A family of modular area- and energy-efficient QRD-accelerator architectures

Scalable Fixed Point QRD Core Using Dynamic Partial Reconfiguration

“…A direct implementation of these operations in the hardware involves large amount of resources and higher latency. To overcome these, many methods are discussed in the literature which approximates these functions using LUT based log domain arithmetic [2,3,7], LUT based Newton-Raphson [4,5], CORDIC based architectures [9], and so forth. In [8], the square root operation is approximated using CORDIC and inverse square root is done by division.…”

“…Implementation of the division operation and the CORDIC requires higher latency and consumes more area. In [4,5], the division operation is replaced by an LUT based Newton-Raphson method.…”

“…Computing the trigonometric functions involves square root and inverse square root operations (4). In [4,5], the inverse square root is calculated using an LUT based NR method and the square root is computed based on CORDIC logic. In this work, we propose a method to compute the square root values from inverse square root values at the expense of just a delay and a multiplier.…”

“…a modified boundary cell (from [4,5]) is proposed (Figure 1(c)) which computes the square root utilizing the same LUT and NR blocks (square root is computed by delaying the input value sufficiently and then multiplying it with its inverse square root value obtained from NR logic), thus reducing the resource utilization. LUT-N method consists of a control logic, LUT blocks, and NR iteration equation.…”

“…There are different algorithms and architectures proposed in the literature which includes Gram-Schmidt orthogonalization, modified Gram-Schmidt orthogonalization [2,3], Givens rotation [4][5][6][7][8][9][10][11], householder transformations [12], and various other hybrid methods [13,14]. Gram-Schmidt (GS) algorithm offers reduced accuracy and stability in fixed precision environment.…”