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Mathematical functions are generally classified into two groups. Functions such as logarithmic or trigonometric functions are called elementary functions, and functions such as sin(1/x), which are a combination of two or more elementary functions, are called combinatorial functions. Mathematical functions have many applications in digital devices, such as digital signal processing, image processing, and telecommunication systems. Although software computation of mathematical functions in digital systems has flexibility and convenience advantage, sometimes it does not keep up with the real-time requirements of modern digital systems. To solve this problem, various algorithms have been proposed to implement mathematical functions on hardware. Hardware implementations tend to have higher throughput compared to software implementations, but usually, they suffer in terms of accuracy. In this paper, we propose a novel method for calculating the elementary trigonometric functions using the CORDIC algorithm based on the dynamic microrotation generation technique. We implement our design on Spartan-6 FPGA. Results show our method outperforms similar works in terms of throughput and power consumption while exploiting less hardware.
Hardware Implementation, FPGA , CORDIC Algorithm, Trigonometric Functions
 T. Lang, E. Antelo. High-throughput CORDIC-based geometry operations for 3D computer graphics. IEEE Transactions on Computers. 54 (2005) 347-61.
 A. Shiri, G.K. Khosroshahi. An FPGA Implementation of Singular Value Decomposition. 2019 27th Iranian Conference on Electrical Engineering (ICEE). IEEE2019. pp. 416-22.
 Y.H. Hu. CORDIC-based VLSI architectures for digital signal processing. IEEE signal processing Magazine. 9 (1992) 16-35.
 C.-S. Peng, Y.-S. Chuang, K.-A. Wen. CORDIC-based architecture with channel state information for OFDM baseband receiver. IEEE Transactions on Consumer Electronics. 51 (2005) 403-12.
 S.-F. Hsiao, Y.H. Hu, T.-B. Juang, C.-H. Lee. Efficient VLSI implementations of fast multiplierless approximated DCT using parameterized hardware modules for silicon intellectual property design. IEEE Transactions on Circuits and Systems I: Regular Papers. 52 (2005) 1568-79.
 M. Terré, M. Bellanger. A systolic QRD-based algorithm for adaptive filtering and its implementation. 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE1993. pp. 373-6.
 J. Harrison, T. Kubaska, S. Story. The computation of transcendental functions on the IA-64 architecture. Intel Technology Journal. Citeseer1999.
 M.D. Ercegovac, T. Lang. Digital arithmetic. Elsevier2004.
 J.H. Mathews, K.D. Fink. Numerical methods using MATLAB. Pearson prentice hall Upper Saddle River, NJ2004.
 J. Volder. The CORDIC computing technique. Papers presented at the the March 3-5, 1959, western joint computer conference1959. pp. 257-61.
 E. Antelo, J. Villalba, J.D. Bruguera, E.L. Zapata. High performance rotation architectures based on the radix-4 CORDIC algorithm. IEEE Transactions on Computers. 46 (1997) 855-70.
 E. Deprettere, P. Dewilde, R. Udo. Pipelined CORDIC architectures for fast VLSI filtering and array processing. ICASSP'84 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE1984. pp. 250-3.
 Y.H. Hu, S. Naganathan. An angle recoding method for CORDIC algorithm implementation. IEEE Transactions on Computers. 42 (1993) 99-102.
 S. Aggarwal, P.K. Meher, K. Khare. Area-time efficient scaling-free CORDIC using generalized micro-rotation selection. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 20 (2011) 1542-6.
 P.K. Meher, S.Y. Park. CORDIC designs for fixed angle of rotation. IEEE transactions on very large scale integration (VLSI) systems. 21 (2012) 217-28.
 S. Wang, V. Piuri, E. Wartzlander. Hybrid CORDIC algorithms. IEEE Transactions on Computers. 46 (1997) 1202-7.
 S. Aggarwal, P.K. Meher, K. Khare. Scale-free hyperbolic CORDIC processor and its application to waveform generation. IEEE Transactions on Circuits and Systems I: Regular Papers. 60 (2012) 314-26.
 R. Shukla, K.C. Ray. Low latency hybrid CORDIC algorithm. IEEE Transactions on Computers. 63 (2013) 3066-78.
 L. Chen, J. Han, W. Liu, F. Lombardi. Algorithm and design of a fully parallel approximate coordinate rotation digital computer (CORDIC). IEEE Transactions on Multi-Scale Computing Systems. 3 (2017) 139-51.
 Y. Luo, Y. Wang, Y. Ha, Z. Wang, S. Chen, H. Pan. Generalized hyperbolic CORDIC and its logarithmic and exponential computation with arbitrary fixed base. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 27 (2019) 2156-69.
 Y. Luo, Y. Wang, H. Sun, Y. Zha, Z. Wang, H. Pan. CORDIC-based architecture for computing Nth root and its implementation. IEEE Transactions on Circuits and Systems I: Regular Papers. 65 (2018) 4183-95.
 H. Mahdavi, S. Timarchi. Improving Architectures of Binary Signed-Digit CORDIC With Generic/Specific Initial Angles. IEEE Transactions on Circuits and Systems I: Regular Papers. 67 (2020) 2297-304.
 T.K. Rodrigues, E.E. Swartzlander. Adaptive CORDIC: Using parallel angle recoding to accelerate rotations. IEEE Transactions on Computers. 59 (2010) 522-31.
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