Pipelined implementation of fixed point square root in FPGA using modified non-restoring algorithm

Square root is one of the fundamental arithmetic operations in signal and image processing algorithms. This article presents a novel pipelined architecture to implement N-bits fixed point square root in FPGA using non-restoring algorithm. Pipelining hazards were avoided by modifying the non-restoring algorithm resulting in a 30% improved latency time. Furthermore, the proposed architecture is flexible and can be modified as per the need of an application. The performance of the proposed system, as a function of execution time and power consumption per operation, has been compared with other floating point pipelined implementations. It is demonstrated that the proposed system is ∼ 2 times efficient compared to its counterparts.

[1]  Ray Andraka,et al.  A survey of CORDIC algorithms for FPGA based computers , 1998, FPGA '98.

[2]  Theodore S. Rappaport,et al.  Wireless communications - principles and practice , 1996 .

[3]  Peter M. Athanas,et al.  Quantitative analysis of floating point arithmetic on FPGA based custom computing machines , 1995, Proceedings IEEE Symposium on FPGAs for Custom Computing Machines.

[4]  José Luis Lázaro,et al.  Implementation in Fpgas of Jacobi Method to Solve the Eigenvalue and Eigenvector Problem , 2006, 2006 International Conference on Field Programmable Logic and Applications.

[5]  Alan H. Karp,et al.  High-precision division and square root , 1997, TOMS.

[6]  Yamin Li,et al.  Implementation of single precision floating point square root on FPGAs , 1997, Proceedings. The 5th Annual IEEE Symposium on Field-Programmable Custom Computing Machines Cat. No.97TB100186).

[7]  I. Sajid,et al.  Design of High Performance FPGA Based Face Recognition System , 2008 .

[8]  Brent E. Nelson,et al.  Tradeoffs of designing floating-point division and square root on Virtex FPGAs , 2003, 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 2003. FCCM 2003..

[9]  Li Shang,et al.  Dynamic power consumption in Virtex™-II FPGA family , 2002, FPGA '02.

[10]  Miriam Leeser,et al.  Area and performance tradeoffs in floating-point divide and square-root implementations , 1996, CSUR.

[11]  James M. Ortega,et al.  An error analysis of Householder's method for the symmetric eigenvalue problem , 1962 .

[12]  R. Benjamin,et al.  The role and scope of digital signal processing in communications systems , 1978 .

[13]  Jan-Ray Liao,et al.  Real-time image reconstruction for spiral MRI using fixed-point calculation , 2000, IEEE Transactions on Medical Imaging.

[14]  J. Miller Numerical Analysis , 1966, Nature.

[15]  Todd A. Cook,et al.  Implementation of IEEE single precision floating point addition and multiplication on FPGAs , 1996, 1996 Proceedings IEEE Symposium on FPGAs for Custom Computing Machines.

[16]  A. Ejnioui,et al.  Design and implementation of double precision floating point division and square root on FPGAs , 2006, 2006 IEEE Aerospace Conference.

[17]  J. H. Wilkinson Error Analysis of Eigenvalue Techniques Based on Orthogonal Transformations , 1962 .

[18]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .