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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. 1074-1082, 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 = {0018-9340}, year = {2000}, pages = {1074-1082}, 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 - 0018-9340 SP1074 EP1082 EPD - 1074-1082 A1 - Naofumi Takagi, A1 - Seiji Kuwahara, PY - 2000 KW - Computer arithmetic KW - Euclidean norm KW - VLSI algorithm KW - digit-recurrence algorithm KW - computer graphics. VL - 49 JA - IEEE Transactions on Computers ER - | |||
Abstract—A digit-recurrence algorithm for computing the Euclidean norm of a three-dimensional (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 carry-propagation-free 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.
[1] N. Takagi and S. Kuwahara, “Digit-Recurrence Algorithm for Computing Euclidean Norm of a 3D Vector,” Proc. 14th Symp. Computer Arithmetic, pp. 86-93, Apr. 1999.
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