The format
The exponent is a balanced-ternary number and the fields are fixed. That removes the incumbent's largest cost — regime decode — and makes the exponent add native on a ternary fabric. The accuracy advantage over takum this page used to report has been withdrawn: restated at equal stored width it does not survive.
[ sign | E = 4 balanced-ternary trits | M = 9 mantissa bits ]. value = (-1)^sign x (1 + M/2^9) x 2^e, where e = the sum of t_i x 3^i, in the range -40 to +40.
Radix-3 economy: 3^4 = 81 exponent values from four trits, and on a ternary fabric the exponent add is native — no binary carry, no base conversion.
This page reported 2.1x lower error against takum16 and 2.6x against takum32. Both are withdrawn. The oracle they were measured against negated wrongly on every negative code, and the budget was nominal rather than equal stored width.
Restated at equal stored width the comparison is a tie, not a win. On the TNF rung of the same ladder: 5.32e-3 against takum16's 5.70e-3 at sixteen bits, 1.20e-7 against takum32's 1.26e-7 at thirty-two. No format wins by more than the width it gives up.
The one measured asymmetry is hardware: a full TNF(4,8) adder is 397 LUT against a true base-3 tekum8 adder's 15,251 — 38x — with TNF the wider format. Decode is 1 LUT against 542. Post-synthesis for xc7, no place-and-route, no silicon.
No universal ranking. Width and range are part of the stated test conditions, and an accuracy claim quoted without them is the error that produced the withdrawn figures above.
The GF-T16 multiplier with the bus widths the arithmetic needs, synthesised for xc7 with hard multipliers disabled.
Two stages, latency one cycle, one result per cycle. Post-route on an XC7A200T with nextpnr-xilinx. 81.35 MHz combinational.
The original declares every port 32 bits wide, though nothing in GF-T16 is: synthesis built a 32x32 multiplier and charged 1,179 LUTs or three DSP blocks for it. Correcting the widths is bit-identical over 321,156 input combinations.
GF-T16 reaches plus or minus 40 in powers of two, roughly plus or minus 12 decades. Fixed fields buy the cheap datapath and the uniform precision; range is the price, so comparisons name their width and range.
Artix-7, on the open flow. Not multi-corner characterisation, and ASIC numbers will differ.
The accuracy comparison uses the published format's own oracle. The cost figures are GF-T's own — writing a competitor's implementation and then reporting it as more expensive would prove nothing.
A licence includes the RTL, the independent reference model and the vectors that prove it — so you can check the claims rather than take them on trust.