Design and Implementation of Decimal Reciprocal Unit
Why this work is in the frame
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Bibliographic record
Abstract
This paper presents the efficient design and implementation of a decimal reciprocal unit according to the Standard for Floating-Point Arithmetic (IEEE-754R), in which the initial approximation of the reciprocal is obtained by using a look-up table and a multiplication. An efficient look-up table creation is described in detail, and the error analysis for the ROMs of different sizes is carefully done in this paper. The presented design utilizes a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> times10 bits ROM followed by three Newton-Raphson iterations. It takes 119 clock cycles to achieve the 16-digit (Decimal-64) accuracy approximation of the reciprocal of a decimal floating-point number. The proposed implementation of decimal reciprocal unit is verified with a Xilinx Virtex-II Pro P70 FPGA device and synthesized by using TMSC 0.18 mum standard cell library.
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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 | 0.001 | 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 | 0.000 |
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