Table 7 Maximum relative error and accuracy values of selected methods including our proposed algorithm for square rooting. The number of clock cycles, required by each method, is also provided for comparison purposes. For our proposed algorithm, a LUT size of 1 KB and a 16-bit precision of \(\cos \theta\) values are assumed.
From: Novel seed generation and quadrature-based square rooting algorithms
Square root method | Clock cycles | MRE | Accuracy (bits) |
|---|---|---|---|
Nonrestoring | 313 | \(8.00 \times 10^{-8}\) | 23.58 |
Newton–Raphson | 89 | \(3.20 \times 10^{-3}\) | 8.29 |
Bakhshali | 92 | \(3.20 \times 10^{-3}\) | 8.29 |
Goldschmidt | 35 | \(9.70 \times 10^{-3}\) | 5.69 |
Polynomial approximation | 39 | \(2.90 \times 10^{-2}\) | 5.11 |
Dianov et al. | 34 | \(5.00 \times 10^{-3}\) | 7.64 |
Proposed algorithm | 85 | \(2.17 \times 10^{-4}\) | 12.17 |
