IP Design And Verification Of High-order Floating Point Matrix Operation

Matrix theory and algorithm can be used to solve many problems in practical engineering projects.These engineering fields usually include digital signal processing,high-speed network information transmission,information encryption and image processing.Matrix operation has a wide application value in these large-scale data analysis fields.Moreover,real-time operation is often needed in the system,and its execution efficiency has a crucial impact on the operation of the whole system.With the increasing complexity of modern science and engineering problems,it is often necessary to solve large-scale linear equations.As a mathematical tool,matrix plays an increasingly prominent role.The commonly used matrix operations include addition,subtraction,multiplication,division,inversion,transposition and other operations.In the field of engineering application,the main difficulty is the inversion operation,while the current matrix inversion has the characteristics of long time-consuming and large hardware resources.In order to improve the current situation,it is necessary to design a high-order matrix inversion which can process double precision floating-point data as a hardware accelerator,and also use appropriate hardware resources to complete the matrix inverter.The main work of this paper is as follows:1.On the basis of in-depth study of the characteristics of diagonally dominant matrix and matrix inversion operation,this paper compares and analyzes the solutions proposed by relevant technical documents at home and abroad,and draws the main conclusion that it is difficult to directly inverse the high-order matrix,which needs to be decomposed and then inversed.This process involves a variety of operation methods of matrix decomposition and triangular matrix inversion After the application scope,algorithm principle and the difficulty degree of realization in the actual project,LU matrix decomposition algorithm is finally selected as the key step in the process of matrix inversion.LU matrix decomposition is widely used in many engineering fields,aiming at solving the practical application of linear system equation,etc.,while the two triangular matrices obtained after LU decomposition are selected to use the primary in the inversion operation Row transformation method and elementary row transformation method are suitable for matrix of any order and have better flexibility.2.Based on the idea that the hardware accelerator can execute specific application programs to improve the ability of data processing,a matrix inversion device with configurable order is designed by connecting the system bus to the processor,including memory module,operation module,address control module,etc.,focusing on the decomposition,triangle matrix inversion and multiplication in the process of matrix operation address control module for detailed description.Whereas the LU decomposition process,triangle matrix inversion process and matrix multiplication process all involve multiplication and accumulation operation,the multiplication and accumulation unit can be reused many times,thus it can reduce the cost of hardware resources and save the chip area.3.Completed the logic synthesis,and the results meet the design requirements.The simulation verification of the inverse of the configurable order matrix is completed.The random matrix which meets the specific requirements is generated by MATLAB as the excitation input in the design to be tested.After the output of the design result,the result of the inverse of the matrix is subtracted from that of MATLAB.If the result is within the allowable range of error,the function of the inverse is correct,and the accuracy of the result of the inverse is 10^-5,After analyzing,the conclusion is: under the same order matrix,the maximum error and average error of the inverse result decrease with the increase of the order of matrix elements,while the error of the inverse result will increase with the increase of the order of matrix elements.Completed hardware resource occupancy analysis and compared it with the same type of literature in terms of performance.The test results show that the configurable order matrix inverter in this paper only needs 10398 clock cycles to process the maximum 30 order matrix,which meets the design requirements.Compared with the same type of matrix inverter,this inverter has faster operation efficiency and lower storage resources.