{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "title": "IEEE P3109 v3.2.0 cross-walk for the playra/numeric-conformance-packs",
  "description": "Maps the formats covered in our conformance packs onto the corresponding IEEE P3109 v3.2.0 named formats. This is an implementor cross-reference, not a compliance assertion. Where the P3109 v3.2.0 working draft and a vendor convention disagree (e.g. FP8 E4M3 overflow-to-NaN vs saturate-to-max), the gap is documented honestly in the pack and in the methodology paper, not hidden.",
  "version": "1.0.0",
  "date_published": "2026-06-13",
  "source_standard": {
    "title": "IEEE P3109 v3.2.0 -- Standard for Arithmetic Formats for Machine Learning",
    "status": "draft",
    "url": "https://github.com/P3109/Public"
  },
  "source_catalog": {
    "title": "playra/numeric-conformance-packs",
    "url": "https://huggingface.co/datasets/playra/numeric-conformance-packs",
    "version": "2.1.0"
  },
  "anchor": {
    "identity": "phi^2 + phi^-2 = 3",
    "sha256_of_identity_string": "218403e344779c890f302ad2c70af21fb765060dd794d793c7eacc1ef8f80e6b"
  },
  "mappings": [
    {
      "pack_format": "fp8_e4m3",
      "p3109_name": "Binary8p3se",
      "p3109_section": "P3109 v3.2.0 -- 8-bit FP family, p=3 (3 exponent bits), s=signed, e=encoded",
      "layout": "1s 4e 3m",
      "bias": 7,
      "infinity": "absent (no infinity encoding)",
      "nan": "single canonical pattern 0x7F / 0xFF",
      "overflow_policy": {
        "ours": "saturate to max finite 448.0 (0x7E) -- tt-metal / AMD convention",
        "p3109_v3_2_0": "draft permits both saturate and overflow-to-NaN (OCP MX v1.0 also permits both); JAX/TPU conventionally uses overflow-to-NaN (0x7F)",
        "honest_note": "Single documented interpretation gap; pack vector input=1000.0 carries our 0x7E with abs_error stated honestly."
      },
      "anchor_3_0_at_bits": "0x44"
    },
    {
      "pack_format": "fp8_e5m2",
      "p3109_name": "Binary8p2se",
      "p3109_section": "P3109 v3.2.0 -- 8-bit FP family, p=2",
      "layout": "1s 5e 2m",
      "bias": 15,
      "infinity": "0x7C / 0xFC (true IEEE-style infinity)",
      "nan": "E=11111 AND M != 0",
      "overflow_policy": "overflow to +/-Inf (true IEEE)",
      "anchor_3_0_at_bits": "0x42"
    },
    {
      "pack_format": "mxfp4",
      "p3109_name": "Binary4p1sf (element); block scale separate (E8M0 = Binary8 scale-only)",
      "p3109_section": "P3109 v3.2.0 element-only mapping; full block format is OCP Microscaling v1.0",
      "layout": "1s 2e 1m (element only, 4 bits)",
      "bias": 1,
      "grid": [0, 0.5, 1, 1.5, 2, 3, 4, 6],
      "infinity": "absent",
      "nan": "absent",
      "overflow_policy": "clamp; note that the conventional clamp bound is 7 (one step above grid max 6), which is a frequent failure point in implementations",
      "anchor_3_0_at_bits": "0x5",
      "block_size_ocp_default": 32,
      "block_scale": "shared E8M0 exponent (Binary8 scale-only in P3109 surface area)"
    },
    {
      "pack_format": "bf16",
      "p3109_name": "out of P3109 scope (P3109 covers 8-bit family only); for cross-reference, this is bfloat16 = IEEE 754 truncated binary32",
      "p3109_section": "n/a",
      "layout": "1s 8e 7m",
      "bias": 127,
      "infinity": "present (IEEE)",
      "nan": "present (IEEE)",
      "overflow_policy": "overflow to +/-Inf (true IEEE)",
      "honest_note": "Accumulation order (sequential vs pairwise vs f64 reference) is the dominant error source in deep reduction trees, not single-op rounding. Pack carries a golden_accumulation section to demonstrate this honestly."
    },
    {
      "pack_format": "e8m0_block",
      "p3109_name": "scale-only Binary8 surface (P3109 v3.2.0 acknowledges OCP MX block-scale wrapper)",
      "p3109_section": "informative cross-reference only; OCP MX v1.0 is the normative source for the block-scale wrapper",
      "layout": "8 exponent bits, no mantissa, no sign",
      "purpose": "Shared exponent scale across an MX block (default 32 elements for MXFP4 / MXFP6 / MXFP8 / MXINT8)",
      "ocp_source": "Open Compute Project Microscaling Formats (MX) Specification v1.0"
    },
    {
      "pack_format": "gf16",
      "p3109_name": "out of P3109 scope (P3109 covers 8-bit family only); GoldenFloat is a separate phi-structured family covered in the GoldenFloat preprint arXiv:2606.05017",
      "p3109_section": "n/a",
      "layout": "1s 6e 9m",
      "bias": 31,
      "anchor_3_0_at_bits": "0x4100",
      "design_rule": "Field-width split chosen so that E/M -> 1/phi ~= 0.618; closed-form: e = round((N-1)/phi^2), m = N-1-e, bias = 2^(e-1) - 1.",
      "silicon_attestation": "Trinity S3AI Gamma tape-out (TTSKY26b shuttle); gf16_v2_mul Verilog frozen pre-tape-out, FPGA-validated on Artix-7 at 323 MHz (35/35 testbench)."
    }
  ],
  "notes_for_implementors": [
    "P3109 v3.2.0 is a working DRAFT; mappings here defer to the FLoPS Lean formalisation (arXiv:2602.15965) on any normative ambiguity.",
    "The FP8 E4M3 overflow-to-NaN vs saturate-to-max gap is a known industry-wide ambiguity; we ship our convention with the abs_error stated honestly, and surface the gap in the methodology paper rather than hiding it.",
    "MXFP4 element layout matches between OCP Microscaling v1.0 and NVFP4 (NVIDIA Blackwell); the difference is block scale (E8M0 for MXFP4 vs E4M3 for NVFP4) and block size (32 vs 16)."
  ],
  "external_references": {
    "p3109_repo": "https://github.com/P3109/Public",
    "flops_lean": "https://arxiv.org/abs/2602.15965",
    "ocp_mx_v1": "https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf",
    "ml_dtypes": "https://github.com/jax-ml/ml_dtypes",
    "takum_counterexample": "https://arxiv.org/abs/2412.20273",
    "goldenfloat_preprint": "https://arxiv.org/abs/2606.05017",
    "catalog_paper": "https://arxiv.org/abs/2606.09686"
  }
}