LUT-Based Multipliers for IEEE-754 Floating Point Arithmetic on FPGAs
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
In the IEEE-754 standard for floating point arithmetic, multipliers with size 24-bits (single precision), 53-bits (double precision)), and 113-bits (quadruple precision) are required. LUTs (Look-Up Tables) are building blocks in FPGAs (Field Programmable Gate Arrays) which are used as accelerators for compute intensive applications. FPGAs include DSP Blocks with embedded hardwired multipliers. Lookup tables (LUTs) can be used to supplement the available on-chip multipliers. Delay and area are competing objectives in multiplier design. This paper describes the results of synthesizing 24-bits, 53/54-bits and 114bits multipliers using LUTs in FPGAs using a divide-and-conquer approach on the Xilinx Artix-7 with the Vivado 2020.2 synthesis tool. This approach is compared to the standard multiplier implementation in VHDL. Experimental results show that the divide-and-conquer approach has resulted in a 13.16% speed improvement with a 1.67% LUTs increase for the single precision. For the double precision, the speed has been reduced by 7.32% but the area has been reduced by 6.18% in terms of LUTs and by 28.14% in terms of registers. For the quadruple precision, the speed has been reduced by 20.41% but the area has been reduced by 9.28% in terms of LUTs and by 43.49% in terms of registers. Results show that by using the Karatsuba-Ofman’s approach, the area can be further reduced.
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 | 0.001 | 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