60 lines
1.3 KiB
Text
60 lines
1.3 KiB
Text
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module NumericError
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import Base: convert, promote_rule, +, -, *, /, ^
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export Measure
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type Measure <: Number
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x::Float64
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σ::Float64
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Measure(x::Real) = new(Float64(x), 0)
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Measure(x::Real, σ::Real) = new(Float64(x), σ)
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end
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Base.show(io::IO, x::Measure) = print(io, string(x.x, " ± ", x.σ))
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Base.convert(::Type{Measure}, x::Real) = Measure(Float64(x), 0.0)
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Base.promote_rule(::Type{Float64}, ::Type{Measure}) = Measure
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Base.promote_rule(::Type{Int64}, ::Type{Measure}) = Measure
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+(a::Measure, b::Measure) = Measure(a.x + b.x, sqrt(a.σ ^ 2 + b.σ ^ 2))
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-(a::Measure, b::Measure) = Measure(a.x - b.x, sqrt(a.σ ^ 2 + b.σ ^ 2))
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-(a::Measure) = Measure(-a.x, a.σ)
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*(a::Measure, b::Measure) = begin
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x = a.x * b.x
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σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
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Measure(x, σ)
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end
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/(a::Measure, b::Measure) = begin
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x = a.x / b.x
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σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
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Measure(x, σ)
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end
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^(a::Measure, b::Float64) = begin
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x = a.x ^ b
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σ = abs(x * b * a.σ / a.x)
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Measure(x, σ)
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end
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Base.sqrt(a::Measure) = a ^ .5
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end # module NumericError
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using NumericError
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# x1 = 100 ± 1.1
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# y1 = 50 ± 1.2
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# x2 = 200 ± 2.2
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# y2 = 100 ± 2.3
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x1 = Measure(100, 1.1)
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y1 = Measure(50, 1.2)
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x2 = Measure(200, 2.2)
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y2 = Measure(100, 2.3)
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d = sqrt((x1 - x2) ^ 2 + (y1 - y2) ^ 2)
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@show x1 y1 x2 y2 sqrt((x1 - x2) ^ 2 + (y1 - y2) ^ 2)
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