凡科做网站要钱,一对一直播网站开发,网站首页html制作代码,律师网站素材FPGA实现Cordic算法——向量模式 FPGA实现Cordic算法——向量模式1.cordic算法基本原理2.FPGA实现cordic算法向量模式i、FPGA串行实现cordicii、FPGA流水线实现cordiciii、实验结果 FPGA实现Cordic算法——向量模式
1.cordic算法基本原理 FPGA中运算三角函数#xff0c;浮点数… FPGA实现Cordic算法——向量模式 FPGA实现Cordic算法——向量模式1.cordic算法基本原理2.FPGA实现cordic算法向量模式i、FPGA串行实现cordicii、FPGA流水线实现cordiciii、实验结果 FPGA实现Cordic算法——向量模式
1.cordic算法基本原理 FPGA中运算三角函数浮点数的能力有限而cordic算法能够将三角函数运算转换为简单的移位和加减法进行迭代得到近似结果能够有效降低运算代价提升运算效率。 如上图所示若已知点矢量终点A 0 _0 0 (x 0 _0 0,y 0 _0 0) 若将该矢量逆时针旋转 θ \theta θ 可以根据三角运算得到B 0 _0 0 (x 1 _1 1,y 1 _1 1)点坐标 { x 0 l ∗ c o s ψ y 0 l ∗ s i n ψ { x 1 l ∗ c o s ( θ ψ ) l ∗ ( c o s θ c o s ψ − s i n θ s i n ψ ) x 0 c o s θ − y 0 s i n θ y 1 l ∗ s i n ( θ ψ ) l ∗ ( s i n θ c o s ψ c o s θ s i n ψ ) x 0 s i n θ y 0 c o s θ \begin{cases} x_0 l*cos\psi \\ y_0 l*sin\psi \\ \end{cases} \\ \begin{cases} x_1 l*cos(\theta\psi)l*(cos\theta cos\psi -sin\theta sin\psi) x_0 cos\theta - y_0 sin\theta\\ y_1 l*sin(\theta\psi)l*(sin\theta cos\psi cos\theta sin\psi) x_0 sin\theta y_0 cos\theta\\ \end{cases} {x0l∗cosψy0l∗sinψ{x1l∗cos(θψ)l∗(cosθcosψ−sinθsinψ)x0cosθ−y0sinθy1l∗sin(θψ)l∗(sinθcosψcosθsinψ)x0sinθy0cosθ 令 θ 1 − θ \theta_1 -\theta θ1−θ,即顺时针旋转 θ \theta θ 角度则 { x 0 c o s θ 1 − y 0 s i n θ 1 x 0 c o s θ y 0 s i n θ x 0 s i n θ 1 y 0 c o s θ 1 y 0 c o s θ − x 0 s i n θ \\ \begin{cases} x_0 cos\theta_1 - y_0 sin\theta_1 x_0 cos\theta y_0 sin\theta \\ x_0 sin\theta_1 y_0 cos\theta_1 y_0 cos\theta - x_0 sin\theta \\ \end{cases} {x0cosθ1−y0sinθ1x0cosθy0sinθx0sinθ1y0cosθ1y0cosθ−x0sinθ 联立上述两个式子引入常数$ d (d-1,1)$ ,因此可得 { x 0 c o s θ − d y 0 s i n θ c o s θ ( x 0 − d y 0 t a n θ ) y 0 c o s θ d x 0 s i n θ c o s θ ( y 0 d x 0 t a n θ ) \\ \begin{cases} x_0 cos\theta - dy_0 sin\theta cos\theta(x_0 - dy_0 tan\theta) \\ y_0 cos\theta dx_0 sin\theta cos\theta(y_0 dx_0 tan\theta) \\ \end{cases} {x0cosθ−dy0sinθcosθ(x0−dy0tanθ)y0cosθdx0sinθcosθ(y0dx0tanθ) 这个算法的核心在于将一系列已知的 t a n θ tan\theta tanθ作为表格键值进行存储而 t a n θ tan\theta tanθ可以约等于 1 2 n \frac{1}{2^n} 2n1并且。 1 2 n \frac{1}{2^n} 2n1在FPGA中可以通过右移进行快速运算。 t a n θ tan\theta tanθ各个已知存储值如下 i i i θ \theta θ t a n θ tan\theta tanθ c o s θ cos\theta cosθ ∏ c o s θ \prod cos\theta ∏cosθ04510.7071067811865480.707106781186548125.565050.500.8944271909999160.632455532033676214.032430.250.9701425001453320.61357199107789737.1250160.1250000000000000.9922778767136680.60883391251775343.5763340.06250000000000000.9980525784828890.60764825625616851.7899100.03125000000000000.9995120760870790.60735177014129660.8951730.01562500000000000.9998779520346950.60727764409352670.4476140.007812500000000000.9999694838187880.60725911229889380.2238100.003906250000000000.9999923706927790.60725447933256390.1119050.001953125000000000.9999980926568240.607253321089875100.0559520.0009765625000000000.9999995231631830.607253031529135110.0279760.0004882812500000000.9999998807907320.607252959138945120.0139880.0002441406250000000.9999999701976790.607252941041397130.0069940.0001220703125000000.9999999925494200.607252936517011140.0034976.10351562500000e-050.9999999981373550.607252935385914150.0017483.05175781250000e-050.9999999995343390.607252935103140 而多次旋转过程中每次旋转的 c o s θ cos\theta cosθ需要连续相乘而多次相乘极限也趋近与0.607252这一个常数因此也可做近似处理。那么现在还有最后一个问题这一系列角度能够通过多次旋转得到任意的角度吗可以看到每个角度是不断降低减半的呈递减的分布从宏观上观察大致是可以进行趋近到某一个常数的。 cordic算法有两个模式 1向量模式已知点坐标(x0,y0),可以求得该向量的角度即arctan(y0/x0)。这种可以理解为需要通过多次旋转将该向量旋转至x轴上即y0 0此时旋转过的角度即为向量角度x最终坐标即为向量的长度。 2旋转模式已知角度 θ \theta θ ,求 s i n θ sin\theta sinθ及 c o s θ cos\theta cosθ { x 0 c o s θ − d y 0 s i n θ c o s θ ( x 0 − d y 0 t a n θ ) y 0 c o s θ d x 0 s i n θ c o s θ ( y 0 d x 0 t a n θ ) \\ \begin{cases} x_0 cos\theta - dy_0 sin\theta cos\theta(x_0 - dy_0 tan\theta) \\ y_0 cos\theta dx_0 sin\theta cos\theta(y_0 dx_0 tan\theta) \\ \end{cases} {x0cosθ−dy0sinθcosθ(x0−dy0tanθ)y0cosθdx0sinθcosθ(y0dx0tanθ)
令y0 0 { c o s θ ( x 0 − d y 0 t a n θ ) c o s θ x 0 c o s θ ( y 0 d x 0 t a n θ ) s i n θ y 0 \begin{cases} cos\theta(x_0 - dy_0 tan\theta) cos\theta x_0\\ cos\theta(y_0 dx_0 tan\theta) sin\theta y_0\\ \end{cases} {cosθ(x0−dy0tanθ)cosθx0cosθ(y0dx0tanθ)sinθy0 什么意思呢类似当前有个单位圆初始点在A(x,0)这一点经过旋转多次可以得到B(x1,y1)。此时 { x 1 c o s ( θ ) y 1 s i n ( θ ) \begin{cases} x_1 cos(\theta)\\ y_1 sin(\theta) \end{cases} {x1cos(θ)y1sin(θ) 但是因为这个旋转变换是伪旋转变换需要乘以一个 c o s θ cos\theta cosθ的系数。
2.FPGA实现cordic算法向量模式 这里以向量模式为例子进行FPGA实现首先构建matlab仿真程序
function [len,theta] cordic_theat(x_in,y_in)
clc;
clear x y z;z_ref[ 45,...26.56505113840103,...14.036243438720703,...7.1250163316726685,...3.5763343572616577,...1.7899105548858643,...0.8951736688613892,...0.4476141333580017,...0.22381049394607544,...0.11190563440322876,...0.05595284700393677,...0.027976393699645996,...0.013988196849822998,...0.006994098424911499,... 0.0034970492124557495,...0.00174852460622787475].*2^(24);times 16;%迭代次数
x zeros(times1,1);
y zeros(times1,1);
z zeros(times1,1);
d 1;y(1,1) abs(y_in)*2^(12);
x(1,1) abs(x_in)*2^(12);
z(1,1) 0;for i 1: timesif( y(i,1) 0 )
% d 1;x(i1,1) x(i,1) - d/2^(i-1)*y(i,1);y(i1,1) y(i,1) d/2^(i-1)*x(i,1);z(i1,1) z(i,1) - d*( z_ref(i) );else
% d -1;x(i1,1) x(i,1) d/2^(i-1)*y(i,1);y(i1,1) y(i,1) - d/2^(i-1)*x(i,1);z(i1,1) z(i,1) d*( z_ref(i) );endendmy_z z(times1,1)/2^(24);
my_x x(times1,1)/2^(12) * 0.607253;len my_x;if( x_in 0 y_in0)theta my_z;
elseif (x_in 0 y_in 0)theta 180 - my_z;
elseif (x_in 0 y_in 0)theta 180 my_z;
elseif (x_in 0 y_in 0)theta 360 - my_z;
endend实际值比对程序
t 0:0.01:2*pi;
xcos(t);
ysin(t);
len zeros( 1,length(t));
theta zeros(1,length(t));for i 1:length(t)[len(i),theta(i)] cordic_theat( x(i),y(i) );
endplot( abs(theta-t/pi*180) );
axis([0 640 -0.5e-3 2e-3]);运行结果显示与真实值相比16次迭代基本上可以满足使用需要 i、FPGA串行实现cordic FPGA流水线实现和串行实现大概的区别是。假如工厂需要加工一个零件这个零件需要六个步骤完成每个步骤10s每个步骤不能同时进行[步骤前后有先后关系]。如果是串行是一个工人完成六道工序也就是每60s加工完成一个零件然后取新的物料进行完成。而流水线实现是安排六个人每个人只完成一道工序也就是正常运行过程中每10s就能取一次物料。从吞吐率来说串行每60s取一次数据而流水线每10s便能取一次数据相应的输出也会更加快。串行速度慢但消耗人工少流水线速度快但消耗六倍人工这是FPGA中典型的空间换取时间的例子。 实现代码如下
module cordic_serial(input sys_clk,input sys_rst_n,input user_data_valid,input [31:0] user_x,input [31:0] user_y,output reg user_data_out_valid,output reg [31:0] user_theat,output [31:0] user_len
);//输入为有符号数(定点数) 高12位[整数] 低12位[小数] 即放大2^(12) - 整数部分最大为 2 ^12 -1 [最高位为符号位]
//角度标幺 按 高8位[整数] 低24位[小数] 即放大2^(24) 进行标幺
//一共迭代16次/****************************************************************************\Parameter/Define
\****************************************************************************/
wire [31:0] ang_p [15:0];
wire [31:0] ang_n [15:0];
localparam K 32h9b74ee; //K0.607253*2^24,32h9b74ee,assign ang_p[0] 32b0_0101101_000000000000000000000000; //2D00 0000 45
assign ang_p[1] 32b0_0011010_100100001010011100110001; //1A90 A731 26.56505113840103 445,687,601
assign ang_p[2] 32b0_0001110_000010010100011101000000; //0E09 4740 14.036243438720703
assign ang_p[3] 32b0_0000111_001000000000000100010010; //0720 0112 7.1250163316726685
assign ang_p[4] 32b0_0000011_100100111000101010100110; //0393 8AA6 3.5763343572616577
assign ang_p[5] 32b0_0000001_110010100011011110010100; //01CA 3794 1.7899105548858643
assign ang_p[6] 32b0_0000000_111001010010101000011010; //00E5 2A1A 0.8951736688613892
assign ang_p[7] 32b0_0000000_011100101001011011010111; //0072 96D7 0.4476141333580017
assign ang_p[8] 32b0_0000000_001110010100101110100101; //0039 4BA5 0.22381049394607544
assign ang_p[9] 32b0_0000000_000111001010010111011001; //001C A5D9 0.11190563440322876
assign ang_p[10] 32b0_0000000_000011100101001011101101; //000E 52ED 0.05595284700393677
assign ang_p[11] 32b0_0000000_000001110010100101110110; //0007 2976 0.027976393699645996
assign ang_p[12] 32b0_0000000_000000111001010010111011; //0003 94BB 0.013988196849822998
assign ang_p[13] 32b0_0000000_000000011100101001011101; //0001 CA5D 0.006994098424911499
assign ang_p[14] 32b0_0000000_000000001110010100101110; //0000 E52E 0.0034970492124557495
assign ang_p[15] 32b0_0000000_000000000111001010010111; //0000 7297 0.00174852460622787475assign ang_n[0] 32b1_1010011_000000000000000000000000; //complement code -45
assign ang_n[1] 32b1_1100101_011011110101100011001111; //complement code -26.56505113840103
assign ang_n[2] 32b1_1110001_111101101011100011000000; //complement code -14.036243438720703
assign ang_n[3] 32b1_1111000_110111111111111011101110; //complement code -7.1250163316726685
assign ang_n[4] 32b1_1111100_011011000111010101011010; //complement code -3.5763343572616577
assign ang_n[5] 32b1_1111110_001101011100100001101100; //complement code -1.7899105548858643
assign ang_n[6] 32b1_1111111_000110101101010111100110; //complement code -0.8951736688613892
assign ang_n[7] 32b1_1111111_100011010110100100101001; //complement code -0.4476141333580017
assign ang_n[8] 32b1_1111111_110001101011010001011011; //complement code -0.22381049394607544
assign ang_n[9] 32b1_1111111_111000110101101000100111; //complement code -0.11190563440322876
assign ang_n[10] 32b1_1111111_111100011010110100010011; //complement code -0.05595284700393677
assign ang_n[11] 32b1_1111111_111110001101011010001010; //complement code -0.027976393699645996
assign ang_n[12] 32b1_1111111_111111000110101101000101; //complement code -0.013988196849822998
assign ang_n[13] 32b1_1111111_111111100011010110100011; //complement code -0.006994098424911499
assign ang_n[14] 32b1_1111111_111111110001101011010010; //complement code -0.0034970492124557495
assign ang_n[15] 32b1_1111111_111111111000110101101001; //complement code -0.00174852460622787475localparam ang_180_p 32b0_1011_0100_0000_0000_0000_0000_0000_000; //180 - Q23
//localparam ang_180_n 32b ; //-180reg [31:0] z_theat;
reg [4:0] iterate_times; //迭代次数最大16次数
reg cordic_start_flag;
reg signed [31:0] cordic_x;
reg signed [31:0] cordic_y;
reg signed [31:0] cordic_z;always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_start_flag 1d0;end else if(iterate_times 5d15) begincordic_start_flag 1d0;end else if(user_data_valid 1b1) begincordic_start_flag 1d1;end
endalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginiterate_times 5d0;end if(user_data_out_valid 1b1)beginiterate_times 5d0;end if(cordic_start_flag 1b1)beginiterate_times iterate_times 5d1;end
endreg [1:0] quadrant; //象限判断标志 I-00 II-10 III-11 IV-01
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginquadrant 2d0;end else if( user_data_valid 1b1 iterate_times 5d0)beginquadrant {user_x[31],user_y[31]};end
endalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x 32d0;cordic_y 32d0;cordic_z 32d0;end else if( user_data_valid 1b1 iterate_times 5d0)begincase ({user_x[31],user_y[31]})2b00: {cordic_x,cordic_y} {user_x, user_y};2b10: {cordic_x,cordic_y} {{1b0,~user_x[30:0]}1b1, user_y};2b11: {cordic_x,cordic_y} {{1b0,~user_x[30:0]}1b1, {1b0,~user_y[30:0]}1b1};2b01: {cordic_x,cordic_y} {user_x, {1b0,~user_y[30:0]}1b1};endcasecordic_z 32d0;end else if( cordic_start_flag 1b1 cordic_y[31] 1 ) begincordic_x cordic_x - ({{cordic_y iterate_times}});cordic_y cordic_y ({{cordic_x iterate_times}});cordic_z cordic_z ang_n[iterate_times];end else if( cordic_start_flag 1b1 cordic_y[31] 0 ) begincordic_x cordic_x ({{cordic_y iterate_times}});cordic_y cordic_y - ({{cordic_x iterate_times}});cordic_z cordic_z ang_p[iterate_times];endendalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginuser_data_out_valid 1b0;end else if(iterate_times 5d15)beginuser_data_out_valid 1b1;end else beginuser_data_out_valid 1b0;end
endalways (*) beginif(user_data_out_valid 1b1)begincase (quadrant)2b00 : user_theat (cordic_z 24);2b10 : user_theat (ang_180_p - (cordic_z 1)) 23;2b11 : user_theat (ang_180_p (cordic_z 1)) 23;2b01 : user_theat (~(cordic_z24)) 1b1 ;endcaseendend//输出*0.607253
assign user_len (user_data_out_valid 1b1)? ( (cordic_x 1) (cordic_x 4) (cordic_x 5) (cordic_x 7) (cordic_x 8) (cordic_x 10)(cordic_x 11) (cordic_x 12)):32d0; endmoduleii、FPGA流水线实现cordic
module cordic_parallel(input sys_clk ,input sys_rst_n ,input user_data_valid,input [31:0] user_x,input [31:0] user_y,output reg user_data_out_valid,output reg [31:0] user_theat,output [31:0] user_len);//输入为有符号数(定点数) 高12位[整数] 低12位[小数] 即放大2^(12) - 整数部分最大为 2 ^12 -1 [最高位为符号位]
//角度标幺 按 高8位[整数] 低24位[小数] 即放大2^(24) 进行标幺
//一共迭代16次/****************************************************************************\Parameter/Define
\****************************************************************************/
wire [31:0] ang_p [15:0];
wire [31:0] ang_n [15:0];
localparam K 32h9b74ee; //K0.607253*2^24,32h9b74ee,assign ang_p[0] 32b0_0101101_000000000000000000000000; //2D00 0000 45
assign ang_p[1] 32b0_0011010_100100001010011100110001; //1A90 A731 26.56505113840103 445,687,601
assign ang_p[2] 32b0_0001110_000010010100011101000000; //0E09 4740 14.036243438720703
assign ang_p[3] 32b0_0000111_001000000000000100010010; //0720 0112 7.1250163316726685
assign ang_p[4] 32b0_0000011_100100111000101010100110; //0393 8AA6 3.5763343572616577
assign ang_p[5] 32b0_0000001_110010100011011110010100; //01CA 3794 1.7899105548858643
assign ang_p[6] 32b0_0000000_111001010010101000011010; //00E5 2A1A 0.8951736688613892
assign ang_p[7] 32b0_0000000_011100101001011011010111; //0072 96D7 0.4476141333580017
assign ang_p[8] 32b0_0000000_001110010100101110100101; //0039 4BA5 0.22381049394607544
assign ang_p[9] 32b0_0000000_000111001010010111011001; //001C A5D9 0.11190563440322876
assign ang_p[10] 32b0_0000000_000011100101001011101101; //000E 52ED 0.05595284700393677
assign ang_p[11] 32b0_0000000_000001110010100101110110; //0007 2976 0.027976393699645996
assign ang_p[12] 32b0_0000000_000000111001010010111011; //0003 94BB 0.013988196849822998
assign ang_p[13] 32b0_0000000_000000011100101001011101; //0001 CA5D 0.006994098424911499
assign ang_p[14] 32b0_0000000_000000001110010100101110; //0000 E52E 0.0034970492124557495
assign ang_p[15] 32b0_0000000_000000000111001010010111; //0000 7297 0.00174852460622787475assign ang_n[0] 32b1_1010011_000000000000000000000000; //complement code -45
assign ang_n[1] 32b1_1100101_011011110101100011001111; //complement code -26.56505113840103
assign ang_n[2] 32b1_1110001_111101101011100011000000; //complement code -14.036243438720703
assign ang_n[3] 32b1_1111000_110111111111111011101110; //complement code -7.1250163316726685
assign ang_n[4] 32b1_1111100_011011000111010101011010; //complement code -3.5763343572616577
assign ang_n[5] 32b1_1111110_001101011100100001101100; //complement code -1.7899105548858643
assign ang_n[6] 32b1_1111111_000110101101010111100110; //complement code -0.8951736688613892
assign ang_n[7] 32b1_1111111_100011010110100100101001; //complement code -0.4476141333580017
assign ang_n[8] 32b1_1111111_110001101011010001011011; //complement code -0.22381049394607544
assign ang_n[9] 32b1_1111111_111000110101101000100111; //complement code -0.11190563440322876
assign ang_n[10] 32b1_1111111_111100011010110100010011; //complement code -0.05595284700393677
assign ang_n[11] 32b1_1111111_111110001101011010001010; //complement code -0.027976393699645996
assign ang_n[12] 32b1_1111111_111111000110101101000101; //complement code -0.013988196849822998
assign ang_n[13] 32b1_1111111_111111100011010110100011; //complement code -0.006994098424911499
assign ang_n[14] 32b1_1111111_111111110001101011010010; //complement code -0.0034970492124557495
assign ang_n[15] 32b1_1111111_111111111000110101101001; //complement code -0.00174852460622787475localparam ang_180_p 32b0_1011_0100_0000_0000_0000_0000_0000_000; //180 - Q23//象限判断标志 I-00 II-10 III-11 IV-01
//16-level-pipelevel
reg signed [31:0] cordic_x0 ,cordic_y0 ,cordic_z0 ,quadrant_0 ;
reg signed [31:0] cordic_x1 ,cordic_y1 ,cordic_z1 ,quadrant_1 ;
reg signed [31:0] cordic_x2 ,cordic_y2 ,cordic_z2 ,quadrant_2 ;
reg signed [31:0] cordic_x3 ,cordic_y3 ,cordic_z3 ,quadrant_3 ;
reg signed [31:0] cordic_x4 ,cordic_y4 ,cordic_z4 ,quadrant_4 ;
reg signed [31:0] cordic_x5 ,cordic_y5 ,cordic_z5 ,quadrant_5 ;
reg signed [31:0] cordic_x6 ,cordic_y6 ,cordic_z6 ,quadrant_6 ;
reg signed [31:0] cordic_x7 ,cordic_y7 ,cordic_z7 ,quadrant_7 ;
reg signed [31:0] cordic_x8 ,cordic_y8 ,cordic_z8 ,quadrant_8 ;
reg signed [31:0] cordic_x9 ,cordic_y9 ,cordic_z9 ,quadrant_9 ;
reg signed [31:0] cordic_x10,cordic_y10,cordic_z10,quadrant_10;
reg signed [31:0] cordic_x11,cordic_y11,cordic_z11,quadrant_11;
reg signed [31:0] cordic_x12,cordic_y12,cordic_z12,quadrant_12;
reg signed [31:0] cordic_x13,cordic_y13,cordic_z13,quadrant_13;
reg signed [31:0] cordic_x14,cordic_y14,cordic_z14,quadrant_14;
reg signed [31:0] cordic_x15,cordic_y15,cordic_z15,quadrant_15;
reg signed [31:0] cordic_x16,cordic_y16,cordic_z16,quadrant_16;//reg [1:0] quadrant; //象限判断标志 I-00 II-10 III-11 IV-01
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginquadrant_0 2d0;end else if( user_data_valid 1b1)beginquadrant_0 {user_x[31],user_y[31]};end
endalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x0 32d0;cordic_y0 32d0;cordic_z0 32d0;end else if( user_data_valid 1b1)begincase ({user_x[31],user_y[31]})2b00: {cordic_x0,cordic_y0} {user_x, user_y};2b10: {cordic_x0,cordic_y0} {{1b0,~user_x[30:0]}1b1, user_y};2b11: {cordic_x0,cordic_y0} {{1b0,~user_x[30:0]}1b1, {1b0,~user_y[30:0]}1b1};2b01: {cordic_x0,cordic_y0} {user_x, {1b0,~user_y[30:0]}1b1};endcasecordic_z0 32d0;endend//iterate 1
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x1 32d0;cordic_y1 32d0;cordic_z1 32d0;end else if(cordic_y0[31] 1) begincordic_x1 cordic_x0 - ({{cordic_y0 0}});cordic_y1 cordic_y0 ({{cordic_x0 0}});cordic_z1 cordic_z0 ang_n[0];end else if(cordic_y0[31] 0) begincordic_x1 cordic_x0 ({{cordic_y0 0}});cordic_y1 cordic_y0 - ({{cordic_x0 0}});cordic_z1 cordic_z0 ang_p[0];endend//iterate 2
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x2 32d0;cordic_y2 32d0;cordic_z2 32d0;end else if(cordic_y1[31] 1) begincordic_x2 cordic_x1 - ({{cordic_y1 1}});cordic_y2 cordic_y1 ({{cordic_x1 1}});cordic_z2 cordic_z1 ang_n[1];end else if(cordic_y1[31] 0) begincordic_x2 cordic_x1 ({{cordic_y1 1}});cordic_y2 cordic_y1 - ({{cordic_x1 1}});cordic_z2 cordic_z1 ang_p[1];endend//iterate 3
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x3 32d0;cordic_y3 32d0;cordic_z3 32d0;end else if(cordic_y2[31] 1) begincordic_x3 cordic_x2 - ({{cordic_y2 2}});cordic_y3 cordic_y2 ({{cordic_x2 2}});cordic_z3 cordic_z2 ang_n[2];end else if(cordic_y2[31] 0) begincordic_x3 cordic_x2 ({{cordic_y2 2}});cordic_y3 cordic_y2 - ({{cordic_x2 2}});cordic_z3 cordic_z2 ang_p[2];endend//iterate 4
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x4 32d0;cordic_y4 32d0;cordic_z4 32d0;end else if(cordic_y3[31] 1) begincordic_x4 cordic_x3 - ({{cordic_y3 3}});cordic_y4 cordic_y3 ({{cordic_x3 3}});cordic_z4 cordic_z3 ang_n[3];end else if(cordic_y3[31] 0) begincordic_x4 cordic_x3 ({{cordic_y3 3}});cordic_y4 cordic_y3 - ({{cordic_x3 3}});cordic_z4 cordic_z3 ang_p[3];endend//iterate 5
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x5 32d0;cordic_y5 32d0;cordic_z5 32d0;end else if(cordic_y4[31] 1) begincordic_x5 cordic_x4 - ({{cordic_y4 4}});cordic_y5 cordic_y4 ({{cordic_x4 4}});cordic_z5 cordic_z4 ang_n[4];end else if(cordic_y4[31] 0) begincordic_x5 cordic_x4 ({{cordic_y4 4}});cordic_y5 cordic_y4 - ({{cordic_x4 4}});cordic_z5 cordic_z4 ang_p[4];endend//iterate 6
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x6 32d0;cordic_y6 32d0;cordic_z6 32d0;end else if(cordic_y5[31] 1) begincordic_x6 cordic_x5 - ({{cordic_y5 5}});cordic_y6 cordic_y5 ({{cordic_x5 5}});cordic_z6 cordic_z5 ang_n[5];end else if(cordic_y5[31] 0) begincordic_x6 cordic_x5 ({{cordic_y5 5}});cordic_y6 cordic_y5 - ({{cordic_x5 5}});cordic_z6 cordic_z5 ang_p[5];endend//iterate 7
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x7 32d0;cordic_y7 32d0;cordic_z7 32d0;end else if(cordic_y6[31] 1) begincordic_x7 cordic_x6 - ({{cordic_y6 6}});cordic_y7 cordic_y6 ({{cordic_x6 6}});cordic_z7 cordic_z6 ang_n[6];end else if(cordic_y6[31] 0) begincordic_x7 cordic_x6 ({{cordic_y6 6}});cordic_y7 cordic_y6 - ({{cordic_x6 6}});cordic_z7 cordic_z6 ang_p[6];endend//iterate 8
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x8 32d0;cordic_y8 32d0;cordic_z8 32d0;end else if(cordic_y7[31] 1) begincordic_x8 cordic_x7 - ({{cordic_y7 7}});cordic_y8 cordic_y7 ({{cordic_x7 7}});cordic_z8 cordic_z7 ang_n[7];end else if(cordic_y7[31] 0) begincordic_x8 cordic_x7 ({{cordic_y7 7}});cordic_y8 cordic_y7 - ({{cordic_x7 7}});cordic_z8 cordic_z7 ang_p[7];endend//iterate 9
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x9 32d0;cordic_y9 32d0;cordic_z9 32d0;end else if(cordic_y8[31] 1) begincordic_x9 cordic_x8 - ({{cordic_y8 8}});cordic_y9 cordic_y8 ({{cordic_x8 8}});cordic_z9 cordic_z8 ang_n[8];end else if(cordic_y8[31] 0) begincordic_x9 cordic_x8 ({{cordic_y8 8}});cordic_y9 cordic_y8 - ({{cordic_x8 8}});cordic_z9 cordic_z8 ang_p[8];endend//iterate 10
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x10 32d0;cordic_y10 32d0;cordic_z10 32d0;end else if(cordic_y9[31] 1) begincordic_x10 cordic_x9 - ({{cordic_y9 9}});cordic_y10 cordic_y9 ({{cordic_x9 9}});cordic_z10 cordic_z9 ang_n[9];end else if(cordic_y9[31] 0) begincordic_x10 cordic_x9 ({{cordic_y9 9}});cordic_y10 cordic_y9 - ({{cordic_x9 9}});cordic_z10 cordic_z9 ang_p[9];endend//iterate 11
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x11 32d0;cordic_y11 32d0;cordic_z11 32d0;end else if(cordic_y10[31] 1) begincordic_x11 cordic_x10 - ({{cordic_y10 10}});cordic_y11 cordic_y10 ({{cordic_x10 10}});cordic_z11 cordic_z10 ang_n[10];end else if(cordic_y10[31] 0) begincordic_x11 cordic_x10 ({{cordic_y10 10}});cordic_y11 cordic_y10 - ({{cordic_x10 10}});cordic_z11 cordic_z10 ang_p[10];endend//iterate 12
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x12 32d0;cordic_y12 32d0;cordic_z12 32d0;end else if(cordic_y11[31] 1) begincordic_x12 cordic_x11 - ({{cordic_y11 11}});cordic_y12 cordic_y11 ({{cordic_x11 11}});cordic_z12 cordic_z11 ang_n[11];end else if(cordic_y11[31] 0) begincordic_x12 cordic_x11 ({{cordic_y11 11}});cordic_y12 cordic_y11 - ({{cordic_x11 11}});cordic_z12 cordic_z11 ang_p[11];endend//iterate 13
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x13 32d0;cordic_y13 32d0;cordic_z13 32d0;end else if(cordic_y12[31] 1) begincordic_x13 cordic_x12 - ({{cordic_y12 12}});cordic_y13 cordic_y12 ({{cordic_x12 12}});cordic_z13 cordic_z12 ang_n[12];end else if(cordic_y12[31] 0) begincordic_x13 cordic_x12 ({{cordic_y12 12}});cordic_y13 cordic_y12 - ({{cordic_x12 12}});cordic_z13 cordic_z12 ang_p[12];endend//iterate 14
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x14 32d0;cordic_y14 32d0;cordic_z14 32d0;end else if(cordic_y13[31] 1) begincordic_x14 cordic_x13 - ({{cordic_y13 13}});cordic_y14 cordic_y13 ({{cordic_x13 13}});cordic_z14 cordic_z13 ang_n[13];end else if(cordic_y13[31] 0) begincordic_x14 cordic_x13 ({{cordic_y13 13}});cordic_y14 cordic_y13 - ({{cordic_x13 13}});cordic_z14 cordic_z13 ang_p[13];endend//iterate 15
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x15 32d0;cordic_y15 32d0;cordic_z15 32d0;end else if(cordic_y14[31] 1) begincordic_x15 cordic_x14 - ({{cordic_y14 14}});cordic_y15 cordic_y14 ({{cordic_x14 14}});cordic_z15 cordic_z14 ang_n[14];end else if(cordic_y14[31] 0) begincordic_x15 cordic_x14 ({{cordic_y14 14}});cordic_y15 cordic_y14 - ({{cordic_x14 14}});cordic_z15 cordic_z14 ang_p[14];endend//iterate 16
always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begincordic_x16 32d0;cordic_y16 32d0;cordic_z16 32d0;end else if(cordic_y15[31] 1) begincordic_x16 cordic_x15 - ({{cordic_y15 15}});cordic_y16 cordic_y15 ({{cordic_x15 15}});cordic_z16 cordic_z15 ang_n[15];end else if(cordic_y15[31] 0) begincordic_x16 cordic_x15 ({{cordic_y15 15}});cordic_y16 cordic_y15 - ({{cordic_x15 15}});cordic_z16 cordic_z15 ang_p[15];endendalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)begin{quadrant_1, quadrant_2, quadrant_3, quadrant_4} 4b0;{quadrant_5, quadrant_6, quadrant_7, quadrant_8} 4b0;{quadrant_9, quadrant_10, quadrant_11, quadrant_12} 4b0;{quadrant_13, quadrant_14, quadrant_15, quadrant_16} 4b0;end else begin{quadrant_1, quadrant_2, quadrant_3, quadrant_4 } {quadrant_0, quadrant_1, quadrant_2, quadrant_3 };{quadrant_5, quadrant_6, quadrant_7, quadrant_8 } {quadrant_4, quadrant_5, quadrant_6, quadrant_7 };{quadrant_9, quadrant_10, quadrant_11, quadrant_12} {quadrant_8, quadrant_9, quadrant_10, quadrant_11};{quadrant_13, quadrant_14, quadrant_15, quadrant_16} {quadrant_12, quadrant_13, quadrant_14, quadrant_15};end
endreg [4:0] iterate_times;
reg start_flag;always (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginstart_flag 1d0;end else if(user_data_valid 1b1) begin start_flag 1d1;end
endalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginiterate_times 5d0;end else if(iterate_times 5d17) begin iterate_times 5d17;end else if(user_data_valid 1b1 || start_flag 1b1 ) beginiterate_times iterate_times 5d1;end
endalways (posedge sys_clk or negedge sys_rst_n) beginif(!sys_rst_n)beginuser_data_out_valid 1b0;end else if(iterate_times 5d16)beginuser_data_out_valid 1b1;end else beginuser_data_out_valid 1b0;end
endalways (*) beginif(user_data_out_valid 1b1)begincase (quadrant_16)2b00 : user_theat (cordic_z16 24);2b10 : user_theat (ang_180_p - (cordic_z16 1)) 23;2b11 : user_theat (ang_180_p (cordic_z16 1)) 23;2b01 : user_theat (~(cordic_z1624)) 1b1 ;endcaseendend//输出*0.607253
assign user_len (user_data_out_valid 1b1)? ( (cordic_x16 1) (cordic_x16 4) (cordic_x16 5) (cordic_x16 7) (cordic_x16 8) (cordic_x16 10)(cordic_x16 11) (cordic_x16 12)):32d0; endmodule以上实现一定要注意不能运算溢出一旦溢出将影响相应判断。
iii、实验结果
