An Energy-Efficient Approximate Divider Based on Logarithmic Conversion and Piecewise Constant Approximation
Bibliographic record
Abstract
Approximate computing (AC) has been considered as a promising paradigm to improve the energy-efficiency of computing hardware for error-tolerant applications, with negligible quality degradation to the output. Dividers frequently limit the performance of a computing system; however, they have not received as much attention as multipliers and adders in AC. In this paper, an energy-efficient and high-performance approximate divider is proposed based on logarithmic conversion and piecewise constant approximation. In this design, the range for the conversion between binary and logarithmic numbers is first expanded from$\mathbf {[{0,1}]}$to$\mathbf {[-0.5,1]}$. A heuristic search algorithm is then devised to find the most accurate constant set to approximate the reciprocal of the divisor, by minimizing a statistical error. The hardware implementation is presented for both floating-point (FP) and integer dividers. With a high configurability, the proposed divider results in a mean relative error distance (MRED) from 2.78% to 0.046%, indicating a high accuracy among state-of-the-art approximate dividers. Compared to the half-precision FP divider, the proposed divider with a MRED of 0.74% can achieve nearly$\mathbf {90\times }$improvement in PDP. Moreover, compared to state-of-the-art approximate dividers, the proposed design is in the Pareto Frontier in terms of power delay product (PDP) and MRED. The three image processing application results demonstrate that the proposed divider can result in the highest peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) even with truncation.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.003 | 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".