Finite Precision Rational Arithmetic: An Arithmetic Unit

P. Kornerup; D.W. Matula

doi:10.1109/TC.1983.1676239

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1983
Issue No. 4 - April
Abstract - Finite Precision Rational Arithmetic: An Arithmetic Unit

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Finite Precision Rational Arithmetic: An Arithmetic Unit (PDF)

April 1983 (vol. 32 no. 4)

pp. 378-388

	ASCII Text	x
	P. Kornerup, D.W. Matula, "Finite Precision Rational Arithmetic: An Arithmetic Unit," IEEE Transactions on Computers, vol. 32, no. 4, pp. 378-388, April, 1983.

	BibTex	x
	@article{ 10.1109/TC.1983.1676239, author = {P. Kornerup and D.W. Matula}, title = {Finite Precision Rational Arithmetic: An Arithmetic Unit}, journal ={IEEE Transactions on Computers}, volume = {32}, number = {4}, issn = {0018-9340}, year = {1983}, pages = {378-388}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1983.1676239}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }

	RefWorks Procite/RefMan/Endnote	x
	TY - JOUR JO - IEEE Transactions on Computers TI - Finite Precision Rational Arithmetic: An Arithmetic Unit IS - 4 SN - 0018-9340 SP378 EP388 EPD - 378-388 A1 - P. Kornerup, A1 - D.W. Matula, PY - 1983 KW - SRT-division KW - Borrow-save and carry-save addition KW - Euclidean algorithm KW - fixed-slash and floating-slash representations KW - rational numbers VL - 32 JA - IEEE Transactions on Computers ER -

P. Kornerup, Department of Computer Science, Aarhus University

D.W. Matula

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.1983.1676239

The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including rounding. Binary implementations are discussed, based on techniques known from SRT division, and utilizing ripple-free borrow-save and carry-save addition. Average time behavior is investigated.

Index Terms:

SRT-division, Borrow-save and carry-save addition, Euclidean algorithm, fixed-slash and floating-slash representations, rational numbers

Citation:

P. Kornerup, D.W. Matula, "Finite Precision Rational Arithmetic: An Arithmetic Unit," IEEE Transactions on Computers, vol. 32, no. 4, pp. 378-388, April 1983, doi:10.1109/TC.1983.1676239

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