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Update differential operators

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This commit is contained in:
Anton Korobeynikov
2025-07-25 15:16:12 -07:00
parent 595abee2c1
commit 9b6730569c
2 changed files with 46 additions and 220 deletions
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6
stdlib/private/DifferentiationUnittest/DifferentiationUnittest.swift.gyb
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@@ -378,14 +378,16 @@ public func gradient<T, U, R: FloatingPoint>(
public func derivative<T: FloatingPoint, R>(
at x: ${Self}<T>, of f: @differentiable(reverse) (${Self}<T>) -> R
) -> R.TangentVector where T.TangentVector == T {
return differential(at: x, of: f)(1)
let diff = differential(at: x, of: f)
return diff(${Self}<T>(1))
}
public func derivative<T: FloatingPoint, U: FloatingPoint, R>(
at x: ${Self}<T>, _ y: ${Self}<U>,
of f: @differentiable(reverse) (${Self}<T>, ${Self}<U>) -> R
) -> R.TangentVector where T.TangentVector == T, U.TangentVector == U {
return differential(at: x, y, of: f)(1, 1)
let diff = differential(at: x, y, of: f)
return diff(${Self}<T>(1), ${Self}<U>(1))
}
public func valueWithGradient<T, R: FloatingPoint>(

260
stdlib/public/Differentiation/DifferentialOperators.swift
View File

@@ -19,272 +19,96 @@ import Swift
// Value with differential
@inlinable
public func valueWithDifferential<T, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
) -> (value: R, differential: (T.TangentVector) -> R.TangentVector) {
return Builtin.applyDerivative_jvp(f, x)
}
@inlinable
public func valueWithDifferential<T, U, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> (value: R,
differential: (T.TangentVector, U.TangentVector) -> R.TangentVector) {
return Builtin.applyDerivative_jvp_arity2(f, x, y)
}
@inlinable
public func valueWithDifferential<T, U, V, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> (value: R,
differential: (T.TangentVector, U.TangentVector, V.TangentVector)
-> (R.TangentVector)) {
return Builtin.applyDerivative_jvp_arity3(f, x, y, z)
public func valueWithDifferential<each T, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> (value: R, differential: (repeat (each T).TangentVector) -> R.TangentVector) {
return Builtin.applyDerivative_jvp(f, repeat each x)
}
// Value with pullback
@inlinable
public func valueWithPullback<T, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
) -> (value: R, pullback: (R.TangentVector) -> T.TangentVector) {
return Builtin.applyDerivative_vjp(f, x)
}
@inlinable
public func valueWithPullback<T, U, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> (value: R,
pullback: (R.TangentVector) -> (T.TangentVector, U.TangentVector)) {
return Builtin.applyDerivative_vjp_arity2(f, x, y)
}
@inlinable
public func valueWithPullback<T, U, V, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> (value: R,
pullback: (R.TangentVector)
-> (T.TangentVector, U.TangentVector, V.TangentVector)) {
return Builtin.applyDerivative_vjp_arity3(f, x, y, z)
public func valueWithPullback<each T, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> (value: R, pullback: (R.TangentVector) -> (repeat (each T).TangentVector)) {
return Builtin.applyDerivative_vjp(f, repeat each x)
}
// Differential
@inlinable
public func differential<T, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
) -> (T.TangentVector) -> R.TangentVector {
return valueWithDifferential(at: x, of: f).1
public func differential<each T, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> (repeat (each T).TangentVector) -> R.TangentVector {
return valueWithDifferential(at: repeat each x, of: f).1
}
@inlinable
public func differential<T, U, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> (T.TangentVector, U.TangentVector) -> R.TangentVector {
return valueWithDifferential(at: x, y, of: f).1
}
@inlinable
public func differential<T, U, V, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> (T.TangentVector, U.TangentVector, V.TangentVector) -> (R.TangentVector) {
return valueWithDifferential(at: x, y, z, of: f).1
}
// Pullback
@inlinable
public func pullback<T, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
) -> (R.TangentVector) -> T.TangentVector {
return Builtin.applyDerivative_vjp(f, x).1
}
@inlinable
public func pullback<T, U, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> (R.TangentVector) -> (T.TangentVector, U.TangentVector) {
return Builtin.applyDerivative_vjp_arity2(f, x, y).1
}
@inlinable
public func pullback<T, U, V, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> (R.TangentVector)
-> (T.TangentVector, U.TangentVector, V.TangentVector) {
return Builtin.applyDerivative_vjp_arity3(f, x, y, z).1
public func pullback<each T, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> (R.TangentVector) -> (repeat (each T).TangentVector) {
return valueWithPullback(at: repeat each x, of: f).1
}
// Derivative
@inlinable
public func derivative<T: FloatingPoint, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
public func derivative<each T: FloatingPoint, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> R.TangentVector
where T.TangentVector == T {
return differential(at: x, of: f)(T(1))
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U {
return differential(at: x, y, of: f)(T(1), U(1))
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
return differential(at: x, y, z, of: f)(T(1), U(1), V(1))
where repeat (each T).TangentVector == each T {
return differential(at: repeat each x, of: f)(repeat (each T).init(1))
}
// Gradient
@inlinable
public func gradient<T, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
) -> T.TangentVector
public func gradient<each T, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> (repeat (each T).TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return pullback(at: x, of: f)(R(1))
}
@inlinable
public func gradient<T, U, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> (T.TangentVector, U.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return pullback(at: x, y, of: f)(R(1))
}
@inlinable
public func gradient<T, U, V, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> (T.TangentVector, U.TangentVector, V.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return pullback(at: x, y, z, of: f)(R(1))
return pullback(at: repeat each x, of: f)(R(1))
}
// Value with derivative
@inlinable
public func valueWithDerivative<T: FloatingPoint, R>(
at x: T, of f: @escaping @differentiable(reverse) (T) -> R
public func valueWithDerivative<each T: FloatingPoint, R>(
at x: repeat each T, of f: @escaping @differentiable(reverse) (repeat each T) -> R
) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T {
let (y, differential) = valueWithDifferential(at: x, of: f)
return (y, differential(T(1)))
}
@inlinable
public func valueWithDerivative<T: FloatingPoint, U: FloatingPoint, R>(
at x: T, _ y: U, of f: @escaping @differentiable(reverse) (T, U) -> R
) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T,
U.TangentVector == U {
let (y, differential) = valueWithDifferential(at: x, y, of: f)
return (y, differential(T(1), U(1)))
}
@inlinable
public func valueWithDerivative<
T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
at x: T, _ y: U, _ z: V, of f: @escaping @differentiable(reverse) (T, U, V) -> R
) -> (value: R, derivative: R.TangentVector)
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
let (y, differential) = valueWithDifferential(at: x, y, z, of: f)
return (y, differential(T(1), U(1), V(1)))
where repeat (each T).TangentVector == each T {
let (y, differential) = valueWithDifferential(at: repeat each x, of: f)
return (y, differential(repeat (each T).init(1)))
}
// Value with gradient
@inlinable
public func valueWithGradient<T, R>(
at x: T, of f: @differentiable(reverse) (T) -> R
) -> (value: R, gradient: T.TangentVector)
public func valueWithGradient<each T, R>(
at x: repeat each T, of f: @differentiable(reverse) (repeat each T) -> R
) -> (value: R, gradient: (repeat (each T).TangentVector))
where R : FloatingPoint, R.TangentVector == R {
let (y, pullback) = valueWithPullback(at: x, of: f)
return (y, pullback(R(1)))
}
@inlinable
public func valueWithGradient<T, U, R>(
at x: T, _ y: U, of f: @differentiable(reverse) (T, U) -> R
) -> (value: R, gradient: (T.TangentVector, U.TangentVector))
where R : FloatingPoint, R.TangentVector == R {
let (y, pullback) = valueWithPullback(at: x, y, of: f)
return (y, pullback(R(1)))
}
@inlinable
public func valueWithGradient<T, U, V, R>(
at x: T, _ y: U, _ z: V, of f: @differentiable(reverse) (T, U, V) -> R
) -> (value: R,
gradient: (T.TangentVector, U.TangentVector, V.TangentVector))
where R : FloatingPoint, R.TangentVector == R {
let (y, pullback) = valueWithPullback(at: x, y, z, of: f)
let (y, pullback) = valueWithPullback(at: repeat each x, of: f)
return (y, pullback(R(1)))
}
// Derivative (curried)
@inlinable
public func derivative<T: FloatingPoint, R>(
of f: @escaping @differentiable(reverse) (T) -> R
) -> (T) -> R.TangentVector
where T.TangentVector == T {
return { x in derivative(at: x, of: f) }
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, R>(
of f: @escaping @differentiable(reverse) (T, U) -> R
) -> (T, U) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U {
return { (x, y) in derivative(at: x, y, of: f) }
}
@inlinable
public func derivative<T: FloatingPoint, U: FloatingPoint, V: FloatingPoint, R>(
of f: @escaping @differentiable(reverse) (T, U, V) -> R
) -> (T, U, V) -> R.TangentVector
where T.TangentVector == T,
U.TangentVector == U,
V.TangentVector == V {
return { (x, y, z) in derivative(at: x, y, z, of: f) }
public func derivative<each T: FloatingPoint, R>(
of f: @escaping @differentiable(reverse) (repeat each T) -> R
) -> (repeat each T) -> R.TangentVector
where repeat (each T).TangentVector == each T {
return { (x: repeat each T) in derivative(at: repeat each x, of: f) }
}
// Gradient (curried)
@inlinable
public func gradient<T, R>(
of f: @escaping @differentiable(reverse) (T) -> R
) -> (T) -> T.TangentVector
public func gradient<each T, R>(
of f: @escaping @differentiable(reverse) (repeat each T) -> R
) -> (repeat each T) -> (repeat (each T).TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return { x in gradient(at: x, of: f) }
}
@inlinable
public func gradient<T, U, R>(
of f: @escaping @differentiable(reverse) (T, U) -> R
) -> (T, U) -> (T.TangentVector, U.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return { x, y in gradient(at: x, y, of: f) }
}
@inlinable
public func gradient<T, U, V, R>(
of f: @escaping @differentiable(reverse) (T, U, V) -> R
) -> (T, U, V) -> (T.TangentVector, U.TangentVector, V.TangentVector)
where R : FloatingPoint, R.TangentVector == R {
return { x, y, z in gradient(at: x, y, z, of: f) }
return { (x: repeat each T) in gradient(at: repeat each x, of: f) }
}