Give tracked reals with a free origin a zero and a one (fixes #172), and pin #126

[devmotion]

#301 triaged #126 and #172 as already passing on master. #126 does; #172 does not, so this branch pins the first and fixes the second.

#126 — test only

gradient(x -> x[], fill(1.0)) was ambiguous between the AbstractRange... and Colon... methods of getindex, because a bare vararg matches zero arguments. 4a50321 fixed it incidentally while fixing #202, by requiring a leading index. Nothing pinned it, and it would come back unnoticed with any future widening of those signatures.

#172 — fix and test

mapping over a tracked array mixes elements that carry an origin with ones that do not, and the resulting eltype leaves the origin free. reducedim_init allocates a reduction's accumulator by asking that eltype for its zero, or one for prod, which reached valtype — defined only for a pinned origin:

julia> ReverseDiff.gradient([1.0, 2.0]) do x
           sum(sum(map(i -> isodd(i) ? x[i] : 2 * x[i], eachindex(x)); dims = 1))
       end
ERROR: MethodError: no method matching valtype(::Type{TrackedReal{Float64, Float64}})

That is the element type in the issue's stack trace. Narrower spellings of "different types" (Real[], Any[]) already worked, which is most likely what produced the triage in #301.

Neither identity depends on the origin, so both are deducible from the type alone, as zero requires. Nothing is the origin zero has always used, and TrackedReal{V,D,Nothing} is an instance of TrackedReal{V,D}, so the documented zero(T) isa T holds. The signature matches that type exactly rather than its subtypes: a Union of two origins is also a subtype, and no single member of it could be returned.

The zero method is the one #173 added and #177 reverted wholesale over #175, whose cause — increment_deriv! indexing into untracked elements — was fixed by #300. one is its counterpart, which #173 never added.

Derivatives still route through the tape, not the origin: the accumulator is a fresh value, never an aliased array slot. Checked against ForwardDiff across randomized sum/prod reductions, jacobian and hessian, and on tape replay with a compiled tape — the committed test uses prod so that a replay reusing stale values would be caught.

detect_ambiguities(ReverseDiff) is unchanged at 877, none involving zero or one. Removing the two methods makes every new #172 assertion fail with the MethodError above, and leaves the #126 ones passing.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 86.93%. Comparing base (cd0a06d) to head (4146188).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #302      +/-   ##
==========================================
+ Coverage   86.92%   86.93%   +0.01%     
==========================================
  Files          19       19              
  Lines        1950     1952       +2     
==========================================
+ Hits         1695     1697       +2     
  Misses        255      255              

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