A Design Framework for Hardware-Efficient Logarithmic Floating-Point Multipliers
Bibliographic record
Abstract
The symbiotic use of logarithmic approximation in floating-point (FP) multiplication can significantly reduce the hardware complexity of a multiplier. However, it is difficult for a limited number of logarithmic FP multipliers (LFPMs) to fit in a specific error-tolerant application, such as neural networks (NNs) and digital signal processing, due to their unique error characteristics. This paper proposes a design framework for generating LFPMs. We consider two FP representation formats with different ranges of mantissas, the IEEE 754 Standard FP Format and the Nearest Power of Two FP Format. For both logarithm and anti-logarithm computation, the applicable regions of inputs are first evenly divided into several intervals, and then approximation methods with negative or positive errors are developed for each sub-region. By using piece-wise functions, different configurations of approximation methods throughout applicable regions are created, leading to LFPMs with various trade-offs between accuracy and hardware cost. The variety of error characteristics of LFPMs is discussed and the generic hardware implementation is illustrated. As case studies, two LFPM designs are presented and evaluated in applications of JPEG compression and NNs. They do not only increase the classification accuracy, but also achieve smaller PDPs compared to the exact FP multiplier, while being more accurate than a recent logarithmic FP design.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".