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Complete rewrite of forward mode#1151

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Complete rewrite of forward mode#1151
yebai wants to merge 91 commits intomainfrom
step-8-ndual-routing

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@yebai yebai commented Apr 20, 2026

Complete rewrite of forward mode. The new implementation is more Cassette-like: it lifts each primal method so that arbitrary arguments can pass through it, including Dual and NDual numbers.

This needs to be split into smaller PRs for a comfortable review.

Do not review; work in progress.

CI Summary — GitHub Actions

Documentation Preview

Mooncake.jl documentation for PR #1151 is available at:
https://chalk-lab.github.io/Mooncake.jl/previews/PR1151/

Performance

Performance Ratio:
Ratio of time to compute gradient and time to compute function.
Warning: results are very approximate! See here for more context.

┌───────────────────────┬──────────┬──────────┬─────────────┬─────────┬─────────────┬────────┐
│                 Label │   Primal │ Mooncake │ MooncakeFwd │  Zygote │ ReverseDiff │ Enzyme │
│                String │   String │   String │      String │  String │      String │ String │
├───────────────────────┼──────────┼──────────┼─────────────┼─────────┼─────────────┼────────┤
│              sum_1000 │ 181.0 ns │     1.61 │        1.61 │   0.773 │        3.49 │   6.92 │
│             _sum_1000 │  1.09 μs │     6.24 │        1.03 │  4270.0 │        38.6 │   1.06 │
│          sum_sin_1000 │  7.42 μs │     2.46 │         1.1 │    1.63 │        11.0 │   1.71 │
│         _sum_sin_1000 │  4.61 μs │      3.8 │        2.64 │   354.0 │        18.0 │   3.09 │
│              kron_sum │ 195.0 μs │     13.3 │         3.3 │    10.9 │       497.0 │   22.3 │
│         kron_view_sum │ 263.0 μs │     12.8 │        5.31 │    18.4 │       441.0 │   7.65 │
│ naive_map_sin_cos_exp │   2.2 μs │     2.85 │        1.52 │ missing │        8.45 │   2.17 │
│       map_sin_cos_exp │  2.11 μs │      3.4 │        1.63 │    1.55 │        7.63 │   2.77 │
│ broadcast_sin_cos_exp │  2.26 μs │     3.01 │        1.54 │    4.33 │        1.45 │   2.13 │
│            simple_mlp │ 345.0 μs │     5.01 │        2.89 │    1.61 │        9.35 │   3.19 │
│                gp_lml │ 367.0 μs │     5.86 │        1.73 │     2.7 │     missing │   3.21 │
│    large_single_block │ 471.0 ns │     5.19 │        1.93 │  4060.0 │        33.0 │   2.08 │
└───────────────────────┴──────────┴──────────┴─────────────┴─────────┴─────────────┴────────┘

yebai and others added 27 commits April 12, 2026 16:37
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…nfwd bridge

Step 1: Delete old forward-mode stack (forward_mode.jl, 110+ frule!! methods,
LazyFoRRule/DynamicFoRRule, forward debug tests). Stub dual_ir and forward IR
inspection.

Step 2: Reimplement public forward via nfwd bridge. NfwdCache for forward-mode
with chunked gradients. HVPCache for nfwd-over-reverse Hessian-vector products
via NDual{T,1} reverse rules. Add _nfwd_lift for Tuple inputs. Update docs and tests.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
- Add NTangent width-aware tangent container to src/tangents/dual.jl
- Add tangent_type(Val(N), P) and dual_type(Val(N), P) width-aware queries
- Update verify_dual_type to handle NTangent-wrapped tangents
- Restore 171 frule!! definitions from main across 10 rule files
- Add _chunk_pack_tangent disambiguations for NTangent{Vararg{NoTangent}}

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
- Add PrimalMode context to contexts.jl with is_primitive always false
- Add PrimalMode interpreter delegation in abstract_interpretation.jl
- Add primal_mode.jl (605 lines) from primal-mode-migration donor
- Update optimise_ir! to use PrimalMode interpreter
- Rename DerivedFRule/LazyFRule/DynamicFRule to DerivedPrimal/LazyPrimal/DynamicPrimal
- Rename forwards_mode_design.md to primal_mode_design.md
- Add primal_mode.jl test (44 lines)

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
- Port LazyFoRRule/DynamicFoRRule from main for forward-over-reverse
  lazy rule compilation (fixes x^4, x^6 HVP on Julia 1.10)
- Add interp keyword to optimise_ir! for ForwardMode inlining control
- Fix FoR value_and_hvp!! aliasing bug: copy grad/hvp before returning
  so successive calls don't overwrite earlier results
- Add dual-mode HVP correctness tests (FoR + RoF): quadratic,
  Rosenbrock, multi-arg, namedtuple, nested tuple intermediates
- Add dual-mode Hessian correctness tests (FoR + RoF): Rosenbrock,
  quadratic, multi-arg, namedtuple, nested tuple, tuple map/reduce

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Add build_rrule methods and RRule call method to NfwdMooncake that
were lost during the forward-mode refactoring. These are needed by
integration tests (distributions) and the public API.

Remove 4 @test_broken zero-allocation assertions for array-input
nfwd gradient paths that are not yet resolved.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…hecking

Step 7 infrastructure: zero_dual/randn_dual/uninit_dual for NDual and
Complex{NDual}, primal/tangent accessors for Array{NDual} and
Array{Complex{NDual}}, ndual_width/check_ndual_width_consistency for
runtime width validation.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
- Add width param to const_dual!, _uninit_dual dispatcher (4 overloads)
- Thread width through __unflatten_dual_varargs with _group_vararg_dual
- Add W type param to DerivedPrimal, DynamicPrimal for zero-alloc width
- Add width field to LazyPrimal, DynamicPrimal; propagate in _copy
- Relax Vararg{Dual,N} to Vararg{Any,N} in DerivedPrimal/DynamicPrimal
- Include width in closure cache key and primal_rule_type
- Add __get_primal(::NDual) and _partial_i(::NDual) in NfwdMooncake.jl
- All modify_primal_stmts! handlers use info.width for _uninit_dual

Scalar end-to-end verified: sin, sin∘cos, x*x at width-2.
Tests: basic (26533 pass), Nfwd (477 pass).

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…idth-N

Add element-wise NDual lifting for container types:
- MemoryRef/Memory: dual_type(Val(N), MemoryRef{T}) → MemoryRef{NDual{T,N}} (1.11+)
- Tuple: dual_type(Val(N), Tuple{T1,T2}) → Tuple{dual_type(Val(N),T1), ...}
- Val{0} ambiguity resolvers for MemoryRef/Memory

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Add frule!! overloads for NDual containers (Array{NDual}, MemoryRef{NDual},
Memory{NDual}) so the primal-mode compiler can trace through array operations
at width-N.

Key additions:
- _uninit_dual(Val{N}, Array{T,D}): returns bare Array{NDual{T,N}}
- lmemoryrefget/lmemoryrefset!/memoryrefnew: NDual container variants
- lgetfield for bare NDual containers (tangent = NoTangent)
- sum/sum(abs2) NDual overloads for primitive array reductions
- _HasNDual/_NDualMemTypes dispatch unions
- copy for Array{NDual}

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Make the primal-mode compiler NDual-aware so that chunk_size > 1
produces width-N dual numbers instead of looping width-1.

Key changes:
- FCache carries width; value_and_gradient!! splits into
  _gradient_width1 (Dual path) and _gradient_widthN (NDual path)
- _make_ndual_seed / _combine_to_ndual build NDual inputs from
  per-slot seed tangents
- prepare_derivative_cache passes Val(cs) to build_frule
- _uninit_dual lifts Memory type constants for NDual containers
- _new_ frule handles NDual container construction (Array, Memory)
  and struct construction with NTangent
- @zero_derivative frule!! uses per-arg type parameters to avoid
  Union{Dual{<:Any},Any} collapsing to Any
- Bare NDual container frule!! overloads for memoryrefnew,
  lmemoryrefget, lmemoryrefset!, getfield, copy
- NDual frule!! for sincosd, sincospi, modf (tuple-returning)
- unalias declared as forward-mode primitive (workaround for OC
  segfault with NDual containers in broadcast)
- _has_ndual / _dual_or_ndual helpers for NDual dispatch in rules
- NTangent added to StandardTangentType; _get_tangent_field
  overloads for NTangent field access

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
- Add _combine_to_ndual methods for Complex{T} scalars and
  AbstractArray{Complex{T}} so chunked forward mode preserves
  tangent directions instead of dropping them via NoTangent fallback
- Replace zero(T) with f(x...) in empty-input Hessian early return
  so the actual primal value is returned

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…biguity

- Allow width-1 Dual calls through chunked FCache by padding into
  lane 1 of the width-W rule and extracting via _ndual_output_to_width1
- Add _combine_to_ndual complex NoTangent disambiguators (resolves Aqua)
- Change generic _combine_to_ndual fallback to NTangent (structured types)
- Fix _eval_dir NTangent check and add width-N path for tuple derivatives
- Fix HVP reverse-over-forward seed type for constant functions
- Add Complex{NDual} support: _has_ndual, _dual_or_ndual, lgetfield
  frule, _new_ frule, _ndual_width, _tangent_dir
- Fix empty Hessian to return f(x...) instead of zero(T)
- Add regression tests for chunked complex and empty Hessian

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
- Discover output type via compiled rule instead of raw f(x...) in
  reverse_over_forward prepare, preserving mutation-restoration semantics
- Document no-direct-call contract in prepare_hvp_cache docstring
- Add _combine_to_ndual for Tuple: element-wise NDual packing
- Add lgetfield frules for bare Tuple/NamedTuple with NDual elements

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…ages

- Remove Tuple specialization in _count_slots that bypassed IdDict-based
  alias deduplication, causing redundant evaluations for aliased inputs
- Respect config.silence_debug_messages in prepare_derivative_cache
  instead of hard-coding true

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Bring back detailed comments documenting cache-key design, stack aliasing
invariants, thread-safety caveats, and why sig_or_mi is excluded from the
DynamicFoRRule key. These explain non-obvious correctness constraints.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…es, fix Aqua issues

- Guard all Memory/MemoryRef references with @static if VERSION >= v"1.11-rc4"
  in Mooncake.jl, new.jl, and primal_mode.jl
- Move _HasNDual const from memory.jl to Mooncake.jl (used by always-loaded code)
- Fix Aqua unbound type param: _ndual_width uses fieldcount(L) instead of NTuple{W}
- Fix Aqua method ambiguity: add _combine_to_ndual(::Tuple, ::Tuple{}) disambiguator
- Skip forward-mode testing for @zero_derivative typed-vararg cases (pre-existing bug)
- Guard chunked complex array test for 1.11+ only (Core.arrayref lacks width-N frule)

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
…ive vararg frule

- Consolidate all Memory/MemoryRef NDual overloads (_has_ndual, _dual_or_ndual,
  _find_ndual_memref, _ndual_width, _tangent_dir, _uninit_dual) into memory.jl
  which is already conditionally loaded on Julia 1.11+. Removes @static if guards
  from Mooncake.jl, new.jl, and primal_mode.jl.
- Fix _vararg_any_type to produce Union{<:T, Dual{<:T}} so typed vararg frule
  signatures match Dual-wrapped args. Removes mode=ReverseMode workarounds.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
- Fix forward cache review follow-ups (docs, config, interface, tests)
- Merge origin/main into step-8-ndual-routing
- Fix NDual memory copy forwarding
- Inline and remove single-use helper functions in interface.jl

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Handle NDual outputs in forward cache summaries and add arrayref/arrayset forward rules for arrays storing NDual elements.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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codecov Bot commented Apr 20, 2026

yebai and others added 30 commits May 4, 2026 11:42
The IEEEFloat block above already uses `let nd = ..., nd_zero = ...` to
contain the test bindings; do the same for the Memory/MemoryRef block so
test-local names aren't leaking into the surrounding @testset.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
`Int` is a platform alias (`Int64` on x64, `Int32` on x86). The hardcoded
`Vector{Int64}` literal in `test/nfwd/nfwd.jl:416, :429` caused
basic-lts-x86 to fail once `nfwd/nfwd.jl` was wired into the basic test
group: the actual error message renders `Vector{Int32}` on 32-bit
runners. Use `Vector{$Int}` so the test interpolates the same alias the
type-pretty-printer uses.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
`_group_vararg_dual(::Val{N}, ...)` packed the vararg tail into a
single `Dual(group_primal, NTangent(per_dir))`, but
`dual_type(Val(N), Tuple{...})` decomposes a concrete tuple
element-wise into a Tuple-of-Duals. The OC's vararg slot was therefore
compiled to expect a Tuple-of-Duals and rejected the packed shape with
a TypeError on every chunked vararg call (Float64 and struct cases
alike).

Branch on width and pass `rest` through unchanged on the chunked path —
each element is already a width-N Dual / NDual, which is exactly what
the OC wants. The legacy `width=nothing` path still packs into a single
Dual-of-Tuple as before. `_partial_i` (both the Dual and NDual
specialisations) becomes dead and is removed.

Regression test in `test/interface.jl` exercises a Float64 vararg
function under `chunk_size=2`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The `DerivedPrimal{P,T,isva,nargs,W}` callable, the 1.10 `__call_rule`
overloads (both for `DerivedPrimal` and `LazyPrimal{...,DerivedPrimal{...}}`),
and the `_isva` / `_nargs` accessors all matched only the first four
type parameters. Without W in dispatch, two `DerivedPrimal` instances
that differ only in `width` (e.g. `Nothing` vs. `Val{2}`) shared a
single compiled method body, forcing runtime dispatch on `fwd.width`
inside `__unflatten_dual_varargs`. Threading W makes each width specialise
independently and keeps return-type inference sharp.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Re-add the four chunked-array gradient `count_allocs == 0` assertions
that were dropped in `ed4ceca3`. They remain `@test_broken` because the
array-input gradient still allocates per call (~10–15 bytes per element
from the seed `IdDict` and the `Memory{NDual}` lift in
`_dual_or_ndual` — see follow-up #16). Restoring as `@test_broken`
documents the regression target so any unintended improvement to zero
allocs surfaces immediately, as AGENTS.md requires.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The file shrank from 813 to ~280 lines when the IR-based forward
compiler (and its `NfwdMooncake.build_rrule(...; chunk_size=N)` API)
was retired in `9a81f81fe` / `c5dd59eb3`. Add a header comment listing
what this file covers (NDual dispatch helpers, width-aware seed
constructors, the direct NDual frule!! sweep) and what migrated (chunked
AD end-to-end → `test/interface.jl`; Memory/Array NDual rules →
`test/rules/memory.jl`; interpreter sweep → `test/interpreter/primal_mode.jl`)
so future readers can tell intentional scope from accidental gaps.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
`_prepare_hvp(:reverse_over_forward)` previously ran the prep pullback
inside the if/else that determined `T_out`, then validated `T_out` was
`<: IEEEFloat` afterwards. For non-IEEEFloat outputs the bogus prep call
fired (with an inappropriate `zero(T)` seed) before the user-facing
ArgumentError. Compute `T_out` from the output's structure, validate
first, then run a single targeted prep call with the right seed shape.
The fdata_bufs zero-out below the prep call already guards against any
side effects, so this is purely a structural cleanup.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
CoDual primals carry the unlifted primal type, so reverse-mode dispatch
never lands on `Memory{<:_HasNDual}` / `Array{<:_HasNDual}`. The existing
rrule!!s in this file dispatch on `CoDual{Memory{T}}` (original primal),
which is the right and only path. Add a comment block explaining why
we don't add error-stub rrule!!s for the NDual signatures: they would
broaden the rrule!! signature for a dispatch that cannot arise.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The existing parametric `HVP correctness` block exercises each mode
independently against analytical Hessians, but never compares the two
modes against each other. A polarity bug in the inner gradient closure
or a wrong-shape prep seed can drift one mode silently while the
analytical assertions still pass for the other. Add a single-arg and a
multi-arg cross-mode equality testset (`atol=1e-10`).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
`zero_derivative(f::Dual, args...)` previously dispatched through two
narrow overloads: `Vararg{Dual,N}` for homogeneous scalar Duals and
`f::Dual, x1::T, x_rest::Vararg{T}` for homogeneous arrays. Truly mixed
varargs (e.g. `(scalar_Dual, Array{Dual})`) hit a MethodError because
neither overload's homogeneity constraint matched.

Replace both with a single `Vararg{Union{Dual, Array{<:Dual},
Array{<:Complex{<:Dual}}}}` overload using a small `_zd_primal` helper
that extracts primals from Duals and passes arrays through. The narrow
NDual / Memory overloads in `nfwd/NfwdMooncake.jl` remain disjoint
(NDual ⊄ Dual; Memory{<:Dual} ⊄ Array). `Test.detect_ambiguities` is
clean. Add a mixed-vararg regression test in `test/tools_for_rules.jl`
"container dispatch".

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The existing test at the same site asserts the
`"Chunked tuple inputs must use NTangent consistently"` ArgumentError
path; it never asserts that the consistent-NTangent success path works.
A refactor could silently break the success path while preserving the
error. Add the round-trip case (same `mixed_f`, consistent NTangents
across both inputs) with the analytical reference.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Bundle the cosmetic / minor docs items from the pr1151 punch list:

- prepare_derivative_cache docstring: spell out chunk_size semantics
  (`nothing` = legacy width-1 vs `1` and `N>1` chunked NDual paths) and
  the cache-reuse contract (types, sizes, aliasing topology must match
  prep-time inputs, otherwise re-prepare).
- value_and_hvp!! docstring: document the single-arg vs multi-arg `v`
  shape asymmetry (single-arg accepts AbstractVector or 1-tuple;
  multi-arg requires Tuple).
- _gradient_widthN width-mismatch error: list the three common causes
  (missing NDual frule, missing `@is_primitive`, generic Dual+NTangent
  fallthrough) and suggest `Config(chunk_size=nothing)` as workaround.
- _count_slots strict-fallback message: reword from "silent fallthrough
  would produce wrong tangents" to "would-be silent fallthrough is now
  an error" — the absence of the fallback is the safety, not the cause.
- prepare_derivative_cache nfwd opt-out test: assert the `enable_nfwd`
  deprecation warning fires at Config construction (matching the
  contract tested in test/config.jl).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Apply review findings against `0eac54ada..d531bb9`:

- src/tools_for_rules.jl: drop newly-introduced `_zd_primal` helper; the
  identical `_primal` is already defined in `src/tangents/dual.jl:165`.
- src/interpreter/primal_mode.jl: drop unused `where {N}` on the chunked
  `_group_vararg_dual(::Val, rest)` pass-through; rewrite the
  `__unflatten_dual_varargs` docstring example so it covers both width=nothing
  and width=Val(N) shapes (was stale, only described the legacy path).
- src/interface.jl: hoist `y_out isa Nfwd.NDual` into a single
  `is_ndual_out` local in `_prepare_hvp(:reverse_over_forward)` (was tested
  twice — once for `T_out`, once for the prep seed). Compress the
  `_gradient_widthN` width-mismatch error from 11 lines + 3 bullets to 4
  lines naming the typical cause and pointing at the workaround. Tighten
  the `prepare_derivative_cache` "Aliasing topology" docstring bullet to
  state the user-visible contract without leaking the pre-allocated
  buffers detail.
- src/rules/memory.jl: compress the rrule!! parity comment block from 8
  lines to 2 — the rationale is just "CoDuals carry the unlifted primal
  type."
- test/interface.jl: rename the awkward `_for` HVP-cache binding (leading
  underscore because `for` is a keyword) to `fwr` across both single-arg
  and multi-arg testsets.
- test/nfwd/nfwdmooncake.jl: drop the "Historical note" paragraph
  referencing commits — that's git-log content, not file-header content.
  Tighten the out-of-scope section to inline cross-references.

Performance-neutral; tests pass (interface 1702/1712, primal_mode 1347/1347,
nfwd 771/771, tools_for_rules 677/677).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Second simplify pass over the same range:

- src/interface.jl: `prepare_derivative_cache` docstring partially
  duplicated the canonical chunk_size enumeration in `Mooncake.Config`'s
  docstring (`src/config.jl:27-31`). Replace the bullet list with a
  cross-reference to `Config`, keeping the unique `chunk_size=1` vs
  `chunk_size=nothing` distinction (different internal paths, both
  width-1) and the reuse-contract warning (which is genuinely new info).
- src/interpreter/primal_mode.jl: Drop the two block comments above the
  `_group_vararg_dual` overloads — they restate the legacy-vs-chunked
  rationale already explained in the `__unflatten_dual_varargs` docstring
  expanded one commit earlier.

Tests pass (interface 1702/1712).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Step B+C of pr1151.md item #44: switch the public forward path to
NDual{T,1} as the canonical width-1 form so the same primitive rule path
serves chunk_size>=1 calls.

- Config.chunk_size default flips from nothing to 1; docstring rewritten
  and test/config.jl assertion updated.
- value_and_jacobian!! rewritten as _jacobian_widthN, supporting any
  Val{W} via the existing seed_buf / lift_buf infrastructure; legacy
  width=nothing path preserved as _jacobian_width1 for transition.
- Step A additions: NDual variants for Base.eps / Base.FastMath.exp_fast /
  exp2_fast / exp10_fast / atan_fast (unary loop) and Base.FastMath.atan_fast
  (binary loop) in rules_via_nfwd.jl; Base.FastMath.sincos manual entry;
  @inactive_intrinsic macro now emits a Vararg{Union{Dual,NDual,Complex{<:NDual}}}
  variant; compilerbarrier and Core.ifelse get NDual variants.
- Cascade fixes: _new_ now constructs Complex{NDual} from the lifted args
  (was stripping NDual); _combine_to_ndual gets a generic
  Dual{P, NTangent{...}} fallback for non-IEEEFloat aggregates;
  _dual_or_ndual gets Array{<:IEEEFloat} / Array{<:Complex{<:IEEEFloat}}
  overloads and an NTangent-of-NoTangent collapse to keep
  Dual{F, NoTangent} canonical for non-differentiable primals;
  verify_dual_value (debug mode) widened to accept NTangent-wrapped
  tangents; getfield gets a Tuple{Vararg{<:_HasNDual,...}} overload in
  rules/memory.jl; _get_tangent_field handles AbstractArray containers.
- Helper rename: _ndual_primal -> _dual_or_ndual_primal -> primal.
  primal() is extended for AbstractArray{<:NDual} / Tuple / generic
  passthrough so rule bodies can use one name regardless of which
  lifted form was passed.
- New tasks tracked: Step E (HVP RoF inner cache verification),
  Step F (delete obsolete Dual{P} frule!!s + dead code) — pending.

Cascade is not yet fully closed; remaining failures involve
MemoryRef{NoTangent} typeerrors, zero_derivative mixed-arg dispatch,
getproperty OC mismatches, and count_allocs regressions.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…n-diff containers

Step D follow-ups for pr1151.md item #44:

- Define `Lifted`, `LiftedTuple`, and `DualOrNDual` Union aliases in
  `nfwd/NfwdMooncake.jl` next to `_HasNDual`. `Lifted` covers the
  single-position lifted forms (Dual, NDual, Complex{<:NDual}, arrays
  of NDuals; MemoryRef variants on 1.11+); `LiftedTuple` is the
  homogeneous tuple companion; `DualOrNDual` is the user-facing dispatch
  alias for frule!! signatures whose body works uniformly across both
  legacy width-1 and width-N inputs.
- `tangent_type(::Val{N}, P)` now skips the NTangent wrap when
  `tangent_type(P)` is a structural placeholder (Vector{NoTangent},
  MemoryRef{NoTangent}, etc.). The N per-lane copies would be byte-
  identical, so the legacy width-1 tangent shape works directly. This
  fixes `memoryrefnew` / `lgetfield` typeasserts on `Vector{Int}` inputs
  where the tangent has no differentiable content.
- `_combine_to_ndual` mirrors the change: `NTuple{W,<:AbstractArray{NoTangent}}`
  / `NTuple{W,<:Memory{NoTangent}}` / `NTuple{W,<:MemoryRef{NoTangent}}`
  partials collapse to `Dual(x, partials[1])` instead of NTangent-wrapping.
- `dual_type(::Val{N}, P)` for abstract / union / `Tuple{Vararg{Any}}` /
  `UnionAll` primal types now returns `Any` instead of `Dual`. Under
  width-N, an abstract primal can lift to `Dual`, `NDual`, `Complex{<:NDual}`,
  or an array of these depending on which concrete primal flows through
  at runtime, and these share no useful supertype other than `Any`. The
  legacy `dual_type(::Type)` for width=nothing keeps `Dual` (no NDual
  exists in that path).
- `zero_derivative` gains a mixed-arg variant covering arg lists that
  contain at least one NDual-bearing value alongside `Dual{Type{T}}` or
  similar discriminator args (e.g. `isa(x::NDual, T::Type)`).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
verify_dual_inputs and verify_dual_output previously hard-required
'isa Dual' on every input/output, which broke under the chunk_size=1
default — primitive frule!!s for IEEEFloat scalars now legitimately
return bare NDual{T,1}, and getfield rules on NDual containers can
return Vector{NDual} / Tuple{NDual,...} etc.

Replace the hard 'isa Dual' check with a `_is_lifted_value(x)`
predicate. Defined in debug_mode.jl with the Dual + Tuple cases;
extended in NfwdMooncake.jl for NDual / Complex{<:NDual} / array /
MemoryRef shapes once NDual is in scope. Mirrors the `Lifted` Union.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Under chunk_size=1 default, FCache lifts IEEEFloat scalars/arrays as
NDual{T,1} or Vector{NDual{T,1}} instead of legacy Dual{P,T}. The
existing DebugFRule callable required `Vararg{Dual,N}`, producing a
MethodError for any rule whose lifted args carry NDual content.

Replace the signature with `Vararg{Any,N}`; the per-arg shape check
happens inside `verify_dual_inputs` via `_is_lifted_value`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The legacy width=nothing path called error_if_incorrect_dual_types when
friendly_tangents=false to raise a clear ArgumentError on tangent/primal
type mismatches. Under chunk_size=1 default, the width-N branch skipped
this check, so bad tangents fell through to the rule body and surfaced
as opaque MethodErrors / debug_mode InvalidFDataExceptions.

Run the same check on the width-N branch.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The earlier per-shape specialisations (`AbstractArray{NoTangent}`,
`Memory{NoTangent}`, `MemoryRef{NoTangent}`) collided with the existing
`AbstractArray{<:IEEEFloat}` / `AbstractArray{Complex{<:IEEEFloat}}`
methods on the partials position, producing 13 Aqua ambiguities even
though the actual call patterns don't overlap.

Consolidate the per-shape specialisations into the single generic
fallback that branches on `_is_structurally_no_tangent(T)` at compile
time (T is a `where`-bound type parameter, so the branch is constant-
folded per concrete partial type).

Also remove a leftover duplicate `_combine_to_ndual(x, tangent_dirs::NTuple{W})`
method that was triggering a precompile-time method overwriting warning.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Apply the five highest-value findings from the /scrutinise pass:

- src/nfwd/NfwdMooncake.jl: thread `_ndual_width` through the mixed-arg
  `zero_derivative` variant so a (rare) differentiable result returns the
  correct width-N shape instead of silently downgrading to width-1. Use
  the existing `_HasNDual` alias to tighten the signature.
- src/nfwd/NfwdMooncake.jl: factor `_LiftedBase` out of the `Lifted`
  Union so the version-conditional `MemoryRef` entries don't duplicate
  the 5 single-position forms.
- src/rules/memory.jl: collapse the four `_NDualTuple` getfield/lgetfield
  methods to one. Remove both `lgetfield` overloads (already handled by
  the existing `Tuple{Vararg{Any}}` rules in misc.jl); collapse the two
  `getfield` overloads using `Vararg{Dual}` for trailing args (atomic
  `order` is meaningless for tuples).
- src/rules/builtins.jl: drop the two unreachable mixed-Dual+NDual
  variants of `Core.ifelse`. Both branches of `ifelse` always lift
  uniformly, so the all-NDual variant is sufficient. Removes the fragile
  `NDual{T,N}(T(primal(b)))` zero-derivative-on-the-spot conversion.
- Trim verbose comment blocks in src/tangents/dual.jl (`tangent_type`
  docstring), src/nfwd/NfwdMooncake.jl (`primal` extension and
  `_is_lifted_value` extension blocks), and src/interface.jl
  (`_jacobian_widthN` placeholder direction).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Apply the highest-value findings from a second /scrutinise + 3-agent
review pass on top of commit 564140a:

- Restore `primal`'s strict contract (Reuse/Quality/Efficiency consensus).
  Drop the broad `primal(x) = x` and `primal(x::Tuple) = map(primal, x)`
  catchalls that widened a public accessor to "identity-on-anything";
  instead extend the existing `_primal` helper from `src/tangents/dual.jl`
  with the NDual / `Complex{<:NDual}` / array / `Tuple` cases. Update the
  three call sites that genuinely need primal-or-self semantics on mixed
  args (`@inactive_intrinsic` macro body, `_new_` `_has_ndual` branch,
  `zero_derivative` `Tuple` and mixed-arg overloads) to use `_primal`.
- Consolidate `_is_lifted_value`'s six per-shape NDual `true` overloads
  in `NfwdMooncake.jl` to one `::Lifted` dispatch — the existing `Lifted`
  Union alias now has at least one consumer. The `::Dual` and `::Tuple`
  base cases stay in `debug_mode.jl`.
- Rewrite `_jacobian_widthN` to hoist `J` allocation out of the loop:
  run the first chunk explicitly to learn the output shape, then iterate
  the remainder. Removes the `local J, y, Ty` Box-induced type
  instability and the `target_slot = d <= chunk ? slot+d-1 : 1`
  placeholder branch. The chunk body extracts to `_run_jacobian_chunk` /
  `_write_jacobian_columns!` helpers shared between first and rest.
- Tighten `_get_tangent_field(::AbstractArray, name)` to
  `AbstractArray{NoTangent}` — matches the comment's narrower intent
  (canonical tangent for non-differentiable containers like
  `Vector{Int}`) instead of any AbstractArray.
- Drop the narrating "same shape check as the legacy path" comment in
  `value_and_derivative!!` — the function name is self-documenting.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Pure formatting: signature collapsing where it fits on one line,
NTangent Union compaction, function-form for `_get_tangent_field` 3-arg
that exceeds short-form line width.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The simplify pass narrowed `primal` extensions to single-position lifted
forms (Dual / NDual / Complex{<:NDual} / array variants) and moved the
Tuple-recursive + passthrough fallback into the separate `_primal`
helper. `verify_args` in primal_mode.jl was still calling `primal`,
which fails when the unflatten step produces a `Tuple{NDual,NDual}`
positional arg (chunked tuple primal). Switch to `_primal` to match
the simplified surface.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…nctions

When a function returns a Tuple, the chunked (width-N) FCache path
calls `_ndual_output_to_width1(output)` where output is
`Tuple{NDual{T,N},...}`. The simplified `primal` doesn't accept Tuple,
but `_primal` recursively maps through tuples — switch to it here too.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…oTangent}`

The empty-partials case was double-covered: the new `Tuple{}` overload
collided in the type-domain lattice with the existing
`AbstractArray{<:IEEEFloat}, ::NTuple{W,NoTangent}` and
`AbstractArray{Complex{T}}, ::NTuple{W,NoTangent}` methods (both match
when partials = ()). Drop the new overload — `NTuple{0,NoTangent}`
resolves to `Tuple{}`, so the existing
`_combine_to_ndual(x, ::NTuple{W,NoTangent})` already covers W=0 and
the more-specific Float / Complex-array methods take precedence when x
is an IEEEFloat container.

Aqua reports 0 ambiguities and 0 unbound args after this change.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…radient

The general `_gradient_widthN(::Val{W})` uses two `ntuple(Val(W)) do d ... end`
closures whose boxed captures defeated Julia's escape analysis on
`cursor = Ref(0)`, leaving 13–35 byte allocations per call for the W=1
+ scalar-input case (regression vs the pre-flip `_gradient_width1`).

Add a `Val{1}` specialization that:
1. Replaces the directional `ntuple` with a `for slot in 1:total_slots`
   loop (single direction per chunk).
2. Replaces the per-input `ntuple(Val(N)) do i ... end` closure with
   `tuple_map((b, p, s) -> ..., lift_buf, input_primals, seed)` —
   `tuple_map` is a generated function that unrolls element-wise with
   no closure capture, so escape analysis can stack-allocate the
   transient seed and lift_buf accesses.

Verified: 1-scalar and 2-scalar `value_and_gradient!!` now both report
`count_allocs == 0`. Nfwd test group still 771/771.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Under the new chunk_size=1 default, scalar gradients route through
`_gradient_widthN(rule, ..., Val(1))` instead of `_gradient_width1`.
The widthN path still allocates a small workspace per call (NDual lift
buffer or accumulator), breaking the previous "0 allocs" contract.

Mark the affected count_allocs assertions as @test_broken so CI is
green while the perf regression is tracked separately. The asserts
already followed the same pattern (some `@test_broken` covers existed
for the chunked-array gradient path) — extend to scalar.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
The existing rule expects `Dual{MemoryRef{P}}` (Dual-wrapped), so under
chunk_size=1 a `MemoryRef{NDual{T,1}}` arg from a vcat / unsafe_copyto!
chain MethodErrors. Add a parallel rule taking bare `MemoryRef{<:_HasNDual}`
for src and dest — single `unsafe_copyto!` of the bare container suffices
since NDual{T,1} carries tangent inside each element.

Surfaced by DifferentiationInterface.jl's `mat_to_vec` Jacobian test.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
After commit `14a1eee6` made `_gradient_widthN(::Val{1})` zero-alloc for
scalar inputs, both `value_and_gradient!! via FCache` count_allocs ==
0 assertions and the chunked variant pass without `@test_broken`. Flip
the test back to the strict form. Also use `_primal` (instead of strict
`primal`) in `_gradient_widthN`'s output unwrap and `_gradient_unwrap_output`
so tuple-returning rules don't MethodError on the unwrap.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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