GF-T: measure its cost, halve its critical path, give it its own page - #635

GF-T: measure its cost, halve its critical path, give it its own page (#635)

* Put GF-T where it belongs: at the top

GF-T was the fourth item in a list halfway down two pages, while the homepage led
with a verification service. That is backwards. The service is competent work
anyone with boards could learn to do; GF-T is the only asset here that measurably
beats a published format on the ground its own author claims as the advantage.

Verified before promoting, because a headline claim is exactly where the last one
went wrong. Re-measured from the claim rather than by re-running the script that
produced it — encode, decode, relative error, binned by magnitude, fixed seed,
same oracles:

    |e| < 8      GF-T16 3.56e-4   tekum16 3.27e-4    0.92x  a tie
    |e| 8-20     GF-T16 3.52e-4   tekum16 1.00e-3    2.84x
    |e| 20-38    GF-T16 3.53e-4   tekum16 1.95e-3    5.53x

The research note's "3x and 5.5x" reproduces exactly. The site now carries the
measured ratios rather than the rounded ones.

One correction fell out of the check, and it was worth making. The note labelled
those bins "dec". They are powers of two. Binned in actual decades the far column
is not a win at all — GF-T16's exponent reaches ±40 in powers of two, roughly ±12
decades, so past that it overflows while tekum16's unbounded regime keeps going.
A reviewer checking the labelled axis would have found overflow where the table
promised a 5.5x win and concluded the number was invented. Axis corrected
upstream in trinity-fpga; the trade is now stated on the pages too, because a
bounded range is the honest price of fixed fields.

Homepage, evidence page and licensing page all lead with it, and the primary
action is licensing rather than a service enquiry.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

* GF-T: measure its cost, halve its critical path, give it its own page

Three things the format needed and did not have: a hardware cost, a frequency,
and a page of its own.

**Cost, and a finding.** Every port in gft_mul is declared 32 bits wide. Nothing
in GF-T16 is 32 bits — the mantissa field is 9, so 1+M is 10, their product is
exactly 20, and the exponent offset never exceeds 80, which is 7. Synthesis
dutifully built a 32x32 multiplier and a 32-bit compare tree and charged full
price: 1,179 LUTs, or three DSP48 blocks. With the widths the values actually
need it is 219 LUTs and one DSP, or 219 LUTs and none. The interface cost five
times the arithmetic.

**Frequency.** Cutting between the product and the renormalisation — the two
natural halves — takes it from 81.35 MHz to 147.32 MHz post-route on an XC7A200T
for one cycle of latency. For context, ALTFP_MUL on a Cyclone IV publishes
119-132 MHz at 6-10 cycles, with ~900 logic elements and 18 embedded multipliers.
GF-T's multiplier is ahead on frequency, area, hard-multiplier count and latency
at once.

**Equivalence, proven both times.** The width correction is checked over 321,156
input combinations: the mantissa space swept in full at offset pairs that exercise
underflow, the middle and saturation, then the offsets swept in full at mantissas
that do and do not carry. The pipelined version is checked over 199,994 cycles
against the combinational one delayed by two. Zero mismatches in both.

**The page.** /gft carries the field layout, the accuracy table against tekum16
with the working shown, the hardware cost, the width finding, and a section on
where it loses — the bounded range being the honest price of fixed fields, and the
fact that no tekum16 RTL exists here, so the cost figures are GF-T's own rather
than a comparison against an implementation I wrote for a competitor.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

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Co-authored-by: Dmitrii Vasilev <admin@t27.ai>
Co-authored-by: Claude Opus 5 <noreply@anthropic.com>