Conversion of fixed-point number to floating-point number of vivado IP core

Vivado IP The fixed-point number of the core is converted to a floating-point number Floating-point

Catalog

Preface

One 、 What is a fixed-point number ？

Two 、 What is a floating point number ？

3、 ... and 、Floating-point IP Core configuration steps

Four 、 Simulation

1. Top level code

2. Simulation code

5、 ... and 、 Simulation analysis

summary

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Preface

         With the continuous development of manufacturing technology , Field programmable logic gate array （FPGA） More and more integration , More and more applications , Among them, some mathematical processing classes must be used when processing digital signals IP nucleus . Recently, research on Spatial Adaptive Anti-jamming Technology is under way FPGA Hardware implementation , Some of them are inevitably used IP nucleus , Today, let's introduce in detail from fixed-point number to floating-point number vivado In the middle of Floating-point This IP Nuclear bar , I hope it can help you in your study .

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Tips ： The following is the main body of this article , All are original by the author , It's not easy to write an article , I hope you will attach a link to this article when reprinting .

One 、 What is a fixed-point number ？

         Fixed-point number ： The decimal position is fixed The number of is called fixed-point number , That is, the decimal point is a number fixed at a certain position . Fixed point numbers are divided into fixed-point integers and fixed-point decimals , Among them, fixed-point integers are divided into signed fixed-point integers and unsigned fixed-point integers , Fixed point decimals are divided into signed fixed-point decimals and unsigned fixed-point decimals . This article focuses on 32 position （1+1+30） Signed fixed-point decimal , The size of digits can be set according to different usage scenarios , The other three categories are relatively simple , I won't introduce it here .

         The position of the decimal point is fixed before the most significant digit 、 After the sign bit , Pictured 1 Shown . The decimal point position of fixed-point decimals is implicitly agreed , The decimal point does not really need to occupy a bit position .

chart 1 Signed fixed-point decimal format

          In the figure 1 in , Symbol bit , When =0 when , Is a positive decimal ; When =1 when , Decimals are negative decimals .n Is the decimal bit width , The width of decimal places will directly affect the accuracy of decimal , A wide n The larger the, the higher the precision .

         stay xilinx vivado Medium IP nucleus , Signed fixed-point numbers are represented by complements , So we must understand the original code 、 Inverse code 、 The relationship among complement . The original code of a positive number 、 Inverse code 、 The complement is the same ; The original code of a negative number is the original code of a positive number after taking the absolute value , Reverse the negative original code bit by bit , That is, we get the inverse code of negative numbers , The negative complement is obtained by adding one to the negative inverse .

          Okay , Don't talk much , Direct example .

        example1:     Suppose a signed 32 position （1 Bit sign bit +1 Bit integer +30 A decimal place ） Fixed point decimals are expressed in binary 32'b0011_0111_0110_1100_1111_0101_1101_0000, So what is the decimal system instead of the decimal system ？ First , Its sign bit is 0, It is known that it is a positive number , So the original code 、 Inverse code 、 The complement is the same ; secondly , The integer bit is 0, The actual corresponding integer bit is also 0; then , Its 30 The decimal part is 30'b11_0111_0110_1100_1111_0101_1101_0000, Convert to decimal number, that is 929887696; Last , We know when 30 All decimal places are 1 The decimal number represented by hour is 1073741823, So by the 929887696/1073741823≈0.8660254 It can be concluded that the fixed-point decimal is reduced to a real number, which is approximately 0.8660254.

        example2:     Suppose a signed 32 position （1 Bit sign bit +1 Bit integer +30 A decimal place ） Fixed point decimals are expressed in binary 32'b1100_1000_1001_0011_0000_1010_0011_0000, So what is the decimal system instead of the decimal system ？ First , Its sign bit is 1, We can see that it is a negative number , that 32'b1100_1000_1001_0011_0000_1010_0011_0000 Indicates its complement , The negative original code is different from the complement , We should find out the original code first , Its original code is 32'b0011_0111_0110_1100_1111_0101_1101_0000; secondly , The integer bit is 0, The actual corresponding integer bit is also 0; According to the previous analysis, the positive decimal represented by this code is approximately 0.8660254, So far, it can be concluded that the fixed-point decimal into a real number is approximately -0.8660254.

Two 、 What is a floating point number ？

         Floating point numbers are a standardized expression , The common standard is IEEE754 standard , Used to approximate real numbers , And we can make a trade-off between the expression range and the expression accuracy , So it is called floating point number .（ About IEEE754 Standards do not understand their own Baidu , I'm not going to repeat it here ）.

        example3:     Suppose a signed 32 Bit floating point （ The single precision is 32 position , The double precision is 64 position ） In binary 32'b0011_1111_0101_1101_1011_0011_1101_0111, So according to IEEE754 According to the standard, the sign bit is 0, It means positive decimal , The index part is 8'b0111_1110, The decimal part is 23'b101_1101_1011_0011_1101_0111, according to IEEE754 According to the standard, the decimal number it represents is 0.8660254.

        example4:     Suppose a signed 32 Bit floating point （ The single precision is 32 position , The double precision is 64 position ） In binary 32'b1011_1111_0101_1101_1011_0011_1101_0111, So according to IEEE754 According to the standard, the sign bit is 1, Means negative decimal , The index part is 8'b0111_1110, The decimal part is 23'b101_1101_1011_0011_1101_0111, according to IEEE754 According to the standard, the decimal number it represents is -0.8660254.

3、 ... and 、Floating-point IP Core configuration steps

        stay vivado Mid search Floating-point, To find the IP After the core, you can complete the corresponding configuration according to the following operations .

        1. First configuration Operation Selection Interface , Pictured 2 Shown .

chart 2 Operation Selection Interface configuration

         2. Next configuration Precision of Inputs Interface , Pictured 3 Shown .

chart 3 Precision of Inputs Interface configuration

         3. Then configure Precision of Result Interface , Pictured 4 Shown .

chart 4 Precision of Result Interface configuration

         4. Then configure Optimizations Interface , Pictured 5 Shown .

chart 5 Optimizations Interface configuration

         5. Final configuration Interface Options Interface , Pictured 6 Shown .

        

chart 5 Interface Options Interface configuration

          above 5 After all the interfaces are configured, you can click on the lower right corner OK Button generation IP nucleus .

Four 、 Simulation

1. Top level code

Build a top-level module , Name it fix_to_float_top, Used to instantiate the just generated IP nucleus .

The code is as follows ：

`timescale 1ns / 1ps
//
// Company:  Chongqing University 
// Engineer: CLG 
// Create Date: 2022/07/22 09:37:43
// Design Name: 
// Module Name: fix_to_float_top
// Project Name: 
// Target Devices: 
// Tool Versions: 
// Description: 
// Dependencies: 
// Revision:1.0
// Revision 0.01 - File Created
// Additional Comments:
//


module fix_to_float_top(
    input   clk,                                                      
    input           s_axis_a_tvalid,       // Input data valid flag signal 
    input   [31:0]  s_axis_a_tdata,        // Input   Fixed-point number   data 
    output m_axis_result_tvalid,           // Output data valid flag signal 
    output  [31:0]  m_axis_result_tdata    // Output  float  data 

    );
        floating_point_ip u1_floating_point_ip(
            .aclk(clk),
            .s_axis_a_tvalid(s_axis_a_tvalid),
            .s_axis_a_tdata(s_axis_a_tdata),
            .m_axis_result_tvalid(m_axis_result_tvalid),
            .m_axis_result_tdata(m_axis_result_tdata)
        );
  
endmodule

2. Simulation code

Build a simulation module , Name it fix_to_float_tb, It is used to simulate the instantiation of the top-level module just now IP nucleus .

The code is as follows ：

`timescale 1ns / 1ps
//
// Company:  Chongqing University 
// Engineer: CLG
// Create Date: 2022/07/22 10:02:05
// Design Name: 
// Module Name: fix_to_float_tb
// Project Name: 
// Target Devices: 
// Tool Versions: 
// Description: 
// Dependencies: 
// Revision:1.0
// Revision 0.01 - File Created
// Additional Comments:
//


module fix_to_float_tb( );
    reg clk;
    reg a_valid_a = 1'b0;
    reg [31:0] a_a = 32'b0;
    wire [31:0] result_a;

    fix_to_float_top u1_fix_to_float_top(
        .clk(clk),
        .s_axis_a_tdata(a_a),
        .s_axis_a_tvalid(a_valid_a),
        .m_axis_result_tdata(result_a),
        .m_axis_result_tvalid(m_axis_result_tvalid)
    );
    always #5 clk=~clk;
    
    initial begin
       clk  =   1'b0;
        #100;
        a_valid_a <=   1'b1;
        a_a <= 32'h376CF5D0;

        #500;
        a_valid_a <=   1'b1;
        a_a <= 32'hc8930a30;
    end
    
    always @(posedge clk) begin
        if (m_axis_result_tvalid == 1'b1)  begin
            a_valid_a <=   1'b0;
        end      
    end

endmodule

5、 ... and 、 Simulation analysis

         The simulation results are shown in the figure 7 Shown , Compare the fixed points listed above 、 Examples of floating point numbers , It can be seen that this module successfully converts fixed-point numbers into floating-point numbers .

chart 7 Simulation results

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summary

         This time, I introduce Fixed-point number 、 Floating point numbers and how to use vivado Medium Floating-point IP The core converts fixed-point numbers 32 Bit floating point .