Initial data commit

Task/Quaternion-type/Swift/quaternion-type.swift

@@ -0,0 +1,134 @@
+import Foundation
+
+struct Quaternion {
+  var a, b, c, d: Double
+
+  static let i = Quaternion(a: 0, b: 1, c: 0, d: 0)
+  static let j = Quaternion(a: 0, b: 0, c: 1, d: 0)
+  static let k = Quaternion(a: 0, b: 0, c: 0, d: 1)
+}
+extension Quaternion: Equatable {
+  static func ==(lhs: Quaternion, rhs: Quaternion) -> Bool {
+    return (lhs.a, lhs.b, lhs.c, lhs.d) == (rhs.a, rhs.b, rhs.c, rhs.d)
+  }
+}
+extension Quaternion: ExpressibleByIntegerLiteral {
+  init(integerLiteral: Double) {
+    a = integerLiteral
+    b = 0
+    c = 0
+    d = 0
+  }
+}
+extension Quaternion: Numeric {
+  var magnitude: Double {
+    return norm
+  }
+  init?<T>(exactly: T) { // stub to satisfy protocol requirements
+    return nil
+  }
+  public static func + (lhs: Quaternion, rhs: Quaternion) -> Quaternion {
+    return Quaternion(
+      a: lhs.a + rhs.a,
+      b: lhs.b + rhs.b,
+      c: lhs.c + rhs.c,
+      d: lhs.d + rhs.d
+    )
+  }
+  public static func - (lhs: Quaternion, rhs: Quaternion) -> Quaternion {
+    return Quaternion(
+      a: lhs.a - rhs.a,
+      b: lhs.b - rhs.b,
+      c: lhs.c - rhs.c,
+      d: lhs.d - rhs.d
+    )
+  }
+  public static func * (lhs: Quaternion, rhs: Quaternion) -> Quaternion {
+    return Quaternion(
+      a: lhs.a*rhs.a - lhs.b*rhs.b - lhs.c*rhs.c - lhs.d*rhs.d,
+      b: lhs.a*rhs.b + lhs.b*rhs.a + lhs.c*rhs.d - lhs.d*rhs.c,
+      c: lhs.a*rhs.c - lhs.b*rhs.d + lhs.c*rhs.a + lhs.d*rhs.b,
+      d: lhs.a*rhs.d + lhs.b*rhs.c - lhs.c*rhs.b + lhs.d*rhs.a
+    )
+  }
+  public static func += (lhs: inout Quaternion, rhs: Quaternion) {
+    lhs = Quaternion(
+      a: lhs.a + rhs.a,
+      b: lhs.b + rhs.b,
+      c: lhs.c + rhs.c,
+      d: lhs.d + rhs.d
+    )
+  }
+  public static func -= (lhs: inout Quaternion, rhs: Quaternion) {
+    lhs = Quaternion(
+      a: lhs.a - rhs.a,
+      b: lhs.b - rhs.b,
+      c: lhs.c - rhs.c,
+      d: lhs.d - rhs.d
+    )
+  }
+  public static func *= (lhs: inout Quaternion, rhs: Quaternion) {
+    lhs = Quaternion(
+      a: lhs.a*rhs.a - lhs.b*rhs.b - lhs.c*rhs.c - lhs.d*rhs.d,
+      b: lhs.a*rhs.b + lhs.b*rhs.a + lhs.c*rhs.d - lhs.d*rhs.c,
+      c: lhs.a*rhs.c - lhs.b*rhs.d + lhs.c*rhs.a + lhs.d*rhs.b,
+      d: lhs.a*rhs.d + lhs.b*rhs.c - lhs.c*rhs.b + lhs.d*rhs.a
+    )
+  }
+}
+extension Quaternion: CustomStringConvertible {
+  var description: String {
+    let formatter = NumberFormatter()
+    formatter.positivePrefix = "+"
+    let f: (Double) -> String = { formatter.string(from: $0 as NSNumber)! }
+    return [f(a), f(b), "i", f(c), "j", f(d), "k"].joined()
+  }
+}
+extension Quaternion {
+  var norm: Double {
+    return sqrt(a*a + b*b + c*c + d*d)
+  }
+  var conjugate: Quaternion {
+    return Quaternion(a: a, b: -b, c: -c, d: -d)
+  }
+  public static func + (lhs: Double, rhs: Quaternion) -> Quaternion {
+    var result = rhs
+    result.a += lhs
+    return result
+  }
+  public static func + (lhs: Quaternion, rhs: Double) -> Quaternion {
+    var result = lhs
+    result.a += rhs
+    return result
+  }
+  public static func * (lhs: Double, rhs: Quaternion) -> Quaternion {
+    return Quaternion(a: lhs*rhs.a, b: lhs*rhs.b, c: lhs*rhs.c, d: lhs*rhs.d)
+  }
+  public static func * (lhs: Quaternion, rhs: Double) -> Quaternion {
+    return Quaternion(a: lhs.a*rhs, b: lhs.b*rhs, c: lhs.c*rhs, d: lhs.d*rhs)
+  }
+  public static prefix func - (x: Quaternion) -> Quaternion {
+    return Quaternion(a: -x.a, b: -x.b, c: -x.c, d: -x.d)
+  }
+}
+
+let q:  Quaternion = 1 + 2 * .i + 3 * .j + 4 * .k // 1+2i+3j+4k
+let q1: Quaternion = 2 + 3 * .i + 4 * .j + 5 * .k // 2+3i+4j+5k
+let q2: Quaternion = 3 + 4 * .i + 5 * .j + 6 * .k // 3+4i+5j+6k
+let r: Double = 7
+
+print("""
+  q  = \(q)
+  q1 = \(q1)
+  q2 = \(q2)
+  r = \(r)
+  -q = \(-q)
+  ‖q‖ = \(q.norm)
+  conjugate of q = \(q.conjugate)
+  r + q = q + r = \(r+q) = \(q+r)
+  q₁ + q₂ = \(q1 + q2) = \(q2 + q1)
+  qr = rq = \(q*r) = \(r*q)
+  q₁q₂ = \(q1 * q2)
+  q₂q₁ = \(q2 * q1)
+  q₁q₂ ≠ q₂q₁ is \(q1*q2 != q2*q1)
+""")