Low-Latency Hardware Implementation of High-Precision Hyperbolic Functions Sinhx and Coshx Based on Improved CORDIC Algorithm

Abstract

CORDIC algorithm is used for low-cost hardware implementation to calculate transcendental functions. This paper proposes a low-latency high-precision architecture for the computation of hyperbolic functions sinhx and coshx based on an improved CORDIC algorithm, that is, the QH-CORDIC. The principle, structure, and range of convergence of the QH-CORDIC are discussed, and the hardware circuit architecture of functions sinhx and coshx using the QH-CORDIC is plotted in this paper. The proposed architecture is implemented using an FPGA device, showing that it has 75% and 50% latency overhead over the two latest prior works. In the synthesis using TSMC 65 nm standard cell library, ASIC implementation results show that the proposed architecture is also superior to the two latest prior works in terms of total time (latency × period), ATP (area × total time), total energy (power × total time), energy efficiency (total energy/efficient bits), and area efficiency (efficient bits/area/total time). Comparison of related works indicates that it is much more favorable for the proposed architecture to perform high-precision floating-point computations on functions sinhx and coshx than the LUT method, stochastic computing, and other CORDIC algorithms.

Digital Fixed-Point Low Powered Area Efficient Function Estimation for Implantable Devices

“…It should be noted that constraining the operational range of the input can also reduce latency such as in [23], which incorporate a fully non-iterative implementation by constraining the input to [0, π 12 ], rather than [0, π 2 ] and can be exploited for a very specific range of applications. Further FPGA implementations of CORDICs can be seen in [11], where the authors build a high precision floating point, lowlatency hyperbolic function estimator which uses no LUTs and claim better performance than stochastic computing and LUT methods. [24], build a low latency CORDIC using parallel techniques.…”

“…CORDIC is a hardware friendly method for the implementation of functions and its roots date back as far as 1956. The CORDIC can calculate a wide range of functions, including trigonometric functions, by taking a vector v i and rotating it in small positive or negative increments in a circular, linear or hyperbolic coordinate system [11]. The CORDIC suffers from several key downfalls, firstly CORDIC is an iterative process leading to latency issues, furthermore it requires large look-up-tables in order to store relative phase angles.…”

High-Throughput Low Power Area Efficient 17-bit 2’s Complement Multilayer Perceptron Components and Architecture for on-Chip Machine Learning in Implantable Devices

“…CORDIC is a hardware friendly method for the implementation of functions and its roots date back as far as 1956. The CORDIC can calculate a wide range of functions, including trigonometric functions, by taking a vector v i and rotating it in small positive or negative increments in a circular, linear or hyperbolic coordinate system [34].The CORDIC suffers from several key downfalls, firstly CORDIC is an iterative process leading to latency issues, furthermore it requires large look-up-tables in order to store relative phase angles. Other methods include the calculation of functions using Taylor's expansion (TE) which consists of calculating an infinite sum of a terms derivatives for a given sample [35], however suffer from complex divisions and large exponential values creating a heavy dependence on multipliers.…”

A Low-Latency RDP-CORDIC Algorithm for Real-Time Signal Processing of Edge Computing Devices in Smart Grid Cyber-Physical Systems

“…It can implement many complex functions and mathematical problems with simple addition, subtraction, and shift operations. Table 1 lists some applications of the CORDIC algorithm, including trigonometric functions [ 20 ], hyperbolic functions [ 21 ], FFT [ 22 ] and singular value decomposition [ 23 ]. Nonetheless, the computational speed of the conventional CORDIC algorithm is limited by the number of iterations, i.e., the more iterations of the CORDIC algorithm, the higher the computational accuracy and the longer the time delay.…”