Year 2020,
, 90 - 104, 01.03.2020
Sivanantham S
,
Jean Jenifer Nesam Jeyakumar
References
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- [2]. M. J. Schulte, J. E. Stine, and J. G. Jansen, “Reduced power dissipation through truncated multiplication,” in Proc. IEEE Alessandro Volta Memorial Workshop on Low Power Design, Como, Italy, pp. 61–69,1999.
- [3]. J. M. Jou, S. R.Kuang, R. D. Chen, “Design of low-error fixed-width multiplier for DSP applications,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal. Process., vol. 46, no. 6, pp. 836–842, Jun. 1999.
- [4]. S.J. Jou, H.H. Wang, "Fixed-width multiplier for DSP application", Proc. IEEE Int. Symp. Computer Design, pp. 318-332, 2000.
- [5]. Y. H. Chen, C. W. Lu, H. C. Chiang, T. Y. Chang and C. Hsia, "A low-error statistical fixed-width multiplier and its applications," 2012 International Symposium on Instrumentation & Measurement, Sensor Network and Automation (IMSNA), Sanya, pp. 39-43, 2012.
- [6]. L. D. Van, S. S. Wang, W. S. Feng, “Design of the lower-error fixed-width multiplier and its application,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal. Process., vol. 47, pp. 1112–1118, Oct. 2000.
- [7]. E. J. King and E. E. Swartzlander Jr., “Data-dependent truncation scheme for parallel multipliers,” in Proc. 31st Asilomar Conf. Signals, Systems, and Computers, vol. 2, Pacific Grove, CA, pp. 1178–1182,1997.
- [8]. E. E. Swartzlander Jr., “Truncated multiplication with approximate rounding,” in Proc. 33rd Asilomar Conf. Signals, Systems, and Computers, vol. 2, pp. 1480–1483, 1999.
- [9]. Yuan-Ho Chen, Chung-Yi Li, Tsin-Yuan Chang, "Area-Effective and Power-Efficient Fixed-Width Booth Multipliers Using Generalized Probabilistic Estimation Bias", Emerging and Selected Topics in Circuits and Systems IEEE Journal on, vol. 1, pp. 277-288, 2011.
- [10]. RomainMichard, Arnaud Tisserand, Nicolas Veyrat-Charvillon, "Carry Prediction and Selection for Truncated Multiplication", Signal Processing Systems Design and Implementation 2006. SIPS '06. IEEE Workshop on, pp. 339-344, 2006.
- [11]. L.-D. Van and C.-C. Yang, "Generalized low-error area-efficient fixed width multipliers," IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 52, no. 8, pp. 1608-1619, Aug. 2005.
- [12]. S. S. Kidambi, F. El-Guibaly, and A. Antoniou, “Area-efficient multipliers for digital signal processing applications,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal. Process., vol. 43, no. 2, pp. 90–94, Feb. 1996.
- [13]. Petra, Nicola, Davide De Caro, Valeria Garofalo, Ettore Napoli, and Antonio GM Strollo. "Truncated binary multipliers with variable correction and minimum mean square error." IEEE Transactions on Circuits and Systems I: Regular Papers57, no. 6 (2010): 1312-1325.
- [14]. I.-C. Wey, C.C. Wang, "Low-error and hardware-efficient fixed width multiplier by using the dual-group minor input correction vector to lower input correction vector compensation error", IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 20, no. 10, pp. 1923-1928, 2012.
- [15]. T.-B. Juang, S.-F. Hsiao, "Low-error carry-free fixed-width multipliers with low-cost compensation circuits", IEEE Trans. Circuits Syst. II, vol. 52, no. 6, pp. 299-303, 2005.
- [16]. De Caro, D., Petra, N., Strollo, A.G.M., Tessitore, F. and Napoli, E., 2013. Fixed-width multipliers and multipliers-accumulators with min-max approximation error. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(9), pp.2375-2388.
- [17]. I.-C. Wey, C.-C. Peng, F.-Y. Liao, "Reliable low-power multiplier design using fixed width replica redundancy block", IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 23, no. 1, pp. 78-87, 2015.
- [18]. Pankaj U. Joshi, Raghavendra B., Venkateshwarlu Gudur, “Self-compensation scheme for truncation error in fixed width multipliers”, IET Circuits, Devices &Systems,Volume: 12, no. 1, pp. 55-62, 2018.
- [19]. T. A. Drane, T. M. Rose and G. A. Constantinides, "On the Systematic Creation of Faithfully Rounded Truncated Multipliers and Arrays," in IEEE Transactions on Computers, vol. 63, no. 10, pp. 2513-2525, Oct. 2014.
- [20]. P. U. Joshi, R. B. Deshmukh and V. Gudur, "Self-compensation scheme for truncation error in fixed width multipliers," in IET Circuits, Devices & Systems, vol. 12, no. 1, pp. 55-62, 2018.
- [21]. S. Venkatachalam, S. B. Ko, "Design of Power and Area Efficient Approximate Multipliers," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 25, no. 5, pp. 1782-1786, May 2017.
- [22]. C. R. Baugh, B. A. Wooley, “A two’s complement parallel array multiplication algorithm,” IEEE Trans. Comp., vol. C-22, no. 12, pp. 1045–1047, Dec. 1973.
- [23]. K. Hwang, Computer Arithmetic: Principles, Architecture, and Design. New York: Wiley, 1979.
- [24]. F. Cavanagh, Digital Computer Arithmetic: Design and Implementation. New York: McGraw-Hill, 1984.
- [25]. M. E. Paul, K. Bruce, C Language Algorithms for Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1991.
- [26]. A.D.Booth, “A Signed Binary Multiplication Technique,” Quarterly J. Mechan. Appl. Math, Vol.IV, pp.236-240, 1951.
- [27]. A. A. Karatsuba: The Complexity of Computations. Proceedings of the Steklov Institute of Mathematics, Vol. 211, 1995, pages 169 – 183.
- [28]. Wallace, C.S.: “A Suggestion for a Fast Multiplier,” IEEE Trans. on Electronic Computers, vol. EC – 13, pp 14 – 17, February 1964.
- [29]. L. Dadda, “On Parallel Digital Multipliers,” Alta Frequenza, vol. 45, pp. 574 – 580, 1976.
- [30]. Xianyang Jiang, Peng Xiao, Meikang Qiu, Gaofeng Wang,“Performance Effects of pipeline architecture on a FPGA-based binary32 floating point multiplier”, Microprocessors and Microsystems, Volume 37, Issue 8, pp. 1183-1191, November 2013.
- [31]. Sertbaş, Ahmet, El-Abdallah Hani, and Fethullah Karabiber. "A fast multiplier hardware design for interval arithmetic." IU-Journal of Electrical & Electronics Engineering 6, no. 2 (2006): 169-174.
Low-Error Reconfigurable Fixed-Width Multiplier for Image Processing Applications
Year 2020,
, 90 - 104, 01.03.2020
Sivanantham S
,
Jean Jenifer Nesam Jeyakumar
Abstract
Compensating the error using additional circuitry is mandatory in a low-error fixed-width multiplier. Instead of compensating the error, reconfiguring n-bit fixed-width multiplier to n/2-bit error-free full-width multiplier using decomposed multiplication is proposed in this paper. The decomposed block multiplication using an area-efficient New Bit Pair Recoding (NBPR) algorithm in fixed-width mode shows a relatively lesser truncation error than existing truncated multipliers. Reconfigurable 16x16 NBPR multiplier in three different modes (8x8, 16x8,16x16) with a fixed 16-bit product is verified on the TSMC 65nm CMOS standard cell library. The experimental results show that the NBPR multiplier consumes a lesser area than standard Booth multipliers. Evaluating the proposed multiplier in imaging shows improved PSNR with minimal error compared to other fixed-width multipliers
References
- [1]. Y.C. Lim, "Single precision multiplier with reduced circuit complexity for signal processing applications", IEEE Trans. Comp., vol. 41, no. 10, pp. 1333-1336, 1992.
- [2]. M. J. Schulte, J. E. Stine, and J. G. Jansen, “Reduced power dissipation through truncated multiplication,” in Proc. IEEE Alessandro Volta Memorial Workshop on Low Power Design, Como, Italy, pp. 61–69,1999.
- [3]. J. M. Jou, S. R.Kuang, R. D. Chen, “Design of low-error fixed-width multiplier for DSP applications,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal. Process., vol. 46, no. 6, pp. 836–842, Jun. 1999.
- [4]. S.J. Jou, H.H. Wang, "Fixed-width multiplier for DSP application", Proc. IEEE Int. Symp. Computer Design, pp. 318-332, 2000.
- [5]. Y. H. Chen, C. W. Lu, H. C. Chiang, T. Y. Chang and C. Hsia, "A low-error statistical fixed-width multiplier and its applications," 2012 International Symposium on Instrumentation & Measurement, Sensor Network and Automation (IMSNA), Sanya, pp. 39-43, 2012.
- [6]. L. D. Van, S. S. Wang, W. S. Feng, “Design of the lower-error fixed-width multiplier and its application,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal. Process., vol. 47, pp. 1112–1118, Oct. 2000.
- [7]. E. J. King and E. E. Swartzlander Jr., “Data-dependent truncation scheme for parallel multipliers,” in Proc. 31st Asilomar Conf. Signals, Systems, and Computers, vol. 2, Pacific Grove, CA, pp. 1178–1182,1997.
- [8]. E. E. Swartzlander Jr., “Truncated multiplication with approximate rounding,” in Proc. 33rd Asilomar Conf. Signals, Systems, and Computers, vol. 2, pp. 1480–1483, 1999.
- [9]. Yuan-Ho Chen, Chung-Yi Li, Tsin-Yuan Chang, "Area-Effective and Power-Efficient Fixed-Width Booth Multipliers Using Generalized Probabilistic Estimation Bias", Emerging and Selected Topics in Circuits and Systems IEEE Journal on, vol. 1, pp. 277-288, 2011.
- [10]. RomainMichard, Arnaud Tisserand, Nicolas Veyrat-Charvillon, "Carry Prediction and Selection for Truncated Multiplication", Signal Processing Systems Design and Implementation 2006. SIPS '06. IEEE Workshop on, pp. 339-344, 2006.
- [11]. L.-D. Van and C.-C. Yang, "Generalized low-error area-efficient fixed width multipliers," IEEE Transactions on Circuits and Systems-I: Regular Papers, vol. 52, no. 8, pp. 1608-1619, Aug. 2005.
- [12]. S. S. Kidambi, F. El-Guibaly, and A. Antoniou, “Area-efficient multipliers for digital signal processing applications,” IEEE Trans. Circuits Syst. II, Analog Digit. Signal. Process., vol. 43, no. 2, pp. 90–94, Feb. 1996.
- [13]. Petra, Nicola, Davide De Caro, Valeria Garofalo, Ettore Napoli, and Antonio GM Strollo. "Truncated binary multipliers with variable correction and minimum mean square error." IEEE Transactions on Circuits and Systems I: Regular Papers57, no. 6 (2010): 1312-1325.
- [14]. I.-C. Wey, C.C. Wang, "Low-error and hardware-efficient fixed width multiplier by using the dual-group minor input correction vector to lower input correction vector compensation error", IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 20, no. 10, pp. 1923-1928, 2012.
- [15]. T.-B. Juang, S.-F. Hsiao, "Low-error carry-free fixed-width multipliers with low-cost compensation circuits", IEEE Trans. Circuits Syst. II, vol. 52, no. 6, pp. 299-303, 2005.
- [16]. De Caro, D., Petra, N., Strollo, A.G.M., Tessitore, F. and Napoli, E., 2013. Fixed-width multipliers and multipliers-accumulators with min-max approximation error. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(9), pp.2375-2388.
- [17]. I.-C. Wey, C.-C. Peng, F.-Y. Liao, "Reliable low-power multiplier design using fixed width replica redundancy block", IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 23, no. 1, pp. 78-87, 2015.
- [18]. Pankaj U. Joshi, Raghavendra B., Venkateshwarlu Gudur, “Self-compensation scheme for truncation error in fixed width multipliers”, IET Circuits, Devices &Systems,Volume: 12, no. 1, pp. 55-62, 2018.
- [19]. T. A. Drane, T. M. Rose and G. A. Constantinides, "On the Systematic Creation of Faithfully Rounded Truncated Multipliers and Arrays," in IEEE Transactions on Computers, vol. 63, no. 10, pp. 2513-2525, Oct. 2014.
- [20]. P. U. Joshi, R. B. Deshmukh and V. Gudur, "Self-compensation scheme for truncation error in fixed width multipliers," in IET Circuits, Devices & Systems, vol. 12, no. 1, pp. 55-62, 2018.
- [21]. S. Venkatachalam, S. B. Ko, "Design of Power and Area Efficient Approximate Multipliers," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 25, no. 5, pp. 1782-1786, May 2017.
- [22]. C. R. Baugh, B. A. Wooley, “A two’s complement parallel array multiplication algorithm,” IEEE Trans. Comp., vol. C-22, no. 12, pp. 1045–1047, Dec. 1973.
- [23]. K. Hwang, Computer Arithmetic: Principles, Architecture, and Design. New York: Wiley, 1979.
- [24]. F. Cavanagh, Digital Computer Arithmetic: Design and Implementation. New York: McGraw-Hill, 1984.
- [25]. M. E. Paul, K. Bruce, C Language Algorithms for Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1991.
- [26]. A.D.Booth, “A Signed Binary Multiplication Technique,” Quarterly J. Mechan. Appl. Math, Vol.IV, pp.236-240, 1951.
- [27]. A. A. Karatsuba: The Complexity of Computations. Proceedings of the Steklov Institute of Mathematics, Vol. 211, 1995, pages 169 – 183.
- [28]. Wallace, C.S.: “A Suggestion for a Fast Multiplier,” IEEE Trans. on Electronic Computers, vol. EC – 13, pp 14 – 17, February 1964.
- [29]. L. Dadda, “On Parallel Digital Multipliers,” Alta Frequenza, vol. 45, pp. 574 – 580, 1976.
- [30]. Xianyang Jiang, Peng Xiao, Meikang Qiu, Gaofeng Wang,“Performance Effects of pipeline architecture on a FPGA-based binary32 floating point multiplier”, Microprocessors and Microsystems, Volume 37, Issue 8, pp. 1183-1191, November 2013.
- [31]. Sertbaş, Ahmet, El-Abdallah Hani, and Fethullah Karabiber. "A fast multiplier hardware design for interval arithmetic." IU-Journal of Electrical & Electronics Engineering 6, no. 2 (2006): 169-174.