LUT-Based Multipliers for IEEE-754 Floating Point Arithmetic on FPGAs
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.013 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".