Low-Complexity High-Precision Method and Architecture for Computing the Logarithm of Complex Numbers

Chen, Hui; Zong-guang, YU; Yong-gang, Zhang; Lu, Zhonghai; Fu, Yuxiang; Li, Li

doi:10.1109/tcsi.2021.3081517

Cited by 5 publications

(1 citation statement)

References 26 publications

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“…The CORDIC algorithm was first proposed in 1959 by E. Volder for computing trigonometric functions, multiplication and division [11,12]. To expand the usage areas, the CORDIC algorithm is applied in the computation of logarithms, exponentials, square roots, arbitrary Nth root, complex operations [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In the implementation of the CORDIC algorithm, the type of computation (addition or subtraction) in the iteration is determined by the rotation direction.…”

Section: Introductionmentioning

confidence: 99%

An optimized hardware implementation of the CORDIC algorithm

Lyu

Wang

et al. 2022

IEICE Electron. Express

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In this paper, we propose a software-based simulator and an optimized hardware implementation of the CORDIC algorithm. The number of iterations and the bit width are selected by their relationship calculated by the simulator to satisfy precision requirement. In the proposed hardware implementation, the addition and subtraction operations share the hardware resources. The two's complement is calculated in two steps: inverting and adding one. The adding one operation is integrated in the addition component of the iteration. In addition, a 3:2 compressor is used to reduce the number of adders, and a carry look-ahead adder is used to reduce the critical path. The synthesized results show that when compared with state-of-the-art designs, our method reduces the area by 53.79% and the delay by 58.97% while maintaining the same precision.

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Section: Introductionmentioning

confidence: 99%

An optimized hardware implementation of the CORDIC algorithm

Lyu

Wang

et al. 2022

IEICE Electron. Express

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Efficient Square Root Computation–An Analysis

Prasanna

Tejeswini

Keerthana

et al. 2022

Lecture Notes in Electrical Engineering

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Digital design of a spatial-pow-STDP learning block with high accuracy utilizing pow CORDIC for large-scale image classifier spatiotemporal SNN

Bahrami,

Nazari

2024

Sci Rep

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The paramount concern of highly accurate energy-efficient computing in machines with significant cognitive capabilities aims to enhance the accuracy and efficiency of bio-inspired Spiking Neural Networks (SNNs). This paper addresses this main objective by introducing a novel spatial power spike-timing-dependent plasticity (Spatial-Pow-STDP) learning rule as a digital block with high accuracy in a bio-inspired SNN model. Motivated by the demand for precise and accelerated computation that reduces high-cost resources in neural network applications, this paper presents a methodology based on COordinate Rotation DIgital Computer (CORDIC) definitions. The proposed designs of CORDIC algorithms for exponential (Exp CORDIC), natural logarithm (Ln CORDIC), and arbitrary power function (Pow CORDIC) are meticulously detailed and evaluated to ensure optimal acceleration and accuracy, which respectively show average errors near 10–9, 10–6, and 10–5 with 4, 4, and 6 iterations. The engineered architectures for the Exp, Ln, and Pow CORDIC implementations are illustrated and assessed, showcasing the efficiency achieved through high frequency, leading to the introduction of a Spatial-Pow-STDP learning block design based on Pow CORDIC that facilitates efficient and accurate hardware computation with 6.93 × 10–3 average error with 9 iterations. The proposed learning mechanism integrates this structure into a large-scale spatiotemporal SNN consisting of three layers with reduced hyper-parameters, enabling unsupervised training in an event-based paradigm using excitatory and inhibitory synapses. As a result, the application of the developed methodology and equations in the computational SNN model for image classification reveals superior accuracy and convergence speed compared to existing spiking networks by achieving up to 97.5%, 97.6%, 93.4%, and 93% accuracy, respectively, when trained on the MNIST, EMNIST digits, EMNIST letters, and CIFAR10 datasets with 6, 2, 2, and 6 training epochs.

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Low-Complexity High-Precision Method and Architecture for Computing the Logarithm of Complex Numbers

Cited by 5 publications

References 26 publications

An optimized hardware implementation of the CORDIC algorithm

An optimized hardware implementation of the CORDIC algorithm

Efficient Square Root Computation–An Analysis

Digital design of a spatial-pow-STDP learning block with high accuracy utilizing pow CORDIC for large-scale image classifier spatiotemporal SNN

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