A VLSI Algorithm for Computing the Euclidean Norm of a 3D Vector
A VLSI Algorithm for Computing the Euclidean Norm of a 3D Vector
复制标题
计算 3D 向量欧氏范数的 VLSI 算法
DOI：
10.1109/12.888043
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
S. Kuwahara
中科院分区：
文献类型：
--
作者：
N. Takagi;S. Kuwahara
针对三维计算机图形学中经常出现的三维矢量的欧氏范数问题，提出了一种数字递推算法。通常计算所需的三个平方中的一个被删除，另外两个平方以及两个加法与平方根重叠。欧几里得范数是通过无进位传播的加法、移位和一位数乘法的迭代来计算的。该算法的不同的具体版本是可能的，这取决于基数，数字集的冗余因子等。该算法的每个版本可以实现为顺序（折叠）电路或组合（展开）电路，其具有适合于VLSI的规则阵列结构。
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.