Efficient unit-checked computation


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SIUnits SIUnits

This package provides efficient unit-checked computations based for units in the SIUnits systems. To use this package use (after installing it using Pkg.add)

using SIUnits

optionally, you may also use

using SIUnits
using SIUnits.ShortUnits

instead, to load a number of abbreviations into the current namespace (e.g. kg instead of KiloGram). These abbreviations are not loaded by default to avoid flooding the namespace where this is not desired. Note that all examples in this README assume that the second form was used. To make the examples work with the first form, just substitute the written out names, e.g. Volt for V and Nano*Meter for nm.


SIUnits.jl integrates into the number promotion system and all the usual arithmetic operations (+,-,*,/,^,sqrt) work as one would expect. In particular, addition and subtraction is allowed between two quantities with the same units:

julia> 1V + 2V
3 kg m²s⁻³A⁻¹

julia> (1//2)s - 1s
-1//2 s

However, you may not add or subtract quantities whose units differ:

julia> 1s + 2V
ERROR: Unit mismatch. Got (s ) + (kg m²s⁻³A⁻¹)

Consistently, multiplication and division increase or decrease the exponents of the base units, e.g.:

julia> 1N
1 kg m s⁻²

julia> 1N/m
1 kg s⁻²

julia> 1N*s^2
1 kg m

You may also take square roots of quantities with units:

julia> sqrt(1s^2)
1.0 s

However, currently, the result must have integral exponents. Support for fractional exponents may be added in the future:

julia> sqrt(1m)
ERROR: InexactError()

Converting between unitful and unitless quantities

SIUnits.jl does not define implicit convert methods to avoid silently losing unit information where this may be undesirable. Instead, SIUnits.jl extends the various forced type conversions e.g. float, float64 and int. Packages writing generic code should use these where a specific unitless value is required.

Implementation details

Where possible (i.e. where the compiler can reason about the type of a variable), there is no runtime overhead. For example:

julia> [1V, 2V, 3V]
3-element Array{SIQuantity{Int64,2,1,-3,-1,0,0,0},1}:
 1 kg m²s⁻³A⁻¹
 2 kg m²s⁻³A⁻¹
 3 kg m²s⁻³A⁻¹

julia> sizeof(ans)

this is the same amount of storage as that taken up by a simple array of three 64bit integers:

julia> sizeof([1 2 3])

This shows that there is no runtime memory overhead. Similarly, the code generated to add two 64bit integers:

julia> code_native(+,(Uint64,Uint64))
    .section    __TEXT,__text,regular,pure_instructions
Filename: int.jl
Source line: 42
    push    RBP
    mov RBP, RSP
Source line: 42
    add RDI, RSI
    mov RAX, RDI
    pop RBP

is exactly the same as the code two add two 64bit integer quantities with units:

julia> code_native(+,typeof((1V,2V)))
    .section    __TEXT,__text,regular,pure_instructions
Filename: /Users/kfischer/.julia/SIUnits/src/SIUnits.jl
Source line: 122
    push    RBP
    mov RBP, RSP
Source line: 122
    add RDI, RSI
Source line: 123
    mov RAX, RDI
    pop RBP

This is achieved by keeping track of the exponents as part of the type rather than of the value. An SIQuantity is defined as

immutable SIQuantity{T<:Number,m,kg,s,A,K,mol,cd} <: Number

where the m,kg,s,A,K,mol,cd type parameters keep track of the exponents of the respective base units. This definition is the core of the package. The rest makes it play nicely with the numeric promotion sytem to make sure that generic code will work just fine on SIQuantities.

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