A Hardware-Efficient Logarithmic Multiplier with Improved Accuracy
Bibliographic record
Abstract
Logarithmic multipliers take the base-2 logarithm of the operands and perform multiplication by only using shift and addition operations. Since computing the logarithm is often an approximate process, some accuracy loss is inevitable in such designs. However, the area, latency, and power consumption can be significantly improved at the cost of accuracy loss. This paper presents a novel method to approximate log2N that, unlike the existing approaches, rounds N to its nearest power of two instead of the highest power of two smaller than or equal to N. This approximation technique is then used to design two improved 16×16 logarithmic multipliers that use exact and approximate adders (ILM-EA and ILM-AA, respectively). These multipliers achieve up to 24.42% and 9.82% savings in area and power-delay product, respectively, compared to the state-of-the-art design in the literature with similar accuracy. The proposed designs are evaluated in the Joint Photographic Experts Group (JPEG) image compression algorithm and their advantages over other approximate logarithmic multipliers are shown.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".