• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2004.05b
• /
• pp.247-250
• /
• 2004

Goldschmidt 알고리즘에 의한 부동소수점 1.f2의 역수는 q=NK1K2....Kn (Ki=1+Aj, j=2i)이다. 본 논문에서는 N과 A 값을 1.f2의 값에 따라서 선정하고 Aj의 값이 유효자리수의 반이하 값을 가지면 연산을 종료하는 개선된 Goldschmidt 부동소수점 역수 알고리즘을 제안한다. 1.f2가 1.01012보다 작으면 N=2-1.f2, A=1.f2-1로 하며, 1.01012보다 크거나 같으면 N=2-0.lf2, A=1-0.lf2로 한다. 한편 Goldschmidt 알고리즘은 곱셈을 반복해서 수행하므로 계산 오류가 누적이 된다. 이러한 누적 오류를 감안하면 배정도실수 역수에서는 2-57, 단정도실수 역수에서는 2-28의 유효자리수까지 연산해야 한다. 따라서 Aj가 배정도실수 역수에서는 2-29, 단정도실수 역수에서는 2-14 보다 작아지면 연산을 종료한다. 본 논문에서 제안한 개선한 Goldschmidt 역수 알고리즘은 N=2-0.1f2, A=1-0.lf2로 계산하는 종래 알고리즘과 비교하여 곱셈 연산 회수가 배정도실수 역수는 22%, 단정도실수 역수는 29% 감소하였다. 본 논문의 연구 결과는 테이블을 사용하는 Goldschmidt 역수 알고리즘에 적용해서 연산 시간을 줄일 수 있다.

• Journal of Korea Multimedia Society
• /
• v.22 no.9
• /
• pp.1029-1035
• /
• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.19 no.10
• /
• pp.2341-2349
• /
• 2015

The commonly used Goldschmidt's floating-point divider algorithm performs two multiplications in one iteration. In this paper, a tentative error corrected K'th Goldschmidt's floating-point number divider algorithm which performs K times multiplications in one iteration is proposed. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation in single precision and double precision divider is derived from many reciprocal tables with varying sizes. In addition, an error correction algorithm, which consists of one multiplication and a decision, to get exact result in divider is proposed. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a divider unit. Also, it can be used to construct optimized approximate reciprocal tables.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.5
• /
• pp.3093-3099
• /
• 2014

Modern graphic processors, multimedia processors and audio processors mostly use floating-point number. Meanwhile, high-level language such as C and Java uses both single-precision and double precision floating-point number. In this paper, an algorithm which computes the reciprocal of double precision floating-point number using a 32 bit multiplier is proposed. It divides the mantissa of double precision floating-point number to upper part and lower part, and calculates the reciprocal of the upper part with Goldschmidt's algorithm, and computes the reciprocal of double precision floating-point number with calculated upper part reciprocal as the initial value is proposed. Since the number of multiplications performed by the proposed algorithm is dependent on the mantissa of floating-point number, the average number of multiplications per an operation is derived from some reciprocal tables with varying sizes.

• Proceedings of the Korean Society for Bio-Environment Control Conference
• /
• 1998.05a
• /
• pp.131-139
• /
• 1998

여름철 고온기를 지나는 하우스 밀감은 착색이 되기 전에 과육이 선숙되는데, 일반적으로 착색은 고온에 의해 지연된다(Goldschmidt, 1988). 소비자들은 충분히 착색되지 않고 녹색을 띤 밀감은 성숙이 안된 것으로 생각하고 있기 때문에 수확 후 에테폰 처리에 의해 착색을 촉진시키고 있으나(Jimenez-Cuesta 등, 1983) 과경부의 꼭지가 쉽게 건조되고 짙은 오렌지색으로 발색되지 않고 연한 노란 색으로 되어 상품성이 높지 못하다. (중략)

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.9 no.1
• /
• pp.188-198
• /
• 2005

The Goldschmidt iterative algorithm for finding a floating point square root calculated it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's square root algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To find the square root of a floating point number F, the algorithm repeats the following operations: $R_i=\frac{3-e_r-X_i}{2},\;X_{i+1}=X_i{\times}R^2_i,\;Y_{i+1}=Y_i{\times}R_i,\;i{\in}\{{0,1,2,{\ldots},n-1} }}'$with the initial value is $'\;X_0=Y_0=T^2{\times}F,\;T=\frac{1}{\sqrt {F}}+e_t\;'$. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than $'e_r=2^{-p}'$. The value of p is 28 for the single precision floating point, and 58 for the doubel precision floating point. Let $'X_i=1{\pm}e_i'$, there is $'\;X_{i+1}=1-e_{i+1},\;where\;'\;e_{i+1}<\frac{3e^2_i}{4}{\mp}\frac{e^3_i}{4}+4e_{r}'$. If '|X_i-1|<2^{\frac{-p+2}{2}}\;'$ is true, $'\;e_{i+1}<8e_r\;'$ is less than the smallest number which is representable by floating point number. So, $\sqrt{F}$ is approximate to $'\;\frac{Y_{i+1}}{T}\;'$. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal square root tables ($T=\frac{1}{\sqrt{F}}+e_i$) with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a square root unit. Also, it can be used to construct optimized approximate reciprocal square root tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.9 no.2
• /
• pp.380-389
• /
• 2005

The Goldschmidt iterative algorithm for a floating point divide calculates it by performing a fixed number of multiplications. In this paper, a variable latency Goldschmidt's divide algorithm is proposed, that performs multiplications a variable number of times until the error becomes smaller than a given value. To calculate a floating point divide '$\frac{N}{F}$', multifly '$T=\frac{1}{F}+e_t$' to the denominator and the nominator, then it becomes ’$\frac{TN}{TF}=\frac{N_0}{F_0}$'. And the algorithm repeats the following operations: ’$R_i=(2-e_r-F_i),\;N_{i+1}=N_i{\ast}R_i,\;F_{i+1}=F_i{\ast}R_i$, i$\in${0,1,...n-1}'. The bits to the right of p fractional bits in intermediate multiplication results are truncated, and this truncation error is less than ‘$e_r=2^{-p}$'. The value of p is 29 for the single precision floating point, and 59 for the double precision floating point. Let ’$F_i=1+e_i$', there is $F_{i+1}=1-e_{i+1},\;e_{i+1}',\;where\;e_{i+1}, If '$[F_i-1]<2^{\frac{-p+3}{2}}$ is true, ’$e_{i+1}<16e_r$' is less than the smallest number which is representable by floating point number. So, ‘$N_{i+1}$ is approximate to ‘$\frac{N}{F}$'. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal tables ($T=\frac{1}{F}+e_t$) with varying sizes. 1'he superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a divider. Also, it can be used to construct optimized approximate reciprocal tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc

• BMB Reports
• /
• v.37 no.5
• /
• pp.522-526
• /
• 2004

Prader-Willi (PWS) and Angelman (AS) are syndromes of developmental impairment that result from the loss of expression of imprinted genes in the paternal (PWS) or maternal (AS) 15q11-q13 chromosome. Diagnosis on a clinical basis is difficult in newborns and young infants; thus, a suitable molecular test capable of revealing chromosomal abnormalities is required. We used a variety of cytogenetic and molecular approaches, such as, chromosome G banding, fluorescent in situ hybridization, a DNA methylation test, and a set of chromosome 15 DNA polymorphisms to characterize a cohort of 27 PWS patients and 24 suspected AS patients. Molecular analysis enabled the reliable diagnosis of 14 PWS and 7 AS patients, and their classification into four groups: (A) 6 of these 14 PWS subjects (44%) had deletions of paternal 15q11-q13; (B) 4 of the 7 AS patients had deletions of maternal 15q11-q13; (C) one PWS patient (8%) had a maternal uniparental disomy (UPD) of chromosome 15; (D) the remaining reliably diagnoses of 7 PWS and 3 AS cases showed abnormal methylation patterns of 15q11-q13 chromosome, but none of the alterations shown by the above groups, although they may have harbored deletions undetected by the markers used. This study highlights the importance of using a combination of cytogenetic and molecular tests for a reliable diagnosis of PWS or AS, and for the identification of genetic alterations.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.35 no.4
• /
• pp.407-411
• /
• 2022

Bulk-sized PbTiO₃ (PT), which is widely known as a high-performance ferroelectric oxide but cannot be fabricated into a monolithic ceramic due to its high c/a ratio, was successfully prepared with a high tetragonality by partially substituting Ni ions for Pb ions using a solid-state reaction method. We found that Ni-doped PT was well-fabricated as a bulk monolith with a significant c/a ratio of ~1.06. X-ray diffraction on as-sintered and crushed samples revealed that NiTiO₃ secondary phase was present at the doping level of more than 2 at.%. Scanning electron microscopic study showed that NiTiO₃ secondary phase grew on the surface of PT specimens regardless of the doping level possibly due to the evaporation of Pb during sintering. We demonstrated that an unconventional introduction of Ni ions into A-site plays a key role on the fabrication of bulk PT, though how Ni ion functions should be studied further. We expect that this study contributes to a further development of displacive ferroelectric oxides with a high c/a ratio.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.35 no.5
• /
• pp.516-521
• /
• 2022

We investigated the microstructure, crystal structure, dielectric, and elecromechanical strain properties of lead-free BaTiO₃ (BT)-modified (Bi_1/2Na_1/2)TiO₃-SrTiO₃ (BNT-ST) piezoelectric ceramics. Samples were prepared by a conventional ceramic processing route. Temperature dependent dielectric properties confirmed that a phase transition from a nonergodic relaxor to an ergodic relaxor was induced when the BT concentration reached 1.5 mol%, interestingly, where the average grain size reached a maximum value of 4.5 ㎛. At the same time, enhanced electromechanical strain (S_max/E_max = 600 pm/V) was obtained. It is suggested that the induced ferroelectric-relaxor phase transition by the BT modification is responsible for the enhancement of electromechanical strain in 1.5 mol% BT-modified BNT-ST ceramics.