FPGA开平方的实现

3种方法：

1.JPL近似的实现方法

`timescale 1ns / 1ps
module    complex_abs#(parameter N=32)(
      clk,
      syn_rst,
      dataa,
      datab,
      ampout);
      
input    clk;
input    [N-1:0]    dataa;
input    [N-1:0]    datab;
input    syn_rst;
output    reg    [N-1:0]ampout;

reg [N-1:0]dataa_reg ;
reg [N-1:0]datab_reg ;
wire [N-2:0]dataa_abs ;
wire [N-2:0]datab_abs ;
reg [N-2:0]dataabs_max,dataabs_min ;
reg [N-1:0]absmin_3 ;

 always @(posedge clk)
   begin
       if(syn_rst == 1'b1)
           begin
               dataa_reg <= 'd0 ;
               datab_reg <= 'd0 ;
           end
       else
         begin
             dataa_reg <= dataa ;
               datab_reg <= datab ;
           end
   end
   
 assign dataa_abs = (dataa_reg[31] == 1'b1) ? (31'd0-dataa_reg[N-2:0]) : dataa_reg[N-2:0] ;
 assign datab_abs = (datab_reg[31] == 1'b1) ? (31'd0-datab_reg[N-2:0]) : datab_reg[N-2:0] ;  
 
 always @(posedge clk)
   begin
        if(dataa_abs > datab_abs)
             begin
                  dataabs_max <= dataa_abs ;
                  dataabs_min <= datab_abs ;
                  absmin_3 <= {1'b0,datab_abs}+{datab_abs,1'b0} ;        
             end
        else
          begin
                  dataabs_max <= datab_abs ;
                  dataabs_min <= dataa_abs ;
                  absmin_3 <= {1'b0,dataa_abs}+{dataa_abs,1'b0} ;        
             end
   end
   
 always @(posedge clk)
   begin
        if(absmin_3 > {1'b0,dataabs_max})
             ampout <= {1'b0,dataabs_max} - {4'b0,dataabs_max[N-2:3]} + {2'b0,dataabs_min[N-2:1]} ;
        else
          ampout <= {1'b0,dataabs_max} + {4'b0,dataabs_min[N-2:3]} ;
   end             

endmodule

 2.调用IP模块的cordic算法实现效果

可选模式可以是fraction或者intergalactic

工程中输入数据的范围是远大于2的，于是我们可以采用实现方法是将所有的数据先归一化成-2~2之间，然后再进一步的采用cordic模块

IP的配置如下

3.牛顿迭代忽略余数的实现方法

`timescale 1ns / 1ps
//////////////////////////////////////////////////////////////////////////////////
// Company: 
// Engineer: 
// 
// Create Date: 2018/08/07 16:26:46
// Design Name: 
// Module Name: sqrt
// Project Name: 
// Target Devices: 
// Tool Versions: 
// Description: 
// 
// Dependencies: 
// 
// Revision:
// Revision 0.01 - File Created
// Additional Comments:
// 
//////////////////////////////////////////////////////////////////////////////////


module sqrt
    #(     
            parameter                                       d_width = 32,
            parameter                                   q_width = d_width/2 - 1,
            parameter                                   r_width = q_width + 1    )
    (
    input            wire                                    clk,
    input            wire                                    rst,
    input            wire                                    i_vaild,
    input            wire            [d_width-1:0]            data_i,//data_21,data_12,data_22, //输入

    output        reg                                    o_vaild,
    output        reg            [q_0]            data_o, //输出
    output        reg            [r_0]            data_r  //余数
    );

//--------------------------------------------------------------------------------

    reg                             [d_width-1:0]         D                [r_1]; //被开方数
    reg                             [q_0]         Q_z            [r_1]; //临时
    reg                             [q_0]         Q_q            [r_1]; //确认
    reg                                                     ivalid_t        [r_1];
//--------------------------------------------------------------------------------
    always@(posedge    clk or posedge    rst)
        begin
            if(rst)
                begin
                    D[r_width] <= 0;
                    Q_z[r_width] <= 0;
                    Q_q[r_width] <= 0;
                    ivalid_t[r_width] <= 0;
                end
            else    if(i_vaild)
                begin
                    D[r_width] <= data_i;//data_11+data_21+data_12+data_22;  //被开方数据
                    Q_z[r_width] <= {1'b1,{q_width{1'b0}}}; //实验值设置
                    Q_q[r_width] <= 0; //实际计算结果
                    ivalid_t[r_width] <= 1;
                end
            else
                begin
                    D[r_width] <= 0;
                    Q_z[r_width] <= 0;
                    Q_q[r_width] <= 0;
                    ivalid_t[r_width] <= 0;
                end
        end
//-------------------------------------------------------------------------------

//        迭代计算过程

//-------------------------------------------------------------------------------
        generate
            genvar i;
                for(i=r_width-1;i>=1;i=i-1)
                    begin:U
                        always@(posedge clk or posedge    rst)
                            begin
                                if(rst)
                                    begin
                                        D[i] <= 0;
                                        Q_z[i] <= 0;
                                        Q_q[i] <= 0;
                                        ivalid_t[i] <= 0;
                                    end
                                else    if(ivalid_t[i+1])
                                    begin
                                        if(Q_z[i+1]*Q_z[i+1] > D[i+1])
                                            begin
                                                Q_z[i] <= {Q_q[i+1][q_i],1'b1,{{i-1}{1'b0}}};
                                                Q_q[i] <= Q_q[i+1];
                                            end
                                        else
                                            begin
                                                Q_z[i] <= {Q_z[i+1][q_i],1'b1,{{i-1}{1'b0}}};
                                                Q_q[i] <= Q_z[i+1];
                                            end
                                        D[i] <= D[i+1];
                                        ivalid_t[i] <= 1;
                                    end
                                else
                                    begin
                                        ivalid_t[i] <= 0;
                                        D[i] <= 0;
                                        Q_q[i] <= 0;
                                        Q_z[i] <= 0;
                                    end
                            end
                    end
        endgenerate
//--------------------------------------------------------------------------------

//    计算余数与最终平方根

//--------------------------------------------------------------------------------
        always@(posedge    clk or posedge    rst) 
            begin
                if(rst)
                    begin
                        data_o <= 0;
                        data_r <= 0;
                        o_vaild <= 0;
                    end
                else    if(ivalid_t[1])
                    begin
                        if(Q_z[1]*Q_z[1] > D[1])
                            begin
                                data_o <= Q_q[1];
                                data_r <= D[1] - Q_q[1]*Q_q[1];
                                o_vaild <= 1;
                            end
                        else
                            begin
                                data_o <= {Q_q[1][q_1],Q_z[1][0]};
                                data_r <= D[1] - {Q_q[1][q_1],Q_z[1][0]}*{Q_q[1][q_1],Q_z[1][0]};
                                o_vaild <= 1;
                            end
                    end
                else
                    begin
                        data_o <= 0;
                        data_r <= 0;
                        o_vaild <= 0;
                    end
            end
//--------------------------------------------------------------------------------
endmodule

三种方法的精度对比以及资源占用情况

JPL近似

 IPcordic使用：

牛顿迭代

可以看出资源占用：newtoon>JPL > IPcordic，精度的估计JPL<newtoon<IPcordic,

其中JPL 的计算速度快，但是误差太高了

单独求倒数的模块    /    快速高精度求平方根倒数的算法