Carry free, bit parallel approximate squarers with linear complexity and constant delay
Bibliographic record
Abstract
This paper presents two simple combinational logic design approaches for bit-parallel approximate squarers of unsigned numbers. The design approaches are suitable for squarers of any bit length, and are particularly well suited for implementation in LUT-based FPGAs. It is shown that the hardware requirements grow linearly with the input bit width, as opposed to recent work where the complexity grows quadratically. This is a consequence of the optimized function selection algorithm which limits the number of input variables to each bit function. It is also shown that the critical path delay is independent of the input bit width. The proposed sets of Boolean equations are very simple to use and lend themselves very well to a parameterized HDL description. For a 7-bit input squarer, the maximum relative error (MRE) and average relative error (ARE) are as low as 9.44% and 2.47%, respectively. For very wide input, the MRE and ARE asymptotically approach 11.3% and 4.5%.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".