Microfloats is a Julia package that implements floating point types and arithmetic for sub-8 bit floating point types, supporting arbitrary combinations of sign, exponent, and mantissa bits.
Instances of a sub-8 bit floating point type are still 8 bits wide in memory; the goal of Microfloat is to serve as a base for arithmetic operations and method dispatch, lending downstream packages a good abstraction for doing bitpacking and hardware acceleration.
We can recreate the Float8 and Float8_4 types exported by Float8s.jl through the Microfloat type constructor, which takes the number of sign, exponent, and mantissa bits as arguments:
using Microfloats
const Float8 = Microfloat(1, 3, 4)
const Float8_4 = Microfloat(1, 4, 3)
# creating a sawed-off Float16 (BFloat8?) becomes trivial:
const Float8_5 = Microfloat(1, 5, 2)Microfloats implements the E4M3, E5M2, E2M3, E3M2, E2M1, and E8M0 types from the Open Compute Project Microscaling Formats (MX) Specification, with most of these using saturated arithmetic (no infinities), and different bit layouts for NaNs. These are exported as MX_E4M3, MX_E5M2, MX_E2M3, MX_E3M2, MX_E2M1, and MX_E8M0, respectively.
For INT8, see FixedPointNumbers.Q1f6.
Warning
MX types may not yet be fully OCP compliant. See issues with the 
Since Microfloats.jl only implements the primitive types, microscaling itself may be done with Microscaling.jl, which includes quantization and bitpacking.
using Pkg
Pkg.Registry.add(url="https://github.com/MurrellGroup/MurrellGroupRegistry")
Pkg.add("Microfloats")