge clk or negedge rst_n)begin//第16次迭代if(!rst_n)beginx16 <= 'b0;y16 <= 'b0;z16 <= 'b0;endelse if(!y15[31]) beginx16 <= x15 + (y15>>>15);y16 <= y15 - (x15>>>15);z16 <= z15 + angle_15;endelse beginx16 <= x15 - (y15>>>15);y16 <= y15 + (x15>>>15);z16 <= z15 - angle_15; end
end wire[31:0] mozhi_tmp;
wire[31:0] mozhi_tmp1;
wire[31:0] mozhi_tmp2;assign mozhi_tmp = x16>>>6;
assign mozhi_tmp1 = mozhi_tmp+mozhi_tmp+mozhi_tmp+mozhi_tmp+mozhi_tmp+mozhi_tmp+mozhi_tmp;
assign mozhi_tmp2 = x16>>>1;always@(posedge clk or negedge rst_n)beginif(!rst_n)beginmozhi <= 'b0;angle <= 'b0;endelse beginmozhi = (mozhi_tmp1 + mozhi_tmp2)>>>16;angle = z16>>>16;end
end endmodule2.3 Testbench B
Testbench代码如下：
`timescale 1ns/1psmodule cordic_Btb();parameter PERIOD = 10;
reg clk;
reg rst_n;
reg signed [31:0] x;
reg signed [31:0] y;
reg start;
wire signed [31:0] angle;
wire signed [31:0] mozhi;
wire finished;
initial beginclk = 0;rst_n = 0;x = 'b0;y = 'b0;start = 0;#100 rst_n = 1;#10 @(posedge clk) start = 1; x = 9'd100 ; y = 9'd100 ;#10 @(posedge clk) x = 9'd10; y = 9'd10;#10 @(posedge clk) x = 9'd3 ; y = 9'd4 ;#10 @(posedge clk) x = 9'd6 ; y = 9'd8 ;#100000 $stop;
endalways #(PERIOD/2) clk = ~clk;cordic_B inst1(.clk(clk),.rst_n(rst_n),.x(x),.y(y),.start(start),.angle(angle),.mozhi(mozhi),.finished(finished));
endmodule相应仿真波形如下图所示：
可以看到，输入的(x,y)为(100,100)时，其夹角θ \thetaθ=45°，模值近似为141。其他情况同理。
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