Julia types for the C-based SoftPosit library - a posit arithmetic emulator.
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 https://posithub.org
If this library doesn't support a desired functionality or for anything else, please raise an issue.
In the Julia REPL do
julia>] add SoftPositwhere ] opens the package manager. Then simply using SoftPosit which enables all of the functionality.
SoftPosit.jl emulates the following Posit number formats Posit(n,es), with n number of bits including es exponent bits: Posit(8,0), Posit(16,1), Posit(32,2) as primitive types called
Posit8, Posit16, Posit32
following the draft standard. Additionally, the following off-standard formats are defined as primitive types, which are internally stored as 32bit (the remaining bits are kept as zeros): Posit(8,1), Posit(8,2), Posit(16,1), Posit(16,2), Posit(24,1), and Posit(24,2) called Posit8_1, Posit8_2, Posit16_1, Posit16_2, Posit24_1, and Posit24_2.
For all the types Posit8, Posit16, Posit32, Posit8_2, Posit16_2, Posit24_2 conversions between Integers and Floats and basic arithmetic operations +, -, *, / and sqrt (among others) are defined. Unfortunately, Posit8_1, Posit16_1, Posit24_1 are not yet fully supported by the underlying C library.
To support quires, Quire8, Quire16 and Quire32 are implemented as 32 / 128 / 512bit types for fused multiply-add and fused multiply-subtract. Additional math functions like exp,log,sin,cos,tan are defined via conversion to Float64 (no support yet of the C library) and therefore do not have error-free rounding.
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"For a comprehensive notebook covering (almost) all the functionality of SoftPosit.jl please read softposit_examples.ipynb
Following the posit standard, posits should underflow between [-minpos/2,0) and (0,minpos/2] and never overflow in (-∞,-maxpos] and [maxpos,∞). Float ±infinity and Not-a-Number are mapped to posit Not-a-Real NaR, and NaR is mapped back to NaN. In the current version v0.4 the implementaion of this rounding mode make a few changes
- Posit8 and Posit32: No underflow, all numbers in [-minpos,0) are mapped to -minpos (and (0,minpos] to minpos)
- Posit16: Underflow occurs at minpos/4 and overflow occurs at floatmax(Float32)/4
Round to nearest, tie to even is implemented for all formats.