--- license: cc-by-4.0 language: - en pretty_name: Numeric Format Catalog (Trinity S3AI / t27) size_categories: - n<1K task_categories: - other multilinguality: - monolingual annotations_creators: - expert-generated language_creators: - machine-generated tags: - numeric-formats - floating-point - conformance - audit-disclosed - catalog - ruler - ieee-754 - goldenfloat - posit - mxfp4 - fp8 - bf16 - trinity-s3ai - t27 paper: - arxiv: 2606.09686 - arxiv: 2606.05017 configs: - config_name: default data_files: - split: catalog path: formats_catalog.jsonl --- # Numeric Format Catalog (Trinity S3AI / t27) **Version:** v3.0 (2026-06-13) -- supersedes v2 (count=81, withdrawn) and v1 (count=77, withdrawn). **Count:** **83 numeric formats across 13 clusters.** **License:** CC-BY-4.0. **Maintainer:** Trinity S3AI -- `admin@t27.ai` -- ORCID [0009-0008-4294-6159](https://orcid.org/0009-0008-4294-6159). **Companion dataset:** [`playra/numeric-conformance-packs`](https://huggingface.co/datasets/playra/numeric-conformance-packs) (bit-exact conformance vectors that instantiate this catalog). **Linked papers:** - **Catalog preprint (84-format ruler):** [arXiv:2606.09686](https://arxiv.org/abs/2606.09686) -- [HF paper page](https://huggingface.co/papers/2606.09686) - **Anchor preprint (GoldenFloat identity):** [arXiv:2606.05017](https://arxiv.org/abs/2606.05017) ## TL;DR A single canonical reference of every numeric format relevant to ML, scientific computing, historical hardware, and the GoldenFloat (GF) phi-structured family. Codegen-generated from a single source of truth (`specs/numeric/formats_catalog.t27` in [`gHashTag/t27`](https://github.com/gHashTag/t27)). ## Count reconciliation (v3.0 -- count=83) | Source | Count | Status | |---|---|---| | `arXiv:2606.09686` Table 1 (paper #3, draft) | 84 | aspirational, MXFP6 split + standalone E8M0 | | `specs/numeric/formats_catalog.t27` SSOT raw `// CATALOG:` lines | **83** | **live ground truth** | | **THIS DATASET v3 (codegen LIVE re-run, post t27 #1065)** | **83** | **converges with SSOT** | | v2 of this dataset (uploaded 2026-06-10) | 81 | parser dropped `gf512` + `gf1024` -- fixed in [#1065](https://github.com/gHashTag/t27/pull/1065) | | v1 of this dataset (uploaded 2026-06-10 AM) | 77 | inherited stale shipped gen | **Why 83 and not 84.** Paper #3 Table 1 carries a draft "84" that splits MXFP6 into two rows and lists a standalone E8M0 row that the SSOT folds into the MXFP6 wrapper. The SSOT keeps a single MXFP6 row and a single E8M0 row, giving 83. This is an honest documentation reconciliation, not a quality claim. A v4 paper revision will harmonise to 83 (or the SSOT will add one row to harmonise to 84) -- whichever lands first. ## Cluster breakdown | Cluster | Count | Notes | |---|---|---| | GoldenFloat | 22 | GF4..GF1024, 17 binary rungs + extras (closed-form `e = round((N-1)/phi^2)`) | | HistoricalVendor | 10 | DEC, IBM, Cray, etc. | | PositUnumIII | 8 | Posit-{8,16,32}, Unum-III variants | | IntegerFixed | 8 | int4 / int8 / fixed-point sweeps | | MlLowPrecision | 7 | FP8 (E4M3, E5M2), NF4, NF8, OFP8 | | Ieee754Binary | 5 | binary16, binary32, binary64, binary128, bfloat16 | | Lns | 4 | Logarithmic Number System variants | | Theoretical | 4 | Takum and similar research formats | | CompressionTrick | 4 | Microscaling + structured sparsity wrappers | | Ieee754Decimal | 3 | decimal64, decimal128 | | ExtendedFloat | 3 | x87 80-bit, double-double, etc. | | Microscaling | 3 | MXFP4, MXFP6, MXFP8 | | QuantTuned | 2 | Tuned-quantisation variants | | **Total** | **83** | **across 13 clusters** | ## File inventory | File | Format | Purpose | |---|---|---| | `formats_catalog.jsonl` | JSONL | One format per line, 83 rows total | | `formats_catalog.json` | JSON | Same data as a single array | | `formats_catalog.md` | Markdown | Human-readable table | | `SHA256SUMS.txt` | Text | SHA-256 manifest for tamper-evidence | ## Row schema (per JSONL line) Each row has the following canonical fields: | Field | Type | Description | |---|---|---| | `id` | string | Canonical identifier (e.g. `binary16`, `gf16`) | | `name` | string | Human-readable name | | `bits` | int | Total bit-width | | `s_bits` | int | Sign bits | | `e_bits` | int | Exponent bits | | `m_bits` | int | Mantissa bits | | `bias` | int | Exponent bias | | `bias_formula` | string | Closed-form bias rule (where applicable) | | `phi_distance` | float | Distance from the phi-structured field-width rule | | `storage` | string | Storage envelope (e.g. `u16`, `u32`) | | `cluster` | string | Cluster label (one of 13) | | `gf_relation` | string | Relation to GoldenFloat (`competitor`, `member`, `wrapper`, ...) | | `status` | string | Verification status (`Verified`, `Conj`, `Risk`, ...) | | `source` | string | Primary standards reference | | `standard` | string | Issuing body / spec | | `use_case` | string | Canonical use case | ## Quick start ```python from datasets import load_dataset # Load the full catalog ds = load_dataset("playra/numeric-format-catalog", split="catalog") print(f"Loaded {len(ds)} formats across {len(set(r['cluster'] for r in ds))} clusters") # Filter to GoldenFloat formats gf = [r for r in ds if r["cluster"] == "GoldenFloat"] print(f"{len(gf)} GoldenFloat rungs") # Find anything close to the phi-distance rule phi_close = sorted(ds, key=lambda r: r["phi_distance"])[:5] for r in phi_close: print(r["id"], r["phi_distance"]) ``` ## Provenance This catalog is **codegen output**, not hand-edited. The pipeline: ``` specs/numeric/formats_catalog.t27 (SSOT in gHashTag/t27) | v tools/gen_formats_catalog.py (codegen, Python stop-gap) | v gen/numeric/formats_catalog.{json,jsonl,md,...} | v This Hugging Face dataset (mirror) ``` To re-derive locally: ```bash git clone https://github.com/gHashTag/t27.git cd t27 python3 tools/gen_formats_catalog.py specs/numeric/formats_catalog.t27 gen/numeric wc -l gen/numeric/formats_catalog.jsonl # 83 ``` ## Considerations for using the data ### Recommended uses - A reference list of numeric formats relevant to AI accelerator design - A discovery aid: "is format X already catalogued? if so, what cluster?" - A standards cross-walk anchor (IEEE 754, OCP, IEEE P3109, posit) - A bibliography of the GoldenFloat family for accelerator-architecture researchers ### Out of scope - **Not a quality ranking.** `phi_distance = 0` means "field widths match the phi rule"; it does not mean "best format". Choose by use case, not by phi-distance. - **Not exhaustive.** Vendor-proprietary in-house formats not published in standards bodies are omitted. - **No silicon performance data.** For end-to-end silicon validation, see [`gHashTag/tt-trinity-corona`](https://github.com/gHashTag/tt-trinity-corona) (Tier 2 of the ruler stack). - **No model accuracy claims.** This is a format-spec catalogue, not a quantisation benchmark. ### Known limitations - **Paper / SSOT count drift (84 vs 83).** Honest documentation note, see "Count reconciliation" above. - **Status labels are non-uniform across clusters.** `Verified` requires silicon or formal proof; `Conj` is theoretical; `Risk` flags numerical or canonicality concerns. - **GF cluster is over-represented (22 of 83 = 27%).** This is by construction -- this catalog originates in the GoldenFloat research line. - **English-only.** No localisation of names / use cases. ### Known biases - **GoldenFloat-centred view.** Formats are ranked and labelled relative to the phi-structured field-width rule. Other research lines may legitimately disagree with the cluster taxonomy. ## Citation ```bibtex @misc{vasilev2026numericrulercatalog, title = {Eighty Formats and a Ruler: A Comprehensive Numeric Format Catalog for Phi-Structured and IEEE Floating-Point Arithmetic}, author = {Vasilev, Daniil and {Trinity S3AI}}, year = {2026}, eprint = {2606.09686}, archivePrefix = {arXiv}, primaryClass = {cs.AR}, url = {https://arxiv.org/abs/2606.09686} } @misc{trinitys3ai2026catalog, title = {Numeric Format Catalog}, author = {{Trinity S3AI}}, year = {2026}, publisher = {Hugging Face}, url = {https://huggingface.co/datasets/playra/numeric-format-catalog} } ``` ## Maintenance and changelog | Date | Version | Count | Change | |---|---|---|---| | 2026-06-10 | v1.0 | 77 | Initial release (shipped gen, stale) | | 2026-06-10 | v2.0 | 81 | Re-derived from SSOT, hit parser bug (`bias_formula` `2^N-1` dropped) | | 2026-06-13 | v3.0 | **83**| Parser fix landed in t27 [#1065](https://github.com/gHashTag/t27/pull/1065); SSOT and codegen now converge; full FAIR / Datasheets / Data Cards upgrade | **Update cadence.** Regenerated whenever the SSOT changes. No fixed cadence. Major version bumps when count changes or schema changes. **Contact.** `admin@t27.ai` -- async-only, ASCII-only. ## Machine-readable metadata - **Croissant JSON-LD:** [`croissant.json`](croissant.json) at repo root (MLCommons Croissant 1.0) - **YAML metadata:** at the top of this file, machine-parseable per HF Hub spec - **SHA-256 manifest:** [`SHA256SUMS.txt`](SHA256SUMS.txt) ## Identity stack - **Maintainer:** Vasilev Daniil (Trinity S3AI) - **Email:** admin@t27.ai (sole canonical contact) - **ORCID:** 0009-0008-4294-6159 - **GitHub:** gHashTag - **HF org:** trinity-s3ai - **Anchor identity:** `phi^2 + 1/phi^2 = 3`