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. Against tekum16: a tie near unity, 2.84x more accurate at mid range and 5.53x at far range.
[ 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.
GF-T16 3.56e-4 against tekum16 3.27e-4. Mean relative error over an encode-decode round trip, 6000 values, random sign.
GF-T16 3.52e-4 against tekum16 1.00e-3.
GF-T16 3.53e-4 against tekum16 1.95e-3. Nine mantissa bits at every magnitude, where tekum16 tapers to about four.
8 August 2026, against the published format's own oracle. The ratios reproduce exactly. Bins are in powers of two, not decades.
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. tekum16's regime is unbounded, so beyond that GF-T16 overflows and tekum16 keeps working. Fixed fields buy the cheap datapath and the uniform precision; range is the price.
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.