Approximate Leading One Detector Design for a Hardware-Efficient Mitchell Multiplier
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We propose two approximate leading one detector (LOD) designs and an approximate adder (for summing two logarithms) that can be used to improve the hardware efficiency of the Mitchell logarithmic multiplier. The first LOD design uses a single fixed value to approximate the `d' least significant bits (LSBs). For d=16 this design reduces the hardware cost by 19.91% compared to the conventional 32-bit Mitchell multiplier and by 15.19% when compared to a recent design in the literature. Our design is smaller by 32.33% and more energy-efficient by 56.77% with respect to a conventional Mitchell design. The second design partitions the `d' bits into smaller fields and increases the accuracy by using a multiplexing scheme that selects a closer approximation to the actual input value. This design reduces the hardware cost by 17.98% compared to the original Mitchell multiplier and by 13.15% when compared to the other recent design. Our design is smaller by 29.17% and more energy-efficient by 56.18% with respect to the conventional Mitchell design. In the approximate adder, the `m' least significant bits are set to a fixed bias of alternating ones and zeros. The optimal values of `d' and `m' are chosen to preserve the full accuracy of the conventional Mitchell multiplier while reducing the hardware cost. The new designs produce increased signed errors for inputs less than or equal to 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</sup> but for larger numbers the accuracy is equal to that of the conventional Mitchell multiplier. The approximation affects only the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</sup> -1 smallest input values out of 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">32</sup> -1. The new approximate multipliers are suitable for applications where approximation errors affecting the least significant digits can be tolerated.
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.
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it