Finally a number type that you can count with your fingers. Super Mario and Zelda would be proud.

Comes in two flavours: Float8 has 3 exponent bits and 4 fraction bits, Float8_4 has 4 exponent bits and 3 fraction bits. Both rely on conversion to Float32 to perform any arithmetic operation, similar to Float16.

CAUTION: Float8_4(::Float32) currently contains a bug for subnormals.

julia> using Float8s

julia> a = Float8(4)
Float8(4.0)

julia> b = Float8(3.14159)
Float8(3.125)

julia> a+b
Float8(7.0)

julia> sqrt(a)
Float8(2.0)

julia> a^2
Inf8

Most arithmetic operations are implemented. If you would like to have an additional feature, raise an issue.

Float8s.jl is registered, just do

pkg> add Float8s

This package was written for the following publication

Klöwer M, PD Düben and TN Palmer, 2020. Number formats, error mitigation and scope for 16-bit arithmetics in weather and climate modelling analyzed with a shallow water model, Journal of Advances in Modeling Earth Systems, 12, e2020MS002246. doi: 10.1029/2020MS002246

If you use this package in your own research, please cite us.