Family Day update

Task/Numeric-error-propagation/Nim/numeric-error-propagation.nim

@@ -0,0 +1,42 @@
+import strformat
+import math
+
+type
+  Imprecise = object
+    x: float
+    σ: float
+
+template `^`(a, b: float): float =
+  pow(a, b)
+template `-`(a: Imprecise): Imprecise =
+  Imprecise(x: -a.x, σ: a.σ)
+template `+`(a, b: Imprecise): Imprecise =
+  Imprecise(x: a.x + b.x, σ: sqrt(a.σ ^ 2 + b.σ ^ 2))
+template `-`(a, b: Imprecise): Imprecise =
+  Imprecise(x: a.x - b.x, σ: sqrt(a.σ ^ 2 + b.σ ^ 2))
+template `*`(a, b: Imprecise): Imprecise =
+  let x = a.x * b.x
+  let σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
+  Imprecise(x: x, σ: σ)
+template `/`(a, b: Imprecise): Imprecise =
+  let x = a.x / b.x
+  let σ = sqrt(x ^ 2 * ((a.σ / a.x) ^ 2 + (b.σ / b.x) ^ 2))
+  Imprecise(x: x, σ: σ)
+template `^`(a: Imprecise, b: float): Imprecise =
+  if b < 0:
+    raise newException(IOError, "Cannot raise to negative power.")
+  let x = a.x ^ b
+  let σ = abs(x * b * a.σ / a.x)
+  Imprecise(x: x, σ: σ)
+template sqrt(a: Imprecise): Imprecise =
+  a ^ 0.5
+
+proc `$`(a: Imprecise): string =
+  fmt"{a.x:.2f} ± {a.σ:.2f}"
+
+var x1 = Imprecise(x: 100, σ: 1.1)
+var y1 = Imprecise(x: 50, σ: 1.2)
+var x2 = Imprecise(x: 200, σ: 2.2)
+var y2 = Imprecise(x: 100, σ: 2.3)
+
+echo $(sqrt((x1 - x2) ^ 2 + (y1 - y2) ^ 2))