# EFFICIENT SERIAL FLOATING-POINT CONSTANT DIVIDER STRUCTURE OF THE FORM 2P±1

### Karthik Mahesh Varadarajan

#### Abstract

Implementation specific computation modules hold the key to the success of fast DSP and Embedded systems. Exponential encoders, dedicated multipliers, barrel shifters and accumulators are common units available on DSPs. The family of constant divider circuits of the form 2p±1, which are useful for image processing, statistical processing like histograms etc., is the specific focus of this paper. This family is largely dominated by the Residue Number System (RNS), Petry and Srinivasan algorithms and the Shuo-Yen Robert-Li algorithm. While these algorithms offer various trade-offs in terms of accuracy, memory footprint, power consumption and timing behavior, none of these methods are suited for processing serialized inputs, dividend inputs with apriori unknown bit length and the circuits have to be replaced with change in input bit length. The circuit size also grows enormously for large input lengths along with a reduction in accuracy. These methods are suited only for integer division and are unsuited for extension to floating/fixed point division. In this paper a novel constant divider algorithm is offered, which overcomes the above mentioned limitations while handling arbitrary length, serial/ parallel data and producing full-precision, full-accuracy, floating point capable results with constant circuit requirements and comparable timing to state of the art methods.

#### References

- A. Th. Schwarzbacher, M. Brutscheck, O. Schwingel, J. B. Foley, 'Constant Divider Structures of the Form 2n ±178, pp. 368-375, Irish Signals And Systems Conference, 2000.
- P. Srinivasan, F. E. Petry, 'Constant-Division Algorithms', IEEE Proc. Computers and Digital Techniques, Vol. 141, No. 6, 2007 (1994).
- A. Th. Schwarzbacher, P. A. Comiskey and J. B. Foley, 'Reduction of the power consumption at the algorithmic level of CMOS circuits', Electronic Systems and Devices Conference, pp. 5-8, June 1998.
- B. Al-Besher, A. Bouridane, A. S. Ashur, 'An RNS-based Division Architecture for Constant Divisors of the Form 2n +1 and 2n-178, Irish Signals & Systems Conference, 1997.
- S. Y. R. Li, 'Fast Constant Division Routines,78 IEEE Transactions on Computers, Vol. C-34, No. 9, September 1985.
- F. E. Petry, P. Srinivasan, 'Division Techniques for Integers of the Form 2n+1 and 2n-178, Int. J. Electronics, Vol. 74, No. 5, 1993.
- R. L. Sites, 'Serial Binary Division by Ten', IEEE Transactions on Computers, vol. 23, no. 12, pp. 1299- 1301, 1974.
- Artzy, E., Hinds, J. A., Saal, H. J., 'A fast division technique for constant divisors', Comm. ACM, February 1976, 19, (Z), pp. 98-101.
- C. Y. Guei, Y. X. Dong, W. B. Shan, 'A fast division technique for constant divisors 2m (2n +/- 1)78, Proceedings of the 1st International Conference on Computers and Applications, 1985, pp. 715-718.
- Johannes, J., Pegden, C., Petry, F., 'Decimal shifting for an exact floating point representation', Computer and Electrical Engineering, 1980.7, (3). pp. 149-155.
- Petry, F. E., 'Two's complement extension of a parallel binary division by ten', Electronics Letters, September 1983, 19, (18), pp. 718-720.

#### Paper Citation

#### in Harvard Style

Varadarajan K. (2011). **EFFICIENT SERIAL FLOATING-POINT CONSTANT DIVIDER STRUCTURE OF THE FORM 2P±1** . In *Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,* ISBN 978-989-8425-48-5, pages 485-490. DOI: 10.5220/0003402904850490

#### in Bibtex Style

@conference{peccs11,

author={Karthik Mahesh Varadarajan},

title={EFFICIENT SERIAL FLOATING-POINT CONSTANT DIVIDER STRUCTURE OF THE FORM 2P±1},

booktitle={Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,},

year={2011},

pages={485-490},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003402904850490},

isbn={978-989-8425-48-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems - Volume 1: PECCS,

TI - EFFICIENT SERIAL FLOATING-POINT CONSTANT DIVIDER STRUCTURE OF THE FORM 2P±1

SN - 978-989-8425-48-5

AU - Varadarajan K.

PY - 2011

SP - 485

EP - 490

DO - 10.5220/0003402904850490