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takum32/64: promote structural -> curated_named bitexact (SW 70->72)
Promote takum32 and takum64 conformance packs from structural (n_vectors=0) to bit-precise via a curated_named vector set (15 vectors each: zero, +1, -1, exp(c/2) grid points for c=+/-2,+/-4,+/-6 both signs). Each named vector is the correctly-rounded f64 of an exact grid value under the Takum decode law (Hunhold 2024, arXiv:2404.18603, value=exp(ell/2)), certified by an independent 400+bit mpmath oracle; abs_error=0 by construction. CURATED-BACKED, NOT exhaustive (2^32/2^64 infeasible) -- distinct from takum16 (exhaustive 2^16). 400k sample probe is supporting evidence only, NOT part of the bitexact claim. INDEX: bitexact 70->72, structural 13->11, total stays 83. WP-18 integrity-gate CLEAN locally (A/B/C/D/D2/E). [verified SW] curated named vectors; NOT [exhaustive]; NOT a silicon claim. Closes #1327
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‎conformance/vectors/INDEX_all_formats.json‎

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"preprint": "https://arxiv.org/abs/2606.05017",
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"total_formats": 83,
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"total_packs": 83,
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"bitexact_packs": 70,
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"bitexact_packs": 72,
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"selfconsistent_packs": 0,
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"structural_packs": 13,
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"structural_packs": 11,
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"packs": [
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{
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"id": "binary16",
@@ -240,18 +240,18 @@
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{
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"id": "takum32",
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"file": "takum32_conformance_v0.json",
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"kind": "structural",
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"n_vectors": 0,
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"source": "generated by gen_all_formats.py",
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"sha256": "3dca713a5bc26040650929100e4bb48cc4c7dd50575b7333f2199152ac0b95b0"
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"kind": "bitexact",
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"n_vectors": 15,
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"source": "curated_named oracle (witness_takum_wide.py, mpmath 1200-bit); see format_notes",
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"sha256": "fd7ec34a74e4ae0577c64999ee2a972788020a6a62b80dd32312cc9082f6cf8a"
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},
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{
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"id": "takum64",
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"file": "takum64_conformance_v0.json",
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"kind": "structural",
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"n_vectors": 0,
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"source": "generated by gen_all_formats.py",
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"sha256": "716629d89176e0cddb6c3acf0e90808fd8a72743bbebe4cbe887e2c5529e0f1a"
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"kind": "bitexact",
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"n_vectors": 15,
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"source": "curated_named oracle (witness_takum_wide.py, mpmath 1200-bit); see format_notes",
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"sha256": "ab1bf903a5de88d784364e6bc6d54faea0e40a19725076bda65e6c8933b7b58e"
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},
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{
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"id": "lns8",

‎conformance/vectors/takum32_conformance_v0.json‎

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Original file line numberDiff line numberDiff line change
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"schema": "t27-conformance/v0.1",
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"format": "TAKUM32",
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"format_name": "takum32",
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"bitexact": false,
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"format_notes": "takum32 -- Hunhold 2024",
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"bitexact": true,
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"format_notes": "takum32 logarithmic (Hunhold 2024, arXiv:2404.18603): value = exp(ell/2). CURATED-BACKED (NOT exhaustive: 2^32 codes infeasible to enumerate) - distinct from takum16 which is exhaustive-backed (2^16). Each named vector is correctly-rounded f64 via an independent 400+-bit mpmath oracle (abs_error=0). Supporting evidence (NOT part of the bitexact claim): a 400k+ randomized+structured sample probe at 600-bit found min midpoint gap 2.27e-7 ULP >> oracle floor 2.5e-175, 0 ambiguous codes - no table-maker's dilemma observed on the sample. Exhaustive guarantee would require libtakum C-parity or an analytic separation bound (Variant B, separate step). zero at 0x0; NaR at MSB-set.",
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"catalog": {
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"id": "takum32",
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"bits": 32,
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"standard": "Hunhold 2024",
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"use_case": "tapered fp32-class",
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"gf_relation": "ally",
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"source": "Hunhold 2024",
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"source": "Hunhold 2024 (arXiv:2404.18603)",
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"phi_distance": -1.0
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},
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"ssot": "https://github.com/gHashTag/t27/blob/master/conformance/FORMAT-SPEC-001.json",
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"preprint": "https://arxiv.org/abs/2606.05017",
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"anchor_identity": "phi^2 + 1/phi^2 = 3",
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"structural_reason": "Takum (Hunhold 2024, arXiv:2404.18603) is a tapered LOGARITHMIC format; its decode is not a plain S:E:M field. takum8 and takum16 are promoted to bit-precise (exhaustive 256 / 65536 codes, independent high-precision witness); this wider rung stays structural pending an external libtakum oracle for the full-domain correctly-rounded gap proof.",
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"anchor_note": "Anchor identity phi^2 + 1/phi^2 = 3 recorded per shared schema.",
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"n_vectors": 0,
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"vectors": []
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}
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"anchor_check": {
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"value": null,
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"expected": 3.0,
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"ieee754_exact": false,
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"note": "3.0 is not an exact grid point of this format at this width"
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},
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"round_trip_policy": "decode: exact bits->f64 (curated_named). encode (reference): round-nearest-ties-even; overflow per format convention. abs_error 0 for representable values.",
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"vector_mode": "curated_named",
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"n_vectors": 15,
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"vectors": [
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{
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"name": "pos_zero",
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"input_f64": 0.0,
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"input_f64_hex": "0x0000000000000000",
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"takum32_bits_hex": "0x00000000",
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"takum32_bits_int": 0,
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"decoded_f64": 0.0,
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"decoded_f64_hex": "0x0000000000000000",
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"abs_error": 0.0,
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"category": "zero"
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},
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{
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"name": "pos_one",
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"input_f64": 1.0,
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"input_f64_hex": "0x3FF0000000000000",
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"takum32_bits_hex": "0x40000000",
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"takum32_bits_int": 1073741824,
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"decoded_f64": 1.0,
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"decoded_f64_hex": "0x3FF0000000000000",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_one",
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"input_f64": -1.0,
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"input_f64_hex": "0xBFF0000000000000",
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"takum32_bits_hex": "0xC0000000",
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"takum32_bits_int": 3221225472,
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"decoded_f64": -1.0,
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"decoded_f64_hex": "0xBFF0000000000000",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "pos_exp_c2",
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"input_f64": 2.718281828459045,
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"input_f64_hex": "0x4005BF0A8B145769",
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"takum32_bits_hex": "0x4C000000",
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"takum32_bits_int": 1275068416,
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"decoded_f64": 2.718281828459045,
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"decoded_f64_hex": "0x4005BF0A8B145769",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_exp_c2",
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"input_f64": -0.36787944117144233,
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"input_f64_hex": "0xBFD78B56362CEF38",
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"takum32_bits_hex": "0xCC000000",
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"takum32_bits_int": 3422552064,
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"decoded_f64": -0.36787944117144233,
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"decoded_f64_hex": "0xBFD78B56362CEF38",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "pos_exp_c-2",
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"input_f64": 0.36787944117144233,
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"input_f64_hex": "0x3FD78B56362CEF38",
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"takum32_bits_hex": "0x34000000",
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"takum32_bits_int": 872415232,
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"decoded_f64": 0.36787944117144233,
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"decoded_f64_hex": "0x3FD78B56362CEF38",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_exp_c-2",
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"input_f64": -2.718281828459045,
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"input_f64_hex": "0xC005BF0A8B145769",
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"takum32_bits_hex": "0xB4000000",
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"takum32_bits_int": 3019898880,
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"decoded_f64": -2.718281828459045,
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"decoded_f64_hex": "0xC005BF0A8B145769",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "pos_exp_c4",
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"input_f64": 7.38905609893065,
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"input_f64_hex": "0x401D8E64B8D4DDAE",
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"takum32_bits_hex": "0x52000000",
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"takum32_bits_int": 1375731712,
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"decoded_f64": 7.38905609893065,
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"decoded_f64_hex": "0x401D8E64B8D4DDAE",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_exp_c4",
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"input_f64": -0.1353352832366127,
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"input_f64_hex": "0xBFC152AAA3BF81CC",
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"takum32_bits_hex": "0xD2000000",
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"takum32_bits_int": 3523215360,
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"decoded_f64": -0.1353352832366127,
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"decoded_f64_hex": "0xBFC152AAA3BF81CC",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "pos_exp_c-4",
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"input_f64": 0.1353352832366127,
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"input_f64_hex": "0x3FC152AAA3BF81CC",
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"takum32_bits_hex": "0x2E000000",
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"takum32_bits_int": 771751936,
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"decoded_f64": 0.1353352832366127,
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"decoded_f64_hex": "0x3FC152AAA3BF81CC",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_exp_c-4",
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"input_f64": -7.38905609893065,
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"input_f64_hex": "0xC01D8E64B8D4DDAE",
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"takum32_bits_hex": "0xAE000000",
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"takum32_bits_int": 2919235584,
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"decoded_f64": -7.38905609893065,
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"decoded_f64_hex": "0xC01D8E64B8D4DDAE",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "pos_exp_c6",
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"input_f64": 20.085536923187668,
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"input_f64_hex": "0x403415E5BF6FB106",
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"takum32_bits_hex": "0x56000000",
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"takum32_bits_int": 1442840576,
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"decoded_f64": 20.085536923187668,
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"decoded_f64_hex": "0x403415E5BF6FB106",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_exp_c6",
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"input_f64": -0.049787068367863944,
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"input_f64_hex": "0xBFA97DB0CCCEB0AF",
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"takum32_bits_hex": "0xD6000000",
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"takum32_bits_int": 3590324224,
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"decoded_f64": -0.049787068367863944,
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"decoded_f64_hex": "0xBFA97DB0CCCEB0AF",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "pos_exp_c-6",
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"input_f64": 0.049787068367863944,
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"input_f64_hex": "0x3FA97DB0CCCEB0AF",
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"takum32_bits_hex": "0x2A000000",
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"takum32_bits_int": 704643072,
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"decoded_f64": 0.049787068367863944,
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"decoded_f64_hex": "0x3FA97DB0CCCEB0AF",
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"abs_error": 0.0,
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"category": "normal"
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},
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{
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"name": "neg_exp_c-6",
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"input_f64": -20.085536923187668,
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"input_f64_hex": "0xC03415E5BF6FB106",
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"takum32_bits_hex": "0xAA000000",
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"takum32_bits_int": 2852126720,
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"decoded_f64": -20.085536923187668,
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"decoded_f64_hex": "0xC03415E5BF6FB106",
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"abs_error": 0.0,
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"category": "normal"
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}
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]
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}

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