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Tuesday, November 17, 2015

Verilog Code for Matrix Multiplication - for 2 by 2 Matrices

Here is the Verilog code for a simple matrix multiplier. The input matrices are of fixed size 2 by 2 and so the output matrix is also fixed at 2 by 2. I have kept the size of each matrix element as 8 bits.

Verilog doesn't allow you to have multi dimensional arrays as inputs or output ports. So I have converted the three dimensional input and output ports to one dimensional array. Inside the module I have created 3D temporary variables which are initialized to the inputs at the beginning of the always statement. 

The matrix multiplier is also synthesisable. When synthesised for Virtex 4 fpga, using Xilinx XST, a maximum combinational path delay of 9 ns was obtained. 

Matrix multiplier:

//Module for calculating Res = A*B
//Where A,B and C are 2 by 2 matrices.
module Mat_mult(A,B,Res);

    //input and output ports.
    //The size 32 bits which is 2*2=4 elements,each of which is 8 bits wide.    
    input [31:0] A;
    input [31:0] B;
    output [31:0] Res;
    //internal variables    
    reg [31:0] Res;
    reg [7:0] A1 [0:1][0:1];
    reg [7:0] B1 [0:1][0:1];
    reg [7:0] Res1 [0:1][0:1]; 
    integer i,j,k;

    always@ (or B)
    begin
    //Initialize the matrices-convert 1 D to 3D arrays
        {A1[0][0],A1[0][1],A1[1][0],A1[1][1]} = A;
        {B1[0][0],B1[0][1],B1[1][0],B1[1][1]} = B;
        i = 0;
        j = 0;
        k = 0;
        {Res1[0][0],Res1[0][1],Res1[1][0],Res1[1][1]} = 32'd0; //initialize to zeros.
        //Matrix multiplication
        for(i=0;< 2;i=i+1)
            for(j=0;< 2;j=j+1)
                for(k=0;< 2;k=k+1)
                    Res1[i][j] = Res1[i][j] + (A1[i][k] * B1[k][j]);
        //final output assignment - 3D array to 1D array conversion.            
        Res = {Res1[0][0],Res1[0][1],Res1[1][0],Res1[1][1]};            
    end 

endmodule

Testbench Code:

module tb;

    // Inputs
    reg [31:0] A;
    reg [31:0] B;
    // Outputs
    wire [31:0] Res;

    // Instantiate the Unit Under Test (UUT)
    Mat_mult uut (
        .A(A), 
        .B(B), 
        .Res(Res)
    );

    initial begin
        // Apply Inputs
        A = 0;  B = 0;  #100;
        A = {8'd1,8'd2,8'd3,8'd4};
        B = {8'd5,8'd6,8'd7,8'd8};
    end
      
endmodule

Simulation waveform:

The codes were simulated using Xilinx ISE 13.1. The following waveform verifies that the design is working correctly.