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takum32/64: promote structural -> curated_named bitexact (SW 70->72) #1328

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Merged
gHashTag merged 2 commits into from
Jul 4, 2026
Merged

takum32/64: promote structural -> curated_named bitexact (SW 70->72) #1328

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d77aa84
takum32/64: promote structural -> curated_named bitexact (SW 70->72)
Jul 4, 2026
9d94e3d
takum32/64: add machine-readable witnesses[] (consistency with bcd pack)
Jul 4, 2026
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20 changes: 10 additions & 10 deletions conformance/vectors/INDEX_all_formats.json
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Expand Up @@ -5,9 +5,9 @@
"preprint": "https://arxiv.org/abs/2606.05017",
"total_formats": 83,
"total_packs": 83,
"bitexact_packs": 70,
"bitexact_packs": 72,
"selfconsistent_packs": 0,
"structural_packs": 13,
"structural_packs": 11,
"packs": [
{
"id": "binary16",
Expand Down Expand Up @@ -240,18 +240,18 @@
{
"id": "takum32",
"file": "takum32_conformance_v0.json",
"kind": "structural",
"n_vectors": 0,
"source": "generated by gen_all_formats.py",
"sha256": "3dca713a5bc26040650929100e4bb48cc4c7dd50575b7333f2199152ac0b95b0"
"kind": "bitexact",
"n_vectors": 15,
"source": "curated_named oracle (witness_takum_wide.py, mpmath 1200-bit); see format_notes",
"sha256": "9743747e70e9da3490a08c6d2c954f49108293a6381a4e1365a6434444478cf0"
},
{
"id": "takum64",
"file": "takum64_conformance_v0.json",
"kind": "structural",
"n_vectors": 0,
"source": "generated by gen_all_formats.py",
"sha256": "716629d89176e0cddb6c3acf0e90808fd8a72743bbebe4cbe887e2c5529e0f1a"
"kind": "bitexact",
"n_vectors": 15,
"source": "curated_named oracle (witness_takum_wide.py, mpmath 1200-bit); see format_notes",
"sha256": "9467083cfdd44436a257b0efedbdbffe0b24ffe5b3ce45f16637d6fdd6739340"
},
{
"id": "lns8",
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210 changes: 202 additions & 8 deletions conformance/vectors/takum32_conformance_v0.json
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Expand Up @@ -2,8 +2,8 @@
"schema": "t27-conformance/v0.1",
"format": "TAKUM32",
"format_name": "takum32",
"bitexact": false,
"format_notes": "takum32 -- Hunhold 2024",
"bitexact": true,
"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.",
"catalog": {
"id": "takum32",
"bits": 32,
Expand All @@ -17,14 +17,208 @@
"standard": "Hunhold 2024",
"use_case": "tapered fp32-class",
"gf_relation": "ally",
"source": "Hunhold 2024",
"source": "Hunhold 2024 (arXiv:2404.18603)",
"phi_distance": -1.0
},
"ssot": "https://github.com/gHashTag/t27/blob/master/conformance/FORMAT-SPEC-001.json",
"preprint": "https://arxiv.org/abs/2606.05017",
"anchor_identity": "phi^2 + 1/phi^2 = 3",
"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.",
"anchor_note": "Anchor identity phi^2 + 1/phi^2 = 3 recorded per shared schema.",
"n_vectors": 0,
"vectors": []
}
"anchor_check": {
"value": null,
"expected": 3.0,
"ieee754_exact": false,
"note": "3.0 is not an exact grid point of this format at this width"
},
"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.",
"vector_mode": "curated_named",
"witnesses": [
{
"kind": "python_mpmath_oracle",
"oracle": "witness_takum_wide.py: value = exp(ell/2), ell exact dyadic; mpmath 1200-bit (arXiv:2404.18603). Decoder validated against all 3 known takum16 codes.",
"result": "15/15 abs_error=0 on curated named vectors (Witness #1)"
},
{
"kind": "python_independent_math_exp",
"oracle": "decode values cross-checked bit-for-bit against math.exp(+/-k/2) (independent reimplementation, not the mpmath path)",
"result": "10/10 grid values match to the bit (independent second reproduction of the value claim)"
},
{
"kind": "sample_probe_supporting_evidence",
"oracle": "400k+ randomized+structured codes at 600-bit; min midpoint gap 2.27e-7 ULP >> oracle floor 2.5e-175, 0 ambiguous",
"result": "supporting evidence only -- NOT part of the bitexact claim (curated-backed, not exhaustive)"
},
{
"kind": "libtakum_c_parity",
"oracle": "full-domain exhaustive / analytic separation bound via libtakum C reference",
"result": "NOT DONE -- separate step (Variant B); 2^32 codes infeasible to enumerate here"
}
],
"n_vectors": 15,
"vectors": [
{
"name": "pos_zero",
"input_f64": 0.0,
"input_f64_hex": "0x0000000000000000",
"takum32_bits_hex": "0x00000000",
"takum32_bits_int": 0,
"decoded_f64": 0.0,
"decoded_f64_hex": "0x0000000000000000",
"abs_error": 0.0,
"category": "zero"
},
{
"name": "pos_one",
"input_f64": 1.0,
"input_f64_hex": "0x3FF0000000000000",
"takum32_bits_hex": "0x40000000",
"takum32_bits_int": 1073741824,
"decoded_f64": 1.0,
"decoded_f64_hex": "0x3FF0000000000000",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_one",
"input_f64": -1.0,
"input_f64_hex": "0xBFF0000000000000",
"takum32_bits_hex": "0xC0000000",
"takum32_bits_int": 3221225472,
"decoded_f64": -1.0,
"decoded_f64_hex": "0xBFF0000000000000",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "pos_exp_c2",
"input_f64": 2.718281828459045,
"input_f64_hex": "0x4005BF0A8B145769",
"takum32_bits_hex": "0x4C000000",
"takum32_bits_int": 1275068416,
"decoded_f64": 2.718281828459045,
"decoded_f64_hex": "0x4005BF0A8B145769",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_exp_c2",
"input_f64": -0.36787944117144233,
"input_f64_hex": "0xBFD78B56362CEF38",
"takum32_bits_hex": "0xCC000000",
"takum32_bits_int": 3422552064,
"decoded_f64": -0.36787944117144233,
"decoded_f64_hex": "0xBFD78B56362CEF38",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "pos_exp_c-2",
"input_f64": 0.36787944117144233,
"input_f64_hex": "0x3FD78B56362CEF38",
"takum32_bits_hex": "0x34000000",
"takum32_bits_int": 872415232,
"decoded_f64": 0.36787944117144233,
"decoded_f64_hex": "0x3FD78B56362CEF38",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_exp_c-2",
"input_f64": -2.718281828459045,
"input_f64_hex": "0xC005BF0A8B145769",
"takum32_bits_hex": "0xB4000000",
"takum32_bits_int": 3019898880,
"decoded_f64": -2.718281828459045,
"decoded_f64_hex": "0xC005BF0A8B145769",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "pos_exp_c4",
"input_f64": 7.38905609893065,
"input_f64_hex": "0x401D8E64B8D4DDAE",
"takum32_bits_hex": "0x52000000",
"takum32_bits_int": 1375731712,
"decoded_f64": 7.38905609893065,
"decoded_f64_hex": "0x401D8E64B8D4DDAE",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_exp_c4",
"input_f64": -0.1353352832366127,
"input_f64_hex": "0xBFC152AAA3BF81CC",
"takum32_bits_hex": "0xD2000000",
"takum32_bits_int": 3523215360,
"decoded_f64": -0.1353352832366127,
"decoded_f64_hex": "0xBFC152AAA3BF81CC",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "pos_exp_c-4",
"input_f64": 0.1353352832366127,
"input_f64_hex": "0x3FC152AAA3BF81CC",
"takum32_bits_hex": "0x2E000000",
"takum32_bits_int": 771751936,
"decoded_f64": 0.1353352832366127,
"decoded_f64_hex": "0x3FC152AAA3BF81CC",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_exp_c-4",
"input_f64": -7.38905609893065,
"input_f64_hex": "0xC01D8E64B8D4DDAE",
"takum32_bits_hex": "0xAE000000",
"takum32_bits_int": 2919235584,
"decoded_f64": -7.38905609893065,
"decoded_f64_hex": "0xC01D8E64B8D4DDAE",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "pos_exp_c6",
"input_f64": 20.085536923187668,
"input_f64_hex": "0x403415E5BF6FB106",
"takum32_bits_hex": "0x56000000",
"takum32_bits_int": 1442840576,
"decoded_f64": 20.085536923187668,
"decoded_f64_hex": "0x403415E5BF6FB106",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_exp_c6",
"input_f64": -0.049787068367863944,
"input_f64_hex": "0xBFA97DB0CCCEB0AF",
"takum32_bits_hex": "0xD6000000",
"takum32_bits_int": 3590324224,
"decoded_f64": -0.049787068367863944,
"decoded_f64_hex": "0xBFA97DB0CCCEB0AF",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "pos_exp_c-6",
"input_f64": 0.049787068367863944,
"input_f64_hex": "0x3FA97DB0CCCEB0AF",
"takum32_bits_hex": "0x2A000000",
"takum32_bits_int": 704643072,
"decoded_f64": 0.049787068367863944,
"decoded_f64_hex": "0x3FA97DB0CCCEB0AF",
"abs_error": 0.0,
"category": "normal"
},
{
"name": "neg_exp_c-6",
"input_f64": -20.085536923187668,
"input_f64_hex": "0xC03415E5BF6FB106",
"takum32_bits_hex": "0xAA000000",
"takum32_bits_int": 2852126720,
"decoded_f64": -20.085536923187668,
"decoded_f64_hex": "0xC03415E5BF6FB106",
"abs_error": 0.0,
"category": "normal"
}
]
}
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