43 lines
1.2 KiB
Nim
43 lines
1.2 KiB
Nim
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import strformat
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import math
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type
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Imprecise = object
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x: float
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σ: float
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template `^`(a, b: float): float =
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pow(a, b)
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template `-`(a: Imprecise): Imprecise =
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Imprecise(x: -a.x, σ: a.σ)
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template `+`(a, b: Imprecise): Imprecise =
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Imprecise(x: a.x + b.x, σ: sqrt(a.σ ^ 2 + b.σ ^ 2))
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template `-`(a, b: Imprecise): Imprecise =
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Imprecise(x: a.x - b.x, σ: sqrt(a.σ ^ 2 + b.σ ^ 2))
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template `*`(a, b: Imprecise): Imprecise =
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let x = a.x * b.x
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let σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
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Imprecise(x: x, σ: σ)
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template `/`(a, b: Imprecise): Imprecise =
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let x = a.x / b.x
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let σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
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Imprecise(x: x, σ: σ)
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template `^`(a: Imprecise, b: float): Imprecise =
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if b < 0:
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raise newException(IOError, "Cannot raise to negative power.")
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let x = a.x ^ b
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let σ = abs(x * b * a.σ / a.x)
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Imprecise(x: x, σ: σ)
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template sqrt(a: Imprecise): Imprecise =
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a ^ 0.5
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proc `$`(a: Imprecise): string =
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fmt"{a.x:.2f} ± {a.σ:.2f}"
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var x1 = Imprecise(x: 100, σ: 1.1)
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var y1 = Imprecise(x: 50, σ: 1.2)
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var x2 = Imprecise(x: 200, σ: 2.2)
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var y2 = Imprecise(x: 100, σ: 2.3)
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echo $(sqrt((x1 - x2) ^ 2 + (y1 - y2) ^ 2))
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