Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
Binary Division Algorithms based on Vedic Mathematics: A Review 1 1,2
Satnam Singh Shergill, 2Arvind Kumar
Dept. of Electronics and Communication, U.I.E.T., P.U., Chandigarh
ABSTRACT – With ever increasing demand of speed, accuracy and space we need better hardware and software. Software can be made better by making faster algorithms. As far as arithmetic algorithms are concerned in digital hardware, division is the least used one, computers experience performance degradation if division is ignored. There are various fields in digital world which demand excessive multiplication and division. For them algorithms based on Vedic Mathematics have proved to be much faster than other algorithms and there is further room for improvement also, which attracts further attention from researchers working on these algorithms.
I. INTRODUCTION Today the computers have evolved very much since their creation. However, one thing has not changed. The main function of computers is to do the mathematical operations to run programs. Computers process lots of binary numbers based addition, multiplication and division. In comparison to other mathematical operations, division is the least used operation. However, if we ignore division, there will be performance. With increasing reliance on technology in every field like payment through NFC, cloud data storage etc. we need better cryptographic solutions, and elliptic curve cryptography is one of them. But elliptic curve cryptography involves calculations on about 200-600 digits and for those calculations to be economical we need arithmetic algorithms to be fast and less space consuming. Improving division algorithm is one those tasks. Also, with the ever rising quality of image and video signals, we need faster algorithms to absorb the effect of more calculation delays associated with their processing. Digital Signal Processing is another area which requires faster processing of high number of bits. So, there is always need for faster and better algorithms in computing world. And algorithms based on Vedic Mathematics have proved to be much faster than other algorithms and there is further room for improvement also, which attracts further attention from researchers working on these algorithms. II. RELATED WORK Prabir Saha et al [1] used Nikhilam Navatascaramam Dasatah (NND) sutra of Vedic Mathematics to develop a Vedic Divider Architecture for binary numbers and it was implemented on spice spectre through existing 90nm CMOS technology. Comparison of new architecture was done with digit recurrence, convergence and series expansion based architectures and found improvement of 50%, 45% and 41% respectively in vedic architecture. Furthermore power consumption was less by 44%, 35% and 27% respectively. They calculated that EDP(Energy Delay Product) was reduced by 73% compared with series 1
expansion based architecture(the best architecture reported so far). Diganta Sengupta et al[2] used Nikhilam Navatascaramam Dasatah (NND) sutra and Parvartya Yojayet sutra to develop a division algorithm for BCD numbers. Their work involved adjusting the divisor and then carrying out other steps of algorithm in which each partial remainder needed to be normalized. To calculate the time taken for division, each division was iterated 10,000 times at each run of the program and compared the time taken by the algorithm with that of Non Restore Type division algorithm for the same set of divisors and dividends. It was found that for 2 digit divisor and dividend vedic division took 0.150µs whereas Non Restore Type division took 0.800µs. For 15 digit dividend and 6 digit divisor vedic division took 2.490µs and Non Restore Type division took 49.290µs. It was seen that the difference in time taken increased with the increase in number of digits proving vedic division much better in division involving large number of digits. Soma BhanuTej[3] of IBM Systems and Technology Group applied Parvartya Yojayet sutra of Vedic Mathematics to develop a high performance divider and comparison of static timing analysis was done between vedic divider and conventional divider. A 32 bit dividend and 16 bit divisor binary vedic divider was synthesised using 180nm and 32nm standard cell libraries on Cadence nclauch and comparison was done with conventional divider and it was found that vedic divider saved power in the range of 109mW and was ~7 times faster and area occupied was ~13 times lesser than conventional divider. Ratiranjan Senapati et al[4] implemented Parvartya Yojayet sutra vedic divider using Xilinx ISE on 90nm CMOS technology. They implemented 8 bit binary dividend by 4 bit binary divisor circuitry and found that propagation delay was only ~19.9ns and consumed ~34mW power. Compared to repetitive subtraction method this algorithm had ~46% less propagation delay and consumed ~27% less power. Shantanu Oke et al[5] used another Vedic Mathematics sutra called Dhwajam sutra to develop Distinctive Division Achitecture and the algorithms was implemented on Xilinx 8.1 ISE and they tested the results on Spartan 3 FPGA platform also. Comparing their algorithm with NewtonRaphson algorithm, it was stated that their algorithm was much less complex and needed less number of steps and their was no need of look up table in their algorithm as was their in Newton-Raphson and SRT algorithm. R. Thamil Chelvan and S. Roobini Priya[6] implemented RSA encryption/ decryption algorithm using Dhvajanka sutra also called Dhwajam sutra for fixed and floating point binary numbers. They implemented the algorithm on FPGA using Xilinx Spartan library using Verilog HDL. It was found that gate delay for RSA circuitry using 8x8 NITTTR, Chandigarh
EDIT-2015
Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
overlay multiplier architecture and 16 bit by 16 bit vedic division was 1.507 µs whereas for Restoring Type division algorithm the gate delay was 2.838 µs and for Non Restore Type division algorithm it was 2.828 µs. Najib Ghatte et al[7] used Vedic Mathematics to implement a IEEE 754 single precision floating point division algorithm using Verilog HDL and simulations were done using ModelSim SE Plus 6.5. It was then synthesised for VirtexTM -5 FPGA family device XC5VLX30. It was found that there was about 12% improvement in utilization of the resources as compared to Restoring/ Non Restoring type division algorithms. The combinational delay was just 5.405ns and power consumption was reduced to 2mW whereas traditional ALU’s consume more power. Surabhi Jain et al[8] developed high speed deconvolution algorithm using Binary division algorithms based on Vedic Mathematics. They used Nikhilam and Parvartya sutra and implementation was done on Xilinx ISE using Verilog HDL. Simulated results showed a reduction in delay of 19% as compared to conventional methods. III. CONCLUSION In this work, our focus was on the application of Vedic Mathematics for binary fixed point and floating point divisions. The work done by the authors referred to in this work has proven that Vedic Division algorithms can be used for the development of faster and less power consuming devices and also it has been shown that the area consumed is less in Vedic Division implementations as compared to other algorithms which makes these algorithms more suitable for mobile application because mobile devices need to have required functionality at the least possible power and space consumption. REFERENCES Prabir Saha, Arindam Banerjee, Partha Bhattacharyya, Anup Dandapat (2011) ‘Vedic Divider: Novel Architecture (ASIC) for High Speed VLSI Applications’, International Symposium on Electronic System Design. Diganta Sengupta, Mahamuda Sultana and Atal Chaudhuri (2013) ‘ Vedivision – A Fast BCD Division Algorithm Facilitated by Vedic Mathematics’, International Journal of Computer Science & Information Technology, Vol. 5, No. 4, pp.67-80. Soma BhanuTej, IBM Systems and Technology Group, Bangalore, India. Ratiranjan Senapati, Bandan Kumar Bhoi, Manoranjan Pradhan (2013) ‘Novel Binary Divider Architecture for high speed VLSI applications’, Proceedings of 2013 I.E.E.E. Conference on Information and Communication Technologies. Shantanu Oke, Suraj Lulla, Prathamesh Lad (2014) ‘VLSI (FPGA) Design for Distinctive Division Architecture using the Vedic Sutra ‘Dhwajam’’, International Conference on Devices, Circuits and Systems(ICDCS). R. Thamil Chelvan, S. Roobini Priya (2013), ‘Implementation of Fixed And Floating Point Division Using Dhvajanka Sutra’, International Journal of VLSI and Embedded Systems-IJVES, Vol. 04, Issue 02, pp. 234-237. Najib Ghatte, Shilpa Patil, Deepak Bhoir (2014) ‘Single Precision Floating Point Division’, IRF International Conference. Surabhi Jain, Mukul Pancholi, Harsh Garg, Sandeep Saini (2014) ‘Binary Division Algorithm and High Speed Deconvolution Algorithm(Based on Ancient Indian Vedic Mathematics)’, IEEE.
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