[Math] ==~ operator applies to any <AlmostEquatable, EquatableWithinEpsilon>

Math/Math/Types.swift

@@ -9,19 +9,36 @@
 import Foundation
 
 public typealias Float = Swift.Float
+public typealias Double = Swift.Double
 
-/** Acceptable tolerance for Float equality. */
-let Epsilon: Float = 1e-6
-
-extension Float {
-    /** Test that `other` is almost equal (i.e. within the +/- Epsilon) to `self`. */
-    func almostEqual(other: Float) -> Bool {
-        return other >= (self - Epsilon) && other <= (self + Epsilon)
-    }
+public protocol AlmostEquatable {
+    @warn_unused_result
+    func ==~(lhs: Self, rhs: Self) -> Bool
 }
 
-/** Custom operator for almost-equality of floats. */
-infix operator =~ { associativity left precedence 130 }
-public func =~(lhs: Float, rhs: Float) -> Bool {
-    return lhs.almostEqual(rhs)
+public protocol EquatableWithinEpsilon: Strideable {
+    static var Epsilon: Self.Stride { get }
+}
+
+extension Float: EquatableWithinEpsilon {
+    public static let Epsilon: Float.Stride = 1e-8
+}
+
+extension Double: EquatableWithinEpsilon {
+    public static let Epsilon: Double.Stride = 1e-16
+}
+
+private func almostEqual<T: EquatableWithinEpsilon>(lhs: T, _ rhs: T, epsilon: T.Stride) -> Bool {
+    return abs(lhs - rhs) <= epsilon
+}
+
+/** Almost-equality of floating point types. */
+infix operator ==~ { associativity left precedence 130 }
+public func ==~<T: protocol<AlmostEquatable, EquatableWithinEpsilon>>(lhs: T, rhs: T) -> Bool {
+    return almostEqual(lhs, rhs, epsilon: T.Epsilon)
+}
+
+infix operator !==~ { associativity left precedence 130 }
+public func !==~<T: AlmostEquatable>(lhs: T, rhs: T) -> Bool {
+    return !(lhs ==~ rhs)
 }