Abstract
Arithmetic accelerators are always in demand for fast computations and logic operations. Here, posit arithmetic plays an important role; it outperforms the traditional IEEE-754 floating-point in terms of accuracy and dynamic range. This paper proposes efficient sequential architectures for the posit adder/subtractor and multiplier that work according to the desired bit size of operands. Here, 32-bit architectures with different exponent sizes (ES) have been designed with a control unit. FPGA implementations of these architectures have been performed on the Xilinx Virtex-7 xc7vx330t-3ffg1157 and the Zynq UltraScale + MPSoC ZCU102 device. In comparison with the existing work, it is observed that the datapath delay is lowered by 64.64% for the 32-bit adder and 52.66% for the 32-bit multiplier on the Xilinx Virtex-7 FPGA device. Furthermore, the area-delay (AD) product is reduced by 52.69% and 69.30% for the 32-bit posit adder and multiplier, respectively. In addition, the proposed design has reduced dynamic power than the existing architectures.
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References
IEEE standard for floating-point arithmetic, IEEE Std 754–2019 (Revision of IEEE 754–2008), pp. 1–84 (2019)
van Dam, L.: Enabling high performance posit arithmetic applications using hardware acceleration (2018)
Gustafson, J.L., Yonemoto, I.T.: Beating floating point at its own game: posit arithmetic. Supercomput. Front. Innov. 4(2), 71–86 (2017)
Sravya, A.M., Swetha, N., Panigrahy, A.K.: Hardware posit numeration system primarily based on arithmetic operations. In: 2022 3rd International Conference for Emerging Technology (INCET), pp. 1–8 (2022)
Gustafson, J.L.: The End of Error: Unum Computing. Chapman and Hall/CRC, Boca Raton (2017)
Buoncristiani, N., Shah, S., Donofrio, D., Shalf, J.: Evaluating the numerical stability of posit arithmetic. In: 2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS), (New Orleans, LA, USA, USA), pp. 612–621. IEEE, 18–22 May 2020
Mallasén, D., Murillo, R., Del Barrio, A.A., Botella, G., Piñuel, L., Prieto-Matias, M.: PERCIVAL: open-source posit RISC-V core with quire capability. IEEE Trans. Emerg. Top. Comput. 10(3), 1241–1252 (2022)
van Dam, L., Peltenburg, J., Al-Ars, Z., Hofstee, H.P.: An accelerator for posit arithmetic targeting posit level 1 blas routines and pair-hmm. In: Proceedings of the Conference for Next Generation Arithmetic 2019, CoNGA 2019, (New York, NY, USA), Association for Computing Machinery (2019)
Jaiswal, M.K., So, H.K.-H.: Architecture generator for type-3 unum posit adder/subtractor. In: 2018 IEEE International Symposium on Circuits and Systems (ISCAS), (Florence, Italy), pp. 1–5. IEEE, 27–13 May 2018
Chaurasiya, R., et al.: Parameterized posit arithmetic hardware generator. In: 2018 IEEE 36th International Conference on Computer Design (ICCD), (Orlando, FL, USA, USA), pp. 334–341. IEEE, 7–10 October 2018
Barua, H.B., Mondal, K.C.: Approximate computing: a survey of recent trends-bringing greenness to computing and communication. J. Inst. Eng. (India) Ser. B 100(6), 619–626 (2019)
MartÃn-Hernando, Y., RodrÃguez-Ramos, L.F., Garcia-Talavera, M.R.: Fixed-point vs. floating-point arithmetic comparison for adaptive optics real-time control computation. In: Adaptive Optics Systems, vol. 7015, p. 70152Z (2008). International Society for Optics and Photonics
Sasidharan, A., Nagarajan, P.: VHDL implementation of IEEE 754 floating point unit. In: International Conference on Information Communication and Embedded Systems (ICICES2014), pp. 1–5 (2014)
Shekhawat, D., Jangir, A., Pandey, J.G.: A hardware generator for posit arithmetic and its FPGA prototyping. In: 2021 25th International Symposium on VLSI Design and Test (VDAT), pp. 1–6. IEEE (2021)
Jaiswal, M.K., So, H.K.-H.: PACoGen: a hardware posit arithmetic core generator. IEEE Access 7, 74586–74601 (2019)
Jaiswal, M.K., So, H.K.H.: Universal number posit arithmetic generator on FPGA. In: 2018 Design, Automation & Test in Europe Conference & Exhibition (DATE), (Dresden, Germany), pp. 1159–1162. IEEE, 19–23 March 2018
Kahan, W.: IEEE standard 754 for binary floating-point arithmetic. Lect. Notes Status IEEE 754(94720–1776), 11 (1996)
Jaiswal, M.K., So, H.K.-H.: Architecture generator for type-3 Unum posit adder/subtractor. In: 2018 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2018)
Gustafson, J.L., Yonemoto, I.T.: Beating floating point at its own game: posit arithmetic. Supercomput. Front. Innov. Int. J. 4, 71–86 (2017)
Hou, J., Zhu, Y., Du, S., Song, S.: Enhancing accuracy and dynamic range of scientific data analytics by implementing posit arithmetic on FPGA. J. Signal Process. Syst. 91, 1137–1148 (2019)
Xiao, F., Liang, F., Wu, B., Liang, J., Cheng, S., Zhang, G.: Posit arithmetic hardware implementations with the minimum cost divider and squareroot. Electronics 9(10), 1622 (2020)
MalÃk, P.: High throughput floating-point dividers implemented in FPGA. In: 2015 IEEE 18th International Symposium on Design and Diagnostics of Electronic Circuits & Systems, pp. 291–294 (2015)
Mallasén, D., Murillo, R., Del Barrio, A.A., Botella, G., Piñuel, L., Prieto-Matias, M.: Customizing the CVA6 RISC-V core to integrate posit and quire instructions. In: 2022 37th Conference on Design of Circuits and Integrated Circuits (DCIS), pp. 01–06. IEEE (2022)
Cococcioni, M., Rossi, F., Ruffaldi, E., Saponara, S.: A lightweight posit processing unit for RISC-V processors in deep neural network applications. IEEE Trans. Emerg. Top. Comput. 10(4), 1898–1908 (2022)
Sharma, N.N., et al.: CLARINET: a quire-enabled RISC-V-based framework for posit arithmetic empiricism. J. Syst. Archit. 135, 102801 (2023)
Lafage, V.: Revisiting what every computer scientist should know about floating-point arithmetic, arXiv preprint arXiv:2012.02492 (2020)
Cococcioni, M., Ruffaldi, E., Saponara, S.: Exploiting posit arithmetic for deep neural networks in autonomous driving applications. In: 2018 International Conference of Electrical and Electronic Technologies for Automotive, pp. 1–6. IEEE (2018)
Gustafson, J.L.: Posit arithmetic. Mathematica Notebook describing the posit number system, vol. 30 (2017)
Acknowledgement
This work has been carried out at Integrated Circuits and Systems Group, CSIR - Central Electronics Engineering Research Institute (CEERI), Pilani, Rajasthan, India. We extend our sincere gratitude to the Director, CSIR-CEERI, Pilani, India, for providing the required resources to carry out this research work.
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Shekhawat, D., Gandhi, J., Santosh, M., Pandey, J.G. (2023). PHAc: Posit Hardware Accelerator for Efficient Arithmetic Logic Operations. In: Gustafson, J., Leong, S.H., Michalewicz, M. (eds) Next Generation Arithmetic. CoNGA 2023. Lecture Notes in Computer Science, vol 13851. Springer, Cham. https://doi.org/10.1007/978-3-031-32180-1_6
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