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Mark G. Arnold, Thomas A. Bailey, John R. Cowles, Mark D. Winkel, "Arithmetic CoTransformations in the Real and Complex Logarithmic Number Systems," IEEE Transactions on Computers, vol. 47, no. 7, pp. 777786, July, 1998.  
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@article{ 10.1109/12.709377, author = {Mark G. Arnold and Thomas A. Bailey and John R. Cowles and Mark D. Winkel}, title = {Arithmetic CoTransformations in the Real and Complex Logarithmic Number Systems}, journal ={IEEE Transactions on Computers}, volume = {47}, number = {7}, issn = {00189340}, year = {1998}, pages = {777786}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.709377}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Arithmetic CoTransformations in the Real and Complex Logarithmic Number Systems IS  7 SN  00189340 SP777 EP786 EPD  777786 A1  Mark G. Arnold, A1  Thomas A. Bailey, A1  John R. Cowles, A1  Mark D. Winkel, PY  1998 KW  Arithmetic cotransforamtions KW  logarithmic number systems KW  complex logarithms. VL  47 JA  IEEE Transactions on Computers ER   
Abstract—The real logarithmic number system, which represents a value with a sign bit and a quantized logarithm, can be generalized to create the complex logarithmic number system, which replaces the sign bit with a quantized angle in a log/polar coordinate system. Although multiplication and related operations are easy in both real and complex systems, addition and subtraction are hard, especially when interpolation is used to implement the system. Both real and complex logarithmic arithmetic benefit from the use of cotransformation, which converts an addition or subtraction from a region where interpolation is expensive to a region where it is easier. Two cotransformations that accomplish this goal are introduced. The first is an approximation based on real analysis of the subtraction logarithm. The second is based on simple algebra that applies for both real and complex values and that works for both addition and subtraction.
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