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| {"id":"gf6","name":"GF6 (rule-derived)","bits":6,"s_bits":1,"e_bits":2,"m_bits":3,"bias":1,"bias_formula":"1","phi_distance":0.049,"storage":"u8_packed","cluster":"GoldenFloat","status":"Open","standard":"this work; rule e=round(5/phi^2)=2; FP6 E2M3 bridge","use_case":"OPEN R&D: bridge GF4-GF8; FP6 E2M3 hint","gf_relation":"experimental","source":"specs/numeric/gf6.t27"} |
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| {"id":"gf_lns_hybrid","name":"GF + LNS hybrid (dual-space)","bits":16,"s_bits":1,"e_bits":6,"m_bits":9,"bias":31,"bias_formula":"31","phi_distance":0.049,"storage":"u16_plus_lns_path","cluster":"GoldenFloat","status":"Experimental","standard":"this work; mul in log-space, accumulate Lucas-closed","use_case":"OPEN R&D: dual-space arithmetic","gf_relation":"experimental","source":"section12.5"} |
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| {"id":"mxgf4","name":"MXGF4 (microscaling GF4)","bits":4,"s_bits":1,"e_bits":1,"m_bits":2,"bias":0,"bias_formula":"0","phi_distance":0.118,"storage":"u8_packed_plus_e8m0","cluster":"GoldenFloat","status":"Experimental","standard":"this work; OCP MX block + GF4","use_case":"OPEN R&D: phi-aligned MX-4 candidate","gf_relation":"experimental","source":"section12.5"} |
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| {"id":"ibm_hfp32","name":"IBM HFP (single)","bits":32,"s_bits":1,"e_bits":7,"m_bits":24,"bias":64,"bias_formula":"64","phi_distance":-1.0,"storage":"u32","cluster":"HistoricalVendor","status":"Historical","standard":"IBM System/360 (1964); base-16 exponent","use_case":"legacy mainframe","gf_relation":"orthogonal","source":"IBM POO"} |
| {"id":"ibm_hfp64","name":"IBM HFP (double)","bits":64,"s_bits":1,"e_bits":7,"m_bits":56,"bias":64,"bias_formula":"64","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"IBM System/360 (1964)","use_case":"legacy mainframe","gf_relation":"orthogonal","source":"IBM POO"} |
| {"id":"ibm_hfp128","name":"IBM HFP (extended)","bits":128,"s_bits":1,"e_bits":7,"m_bits":120,"bias":64,"bias_formula":"64","phi_distance":-1.0,"storage":"u128","cluster":"HistoricalVendor","status":"Historical","standard":"IBM z/Architecture","use_case":"legacy mainframe","gf_relation":"orthogonal","source":"IBM POO"} |
| {"id":"ms_mbf32","name":"Microsoft MBF (single)","bits":32,"s_bits":1,"e_bits":8,"m_bits":23,"bias":129,"bias_formula":"129","phi_distance":-1.0,"storage":"u32","cluster":"HistoricalVendor","status":"Historical","standard":"MS BASIC / MS-DOS (pre-IEEE)","use_case":"MS BASIC legacy","gf_relation":"orthogonal","source":"MS-DOS docs"} |
| {"id":"ms_mbf64","name":"Microsoft MBF (double)","bits":64,"s_bits":1,"e_bits":8,"m_bits":55,"bias":129,"bias_formula":"129","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"MS BASIC","use_case":"MS BASIC legacy","gf_relation":"orthogonal","source":"MS-DOS docs"} |
| {"id":"vax_f","name":"VAX F-float","bits":32,"s_bits":1,"e_bits":8,"m_bits":23,"bias":128,"bias_formula":"128","phi_distance":-1.0,"storage":"u32","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX","use_case":"DEC legacy","gf_relation":"orthogonal","source":"VAX Architecture Reference"} |
| {"id":"vax_d","name":"VAX D-float","bits":64,"s_bits":1,"e_bits":8,"m_bits":55,"bias":128,"bias_formula":"128","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX","use_case":"DEC legacy double","gf_relation":"orthogonal","source":"VAX Architecture Reference"} |
| {"id":"vax_g","name":"VAX G-float","bits":64,"s_bits":1,"e_bits":11,"m_bits":52,"bias":1024,"bias_formula":"1024","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX (IEEE-like)","use_case":"DEC legacy","gf_relation":"orthogonal","source":"VAX Architecture Reference"} |
| {"id":"vax_h","name":"VAX H-float","bits":128,"s_bits":1,"e_bits":15,"m_bits":112,"bias":16384,"bias_formula":"16384","phi_distance":-1.0,"storage":"u128","cluster":"HistoricalVendor","status":"Historical","standard":"DEC VAX","use_case":"DEC quad","gf_relation":"orthogonal","source":"VAX Architecture Reference"} |
| {"id":"cray_float","name":"Cray float","bits":64,"s_bits":1,"e_bits":15,"m_bits":48,"bias":16384,"bias_formula":"16384","phi_distance":-1.0,"storage":"u64","cluster":"HistoricalVendor","status":"Historical","standard":"Cray-1 (1976); no NaN/Inf, unrounded mul","use_case":"Cray legacy","gf_relation":"orthogonal","source":"Cray-1 Hardware Reference"} |
| {"id":"minifloat","name":"minifloat (arbitrary E:M, <=16 bits)","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"Theoretical","status":"Experimental","standard":"parametric framework","use_case":"design space of GF4/GF8/GF12/GF16","gf_relation":"ally","source":"Higham 1996"} |
| {"id":"unum_i","name":"Unum I (tapered + ubound)","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"Theoretical","status":"Experimental","standard":"Gustafson 2015 (predecessor to posit)","use_case":"interval arithmetic","gf_relation":"ally","source":"Gustafson 2015 (The End of Error)"} |
| {"id":"unum_ii","name":"Unum II (SORN projective)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"lookup_table","cluster":"Theoretical","status":"Experimental","standard":"Gustafson 2016","use_case":"lookup-table real arithmetic; not GF-comparable","gf_relation":"orthogonal","source":"Gustafson 2016"} |
| {"id":"tapered_fp","name":"tapered floating point","bits":0,"s_bits":1,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"Theoretical","status":"Experimental","standard":"Morris 1971; posit ancestor","use_case":"variable mantissa via regime bits","gf_relation":"ally","source":"Morris 1971 (IEEE TC)"} |
| {"id":"block_fp","name":"block floating point (BFP)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"CompressionTrick","status":"Verified","standard":"Wilkinson 1965; modern revivals","use_case":"per-tile shared exponent","gf_relation":"ally","source":"Darvish-Rouhani 2020"} |
| {"id":"shared_exp","name":"shared-exponent formats","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"CompressionTrick","status":"Verified","standard":"generalised BFP","use_case":"LLM quantization","gf_relation":"ally","source":"Darvish-Rouhani 2020"} |
| {"id":"per_channel_scale","name":"INT8 with per-channel scale","bits":8,"s_bits":1,"e_bits":0,"m_bits":7,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"u8_plus_fp32_scale","cluster":"CompressionTrick","status":"Verified","standard":"Jacob 2018 (TFLite)","use_case":"standard quant inference","gf_relation":"competitor","source":"Jacob 2018 (CVPR)"} |
| {"id":"stochastic_rounding","name":"stochastic rounding (technique)","bits":0,"s_bits":0,"e_bits":0,"m_bits":0,"bias":0,"bias_formula":"0","phi_distance":-1.0,"storage":"varies","cluster":"CompressionTrick","status":"Verified","standard":"Gupta 2015","use_case":"training small networks at low precision","gf_relation":"ally","source":"Gupta 2015 (ICML)"} |
|
|
