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Naofumi Takagi, Seiji Kuwahara, "A VLSI Algorithm for Computing the Euclidean Norm of a 3D Vector," IEEE Transactions on Computers, vol. 49, no. 10, pp. 10741082, October, 2000.  
BibTex  x  
@article{ 10.1109/12.888043, author = {Naofumi Takagi and Seiji Kuwahara}, title = {A VLSI Algorithm for Computing the Euclidean Norm of a 3D Vector}, journal ={IEEE Transactions on Computers}, volume = {49}, number = {10}, issn = {00189340}, year = {2000}, pages = {10741082}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.888043}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A VLSI Algorithm for Computing the Euclidean Norm of a 3D Vector IS  10 SN  00189340 SP1074 EP1082 EPD  10741082 A1  Naofumi Takagi, A1  Seiji Kuwahara, PY  2000 KW  Computer arithmetic KW  Euclidean norm KW  VLSI algorithm KW  digitrecurrence algorithm KW  computer graphics. VL  49 JA  IEEE Transactions on Computers ER   
Abstract—A digitrecurrence algorithm for computing the Euclidean norm of a threedimensional (3D) vector which often appears in 3D computer graphics is proposed. One of the three squarings required for the usual computation is removed and the other two squarings, as well as the two additions, are overlapped with the square rooting. The Euclidean norm is computed by iteration of carrypropagationfree additions, shifts, and multiplications by one digit. Different specific versions of the algorithm are possible, depending on the radix, the redundancy factor of the digit set, and etc. Each version of the algorithm can be implemented as a sequential (folded) circuit or a combinational (unfolded) circuit, which has a regular array structure suitable for VLSI.
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