Rename `move(along:)` to `move(by:)` based on the proposal feedback. The main argument for the change is that tangent vectors specify both a direction and a magnitude, whereas `along:` does not indicate that `self` is being moved by the specified magnitude.
`Differentiable` conformance derivation now supports
`Differentiable.zeroTangentVectorInitializer`.
There are two potential cases:
1. Memberwise derivation: done when `TangentVector` can be initialized memberwise.
2. `{ TangentVector.zero }` derivation: done as a fallback.
`zeroTangentVectorInitializer` is a closure that produces a zero tangent vector,
capturing minimal necessary information from `self`.
It is an instance property, unlike the static property `AdditiveArithmetic.zero`,
and should be used by the differentiation transform for correctness.
Remove `Differentiable.zeroTangentVectorInitializer` dummy default implementation.
Update stdlib `Differentiable` conformances and tests.
Clean up DerivedConformanceDifferentiable.cpp cruft.
Resolves TF-1007.
Progress towards TF-1008: differentiation correctness for projection operations.
* Add all [differential operators](https://github.com/apple/swift/blob/master/docs/DifferentiableProgramming.md#list-of-differential-operators).
* Add `withoutDerivative(at:)`, used for efficiently stopping the derivative propagation at a value and causing the derivative at the value to be zero.
* Add utility `differentiableFunction(from:)`, used for creating a `@differentiable` function from an original function and a derivative function.
Mostly work done by @marcrasi and @dan-zheng.
Partially resolves TF-843.
TODO:
* Add `AnyDerivative`.
* Add `Array.differentiableMap(_:)` and `differentiableReduce(_:_:)`.
Add `Differentiable` conformances for floating-point types to the
`_Differentiation` module. The `TangentVector` associated type for
floating-point types is `Self`.
This design adheres to the differentiable programming manifesto:
docs/DifferentiableProgramming.md.
Partially resolves TF-1052.
The `_Differentiation` module is the experimental support library for
differentiable programming. It is built when the build-script flag
`--enable-experimental-differentiable-programming` is enabled.
The `Differentiable` protocol generalizes all types that work with
differentiation. It is a core piece of the differentiable programming
project. Other parts depending on the `Differentiable` protocol will
be upstreamed piece by piece.
The `Differentiable` protocol is compiler-known and will be used during
type-checking, SILGen, and the SIL differentiation transform.
