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The full adder made the cost claim comparable

2026-08-18 · 5 min read

A merged FPGA-repository PR replaces a magnitude-only comparison with a full adder and reports 3000 oracle checks, 0 errors, and a 440-LUT post-synthesis result.

[Measured — Yosys] A merged pull request in gHashTag/trinity-fpga adds a complete TEF/TNF floating-point adder, tef_add_full.v. It exists because an earlier area comparison put a magnitude-only circuit beside a complete tapered-field model: the two sides did not implement the same operation.

The new circuit has sign input and output, effective subtraction when signs differ, round-to-nearest-even from guard/round/sticky bits, full leading-zero normalisation, and the format’s overflow row. The correction is about making the cost question comparable; it is not a claim that this format is better than a published competitor.

The oracle came before the area table

Against the conformance oracle’s own encode, 3000 random pairs produced 0 errors. That check exposed two mistakes in the hand-written golden model: it divided the mantissa by 512 + 1 instead of 512, and it saturated overflow to the largest finite value instead of the Inf row. The first mistake changed 133 of 3000 results by one ulp. A third fault was real RTL: a carry-out bit was dropped instead of being folded into sticky.

A like-for-like synthesis table

On this Yosys 0.65 run with synth_xilinx, xc7 family and DSP disabled, the full circuit is about 2.7× smaller than the internal reference model in LUT count. The missing rounding, subtraction and normalisation account for 343 LUT, or about 4.5× the magnitude-only circuit. These are post-synthesis cell counts, not a board measurement.

What the comparison does and does not say

• It shows why a magnitude-only accumulator cannot support a full-adder cost claim.
• It gives a reproducible RTL artefact, an oracle check, and a named synthesis configuration.
• The 1182-LUT opponent is an internal linear structural model, not the published takum format.
• No place-and-route, AX7203 board run, throughput, energy, or accuracy comparison with takum is established.
• The result does not establish a general advantage for a format or a complete hardware story.

Before comparing formats, compare the operations they actually implement.

The engineering use is narrow but practical: keep magnitude-only, full arithmetic, oracle validation and synthesis configuration as separate fields in every area claim. Otherwise an asymmetry in the circuit can masquerade as a property of the format.