Numeric error propagation: Difference between revisions

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 {{out}}
 <pre>111.80339887498948 ±2.938366893361004</pre>
+=={{header|Swift}}==
+<lang swift>import Foundation
+precedencegroup ExponentiationGroup {
+  higherThan: MultiplicationPrecedence
+}
+infix operator ** : ExponentiationGroup
+infix operator ±
+func ±(_ lhs: Double, _ rhs: Double) -> UncertainDouble { UncertainDouble(value: lhs, error: rhs) }
+struct UncertainDouble {
+  var value: Double
+  var error: Double
+  static func +(_ lhs: UncertainDouble, _ rhs: UncertainDouble) -> UncertainDouble {
+    return UncertainDouble(value: lhs.value + rhs.value, error: pow(pow(lhs.error, 2) + pow(rhs.error, 2), 0.5))
+  }
+  static func +(_ lhs: UncertainDouble, _ rhs: Double) -> UncertainDouble {
+    return UncertainDouble(value: lhs.value + rhs, error: lhs.error)
+  }
+  static func -(_ lhs: UncertainDouble, _ rhs: UncertainDouble) -> UncertainDouble {
+    return UncertainDouble(value: lhs.value - rhs.value, error: pow(pow(lhs.error, 2) + pow(rhs.error, 2), 0.5))
+  }
+  static func -(_ lhs: UncertainDouble, _ rhs: Double) -> UncertainDouble {
+    return UncertainDouble(value: lhs.value - rhs, error: lhs.error)
+  }
+  static func *(_ lhs: UncertainDouble, _ rhs: UncertainDouble) -> UncertainDouble {
+    let val = lhs.value * rhs.value
+    return UncertainDouble(
+      value: val,
+      error: pow(pow(val, 2) * (pow(lhs.error / lhs.value, 2) + pow(rhs.error / rhs.value, 2)), 0.5)
+    )
+  }
+  static func *(_ lhs: UncertainDouble, _ rhs: Double) -> UncertainDouble {
+    return UncertainDouble(value: lhs.value * rhs, error: abs(lhs.error * rhs))
+  }
+  static func /(_ lhs: UncertainDouble, _ rhs: UncertainDouble) -> UncertainDouble {
+    let val = lhs.value / rhs.value
+    return UncertainDouble(
+      value: val,
+      error: pow(val, 2) * (pow(lhs.error / lhs.value, 2) + pow(rhs.error / rhs.value, 2))
+    )
+  }
+  static func /(_ lhs: UncertainDouble, _ rhs: Double) -> UncertainDouble {
+    return UncertainDouble(value: lhs.value / rhs, error: abs(lhs.error * rhs))
+  }
+  static func **(_ lhs: UncertainDouble, _ power: Double) -> UncertainDouble {
+    let val = pow(lhs.value, power)
+    return UncertainDouble(value: val, error: abs((val * power) * (lhs.error / lhs.value)))
+  }
+}
+extension UncertainDouble: CustomStringConvertible {
+  public var description: String { "\(value) ± \(error)" }
+}
+let (x1, y1) = (100 ± 1.1, 50 ± 1.2)
+let (x2, y2) = (200 ± 2.2, 100 ± 2.3)
+let d = ((x2 - x1) ** 2 + (y2 - y1) ** 2) ** 0.5
+print(d)</lang>
+{{out}}
+<pre>111.80339887498948 ± 2.4871670631463423</pre>
 =={{header|Tcl}}==