부동소수점수 N차 제곱근 K차 골드스미스 알고리즘 = Floating Point Number N’th Root K’th Order Goldschmidt Algorithm

다국어 초록 (Multilingual Abstract)

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.

참고문헌 (Reference)

1 조경연, "오차 교정 K차 골드스미트 부동소수점 나눗셈" 한국정보통신학회 19 (19): 2341-2349, 2015

2 송인호, "디스플레이 상관 색온도에 따른 색 보정매트릭스를 이용한 3D 영상 재생" 한국멀티미디어학회 22 (22): 55-61, 2019

3 김성기, "가변 시간 뉴톤-랍손 부동소수점 역수 제곱근 계산기" 한국정보처리학회 12 (12): 413-420, 2005

4 김성기, "가변 시간 골드스미트 부동소수점 제곱근 계산기" 한국정보통신학회 9 (9): 188-198, 2005

5 S. Borkar, "The Future of Microprocessors" 54 (54): 67-77, 2011

6 Y. Li, "On the Improved Implementations and Performance Evaluation of Digit-by-Digit Integer Restoring and Nonrestoring Cube Root Algorithms" 1-5, 2016

7 P. D. Proinov, "On the Convergence of Halley’s Method for Multiple Polynomials Zeros" 12 (12): 555-572, 2015

8 F. Dubeau, "Nth Root Extraction : Double Iteration Process and Newtons’s Method" 91 (91): 191-198, 1998

9 F. Dubeau, "Newton’s Method and High-order Algorithm for the Nth Root Computation" 224 (224): 66-76, 2009

10 D. D. Sarma, "Measuring and Accuracy of ROM Reciprocal Tables" 43 (43): 932-930, 1994

11 IEEE, "IEEE Standard for Binary Floating-Point Arithmetic"

12 S. G. Chen, "Fast Computation of the Nth Root" 17 (17): 1423-1427, 1989

13 C. S. Yan, "Design and Implementation of a 64/32-bit Floatingpoint Division, Reciprocal, Square root, and Inverse Square root Unit" 1976-1979, 2006

14 S. F. Oberman, "Design Issues in Division and Other Floating Point Operations" 46 (46): 154-161, 1997

15 J. M. Gutierrez, "Calculus of Nth Roots and Third Order Iterative Methods" 47 (47): 2875-2880, 2001

16 Y. Luo, "CORDIC-Based Architecture for Computing Nth Root and Its Implementation" 65 (65): 4183-4195, 2018

17 P. Montuschi, "A Digit-by-Digit Algorithm for mth Root Extraction" 56 (56): 1696-1708, 2007