• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.46 no.3
• /
• pp.20-25
• /
• 2009

We propose hardware architecture of floating-point square root and inverse square root arithmetic units using lookup tables. They are used for lighting engines and shader processor for 3D graphic processing. The architecture is based on Taylor series expansion and consists of lookup tables and correction units so that the size of look-up tables are reduced. It can be applied to 32 bit floating point formats of IEEE-754 and reduced 24 bit floating point formats. The square root and inverse square root arithmetic units for 32 bit and 24 bit floating format number are designed as the proposed architecture. They can operation in a single cycle, and satisfy the precision of $10^{-5}$ required by OpenGL 1.x ES. They are designed using Verilog-HDL and the RTL codes are verified using an FPGA.

• Communications of the Korean Mathematical Society
• /
• v.29 no.3
• /
• pp.489-496
• /
• 2014

We drive a closed-form expression for the price of a European quanto call option in the double square root stochastic volatility model.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.65 no.6
• /
• pp.1019-1025
• /
• 2016

This paper proposes a parallel reduced-order square-root unscented Kalman filter for state estimation of a sensorless permanent-magnet synchronous motor. The appearance of an unscented Kalman filter is caused by the linearization process error between a real system and classical Kalman model. The unscented transformation can make a more accurate Kalman model. However, the complexity is its main drawback. This paper investigates the design and implementation of the proposed filter with Potter and Carlson square-root form. The proposed parallel reduced-order square-root unscented Kalman filter reduces memory and code size, and improves numerical computation. And the performance is not significantly different from the unscented Kalman filter. The experimentation is performed for the verification of the proposed filter.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1523-1537
• /
• 2022

We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.37A no.12
• /
• pp.1031-1037
• /
• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• Kyungpook Mathematical Journal
• /
• v.52 no.3
• /
• pp.347-357
• /
• 2012

When Newton's method, or Halley's method is used to approximate the pth root of 1-z, a sequence of rational functions is obtained. In this paper, a beautiful formula for these rational functions is proved in the square root case, using an interesting link to Chebyshev's polynomials. It allows the determination of the sign of the coefficients of the power series expansion of these rational functions. This answers positively the square root case of a proposed conjecture by Guo(2010).

• East Asian mathematical journal
• /
• v.29 no.5
• /
• pp.511-519
• /
• 2013

There are various methods for evaluating a matrix square root, which is a solvent of the quadratic matrix equation $X^2-A=0$. We consider new iterative methods for solving matrix square roots of M-matrices. Particulary we show that the relaxed binomial iteration is more efficient than Newton-Schulz iteration in some cases. And we construct a formula to find relaxation coefficients through statistical experiments.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.38A no.9
• /
• pp.759-764
• /
• 2013

We present a square root algorithm in $F_q$ which generalizes Atkin's square root algorithm [9] for finite field $F_q$ of q elements where $q{\equiv}5$ (mod 8) and Kong et al.'s algorithm [11] for the case $q{\equiv}9$ (mod 16). Our algorithm precomputes ${\xi}$ a primitive $2^s$-th root of unity where s is the largest positive integer satisfying $2^s|q-1$, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favorably compared with the algorithms of Atkin, M$\ddot{u}$ller and Kong et al.

• Food Science and Preservation
• /
• v.24 no.6
• /
• pp.778-785
• /
• 2017

This study was conducted to develop a predictive model for the growth of Escherichia coli strain RC-4-D isolated from red kohlrabi sprout seeds. We collected E. coli kinetic growth data during red kohlrabi seed sprouting under isothermal conditions (10, 15, 20, 25, and $30^{\circ}C$). Baranyi model was used as a primary order model for growth data. The maximum growth rate (${\mu}max$) and lag-phase duration (LPD) for each temperature (except for $10^{\circ}C$ LPD) were determined. Three kinds of secondary models (suboptimal Ratkowsky square-root, Huang model, and Arrhenius-type model) were compared to elucidate the influence of temperature on E. coli growth rate. The model performance measures for three secondary models showed that the suboptimal Huang square-root model was more suitable in the accuracy (1.223) and the suboptimal Ratkowsky square-root model was less in the bias (0.999), respectively. Among three secondary order model used in this study, the suboptimal Ratkowsky square-root model showed best fit for the secondary model for describing the effect of temperature. This model can be utilized to predict E. coli behavior in red kohlrabi sprout production and to conduct microbial risk assessments.

• Proceedings of the IEEK Conference
• /
• 2001.06b
• /
• pp.365-368
• /
• 2001

This paper described a design and implementation of the division/square-root for a redundant floating point binary number using high-speed quotient selector. This division/square-root used the method of a redundant binary addition with 25MHz clock speed. The addition of two numbers can be performed in a constant time independent of the word length since carry propagation can be eliminated. We have developed a 16-bit VLSI circuit for division and square-root operations used extensively in each iterative step. It peformed the division and square-root by a redundant binary addition to the shifted binary number every 16 cycles. Also the circuit uses the nonrestoring method to obtain a quotient. The quotient selection logic used a leading three digits of partial remainders in order to be implemented in a simple circuit. As a result, the performance of the proposed scheme is further enhanced in the speed of operation process by applying new quotient selection addition logic which can be parallelly process the quotient decision field. It showed the speed-up of 13% faster than previously presented schemes used the same algorithms.