gfloat: Generic floating-point types in Python

An implementation of generic floating point encode/decode logic, handling various current and proposed floating point types:

• IEEE 754: Binary16, Binary32
• OCP Float8: E5M2, E4M3
• IEEE WG P3109: P3109_{K}p{P} for K > 2, and 1 <= P < K.
• OCP MX Formats: E2M1, M2M3, E3M2, E8M0, INT8, and the MX block formats.

The library favours readability and extensibility over speed (although the *_ndarray functions are reasonably fast for large arrays, see the benchmarking notebook). For other implementations of these datatypes more focused on speed see, for example, ml_dtypes, bitstring, MX PyTorch Emulation Library.

See https://gfloat.readthedocs.io for documentation, or dive into the notebooks to explore the formats.

For example, here's a table from the 02-value-stats notebook:

name	B: Bits in the format	P: Precision in bits	E: Exponent field width in bits	0<x<1	1<x<Inf	minSubnormal	maxSubnormal	minNormal	maxNormal	Exact in float16?	Exact in float32?
p3109_k3p2sf	3	2	1	1	1	0.5	0.5	1	1.5	True	True
ocp_e2m1	4	2	2	1	5	0.5	0.5	1	6	True	True
p3109_k4p2sf	4	2	2	3	3	0.25	0.25	0.5	3	True	True
ocp_e2m3	6	4	2	7	23	0.125	0.875	1	7.5	True	True
ocp_e3m2	6	3	3	11	19	0.0625	0.1875	0.25	28	True	True
p3109_k6p3sf	6	3	3	15	15	0.03125	0.09375	0.125	14	True	True
p3109_k6p4sf	6	4	2	15	15	0.0625	0.4375	0.5	3.75	True	True
ocp_e4m3	8	4	4	55	70	2^-9	7/4*2^-7	0.015625	448	True	True
ocp_e5m2	8	3	5	59	63	2^-16	3/2*2^-15	2^-14	57344	True	True
p3109_k8p1se	8	1	7	63	62	n/a	n/a	2^-63	2^62	False	True
p3109_k8p1ue	8	1	8	127	125	n/a	n/a	2^-127	2^125	False	True
p3109_k8p3se	8	3	5	63	62	2^-17	3/2*2^-16	2^-15	49152	True	True
p3109_k8p3sf	8	3	5	63	63	2^-17	3/2*2^-16	2^-15	57344	True	True
p3109_k8p3ue	8	3	6	127	125	2^-33	3/2*2^-32	2^-31	5/4*2^31	False	True
p3109_k8p3uf	8	3	6	127	126	2^-33	3/2*2^-32	2^-31	3/2*2^31	False	True
p3109_k8p4se	8	4	4	63	62	2^-10	7/4*2^-8	0.0078125	224	True	True
p3109_k8p4sf	8	4	4	63	63	2^-10	7/4*2^-8	0.0078125	240	True	True
p3109_k8p4ue	8	4	5	127	125	2^-18	7/4*2^-16	2^-15	53248	True	True
p3109_k8p4uf	8	4	5	127	126	2^-18	7/4*2^-16	2^-15	57344	True	True
p3109_k8p7sf	8	7	1	63	63	0.015625	63/32*2^-1	1	127/64*2^0	True	True
p3109_k8p8uf	8	8	1	127	126	0.0078125	127/64*2^-1	1	127/64*2^0	True	True
binary16	16	11	5	15359	16383	2^-24	1023/512*2^-15	2^-14	65504	True	True
bfloat16	16	8	8	16255	16383	2^-133	127/64*2^-127	2^-126	255/128*2^127	False	True
ocp_e8m0	8	1	8	127	127	n/a	n/a	2^-127	2^127	False	True
ocp_int8	8	8	0	63	63	0.015625	127/64*2^0	n/a	n/a	True	True

Notes

All NaNs are the same, with no distinction between signalling or quiet, or between differently encoded NaNs.