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JaapWijnenJaapWijnen
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feat: add Differentiable conformance to InlineArray 
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‎.github/workflows/pull_request.yml‎

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name: Test Swift ${{ matrix.swift }} Ubuntu Latest
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strategy:
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matrix:
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swift: ["6.0.3", "6.1", "6.2"]
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swift: ["6.2"]
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runs-on: ubuntu-latest
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container: swift:${{ matrix.swift }}
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steps:
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name: Test Swift ${{ matrix.swift }} macOS
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strategy:
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matrix:
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swift: ["6.0.3", "6.1", "6.2"]
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swift: ["6.2"]
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runs-on: macos-15
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steps:
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- uses: actions/checkout@v4

‎Package.swift‎

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// swift-tools-version: 6.0
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// swift-tools-version: 6.2
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// The swift-tools-version declares the minimum version of Swift required to build this package.
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import PackageDescription
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let package = Package(
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name: "swift-differentiation",
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platforms: [
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// we only support the latest versions of OSes as `@available(...)` is not yet supported for differentiation.
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.macOS("26"),
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.iOS("26"),
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],
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products: [
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.library(
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name: "Differentiation",

‎Sources/Differentiation/InlineArray+Differentiation.swift‎

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#if canImport(_Differentiation)
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import _Differentiation
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extension InlineArray: @retroactive Differentiable where Element: Differentiable {
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public typealias TangentVector = InlineArray<count, Element.TangentVector>
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@inlinable
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public mutating func move(by offset: TangentVector) {
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for i in self.indices {
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self[i].move(by: offset[i])
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}
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}
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@derivative(of: init)
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@_alwaysEmitIntoClient
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public static func _vjpInit(repeating value: Element) -> (value: Self, pullback: (TangentVector) -> Element.TangentVector) {
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(
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value: Self(repeating: value),
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pullback: { v in
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var result: Element.TangentVector = .zero
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for i in v.indices {
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result += v[i]
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}
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return result
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}
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)
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}
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@inlinable
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public func read(_ i: Index) -> Element {
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self[i]
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}
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@derivative(of: read)
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@inlinable
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public func _vjpRead(_ i: Index) -> (value: Element, pullback: (Element.TangentVector) -> TangentVector) {
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(
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value: self[i],
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pullback: { v in
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var array = InlineArray<count, Element.TangentVector>(repeating: .zero)
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array[i] = v
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return array
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}
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)
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}
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@inlinable
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public mutating func update(at i: Index, with value: Element) {
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self[i] = value
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}
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@derivative(of: update)
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@inlinable
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public mutating func _vjpUpdate(
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at i: Index,
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with value: Element
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) -> (value: Void, pullback: (inout TangentVector) -> Element.TangentVector) {
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self[i] = value
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return (
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value: (),
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pullback: { (v: inout TangentVector) in
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let dElement = v[i]
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v[i] = Element.TangentVector.zero
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return dElement
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}
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)
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}
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}
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extension InlineArray: @retroactive AdditiveArithmetic where Element: AdditiveArithmetic {
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@inlinable
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public static var zero: InlineArray<count, Element> {
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.init(repeating: .zero)
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}
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@inlinable
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public static func + (lhs: InlineArray<count, Element>, rhs: InlineArray<count, Element>) -> InlineArray<count, Element> {
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InlineArray<count, Element> { lhs[$0] + rhs[$0] }
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}
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@inlinable
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public static func - (lhs: InlineArray<count, Element>, rhs: InlineArray<count, Element>) -> InlineArray<count, Element> {
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InlineArray<count, Element> { lhs[$0] - rhs[$0] }
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}
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}
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extension InlineArray where Element: Differentiable & AdditiveArithmetic {
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@derivative(of: +)
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@inlinable
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public static func _vjpAdd(
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lhs: InlineArray<count, Element>,
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rhs: InlineArray<count, Element>
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) -> (
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value: InlineArray<count, Element>,
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pullback: (InlineArray<count, Element.TangentVector>) -> (
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InlineArray<count, Element.TangentVector>,
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InlineArray<count, Element.TangentVector>
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)
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) {
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(
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value: lhs + rhs,
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pullback: { v in
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(v, v)
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}
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)
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}
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@derivative(of: -)
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@inlinable
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public static func _vjpSubtract(
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lhs: InlineArray<count, Element>,
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rhs: InlineArray<count, Element>
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) -> (
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value: InlineArray<count, Element>,
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pullback: (InlineArray<count, Element.TangentVector>) -> (
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InlineArray<count, Element.TangentVector>,
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InlineArray<count, Element.TangentVector>
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)
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) {
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(
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value: lhs - rhs,
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pullback: { v in
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(v, .zero - v)
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}
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)
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}
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}
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// Temporary conformance to `Equatable` as this will eventually land in the stdlib
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extension InlineArray: @retroactive Equatable where Element: Equatable {
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@inlinable
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public static func == (lhs: InlineArray<count, Element>, rhs: InlineArray<count, Element>) -> Bool {
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for i in lhs.indices {
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if lhs[i] != rhs[i] { return false }
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}
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return true
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}
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}
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#endif

‎Tests/DifferentiationTests/InlineArrayTests.swift‎

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import Differentiation
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import Testing
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#if canImport(_Differentiation)
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@Suite
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struct InlineArrayTests {
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// Test that the zero additive arithmetic gives an array of zeros
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@Test("zero produces repeating zero elements")
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func zeroProducesZeros() {
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let z = InlineArray<2, Double>.zero
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#expect(z[0] == 0.0)
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#expect(z[1] == 0.0)
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}
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// Test + and - work elementwise
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@Test("additive arithmetic + and − are elementwise")
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func additiveArithmeticAddSubtract() {
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let a = InlineArray<2, Double>(repeating: 1.5) // [1.5, 1.5]
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let b: InlineArray<2, Double> = [2.0, 3.0]
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let sum = a + b
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#expect(sum[0] == 3.5)
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#expect(sum[1] == 4.5)
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let diff = b - a
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#expect(diff[0] == 0.5)
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#expect(diff[1] == 1.5)
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}
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// Test differentiable init(repeating:)
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@Test("vjp of init(repeating:) aggregates tangent inputs correctly")
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func testVJPInitRepeating() {
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// For differentiable init(repeating:), the pullback should sum all elements of the tangent vector
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let repeated = InlineArray<2, Double>(repeating: 4.0)
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// forward run
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// Now test pullback: apply VJP
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// The API for using VJP: call `valueWithPullback` or similar
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let (value, pullback) = valueWithPullback(at: 4.0, of: { value in InlineArray<2, Double>(repeating: value) })
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// value should equal what init(repeating:) produces
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#expect(value == repeated)
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// construct some tangent vector
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let tv: InlineArray<2, Double> = [10.0, 20.0]
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// apply pullback
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let back = pullback(tv)
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// Should equal sum of elements, i.e. 10 + 20 == 30, as Double’s tangent
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#expect(back == 30.0)
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}
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@Test("vjp of read is correct")
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func testVJPRead() {
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let arr: InlineArray<2, Double> = [5.0, 7.0]
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let index = 1
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let (value, pullback) = valueWithPullback(at: arr, of: { value in value.read(index) })
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#expect(value == 7.0)
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// Tangent vector for output
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let outTangent = 3.0
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let backVec = pullback(outTangent) // this returns a T2
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// It should have zero except at that index where it's outTangent
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#expect(backVec[0] == 0.0)
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#expect(backVec[1] == 3.0)
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}
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@Test("vjp of update mutating works")
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func testVJPUpdate() {
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let arr: InlineArray<2, Double> = [1.0, 2.0]
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let index = 0
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let newValue = 100.0
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// Apply the derivative via VJP of update
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// Because update is mutating, the pullback signature is a bit different
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// Use the manual _vjpUpdate
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let (value, pullback) = valueWithPullback(
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at: arr, newValue,
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of: { arr, newValue in
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var arr = arr
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arr.update(at: index, with: newValue)
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return arr
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}
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)
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// After update, arr[0] should be newValue
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#expect(value[0] == 100.0)
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#expect(value[1] == 2.0)
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// Suppose we have a tangent vector v for the whole array
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let tangent: InlineArray<2, Double> = [10.0, 20.0]
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// Pullback should take and zero out the tangent component at `index`, returning the old tangent at that index
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let result = pullback(tangent)
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#expect(result.1 == 10.0)
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// After pullback, tangent[0] should be zero, tangent[1] remains 20
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#expect(result.0[0] == 0.0)
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#expect(result.0[1] == 20.0)
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}
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// You could test move(by:) on the tangent vector space
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@Test("move(by:) translates elements correctly")
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func testMoveBy() {
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var arr: InlineArray<2, Double> = [1.0, 2.0]
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let offset: InlineArray<2, Double> = [1.0, 2.0]
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arr.move(by: offset)
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// After move, arr should be [1+1, 2+2] == [2,4]
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#expect(arr[0] == 2.0)
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#expect(arr[1] == 4.0)
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}
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}
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#endif

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