Title: A novel approach for computation of cosine function

Authors: Abul Hasnat; Santanu Halder; Azizul Hoque; Debotosh Bhattacharjee

Addresses: Government College of Engineering and Textile Technology, 4, Cantonment Road, Berhampore, West Bengal, PIN-742101, India ' Government College of Engineering and Leather Technology, Block – LB 11, Sector-III, Salt Lake, Kolkata-700106, India ' Sreegopal Banerjee College, Bagati Kantapukur Rd, Boropukur Area, Mogra, Amodghata, West Bengal, PIN-712503, India ' Department of Computer Science and Engineering, Jadavpur University, West Bengal, India

Abstract: Objective of trigonometric function approximation in digital systems are faster computation in less number of clock cycles, optimising hardware resources, accuracy in more number of bits, etc. This study proposes a novel method for cosine function computation and respective FPGA-based architecture. A triangle is presumably located in the first quadrant of a circle with unit radius whose one vertex is the centre, other two vertices touches the perimeter. Using the area of the triangle, it is observed that the y coordinate of the third vertex of the triangle is the sine value. The error is the difference between arch length and side length. Newton's interpolation method is used to formulate the error approximation function. This method is synthesised on Xilinx Spartan 3 xc3s200-5ft256 FPGA kit. The proposed method gives accuracy up to 14 bits or more in 96% cases in 11 clock cycles only at maximum speed of 89.977 MHz.

Keywords: transcendental functions; coordinate rotation digital computing; CORDIC; cosine; FPGA; numerical method; Newton's interpolation method; triangle; unit circle.

DOI: 10.1504/IJNP.2019.104257

International Journal of Nanoparticles, 2019 Vol.11 No.4, pp.265 - 282

Received: 15 Feb 2018
Accepted: 14 Oct 2018
Published online: 23 Dec 2019 *

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