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Course 3: GoldenFloat, one rule for seventeen float widths
[the browser compiler runs a spec's constant asserts, not its function tests; 7 lesson-spec fixes wait on gHashTag/t27 PR 7496; no lesson claims a speed or a hardware result] A new course on the GoldenFloat family: one rule, E = round((N - 1) / phi^2), splits every width from GF4 to GF1024. 27 lessons in 9 modules of 3, each opening a table drawn from one spec and the spec itself.
Course 3 is GoldenFloat: one family of float formats from arXiv:2606.05017, where one rule picks the split for every width. Of the N - 1 bits after the sign, round((N - 1) / phi^2) go to the exponent and the rest to the mantissa. The family spec lists 17 widths, from GF4 to GF1024, and marks GF16 primary.
What each lesson opens
Each of the 27 lessons opens a black-and-white table drawn from one spec: the fields of one format, its bias and its distance from 1 / phi, or the values a test checks. Every number in a table is a constant or a test value of the spec the lesson opens, or arithmetic of them. Where a test writes its value in rather than computing it, as in gf_competitive.t27, the lesson says so. Where a comment and the code of a spec disagree, the lesson says which is which: in gf8.t27 a comment gives 15.5 as the largest value and the code computes 31.
The 27 lessons sit in 9 modules of 3: the rule and its numbers; why phi, why three; GF4 to GF8; ten to fourteen bits; GF16 at work; GF32 to GF64; GF96 to GF256; the widest rungs, then trits; more trits, then the decode. 7 lesson specs (phi_ratio, phi_split_optimality, radix_economy, gf8, gf12, gf24, gf32) did not compile clean in the browser compiler; each got the smallest change that makes it compile, and the same change is proposed upstream as gHashTag/t27 PR 7496.
The 27 lessons
| # | Lesson | Spec | Widget |
|---|---|---|---|
| 1 | A float cut by phi | numeric/goldenfloat_family.t27 | table |
| 2 | Phi as a ratio | numeric/phi_ratio.t27 | table |
| 3 | Lucas numbers stay whole | numeric/lucas_accumulator.t27 | table |
| 4 | Why the split is phi | math/phi_split_optimality.t27 | table |
| 5 | Why base three | math/radix_economy.t27 | table |
| 6 | Phi in sixteen bits | numeric/gf_competitive.t27 | table |
| 7 | GF4: four bits | numeric/gf4.t27 | table |
| 8 | GF6: six bits | numeric/gf6.t27 | table |
| 9 | GF8: one byte | numeric/gf8.t27 | table |
| 10 | GF10: ten bits | numeric/gf10.t27 | table |
| 11 | GF12: twelve bits | numeric/gf12.t27 | table |
| 12 | GF14: fourteen bits | numeric/gf14.t27 | table |
| 13 | GF16: the primary format | numeric/gf16.t27 | table |
| 14 | Two products, one sum | ternary/gft_dot2.t27 | table |
| 15 | GF20 and GF24 | numeric/gf24.t27 | table |
| 16 | GF32: a single | numeric/gf32.t27 | table |
| 17 | GF48: forty-eight bits | numeric/gf48.t27 | table |
| 18 | GF64: a double | numeric/gf64.t27 | table |
| 19 | GF96: ninety-six bits | numeric/gf96.t27 | table |
| 20 | GF128: a quad | numeric/gf128.t27 | table |
| 21 | GF256: two hundred fifty-six bits | numeric/gf256.t27 | table |
| 22 | GF512: five hundred twelve bits | numeric/gf512.t27 | table |
| 23 | GF1024: one kilobit | numeric/gf1024.t27 | table |
| 24 | GF-T8: an exponent in trits | numeric/gft8.t27 | table |
| 25 | GF-T16: six trits | numeric/gft16.t27 | table |
| 26 | GF-T32: twelve trits | numeric/gft32.t27 | table |
| 27 | Decode in one step | math/gf_competitive.t27 | table |
What this course does not claim
No lesson claims a speed, an accuracy on a model or a result on hardware. The decode lesson counts steps as the spec writes them, not a timing. Each format spec says its bias is an open question: it is chosen per format, not derived from the closed form.
What this does not settle
- 7 lesson specs compile clean here after the smallest fix; the same fix waits for review upstream in gHashTag/t27 PR 7496.
- Every format spec says its bias is open: chosen per format, not derived from the closed form.
- The values in gf_competitive.t27 are written into its tests, not produced by an encoder.
Receipts
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