80 lines
3.2 KiB
Julia
80 lines
3.2 KiB
Julia
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# This file is a part of Julia. License is MIT: https://julialang.org/license
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# Here we implement a minimal dimensionful type Furlong, which is used
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# to test dimensional correctness of various functions in Base. Furlong
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# is exported by the TestHelpers module.
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# represents a quantity in furlongs^p
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struct Furlong{p,T<:Number} <: Number
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val::T
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Furlong{p,T}(v::Number) where {p,T} = new(v)
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Furlong{p,T}(x::Furlong{p}) where {p,T} = new(x.val)
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end
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Furlong{T<:Number}(x::T) = Furlong{1,T}(x)
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(::Type{T}){p,T}(x::Furlong{p,T}) = x.val
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(::Type{Furlong{p}}){p}(v::Number) = Furlong{p,typeof(v)}(v)
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Base.convert{T,p,S}(::Type{Furlong{p,T}}, x::Furlong{p,S}) = Furlong{p,T}(convert(T,x.val))
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Base.convert{T}(::Type{Furlong{0,T}}, x::Furlong{0}) = Furlong{0,T}(convert(T, x.val))
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Base.convert{T<:Number}(::Type{T}, x::Furlong{0}) = convert(T, x.val)
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Base.convert{T}(::Type{Furlong{0,T}}, x::Number) = Furlong{0,T}(convert(T, x))
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Base.promote_type{p,T,S}(::Type{Furlong{p,T}}, ::Type{Furlong{p,S}}) =
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(Base.@_pure_meta; Furlong{p,promote_type(T,S)})
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Base.one{p,T}(x::Furlong{p,T}) = one(T)
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Base.one{p,T}(::Type{Furlong{p,T}}) = one(T)
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Base.zero{p,T}(x::Furlong{p,T}) = Furlong{p,T}(zero(T))
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Base.zero{p,T}(::Type{Furlong{p,T}}) = Furlong{p,T}(zero(T))
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Base.iszero(x::Furlong) = iszero(x.val)
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# convert Furlong exponent p to a canonical form. This
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# is not type stable, but it doesn't matter since it is used
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# at compile time (in generated functions), not runtime
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canonical_p(p) = isinteger(p) ? Int(p) : Rational{Int}(p)
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Base.abs{p}(x::Furlong{p}) = Furlong{p}(abs(x.val))
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@generated Base.abs2{p}(x::Furlong{p}) = :(Furlong{$(canonical_p(2p))}(abs2(x.val)))
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@generated Base.inv{p}(x::Furlong{p}) = :(Furlong{$(canonical_p(-p))}(inv(x.val)))
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Base.sylvester(a::Furlong,b::Furlong,c::Furlong) = -c / (a + b)
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for f in (:isfinite, :isnan, :isreal)
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@eval Base.$f(x::Furlong) = $f(x.val)
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end
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for f in (:real,:imag,:complex,:middle,:+,:-)
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@eval Base.$f{p}(x::Furlong{p}) = Furlong{p}($f(x.val))
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end
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import Base: +, -, ==, !=, <, <=, isless, isequal, *, /, //, div, rem, mod, ^,
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middle, hypot
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for op in (:+, :-, :middle, :hypot)
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@eval function $op{p}(x::Furlong{p}, y::Furlong{p})
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v = $op(x.val, y.val)
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Furlong{p}(v)
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end
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end
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for op in (:(==), :(!=), :<, :<=, :isless, :isequal)
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@eval $op{p}(x::Furlong{p}, y::Furlong{p}) = $op(x.val, y.val)
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end
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# generated functions to allow type inference of the value of the exponent:
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for (f,op) in ((:_plus,:+),(:_minus,:-),(:_times,:*),(:_div,://))
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@eval @generated function $f{T,p,q}(v::T, ::Furlong{p}, ::Union{Furlong{q},Type{Val{q}}})
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s = $op(p, q)
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:(Furlong{$(canonical_p(s)),$T}(v))
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end
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end
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for (op,eop) in ((:*, :_plus), (:/, :_minus), (://, :_minus), (:div, :_minus))
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@eval begin
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$op{p,q}(x::Furlong{p}, y::Furlong{q}) =
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$eop($op(x.val, y.val),x,y)
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$op{p,S<:Number}(x::Furlong{p}, y::S) = $op(x,Furlong{0,S}(y))
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$op{p,S<:Number}(x::S, y::Furlong{p}) = $op(Furlong{0,S}(x),y)
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end
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end
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for op in (:rem, :mod)
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@eval begin
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$op{p}(x::Furlong{p}, y::Furlong) = Furlong{p}($op(x.val, y.val))
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$op{p}(x::Furlong{p}, y::Number) = Furlong{p}($op(x.val, y))
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end
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end
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Base.sqrt(x::Furlong) = _div(sqrt(x.val), x, Val{2})
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