+ {c ? c.eyebrow : 'The format'} +
++ {c ? c.h1 : 'GF-T — a float whose exponent is ternary.'} +
++ {c ? c.lede : 'The exponent is a balanced-ternary number and the fields are fixed. That removes the incumbent’s largest cost and makes the exponent add native on a ternary fabric. Against tekum16: a tie near unity, 2.84× more accurate at mid range and 5.53× at far range.'} +
+ ++ {c ? c.layoutTitle : 'The layout'} +
+
+{`GF-T16 = [ sign | E = 4 balanced-ternary trits | M = 9 mantissa bits ]
+
+value = (-1)^sign · (1 + M/2^9) · 2^e, e = Σ tᵢ·3ⁱ ∈ [−40, +40]`}
+
+ + {c ? c.accuracyTitle : 'Accuracy against tekum16'} +
++ {c ? c.accuracyNote : 'Mean relative error over an encode → decode round trip, 6000 values, random sign. Re-measured independently on 8 August 2026 against the same oracles: the ratios reproduce exactly. Bins are in powers of two.'} +
+| {h} | )}
|---|
| {cell} | + ))} +
+ {c ? c.whyTitle : 'Why it is cheaper on a ternary fabric'} +
+{name}
+{text}
++ {c ? c.costTitle : 'What it costs in hardware'} +
++ {c ? c.costNote : 'The GF-T16 multiplier, synthesised for xc7 and routed on an XC7A200T with nextpnr-xilinx, hard multipliers disabled. All three variants are bit-equivalent — proven over 321,156 input combinations and 199,994 pipeline cycles.'} +
+| {h} | )}
|---|
| 0 ? 'var(--accent)' : undefined, fontWeight: ri === 2 && i > 0 ? 700 : 400 }}>{cell} | + ))} +
+ {c ? c.widthTitle : 'A finding: the interface cost five times more than the arithmetic'} +
++ {c ? c.widthBody : 'The original module declares every port 32 bits wide, though nothing in GF-T16 is 32 bits: the mantissa field is 9, so (1+M) is 10, their product is 20, and the exponent offset never exceeds 80, which is 7. Synthesis dutifully built a 32×32 multiplier and a 32-bit compare tree and charged full price for it: 1,179 LUTs, or three DSP48 blocks. With the widths the values actually need it comes to 219 LUTs and no DSP at all, bit-identical over 321,156 input combinations.'} +
++ {c ? c.limitsTitle : 'Where it loses'} +
+{name}
+{text}
++ {c ? c.ctaTitle : 'Put GF-T in your design'} +
++ {c ? c.ctaBody : '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.'} +
+ + + {EMAIL} + +