GoldenFloats.jl

Julia reference implementation of the GoldenFloat family of phi-structured floating-point formats. Companion to the Verilog RTL in gHashTag/tt-trinity-gamma, the canonical .t27 SSOT in gHashTag/t27, and the Zig reference in gHashTag/zig-golden-float.

What this is

A small, dependency-free Julia harness for the GoldenFloat width ladder (GF4 ... GF256) and the Lucas-EII integer-exact accumulator. The package is intentionally minimal so it can be dropped into existing numerical linear algebra benchmark suites (e.g. takum-arithmetic/MuFoLAB) for side-by-side comparison against posit, takum, OCP MX, and IEEE binary formats.

Claim status

• [Verified] -- the one closed-form ladder rule e = round((N-1)/phi^2) reproduces all 9 GoldenFloat field-width splits (GF4, GF8, GF12, GF16, GF20, GF24, GF32, GF64, GF256) exactly.
• [Verified] -- the identity phi^2 + phi^-2 = 3 = L_2 (Lucas L_2, classical 1878, not original to this project). More generally phi^(2n) + phi^(-2n) = L_{2n} is verified to 60 decimal digits with mpmath over n=0..12; max residual 7.1e-56. See lucas_accumulator.t27 in the t27 SSOT.
• [Open conjecture] -- whether the phi-ladder is numerically superior to an equally-tuned posit / OCP-MX / takum family. This is FL-002 in gHashTag/trios-trainer-igla src/ledger.rs and is not settled by this package. The point of this Julia port is to make the conjecture testable side-by-side under matched harnesses.

Install

using Pkg
Pkg.add(url="https://github.com/gHashTag/GoldenFloats.jl")

Quick start

using GoldenFloats

# 1. Inspect the 9-rung ladder
for fmt in GOLDEN_FLOAT_FAMILY
    println(fmt)
end

# 2. The single closed rule that derives every width
GoldenFloats.verify_ladder()    # -> true

# 3. Encode / decode a GF16 value
raw = encode(GF16, 1.5)
decode(GF16, raw)               # -> 1.5 (rtol 1e-2)

# 4. Lucas-EII integer-exact accumulator
acc = LucasAcc()
push!(acc, 1)   # add L_2 = 3
push!(acc, 2)   # add L_4 = 7
push!(acc, 3)   # add L_6 = 18
sum(acc)        # -> 28 (BigInt, exact)

# 5. The L5 identity that anchors the family
phi_acc(1)      # 3.0   == lucas(2)
phi_acc(6)      # 322.0 == lucas(12)

Format ladder

Name	Bits	Sign	Exp	Mant	Bias
GF4	4	1	1	2	0
GF8	8	1	3	4	3
GF12	12	1	4	7	7
GF16	16	1	6	9	31
GF20	20	1	7	12	63
GF24	24	1	9	14	255
GF32	32	1	12	19	2047
GF64	64	1	24	39	8388607
GF256	256	1	97	158	2^96 - 1

Field widths follow t27/specs/numeric/goldenfloat_family.t27 verbatim. Bias values match t27/specs/numeric/gf{N}.t27.

Why Julia

The numerical linear algebra benchmark ecosystem this package targets is Julia-native: Posits.jl, Takums.jl, SuiteSparse.jl, MuFoLAB. A Julia reference impl drops directly into those harnesses without a foreign-call boundary.

Related work and prior art

• Posits (J. L. Gustafson, Unum III, 2017) -- tapered precision, regime-coded exponent.
• Takums (L. Hunhold, Beating Posits at Their Own Game, CoNGA 2024, arXiv:2404.18603; Integer Representations of Real Numbers, 2024, arXiv:2412.20273) -- IEEE-754-backward-compatible tapered.
• OCP MX (Rouhani et al., 2023, arXiv:2310.10537) -- block-scaled microfloats.
• Tekum balanced ternary (Hunhold, 2025, arXiv:2512.10964).
• IEEE P3109 -- ML binary8 working group; FLoPS Lean formalization at arXiv:2602.15965.
• Zeckendorf / base-phi integer arithmetic (Ahlbach, Usatine, Pippenger, 2012, arXiv:1207.4497) -- linear-time arithmetic in base phi, the theoretical anchor for the Lucas-EII track.

License

Apache-2.0. See LICENSE.

Citation

If you use this package in research, please cite the upcoming Corona open-silicon paper (in preparation, ARITH 2027 target):

@misc{vasilev2026goldenfloats,
  author = {Vasilev, Dmitrii},
  title  = {GoldenFloats.jl: A phi-structured floating-point reference in Julia},
  year   = {2026},
  howpublished = {\url{https://github.com/gHashTag/GoldenFloats.jl}},
  note   = {Apache-2.0}
}

Contact

Dmitrii Vasilev -- admin@t27.ai -- GitHub @gHashTag ORCID 0009-0008-4294-6159