Sub-Tasks:

• SR-13660 SIL: differentiability witness data structure, parsing and serialization
• SR-13661 Sema: lift "same-file-only derivative registration" limitation
• SR-13662 SILGen: generate differentiability witnesses from @differentiable/@differentiating attributes
• SR-13663 IRGen: lower differentiability witness
• SR-13664 Add differentiability_witness_function instruction
• SR-13665 IRGen: lower differentiability_witness_function instruction
• SR-13666 Differentiation: revamp transform to generate differentiability witnesses
• SR-13667 Differentiation: revamp transform to generate differentiability witness function instructions
• SR-13668 SILOptimizer: devirtualize differentiability_witness_function instructions
• SR-13669 Differentiation: revamp transform to directly canonicalize differentiability witnesses
• SR-13670 Sema/SILGen: lower @derivative attribute directly to SIL differentiability witnesses
• SR-13671 Sema: default @differentiable attribute's derivative generic signature to the original declaration's generic signature
• SR-13672 SIL: remove SILDifferentiableAttr
• SR-13673 Separate registered derivatives from the standard library
• SR-13674 Use @derivative in stdlib instead of @differentiable(jvp:vjp:)
• SR-13675 Use @derivative in tensorflow/swift-apis instead of @differentiable(vjp:)
• SR-13676 Remove '@differentiable' attribute 'jvp:' and 'vjp:' arguments
• SR-13677 diagnose when jvp and vjp have differing access levels
• SR-13678 Investigate low-hanging differentiability witness compile time improvements
• SR-13679 Miscellaneous todos
• SR-13680 figure out correct linkage for all ad symbols
• SR-13681 make sil_differentiability_witness more opaque
• SR-13682 incorrect (?) "function not differentiable" error
• SR-13683 multiple internal derivatives of the same function cause symbol redefinition linker error
• SR-13684 sema forbids private derivatives in different scopes
• SR-13685 diagnose duplicate derivatives for derivatives defined in other modules
• SR-13686 @derivative attribute SILGen crash for foreign original declaration
• SR-13687 Remove -Xfrontend -enable-experimental-cross-file-derivative-registration flag
• SR-13688 Require @derivative functions to have same access level as original declaration
• SR-13689 derivative of @_alwaysEmitIntoClient function
• SR-13690 test/AutoDiff/downstream/cross_module_derivative_attr_e2e.swift fails in optimized mode
• SR-13691 remove "jvp:" and "vjp:" arguments from "@differentiable" decl attribute

blocks:

• TF-911 Upstream SILDifferentiabilityWitness: definition, parsing, printing

is duplicated by:

• TF-136 Retroactive differentiability
• TF-280 Enable cross-file/cross-module differentiability

Issue Description:

Retroactive derivative registration: register derivatives for functions in other modules.

Previously:

• If module A defines func foo, then its derivatives must be in the same module.

With retroactive derivative registration:

• If module A defines func foo;

• And if module B imports module A and defines @derivative(of: foo) func derivativeFoo:

• Then module C can import modules A and B and differentiate func foo (e.g. via differentiation APIs).

Retroactive derivative registration enables the following:

• Defining derivatives in a separate module from original functions. This enables modularity: libraries like swift-numerics can define a separate "derivatives" module.

• Derivative registration for imported C functions. Early demo here.