gfloat 0.4

Generic floating point handling in Python

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: P{p} for p in 1..7
• 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	Exact in float16?	maxFinite	minFinite	maxNormal	minNormal	minSubnormal	maxSubnormal
ocp_e2m1	4	2	2	1	5	True	6	-6	6	1	0.5	0.5
ocp_e2m3	6	4	2	7	23	True	7.5	-7.5	7.5	1	0.125	0.875
ocp_e3m2	6	3	3	11	19	True	28	-28	28	0.25	0.0625	0.1875
ocp_e4m3	8	4	4	55	70	True	448	-448	448	0.015625	1*2^-9	7/4*2^-7
ocp_e5m2	8	3	5	59	63	True	57344	-57344	57344	1*2^-14	1*2^-16	3/2*2^-15
p3109_p1	8	1	7	62	63	False	1*2^63	-1*2^63	1*2^63	1*2^-62	nan	nan
p3109_p2	8	2	6	63	62	False	1*2^31	-1*2^31	1*2^31	1*2^-31	1*2^-32	1*2^-32
p3109_p3	8	3	5	63	62	True	49152	-49152	49152	1*2^-15	1*2^-17	3/2*2^-16
p3109_p4	8	4	4	63	62	True	224	-224	224	0.0078125	1*2^-10	7/4*2^-8
p3109_p5	8	5	3	63	62	True	15	-15	15	0.125	0.0078125	15/8*2^-4
p3109_p6	8	6	2	63	62	True	3.875	-3.875	3.875	0.5	0.015625	31/16*2^-2
bfloat16	16	8	8	16255	16383	False	255/128*2^127	-255/128*2^127	255/128*2^127	1*2^-126	1*2^-133	127/64*2^-127
ocp_int8	8	8	0	63	63	True	127/64*2^0	-2	nan	nan	0.015625	127/64*2^0
ocp_e8m0	8	1	8	127	127	False	1*2^127	1*2^-127	1*2^127	1*2^-127	nan	nan

Notes

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