FPGA使用查表法实现正弦和余弦函数 - 变形方法1_quartus 三角函数

作者：笔触狂放9 | 2024-05-26 05:41:23

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quartus 三角函数

FPGA使用查表法实现正弦和余弦函数

在上篇文章中，设置的输入角度范围是[0,2*pi)。但根据三角函数公式，其实我们可以将[0,2*pi)分成4段，这样就能将输入角度范围缩小到[0,pi/2)了。

1、修改matlab代码


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Zheng Wei, 2022/12/05
%% 
%% 输入角度范围：[0,pi/2); 输入数据量化位数：10bit;
%% 输出结果范围：[0,1];    输出数据量化位数：16bit;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
clc;        % 清理命令行
close all;  % 关闭所有图形窗口 
clear all;  % 清理所有工作区变量
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 参数定义
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
in_quantify_bit = 10;        % 输入数据量化位数（无符号数）
alpha = 0:(pi/2/2^in_quantify_bit):(pi/2-pi/2/2^in_quantify_bit);  % 弧度
 
out_quantify_bit = 16;       % 输出数据量化位数（有符号数）
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 获取三角函数值
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
cos_alpha = cos(alpha);  % 获得cos函数值
sin_alpha = sin(alpha);  % 获得sin函数值
                                                                               
cos_alpha_q = round(cos_alpha *(2^(out_quantify_bit-1)-1));  % 16bit量化
sin_alpha_q = round(sin_alpha *(2^(out_quantify_bit-1)-1));  % 16bit量化
 
% figure(1); subplot(2,1,1);plot(alpha,cos_alpha);subplot(2,1,2);plot(alpha,cos_alpha_q);
% figure(2); subplot(2,1,1);plot(alpha,sin_alpha);subplot(2,1,2);plot(alpha,sin_alpha_q);
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 生成coe文件，第一行定义数据格式, 16代表ROM的数据格式为16进制。
%% 高16bit代表sin值，低16bit代表cos值，各自最高的1bit是符号位。
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
% 因为都是正数，所以不需要取补码
% for i = 1:1:(2^in_quantify_bit)
%     if (cos_alpha_q(i)<0)
%        cos_alpha_q(i) = cos_alpha_q(i) + 2^(out_quantify_bit); % 负数用补码表示
%     else
%        cos_alpha_q(i) = cos_alpha_q(i); % 正数的补码为原码
%     end
%                                                                                          
%     if (sin_alpha_q(i)<0)
%        sin_alpha_q(i) = sin_alpha_q(i) + 2^(out_quantify_bit); % 负数用补码表示
%     else
%        sin_alpha_q(i) = sin_alpha_q(i); % 正数的补码为原码
%     end
% end
 
cos_alpha_q = dec2hex(cos_alpha_q); 
sin_alpha_q = dec2hex(sin_alpha_q);
 
% 将cos和sin拼接为32bit(各自16bit)，此数据输出到FPGA
fid=fopen('cos_sin_lut_2.coe','wt');
fprintf( fid, 'MEMORY_INITIALIZATION_RADIX = 16;\n');                     
fprintf( fid, 'MEMORY_INITIALIZATION_VECTOR =\n');
 
for i = 1:1:(2^in_quantify_bit)
    s=strcat(sin_alpha_q(i,1),sin_alpha_q(i,2),sin_alpha_q(i,3),sin_alpha_q(i,4),cos_alpha_q(i,1),cos_alpha_q(i,2),cos_alpha_q(i,3),cos_alpha_q(i,4));
    fprintf(fid,'%c%c%c%c%c%c%c%c',s); 
    if (i < 2^in_quantify_bit)
        fprintf(fid,',\n'); 
    else
        fprintf(fid,';\n');  % 分号(;) 结束标志位
    end    
end
fclose(fid);

2、将重新生成的coe文件写入ROM核中

3、通过查表得到角度所对应的正弦值和余弦值


/*----------------------------------------------------------------------
    Author:  Zheng Wei
    Date:    2022-12-05
    Version: 1.0
    Description: It is a cos_sin_lut_2 testbench.
-----------------------------------------------------------------------*/
 
`timescale 1ns / 1ps
 
module tb;
                                                 
                                                  
    reg                         i_sys_clk       ; 
    reg                         i_sys_rst       ;
                                                 
    reg             [11:0]      r_rom_phase     ;
    reg             [11:0]      r_rom_phase_ff  ;
    reg             [11:0]      r_rom_phase_2ff ;
    reg             [11:0]      r_rom_phase_3ff ;
    reg             [09:0]      r_rom_addr      ;
    wire            [15:0]      w_cos_rom_val   ; // ROM readout value [0, pi/2)
    wire            [15:0]      w_sin_rom_val   ; // ROM readout value [0, pi/2)
    reg             [16:0]      r_cos_val       ; // transform output value[0, 2*pi)
    reg             [16:0]      r_sin_val       ; // transform output value[0, 2*pi)
    wire            [15:0]      o_cos_val       ; // final output value, drop the least 1bit
    wire            [15:0]      o_sin_val       ; // final output value, drop the least 1bit    
                                                                                             
                                                                                             
                                                                                               
    //  clock generate module
    parameter  period = 6.67;           // 150MHz
    initial begin
        i_sys_clk = 1'b0;
        forever     #(period/2)  i_sys_clk = ~i_sys_clk;
    end
                                                                         
	//-------------------------------------------------------------------
	
	//  system initialization
	task task_sysinit;
		begin		 
            r_rom_phase = 12'd0;
		end
	endtask
	
	//  system reset
	task task_reset;
        begin
            i_sys_rst = 1'b1;
            repeat(20)  @(negedge i_sys_clk);
            i_sys_rst = 1'b0;
        end
    endtask                                                      
                                                          
                                                          
                                                          
    initial begin
        task_sysinit;
	    task_reset  ;
                                            
        repeat(10)  @(posedge i_sys_clk);                                                                            
                                          
                                         
        repeat(100000) @(posedge i_sys_clk);
		                                  
		$stop;                          
    end
                                                                                          
                                                                                         
    always @(posedge i_sys_clk or posedge i_sys_rst) begin
        if (i_sys_rst) begin
            r_rom_phase <= 12'd0;       
        end                  
        else begin           
            r_rom_phase <= r_rom_phase + 12'd1; 
        end
    end                                                                                      
                                                                                         
    always @(posedge i_sys_clk) begin
        r_rom_phase_ff  <= r_rom_phase;   
        r_rom_phase_2ff <= r_rom_phase_ff;
        r_rom_phase_3ff <= r_rom_phase_2ff;         
    end    
                                                                                         
    always @(posedge i_sys_clk or posedge i_sys_rst) begin
        if (i_sys_rst) begin
            r_rom_addr <= 10'd0;       
        end                  
        else begin           
            r_rom_addr <= r_rom_phase[9:0]; 
        end
    end
                                                                                          
                                                                                         
    always @(posedge i_sys_clk) begin          
        case (r_rom_phase_3ff[11:10])
            2'b00: begin // [0, pi/2)
                r_cos_val <=  {1'b0, w_cos_rom_val};
                r_sin_val <=  {1'b0, w_sin_rom_val};
            end
                                                  
            2'b01: begin // [pi/2, pi)
                r_cos_val <= ~{1'b0, w_sin_rom_val} + 1'b1;
                r_sin_val <=  {1'b0, w_cos_rom_val};
            end
                                                  
            2'b10: begin // [pi, 3*pi/2)
                r_cos_val <= ~{1'b0, w_cos_rom_val} + 1'b1;
                r_sin_val <= ~{1'b0, w_sin_rom_val} + 1'b1;
            end
                                                  
            2'b11: begin // [3*pi/2, 2*pi)
                r_cos_val <=  {1'b0, w_sin_rom_val};
                r_sin_val <= ~{1'b0, w_cos_rom_val} + 1'b1;
            end                              
        endcase
    end
                                                                                        
    assign  o_cos_val = r_cos_val[16:1];                                                                                   
    assign  o_sin_val = r_sin_val[16:1];                                                                                   
                                                                                         
//-----------------------------------------------------------------------------------------------                                                         
                                                            
    cos_sin_lut_2  u_cos_sin_lut_2(
        .clka   ( i_sys_clk                    ),  // input wire clka
        .addra  ( r_rom_addr                   ),  // input wire [9 : 0] addra
        .douta  ({w_sin_rom_val, w_cos_rom_val})   // output wire [31 : 0] douta
    );
                                                                                                 
                                                                                                  
                                                                                                 
endmodule

4、仿真结果

5、关键代码分析

使用10bit数据来量化pi/2，即pi/2 = 2^10 也即r_rom_phase = 12'b0100_0000_0000；
所以我们只需要根据r_rom_phase[11:10]来判断输入角度处于4段的哪一段；
$\beta = \varphi [9:0]$ ，即只需要根据r_rom_phase[9:0]来计算三角函数值；
然后根据三角函数公式调整最终输出值。

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