[AutoDiff] Split forward_mode.swift test into separate files. (#33728)

Splits the large `forward_mode.swift` test file into 3 files:

- `forward_mode_simple.swift`
- `forward_mode_array.swift`
- `forward_mode_simd.swift`

This significantly speeds up testing time when tests are run in parallel.

test/AutoDiff/validation-test/forward_mode_array.swift

@@ -0,0 +1,117 @@
+// RUN: %target-run-simple-swift(-Xfrontend -enable-experimental-forward-mode-differentiation)
+// REQUIRES: executable_test
+
+import StdlibUnittest
+import DifferentiationUnittest
+
+var ForwardModeTests = TestSuite("ForwardModeDifferentiation")
+
+//===----------------------------------------------------------------------===//
+// Array methods from ArrayDifferentiation.swift
+//===----------------------------------------------------------------------===//
+
+typealias FloatArrayTan = Array<Float>.TangentVector
+
+ForwardModeTests.test("Array.+") {
+  func sumFirstThreeConcatenating(_ a: [Float], _ b: [Float]) -> Float {
+    let c = a + b
+    return c[0] + c[1] + c[2]
+  }
+
+  expectEqual(3, differential(at: [0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([1, 1]), .init([1, 1])))
+  expectEqual(0, differential(at: [0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([0, 0]), .init([0, 1])))
+  expectEqual(1, differential(at: [0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([0, 1]), .init([0, 1])))
+  expectEqual(1, differential(at: [0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([1, 0]), .init([0, 1])))
+  expectEqual(1, differential(at: [0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([0, 0]), .init([1, 1])))
+  expectEqual(2, differential(at: [0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([1, 1]), .init([0, 1])))
+
+  expectEqual(
+    3,
+    differential(at: [0, 0, 0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([1, 1, 1, 1]), .init([1, 1])))
+  expectEqual(
+    3,
+    differential(at: [0, 0, 0, 0], [0, 0], in: sumFirstThreeConcatenating)(.init([1, 1, 1, 0]), .init([0, 0])))
+
+  expectEqual(
+    3,
+    differential(at: [], [0, 0, 0, 0], in: sumFirstThreeConcatenating)(.init([]), .init([1, 1, 1, 1])))
+  expectEqual(
+    0,
+    differential(at: [], [0, 0, 0, 0], in: sumFirstThreeConcatenating)(.init([]), .init([0, 0, 0, 1])))
+}
+
+ForwardModeTests.test("Array.init(repeating:count:)") {
+  @differentiable
+  func repeating(_ x: Float) -> [Float] {
+    Array(repeating: x, count: 10)
+  }
+  expectEqual(Float(10), derivative(at: .zero) { x in
+    repeating(x).differentiableReduce(0, {$0 + $1})
+  })
+  expectEqual(Float(20), differential(at: .zero, in: { x in
+    repeating(x).differentiableReduce(0, {$0 + $1})
+  })(2))
+}
+
+ForwardModeTests.test("Array.DifferentiableView.init") {
+  @differentiable
+  func constructView(_ x: [Float]) -> Array<Float>.DifferentiableView {
+    return Array<Float>.DifferentiableView(x)
+  }
+
+  let forward = differential(at: [5, 6, 7, 8], in: constructView)
+  expectEqual(
+    FloatArrayTan([1, 2, 3, 4]),
+    forward(FloatArrayTan([1, 2, 3, 4])))
+}
+
+ForwardModeTests.test("Array.DifferentiableView.base") {
+  @differentiable
+  func accessBase(_ x: Array<Float>.DifferentiableView) -> [Float] {
+    return x.base
+  }
+
+  let forward = differential(
+    at: Array<Float>.DifferentiableView([5, 6, 7, 8]),
+    in: accessBase)
+  expectEqual(
+    FloatArrayTan([1, 2, 3, 4]),
+    forward(FloatArrayTan([1, 2, 3, 4])))
+}
+
+ForwardModeTests.test("Array.differentiableMap") {
+  let x: [Float] = [1, 2, 3]
+  let tan = Array<Float>.TangentVector([1, 1, 1])
+
+  func multiplyMap(_ a: [Float]) -> [Float] {
+    return a.differentiableMap({ x in 3 * x })
+  }
+  expectEqual([3, 3, 3], differential(at: x, in: multiplyMap)(tan))
+
+  func squareMap(_ a: [Float]) -> [Float] {
+    return a.differentiableMap({ x in x * x })
+  }
+  expectEqual([2, 4, 6], differential(at: x, in: squareMap)(tan))
+}
+
+ForwardModeTests.test("Array.differentiableReduce") {
+  let x: [Float] = [1, 2, 3]
+  let tan = Array<Float>.TangentVector([1, 1, 1])
+
+  func sumReduce(_ a: [Float]) -> Float {
+    return a.differentiableReduce(0, { $0 + $1 })
+  }
+  expectEqual(1 + 1 + 1, differential(at: x, in: sumReduce)(tan))
+
+  func productReduce(_ a: [Float]) -> Float {
+    return a.differentiableReduce(1, { $0 * $1 })
+  }
+  expectEqual(x[1] * x[2] + x[0] * x[2] + x[0] * x[1], differential(at: x, in: productReduce)(tan))
+
+  func sumOfSquaresReduce(_ a: [Float]) -> Float {
+    return a.differentiableReduce(0, { $0 + $1 * $1 })
+  }
+  expectEqual(2 * x[0] + 2 * x[1] + 2 * x[2], differential(at: x, in: sumOfSquaresReduce)(tan))
+}
+
+runAllTests()