Low-Power Approximate Logarithmic Squaring Circuit Design for DSP Applications
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Bibliographic record
Abstract
The squaring function is widely used in Digital Signal Processing (DSP). There are many DSP applications with noisy inputs for which simplifying approximations of the squaring function implementation have a minor impact on the output quality, while permitting significant reductions in the hardware cost. This article proposes a Low-Error Squaring Function (LESF) and its low-power hardware implementation. Unlike the existing logarithmic squaring functions, LESF benefits from a double-sided error distribution and, consequently, error cancellation in larger calculations. LESF approximates a base-2 logarithmic function with a linear polynomial, i.e., <inline-formula><tex-math notation="LaTeX">$\mathrm{log_2}\;f(x) \approx ax+b$</tex-math></inline-formula> . Since input <inline-formula><tex-math notation="LaTeX">$b$</tex-math></inline-formula> in this sum is a constant, LESF replaces the conventional full-adder with a compact specialized adder for hardware efficiency. Our simulation results show that the 16-bit LESF is 23.23 percent more accurate (in the mean relative error distance) than the baseline Mitchell approximate logarithmic squaring function while being 1.8× faster and 39 percent more energy-efficient. LESF and other logarithmic squaring functions are evaluated for the square-law detector application. LESF is shown to be more than 3× more accurate in this application (with respect to the Euclidean distance) than the next most accurate design in the literature, which uses an iterative error compensation technique.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it