Generalized Hyperbolic CORDIC and Its Logarithmic and Exponential Computation With Arbitrary Fixed Base

@article{Luo2019GeneralizedHC,
  title={Generalized Hyperbolic CORDIC and Its Logarithmic and Exponential Computation With Arbitrary Fixed Base},
  author={Yuanyong Luo and Yuxuan Wang and Yajun Ha and Zhongfeng Wang and Siyuan Chen and Hongbing Pan},
  journal={IEEE Transactions on Very Large Scale Integration (VLSI) Systems},
  year={2019},
  volume={27},
  pages={2156-2169}
}
  • Yuanyong LuoYuxuan Wang H. Pan
  • Published 18 June 2019
  • Computer Science, Mathematics
  • IEEE Transactions on Very Large Scale Integration (VLSI) Systems
This paper proposes a generalized hyperbolic COordinate Rotation Digital Computer (GH CORDIC) to directly compute logarithms and exponentials with an arbitrary fixed base. [] Key Method This new parameter can be used to specify the base with respect to the computation of logarithms and exponentials. As a result, the constant multiplier is no longer needed to convert base $e$ (Euler’s number) to other values because the base of GH CORDIC is adjustable.

Hyperbolic CORDIC-Based Architecture for Computing Logarithm and Its Implementation

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GH CORDIC-Based Architecture for Computing $N$ th Root of Single-Precision Floating-Point Number

Hardware implementation for computing arbitrary roots of a single-precision floating-point number based on Generalized Hyperbolic COordinate Rotation Digital Computer (GH CORDIC) algorithm and simulation results indicate that the proposed method is capable of calculating the LaTeX root with a relative error of 10−7 approximately.

CORDIC as a Switched Nonlinear System

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  • Computer Science
    Circuits Syst. Signal Process.
  • 2020
A control perspective to the COordinate Rotation DIgital Computer is given by describing it as a switched autonomous nonlinear discrete system and a novel architecture is developed for reducing latency without any compromise on the metrics.

CORDIC as a Switched Nonlinear System

  • L. Vachhani
  • Computer Science
    Circuits, Systems, and Signal Processing
  • 2019
A control perspective to the COordinate Rotation DIgital Computer is given by describing it as a switched autonomous nonlinear discrete system and a novel architecture is developed for reducing latency without any compromise on the metrics.

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A Novel Implementation of CORDIC Algorithm Based on Dynamic Microrotation Generation

This paper proposes a novel method for calculating the elementary trigonometric functions using the CORDIC algorithm based on the dynamic microrotation generation technique that outperforms similar works in terms of throughput and power consumption while exploiting less hardware.

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References

SHOWING 1-10 OF 39 REFERENCES

A fixed-point implementation of the expanded hyperbolic CORDIC algorithm

A fixed-point implementation of the hyperbolic CORDIC algorithm with the expansion scheme proposed by Hu et al. (1991) is presented and was targeted to a Stratix FPGA.

The CORDIC Trigonometric Computing Technique

The trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.

50 Years of CORDIC: Algorithms, Architectures, and Applications

A brief overview of the key developments in the CORDIC algorithms and architectures along with their potential and upcoming applications is presented.

Scale-Free Hyperbolic CORDIC Processor and Its Application to Waveform Generation

A pipeline hyperbolic CORDIC processor to implement a direct digital synthesizer (DDS) and an efficient arbitrary waveform generator (AWG), where a pseudo-random number generator modulates the linear increments of phase to produce random phase-modulated waveform.

Algorithm and architecture for logarithm, exponential, and powering computation

A sequential implementation of the algorithm, with a control unit which allows the independent computation of logarithm and exponential, is proposed and the execution times and hardware requirements are estimated for single and double-precision floating-point computations.

An Optimized Logarithmic Converter With Equal Distribution of Relative Errors

This work presents a relative error equal distribution (REED) algorithm that performs the nonuniform piecewise linear interpolation of logarithm and achieves over 70% reduction of average relative errors for the benchmark graphics application, compared to both the state-of-the-art uniform and non uniform methods.

Accurate Fixed-Point Logarithmic Converter

A rigorous technique that allows computing the optimal segmentation and the coefficients values for a prescribed precision is described in this brief, and allows obtaining a sensibly lower error, for the same number of nonuniform segments, compared with previously published results.

Improved Decimal Floating-Point Logarithmic Converter Based on Selection by Rounding

The delay estimation results of the proposed architecture show that its latency is close to that of the binary radix-16 logarithmic converter, and that it has a significant decrease on latency compared with a recently published high performance CORDIC implementation.

A unified algorithm for elementary functions

This paper describes a single unified algorithm for the calculation of elementary functions including multiplication, division, sin, cos, tan, arctan, sinh, cosh, tanh, arctanh, In, exp and

Accelerating hardware Gaussian random number generation using Ziggurat and CORDIC algorithms

An effective method for parallel accessing the coefficients required by the Ziggurat algorithm is presented and the implementation of the proposed architecture on Xilinx's Kintex-7 KC705 device resulted in a throughput of 689.2 million samples per second.