On the fast computation of decimal logarithm
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
The paper presents a new and fast algorithm to efficiently compute radix-10 logarithm of a decimal number. The algorithm uses 32-bit floating-point arithmetic, and is based on a digit-by-digit iterative computation that does not require look-up tables, curve fitting, decimal-binary conversion, or division operations; the number of iterations depends on the user defined precision. The algorithm produces error-free (infinite precision) results up to 7 decimal digits. A numerical example is shown for the purpose of illustration. The accuracy is analyzed for several decimal digits showing compliance with the IEEE 754-2008 standard. When implemented on to the Xilinx VirtexII FPGA, the architecture costs only 1,053 logic cells, runs at a maximum frequency of 44 MHz, and consumes 79 mW of power.
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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 | 0.000 | 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 | 0.000 |
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