Reconfiguration of Memory for High Speed Matrix Multiplication

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Reconfiguration of Memory for High Speed Matrix Multiplication Ms. Shamshad Shirgeri 1,Ms. Pallavi Umesh Naik 2,Mrs. Rohini 3, Prof. Krishnananda Shet 4 1,2,3 Student, M.Tech in Industrial Electronics, 4 - Research Scholar, 1,2,3-KLS s VDRIT,Haliyal affiliated to VTU,Belgaum, 4- Kuvempu University, Shivamogga, Karnataka, India. Abstract The paper entitled RECONFIGURATION OF MEMORY FOR HIGH SPEED MATRIX MULTIPLICATION is basically an enhancement in speed of matrix multiplication. The project aims at reducing the time involved in the operation. The system presented here makes use of three RAMS designated as MAT- RAM-A, MAT-RAM-B and MAT-RAM-C and system also consists of a control circuitry. This system works in two modes i.e., mode-1 and mode-2. In mode-1 the RAM s act as extensions of existing memory of the processor and in mode-2 the two RAMs MAT-RAM-A and MAT-RAM-B are configured as source for hardware with MAT-RAM-C working as destination for storage or resultant matrix after multiplication. The RAMs are configured back in mode-1, so that data can be read from MAT-RAM-C. Keywords: RAM, MAT-RAM-A, MAT- RAM-B and MAT-RAM-C, SIMD. 1. INTRODUCTION In the present electronic era, speed plays a very crucial role. Speed size ad economics are the present buzzwords in the electronic industry. Any designer will have to take all the three outlined factors into account before starting any design. The trend now-adays is miniaturization coupled with fast access time. The technique presented here uses additional RAMs which will act as extension of the existing RAMs of computers. These RAM devices are switched in a special configuration to provide high speed matrix multiplication. In vector computers, special vector registers within the CPU are used for handling vector operations. The hardware and associated software will have to take care of transferring data approximately. This is quite an involved task and it involves substantial hardware and software overheads. In SIMD architecture the multiplication of two matrices involves a number of load and store instructions. Moreover this requires N processors for N x N matrix operation. Also in this case the data will have to be stored column wise in each machine and then load and store instructions have to be executed for N times. The technique presented here overcomes these problems and provides a very convenient and economical solution for high speed matrix multiplication. 2. PREAMBLE 2.1 Statement of problem Traditional method for matrix multiplication consumes lot of time, as it involves reading from memory, multiplying them and again storing the result back in memory and this process has to be repeated for each element of the matrix. This process 1904

obviously wastes processors time. Processors time can be judiciously utilized by the technique presented here. 2.2 Scope of Study This system provides a very convenient and economical solution for high speed matrix multiplication. The speed is quite high and is limited only by the access time of the RAM devices used for this purpose. 2.3 Methodology Splitting the design into functional modules. The complete design to be implemented to be broken into smaller modules catering to the different functions. Adding the designed modules to the library. The design modules are added to the library so that they can be accessed whenever necessary. This method reduces length of coding. Interconnecting all the modules to complete the circuit. The various modules required for are called from the library and then are interconnected as required. 2.4 Limitation of the system The speed of the system is limited only by the access time of the RAMS used in the circuit. External control unit RAM s This system operates in one of the two modes in mode-1 these can be used as RAM s of the main processor, connected just as an extension RAM s of the main processor. In this mode the necessary control signals of the RAM s are connected to the processors data bus. In mode-2, these are used for matrix multiplication process. In this mode the RAM s are isolated from the main processor MATRAM-A and MATRAM-B store the input data matrix and output of the operation is stored in MATRAM-C. The necessary control signals are obtained from the external circuit. 3.1 Switching unit The switching part consists of two multiplexers one for transferring data between RAM and external control unit. The other multiplexer is used for routing the control signals to RAM either from the processor or from an external control unit. Depending upon the select input switching unit connect the RAM s either to the processor or the external control unit. The system operates in two modes, the mode of operation is decided by the input applied to select pin of switching unit. 3. BLOCK DIAGRAM OF RECONFIGURATION OF MEMORY FOR HIGH SPEED MATRIX MULTIPLICATION Figure2. Switching Unit Figure1. Block Diagram of reconfiguration of memory for high speed matrix multiplication The system presented here consists of Processor Switching unit 1905

3.2 External control unit Figure3. External Control Unit It consists of A Multiplier An 8 bit parallel adder A register Three counters A clock 3.2.3 Register Used for storing the sum from the adder block temporarily. Register initially contains zero. Register gets reset once the resultant matrix element is generated. 3.2.4 Counters The counters used here are binary up counters that generate addresses of RAMs during Mode-2 operation along with the addresses, and bi-directional multiplexers used I the circuit that controls the mode of operation of the system. The counter has a register in it, which should be loaded with the number of elements of the matrix. The counter counts until the loaded value, during which the select signal generated by the counter is at logic high and hence the system operates I mode-2, as soon as the count equals the stored value the select signal becomes low, now the system is switched back to mode- 1. 3.2.1 Multiplier Used for the multiplication of the matrix elements. It takes the inputs from the two matrices, namely MATRAM-A and MATRAM-B. It generates the partial product and this becomes the input for the order block. 3.2.2 8 bit Parallel adder Used for the summation purpose. It has two inputs one is partial product from the multiplier block and the other input is the previous sum from the register block. Figure4. 8 bit parallel adder 3.3 RAM s Figure5. Counters MATRAM-A, MATRAM-B and MATRAM- C which are present in the system are just an extension of existing RAM s of the main processor during mode-1 and in this mode the address lines are generated by the processor and input data are given by the processor itself. MATRAM-A and MATRAM-B are configured as source for the hardware. MATRAM-C works as destination matrix to store the resultant. During mode-2 their address lines are generated by the external circuit. The RAM s are again configured back in mode-1, so that data can be read from MATRAM-C. 1906

4. MODES OF OPERATION 4.1 Mode-1 In mode-1, the input to the select pin of external circuit is at logic low. Under this condition the RAM s are connected to the processor. Under this mode, the RAM s are connected to the processor and are isolated from the external circuit. In this mode the address and control signals for the RAM s are obtained from the processor, and processor data bus is connected to the RAM s data bus. Hence reading from or writing into the RAM is under the control of the processor. 4.2 Mode-2 In the mode-2 the input to the select pin is high. Under this condition the RAM s are connected to the external circuit. The RAM s are completely isolated from main processor. In this mode, the address of the RAM s are obtained from the external control unit, the data buses of RAM-A and RAM-B are connected to the multiplier input and the data bus of RAM-C is connected to the output of the adder. Figure6. Implementation of Reconfiguration of memory for high speed matrix multiplication using VHDL. 6. GRAPHICAL COMPARISION 5. VHDL IMPLEMENTATION Figure7. Graphical comparison of Reconfiguration of memory for high speed matrix multiplication 1907

7. CONCLUSION It provides a much faster and an economic technique for matrix multiplication operation. The speed in this technique will be more than ten times faster compared to Pentium processor. Cost involved will be less compared to that of a vector machine or a SMID machine. The speed of the operation is only limited by the access time of the RAM chip used in the circuit. 8. REFERENCES P.H.W. Leong, M.P. Leong, O.Y.H. Cheung, T. Tung, C.M. Kwok, and K.H. Lee, Pilchard A Reconfigurable Computing Platform with Memory Interface. Xilinx, Virtex-E 1.8 V Field Programmable Gate Arrays. Randall Hyde, "The Art of Assembly Language Programming". http://webster.cs.ucr.edu/page_aoa Linux/HTML/AoATOC.html IEEE international conference on An FPGA based floating-point processor array supporting a high-precision dot product by Fritz Mayer. 1908

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