Why this work is in the frame
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Bibliographic record
Abstract
We present efficient squaring formulae based on the Toom-Cook multiplication algorithm. The latter always requires at least one non-trivial constant division in the interpolation step. We show such non-trivial divisions are not needed in the case two operands are equal for three, four and five-way squarings. Our analysis shows that our 3-way squaring algorithms have much less overhead than the best known 3-way Toom-Cook algorithm. Our experimental results show that one of our new 3-way squaring methods performs faster than mpz_mul ( ) in GNU multiple precision library (GMP) for squaring integers of approximately 2400-6700 bits on Pentium IV Prescott 3.2 GHz. For squaring in Z[ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> ], our 3-way squaring algorithms are much superior to other known squaring algorithms for small input size. In addition, we present 4-way and 5-way squaring formulae which do not require any constant divisions by integers other than a power of 2. Under some reasonable assumptions, our 5-way squaring formula is faster than the recently proposed Montgomery's 5-way Karatsuba-like formulae.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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