[API] Derive conformances for AdditiveArithmetic and VectorNumeric.

[dan-zheng]

Implement AdditiveArithmetic and VectorNumeric derived conformances for
struct types.

• AdditiveArithmetic conformances can be derived for struct types whose
  members all conform to AdditiveArithmetic.
• VectorNumeric conformances can be derived for struct types whose members
  all conform to VectorNumeric and all share the same Scalar associated
  type.

Derived conformances improve the usability of these math protocols for
user-defined types.
Derived conformances can be extended for enum types in the future.

Examples:

struct IntFloat: AdditiveArithmetic {
  // Synthesis requirement: all members must conform to `AdditiveArithmetic`.
  var int: Int
  var float: Float

  // Compiler synthesizes:
  // static var zero: IntFloat {
  //   return IntFloat(int: Int.zero, float: Float.zero)
  // }
  // static func + (lhs: IntFloat, rhs: IntFloat) -> IntFloat {
  //   return IntFloat(int: lhs.int + rhs.int, float: lhs.float + rhs.float)
  // }
  // static func - (lhs: IntFloat, rhs: IntFloat) -> IntFloat {
  //   return IntFloat(int: lhs.int - rhs.int, float: lhs.float - rhs.float)
  // }
}

// Generic type.
struct Vector2<T : VectorNumeric>: VectorNumeric {
  // Synthesis requirement: all members must conform to `VectorNumeric`
  // and share the same `Scalar` type.
  var x: T
  var y: T

  // Compiler synthesizes:
  // <all three `AdditiveArithmetic` requirements from above>
  // typealias Scalar = T.Scalar
  // static func * (lhs: Scalar, rhs: Vector2) -> Vector2 {
  //   return Vector2(x: lhs * rhs.x, y: lhs * rhs.y)
  // }
}

// Nested generic type.
struct NestedGeneric: VectorNumeric {
  var vec2: Vector2<Float>
  var float: Float

  // Compiler synthesizes:
  // typealias Scalar = Float
  // <all other `VectorNumeric` requirements from above>
}

[rxwei]

Excellent!

[dan-zheng]

@swift-ci Please test tensorflow

[rxwei]

One request I have is that you make the derived methods and properties be @inlinable, as this will be very important for GPE in TensorFlow use cases. You could do that in a separate patch in case of any hurdles in re-triggering the CI.

[dan-zheng]

One request I have is that you make the derived methods and properties be @inlinable, as this will be very important for GPE in TensorFlow use cases. You could do that in a separate patch in case of any hurdles in re-triggering the CI.

Good point! I'd prefer to add @inlinable in a follow-up patch as I've started working on another PR.

[rxwei]

I suspect something's wrong with our GPU test machines. Please disregard GPU test failures for now since they are not connected to AD.