FPGA使用查表法实现正弦和余弦函数 - 变形方法2的一点扩展_verilog查表法求正余弦

在前面几篇文章中，输出数据量化位数都是16bit，但如果想实现非半字节的量化位数，比如18bit，那怎么办呢？只需要修改下matlab程序，产生18bit的输出数据，verilog程序修改起来就比较简单了。

修改后的matlab程序如下所示：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Zheng Wei, 2022/12/08
%% 
%% 输入角度范围：[0,pi/4); 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：18bit;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
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/4/2^in_quantify_bit):(pi/4-pi/4/2^in_quantify_bit);  % 弧度
 
out_quantify_bit = 18;       % 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));  % 18bit量化
sin_alpha_q = round(sin_alpha *(2^(out_quantify_bit-1)-1));  % 18bit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 = dec2bin(cos_alpha_q,18); 
sin_alpha_q = dec2bin(sin_alpha_q,18);
s=strcat(sin_alpha_q,cos_alpha_q);
s=bin2dec(s);
s=dec2hex(s);
 
% 将cos和sin拼接为36bit(各自18bit)，此数据输出到FPGA
fid=fopen('cos_sin_lut_4.coe','wt');
fprintf( fid, 'MEMORY_INITIALIZATION_RADIX = 16;\n');                     
fprintf( fid, 'MEMORY_INITIALIZATION_VECTOR =\n');
 
for i = 1:1:(2^in_quantify_bit)
    fprintf(fid,'%c%c%c%c%c%c%c%c',s(i,:));
    if (i < 2^in_quantify_bit)
        fprintf(fid,',\n'); 
    else
        fprintf(fid,';\n');  % 分号(;) 结束标志位
    end    
end
fclose(fid);

有几点需要注意的地方：

1. 因为是非半字节，所以不能直接去做数据拼接，而是需要先将10进制转换成2进制；
2. 因为matlab没有2进制直接转16进制的函数，所以拼接完了之后需要先将2进制转换成10进制，然后再将10进制转成16进制；
3. 10进制转2进制的时候注意制定转换位宽，否则数据拼接的结果就会出现问题。