id stringlengths 3 19 | name stringlengths 3 36 | bits int64 0 1.02k | s_bits int64 0 4 | e_bits int64 0 391 | m_bits int64 0 632 | bias float64 -2 79,228,162,514,264,340,000B | bias_formula stringlengths 1 29 | phi_distance float64 -1 1.88 | storage stringlengths 2 21 | cluster stringclasses 13
values | status stringclasses 4
values | standard stringlengths 6 102 | use_case stringlengths 8 68 | gf_relation stringclasses 5
values | source stringlengths 7 67 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
binary16 | binary16 (fp16, half) | 16 | 1 | 5 | 10 | 15 | 15 | 0.118 | u16 | Ieee754Binary | Verified | IEEE 754-2008 | GPU activations, inference | competitor | IEEE 754-2008 |
binary32 | binary32 (fp32, single) | 32 | 1 | 8 | 23 | 127 | 127 | 0.27 | u32 | Ieee754Binary | Verified | IEEE 754-1985 | industry default | competitor | IEEE 754-1985 |
binary64 | binary64 (fp64, double) | 64 | 1 | 11 | 52 | 1,023 | 1023 | 0.406 | u64 | Ieee754Binary | Verified | IEEE 754-1985 | scientific computing | competitor | IEEE 754-1985 |
binary128 | binary128 (fp128, quad) | 128 | 1 | 15 | 112 | 16,383 | 16383 | 0.484 | u128 | Ieee754Binary | Verified | IEEE 754-2008 | high-precision simulations | competitor | IEEE 754-2008 |
binary256 | binary256 (octuple) | 256 | 1 | 19 | 236 | 262,143 | 262143 | 0.538 | u256_software | Ieee754Binary | Verified | IEEE 754-2008 | astronomy, cryptography | competitor | IEEE 754-2008 |
decimal32 | decimal32 | 32 | 1 | 11 | 20 | 101 | 101 | -1 | u32 | Ieee754Decimal | Verified | IEEE 754-2008 (DPD/BID) | banking, GAAP | orthogonal | IEEE 754-2008 |
decimal64 | decimal64 | 64 | 1 | 13 | 50 | 398 | 398 | -1 | u64 | Ieee754Decimal | Verified | IEEE 754-2008 | financial databases | orthogonal | IEEE 754-2008 |
decimal128 | decimal128 | 128 | 1 | 17 | 110 | 6,176 | 6176 | -1 | u128 | Ieee754Decimal | Verified | IEEE 754-2008 | audit ledgers | orthogonal | IEEE 754-2008 |
x87_fp80 | x87 FP80 | 80 | 1 | 15 | 64 | 16,383 | 16383 | -1 | u80_padded | ExtendedFloat | Historical | Intel x87 (explicit integer bit) | legacy long double on x86 | orthogonal | Intel SDM |
double_double | double-double | 128 | 2 | 22 | 104 | 0 | 0 | -1 | two_u64 | ExtendedFloat | Verified | Bailey/Hida (software) | software extended precision | orthogonal | Bailey-Hida 2001 |
quad_double | quad-double | 256 | 4 | 44 | 208 | 0 | 0 | -1 | four_u64 | ExtendedFloat | Verified | Bailey/Hida (software) | astrophysics, quad-precision sims | orthogonal | Bailey-Hida 2001 |
bfloat16 | bfloat16 (BF16) | 16 | 1 | 8 | 7 | 127 | 127 | 0.525 | u16 | MlLowPrecision | Verified | Google Brain | training (range > precision) | competitor | Wang-Kanwar 2019 |
tf32 | TensorFloat-32 (TF32) | 19 | 1 | 8 | 10 | 127 | 127 | 0.27 | u32_padded | MlLowPrecision | Verified | NVIDIA Ampere | A100/H100 mixed precision | competitor | NVIDIA Ampere whitepaper |
fp8_e4m3 | FP8 E4M3 | 8 | 1 | 4 | 3 | 7 | 7 | 0.715 | u8 | MlLowPrecision | Verified | OCP / NVIDIA / Arm / Intel | inference, gradient ranges | competitor | Micikevicius 2022 (arXiv:2209.05433) |
fp8_e5m2 | FP8 E5M2 | 8 | 1 | 5 | 2 | 15 | 15 | 1.882 | u8 | MlLowPrecision | Verified | OCP / NVIDIA | activations, wide range | competitor | Micikevicius 2022 |
fp6_e3m2 | FP6 E3M2 | 6 | 1 | 3 | 2 | 3 | 3 | 0.882 | u8_packed | MlLowPrecision | Verified | OCP MX | aggressive quant inference | competitor | OCP MX v1.0 (2023) |
fp6_e2m3 | FP6 E2M3 | 6 | 1 | 2 | 3 | 1 | 1 | 0.049 | u8_packed | MlLowPrecision | Verified | OCP MX | mantissa-heavy quant | ally | OCP MX v1.0 (2023) |
fp4_e2m1 | FP4 E2M1 | 4 | 1 | 2 | 1 | 1 | 1 | 1.382 | u8_packed | MlLowPrecision | Verified | OCP MX | extreme quant inference | competitor | OCP MX v1.0 (2023) |
mxfp8 | MXFP8 | 8 | 1 | 4 | 3 | 7 | 7 | 0.715 | u8_plus_shared_e8m0 | Microscaling | Verified | OCP MX v1.0 | LLM inference | ally | Rouhani 2023 (arXiv:2310.10537) |
mxfp6 | MXFP6 | 6 | 1 | 3 | 2 | 3 | 3 | 0.882 | u8_packed_plus_e8m0 | Microscaling | Verified | OCP MX v1.0 | aggressive inference | ally | Rouhani 2023 |
mxfp4 | MXFP4 | 4 | 1 | 2 | 1 | 1 | 1 | 1.382 | u8_packed_plus_e8m0 | Microscaling | Verified | OCP MX v1.0 | extreme quant | ally | Rouhani 2023 |
nf4 | NF4 (NormalFloat 4-bit) | 4 | 0 | 0 | 4 | 0 | 0 | -1 | u8_packed | QuantTuned | Verified | Dettmers 2023 (QLoRA) | LLM weight quantization (quantile-based on N(0,1)) | orthogonal | Dettmers 2023 (arXiv:2305.14314) |
afp | AFP (Adaptive Floating-Point) | 16 | 1 | 8 | 7 | 127 | 127 | -1 | u16_plus_tensor_shift | QuantTuned | Verified | Tambe 2020 | efficient training | orthogonal | Tambe 2020 (DAC) |
posit8 | Posit8 | 8 | 1 | 2 | 0 | 0 | 0 | -1 | u8 | PositUnumIII | Verified | Posit Standard 2022 (es=2) | inference | ally | Posit Standard 2022 (posithub.org) |
posit16 | Posit16 | 16 | 1 | 2 | 0 | 0 | 0 | -1 | u16 | PositUnumIII | Verified | Posit Standard 2022 (es=2) | mixed-precision training | ally | Posit Standard 2022 |
posit32 | Posit32 | 32 | 1 | 2 | 0 | 0 | 0 | -1 | u32 | PositUnumIII | Verified | Posit Standard 2022 (es=2) | f32 replacement | ally | Posit Standard 2022 |
posit64 | Posit64 | 64 | 1 | 2 | 0 | 0 | 0 | -1 | u64 | PositUnumIII | Verified | Posit Standard 2022 (es=2) | f64 replacement | ally | Posit Standard 2022 |
takum8 | takum8 | 8 | 1 | 0 | 0 | 0 | 0 | -1 | u8 | PositUnumIII | Verified | Hunhold 2024 (tapered-precision) | IEEE-754 backward-compatible tapered | ally | Hunhold 2024 (arXiv:2412.20273) |
takum16 | takum16 | 16 | 1 | 0 | 0 | 0 | 0 | -1 | u16 | PositUnumIII | Verified | Hunhold 2024 | single-rule ladder counterexample | ally | Hunhold 2024 (arXiv:2412.20273) |
takum32 | takum32 | 32 | 1 | 0 | 0 | 0 | 0 | -1 | u32 | PositUnumIII | Verified | Hunhold 2024 | tapered fp32-class | ally | Hunhold 2024 |
takum64 | takum64 | 64 | 1 | 0 | 0 | 0 | 0 | -1 | u64 | PositUnumIII | Verified | Hunhold 2024 | tapered fp64-class | ally | Hunhold 2024 |
lns8 | LNS-8 | 8 | 1 | 7 | 0 | 0 | 0 | -1 | u8 | Lns | Verified | Arnold 1990; LNS-Madam (2021) | DSP, signal processing | orthogonal | Alam 2021 (arXiv:2106.13914) |
lns16 | LNS-16 | 16 | 1 | 15 | 0 | 0 | 0 | -1 | u16 | Lns | Verified | LNS-Madam (2021) | log-domain training (mul -> add) | orthogonal | Alam 2021 |
lns32 | LNS-32 | 32 | 1 | 31 | 0 | 0 | 0 | -1 | u32 | Lns | Verified | LNS-Madam (2021) | log-domain DSP | orthogonal | Alam 2021 |
lns64 | LNS-64 | 64 | 1 | 63 | 0 | 0 | 0 | -1 | u64 | Lns | Verified | LNS-Madam (2021) | scientific log-domain | orthogonal | Alam 2021 |
gfternary | GFTernary | 2 | 1 | 0 | 2 | 0 | 0 | 0 | u2 | GoldenFloat | Verified | this work; {-phi, 0, +phi} | bulk layers (hybrid) | self | BENCH-007 |
gf4 | GF4 | 4 | 1 | 1 | 2 | 0 | 0 | 0.118 | u8 | GoldenFloat | Experimental | this work; F0 minimal | proof-of-concept | self | specs/numeric/gf4.t27 |
gf8 | GF8 | 8 | 1 | 3 | 4 | 3 | 3 | 0.132 | u8 | GoldenFloat | Verified | this work; L1 Lucas | edge / sensors | self | BENCH-007 (specs/numeric/gf8.t27) |
gf12 | GF12 | 12 | 1 | 4 | 7 | 7 | 7 | 0.047 | u16 | GoldenFloat | Verified | this work; L0/F3 | mid-range / audio | self | BENCH-007 (specs/numeric/gf12.t27) |
gf16 | GF16 | 16 | 1 | 6 | 9 | 31 | 31 | 0.049 | u16 | GoldenFloat | Verified | this work; PHI_BIAS=60; FPGA 35/35 at 323 MHz Artix-7 | training and inference (production) | self | specs/numeric/gf16.t27; zenodo 10.5281/zenodo.19227877 (HW archive) |
gf20 | GF20 | 20 | 1 | 7 | 12 | 63 | 63 | 0.035 | u32 | GoldenFloat | Experimental | this work; 17-squared empirical PHI_BIAS=289 | high-precision edge | self | specs/numeric/gf20.t27 (spec only) |
gf24 | GF24 | 24 | 1 | 9 | 14 | 255 | 255 | 0.025 | u32 | GoldenFloat | Experimental | this work; rule e=round(23/phi^2)=9; normative bias=2^(e-1)-1=255; empirical PHI_BIAS=1364 (=L15) OPEN | server inference | self | specs/numeric/gf24.t27 (spec only) |
gf32 | GF32 | 32 | 1 | 12 | 19 | 2,047 | 2047 | 0.014 | u32 | GoldenFloat | Verified | this work; F0 resolved | fp32 drop-in | self | BENCH-012 (specs/numeric/gf32.t27) |
gf64 | GF64 | 64 | 1 | 24 | 39 | 8,388,607 | 8388607 | 0.003 | u64 | GoldenFloat | Verified | this work; EXP_MAX - BIAS | scientific / double | self | BENCH-007b (specs/numeric/gf64.t27) |
gf6 | GF6 (rule-derived) | 6 | 1 | 2 | 3 | 1 | 1 | 0.049 | u8_packed | GoldenFloat | Open | this work; rule e=round(5/phi^2)=2; FP6 E2M3 bridge | OPEN R&D: bridge GF4-GF8; FP6 E2M3 hint | experimental | specs/numeric/gf6.t27 |
gf10 | GF10 (rule-derived) | 10 | 1 | 3 | 6 | 3 | 3 | 0.118 | u16 | GoldenFloat | Open | this work; rule e=round(9/phi^2)=3; bridge GF8-GF12 | OPEN R&D: tight-precision activations | experimental | specs/numeric/gf10.t27 |
gf14 | GF14 (rule-derived) | 14 | 1 | 5 | 8 | 15 | 15 | 0.007 | u16 | GoldenFloat | Open | this work; rule e=round(13/phi^2)=5; bridge GF12-GF16; lowest phi-dist below GF48 | OPEN R&D: drop-in for fp16 with tighter phi alignment | experimental | specs/numeric/gf14.t27 |
gf48 | GF48 (rule-derived) | 48 | 1 | 18 | 29 | 131,071 | 131071 | 0.003 | u64_padded | GoldenFloat | Open | this work; rule e=round(47/phi^2)=18 | OPEN R&D: between GF32 and GF64; tightest phi-dist of the wide rungs | experimental | specs/numeric/gf48.t27 |
gf96 | GF96 (rule-derived) | 96 | 1 | 36 | 59 | 34,359,738,367 | 34359738367 | 0.008 | u128_padded | GoldenFloat | Open | this work; rule e=round(95/phi^2)=36 | OPEN R&D: between GF64 and GF128 (phi-aligned extended) | experimental | specs/numeric/gf96.t27 |
gf128 | GF128 (rule-derived) | 128 | 1 | 49 | 78 | 281,474,976,710,655 | 281474976710655 | 0.01 | u128 | GoldenFloat | Open | this work; rule e=round(127/phi^2)=49 (corrects v1.1 typo e=48) | OPEN R&D: phi-aligned binary128 alternative | experimental | specs/numeric/gf128.t27 |
gf256 | GF256 (rule-derived) | 256 | 1 | 97 | 158 | 79,228,162,514,264,340,000,000,000,000 | 79228162514264337593543950335 | 0.004 | u256_software | GoldenFloat | Open | this work; rule e=round(255/phi^2)=97; normative bias=2^96-1 | OPEN R&D: phi-aligned binary256 alternative | experimental | specs/numeric/gf256.t27 |
gf512 | GF512 (rule-derived) | 512 | 1 | 195 | 316 | -2 | 2^194-1 | 0.0009 | u512_software | GoldenFloat | Open | this work; rule e=round(511/phi^2)=195 | OPEN R&D: ultra-wide phi-aligned (extrapolation, no RTL) | experimental | specs/numeric/gf512.t27 |
gf1024 | GF1024 (rule-derived) | 1,024 | 1 | 391 | 632 | -2 | 2^390-1 | 0.0006 | u1024_software | GoldenFloat | Open | this work; rule e=round(1023/phi^2)=391; lowest phi-distance in the ladder | OPEN R&D: limit-of-ladder phi alignment (extrapolation, no RTL) | experimental | specs/numeric/gf1024.t27 |
gf8_bfp | GF8-BFP (block FP atop GF8) | 8 | 1 | 3 | 4 | 3 | 3 | 0.132 | u8_plus_shared_exp | GoldenFloat | Experimental | this work; per-tile shared exponent | OPEN R&D: LLM-quantization-friendly GF8 | experimental | section12.5 |
gf_lns_hybrid | GF + LNS hybrid (dual-space) | 16 | 1 | 6 | 9 | 31 | 31 | 0.049 | u16_plus_lns_path | GoldenFloat | Experimental | this work; mul in log-space, accumulate Lucas-closed | OPEN R&D: dual-space arithmetic | experimental | section12.5 |
mxgf6 | MXGF6 (microscaling GF6) | 6 | 1 | 2 | 3 | 1 | 1 | 0.05 | u8_packed_plus_e8m0 | GoldenFloat | Experimental | this work; OCP MX block + GF6 | OPEN R&D: phi-aligned MX-6 candidate | experimental | section12.5 |
mxgf4 | MXGF4 (microscaling GF4) | 4 | 1 | 1 | 2 | 0 | 0 | 0.118 | u8_packed_plus_e8m0 | GoldenFloat | Experimental | this work; OCP MX block + GF4 | OPEN R&D: phi-aligned MX-4 candidate | experimental | section12.5 |
int4 | INT4 / UINT4 | 4 | 1 | 0 | 3 | 0 | 0 | -1 | u8_packed | IntegerFixed | Verified | two complement | aggressive quantization | competitor | ISO/IEC 9899 |
int8 | INT8 / UINT8 | 8 | 1 | 0 | 7 | 0 | 0 | -1 | u8 | IntegerFixed | Verified | two complement | INT8 inference, per-channel scale | competitor | ISO/IEC 9899 |
int16 | INT16 / UINT16 | 16 | 1 | 0 | 15 | 0 | 0 | -1 | u16 | IntegerFixed | Verified | two complement | DSP, embedded ML | competitor | ISO/IEC 9899 |
int32 | INT32 / UINT32 | 32 | 1 | 0 | 31 | 0 | 0 | -1 | u32 | IntegerFixed | Verified | two complement | general CPU integer | competitor | ISO/IEC 9899 |
int64 | INT64 / UINT64 | 64 | 1 | 0 | 63 | 0 | 0 | -1 | u64 | IntegerFixed | Verified | two complement | databases, timestamps | competitor | ISO/IEC 9899 |
int128 | INT128 / UINT128 | 128 | 1 | 0 | 127 | 0 | 0 | -1 | u128 | IntegerFixed | Verified | two complement | crypto, big-int | competitor | Rust/Clang u128 |
q_format | Q-format (Qm.n) | 0 | 1 | 0 | 0 | 0 | 0 | -1 | varies | IntegerFixed | Verified | TI fixed-point | audio DSP, fixed-point ML | orthogonal | TI SPRA704 |
bcd | BCD (binary-coded decimal) | 0 | 0 | 0 | 0 | 0 | 0 | -1 | u4_per_digit | IntegerFixed | Historical | IBM 1959 | calculators, GAAP | orthogonal | ISO/IEC 8859 |
ibm_hfp32 | IBM HFP (single) | 32 | 1 | 7 | 24 | 64 | 64 | -1 | u32 | HistoricalVendor | Historical | IBM System/360 (1964); base-16 exponent | legacy mainframe | orthogonal | IBM POO |
ibm_hfp64 | IBM HFP (double) | 64 | 1 | 7 | 56 | 64 | 64 | -1 | u64 | HistoricalVendor | Historical | IBM System/360 (1964) | legacy mainframe | orthogonal | IBM POO |
ibm_hfp128 | IBM HFP (extended) | 128 | 1 | 7 | 120 | 64 | 64 | -1 | u128 | HistoricalVendor | Historical | IBM z/Architecture | legacy mainframe | orthogonal | IBM POO |
ms_mbf32 | Microsoft MBF (single) | 32 | 1 | 8 | 23 | 129 | 129 | -1 | u32 | HistoricalVendor | Historical | MS BASIC / MS-DOS (pre-IEEE) | MS BASIC legacy | orthogonal | MS-DOS docs |
ms_mbf64 | Microsoft MBF (double) | 64 | 1 | 8 | 55 | 129 | 129 | -1 | u64 | HistoricalVendor | Historical | MS BASIC | MS BASIC legacy | orthogonal | MS-DOS docs |
vax_f | VAX F-float | 32 | 1 | 8 | 23 | 128 | 128 | -1 | u32 | HistoricalVendor | Historical | DEC VAX | DEC legacy | orthogonal | VAX Architecture Reference |
vax_d | VAX D-float | 64 | 1 | 8 | 55 | 128 | 128 | -1 | u64 | HistoricalVendor | Historical | DEC VAX | DEC legacy double | orthogonal | VAX Architecture Reference |
vax_g | VAX G-float | 64 | 1 | 11 | 52 | 1,024 | 1024 | -1 | u64 | HistoricalVendor | Historical | DEC VAX (IEEE-like) | DEC legacy | orthogonal | VAX Architecture Reference |
vax_h | VAX H-float | 128 | 1 | 15 | 112 | 16,384 | 16384 | -1 | u128 | HistoricalVendor | Historical | DEC VAX | DEC quad | orthogonal | VAX Architecture Reference |
cray_float | Cray float | 64 | 1 | 15 | 48 | 16,384 | 16384 | -1 | u64 | HistoricalVendor | Historical | Cray-1 (1976); no NaN/Inf, unrounded mul | Cray legacy | orthogonal | Cray-1 Hardware Reference |
minifloat | minifloat (arbitrary E:M, <=16 bits) | 0 | 1 | 0 | 0 | 0 | 0 | -1 | varies | Theoretical | Experimental | parametric framework | design space of GF4/GF8/GF12/GF16 | ally | Higham 1996 |
unum_i | Unum I (tapered + ubound) | 0 | 1 | 0 | 0 | 0 | 0 | -1 | varies | Theoretical | Experimental | Gustafson 2015 (predecessor to posit) | interval arithmetic | ally | Gustafson 2015 (The End of Error) |
unum_ii | Unum II (SORN projective) | 0 | 0 | 0 | 0 | 0 | 0 | -1 | lookup_table | Theoretical | Experimental | Gustafson 2016 | lookup-table real arithmetic; not GF-comparable | orthogonal | Gustafson 2016 |
tapered_fp | tapered floating point | 0 | 1 | 0 | 0 | 0 | 0 | -1 | varies | Theoretical | Experimental | Morris 1971; posit ancestor | variable mantissa via regime bits | ally | Morris 1971 (IEEE TC) |
block_fp | block floating point (BFP) | 0 | 0 | 0 | 0 | 0 | 0 | -1 | varies | CompressionTrick | Verified | Wilkinson 1965; modern revivals | per-tile shared exponent | ally | Darvish-Rouhani 2020 |
shared_exp | shared-exponent formats | 0 | 0 | 0 | 0 | 0 | 0 | -1 | varies | CompressionTrick | Verified | generalised BFP | LLM quantization | ally | Darvish-Rouhani 2020 |
per_channel_scale | INT8 with per-channel scale | 8 | 1 | 0 | 7 | 0 | 0 | -1 | u8_plus_fp32_scale | CompressionTrick | Verified | Jacob 2018 (TFLite) | standard quant inference | competitor | Jacob 2018 (CVPR) |
stochastic_rounding | stochastic rounding (technique) | 0 | 0 | 0 | 0 | 0 | 0 | -1 | varies | CompressionTrick | Verified | Gupta 2015 | training small networks at low precision | ally | Gupta 2015 (ICML) |
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