SoftPosit.jl

A pure Julia implementation for posit arithmetic. Posit numbers are an alternative to floating-point numbers. Posits extend floats by introducing regime bits that allow for a higher precision around one, yet a wide dynamic range of representable numbers. For further information see posithub.org.

v0.5 respects the 2022 Standard for Posit Arithmetic but drops quire support. v0.4 implements the previous standard, has quire support but depends on the C implementation of SoftPosit.

If this library doesn't support a desired functionality or for anything else, please raise an issue.

Installation

In the Julia REPL do

julia>] add SoftPosit

where ] opens the package manager. Then simply using SoftPosit which enables all of the functionality.

Posit formats

SoftPosit.jl emulates and exports the following Posit number formats

Posit8, Posit16, Posit32
Posit16_1

Posit8, Posit16, Posit32 are the standard formats with 2 exponent bits. The off-standard format Posit(16,1) (16 bits with 1 exponent bit, exported as Posit16_1) was part of the previous posit arithmetic draft standard.

For all the formats conversions between integers and floats and basic arithmetic operations +, -, *, / and sqrt (among others) are defined.

Examples

Conversion to and from Float64 and computing a square root

julia> using SoftPosit
julia> p = Posit16(16)
Posit16(16.0)

julia> sqrt(p)
Posit16(4.0)

And the bitwise representation split into sign, regime, exponent and mantissa bits using bitstring(p,:split)

julia> bitstring(Posit32(123456.7),:split)
"0 111110 00 11100010010000001011010"

Or solving a linear equation system with Posit8

julia> A = Posit8.(randn(3,3))
3×3 Matrix{Posit8}:
 Posit8(1.125)      Posit8(-0.5625) Posit8(0.0390625)
 Posit8(-1.5)       Posit8(0.0625)  Posit8(1.25)
 Posit8(-0.40625)   Posit8(1.875)   Posit8(1.125)

julia> b = Posit8.(randn(3))
3-element Vector{Posit8}:
 Posit8(1.25)
 Posit8(-1.375)
 Posit8(-0.6875)

julia> A\b
3-element Vector{Posit8}:
 Posit8(1.0)
 Posit8(-0.21875)
 Posit8(0.125)

For an (outdated) comprehensive notebook covering (almost) all the functionality of SoftPosit.jl please read softposit_examples.ipynb

Rounding mode

Following the 2022 posit standard, posits should never underflow nor overflow. This is in v0.5 generally respected, but there are some caveats: Posits currently do underflow below about 4*floatmin of the float format you are converting from. In practice this is of little importance as even floatmin(::PositN)^2 is larger than that

julia> floatmin(Posit16)
Posit16(1.3877788e-17)

julia> floatmin(Posit16)*floatmin(Posit16)
Posit16(1.3877788e-17)

and similar for other posit formats. So in Posit16 arithmetic we have 1e-17*1e-17 = 1e-17 (no underflow) and 1e17*1e17 = 1e17 (no overflow).

Citation

If you use this package please cite us

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. 10.1029/2020MS002246