Fix ternary hypot flattening Duals with different tags

[devmotion]

Fixes #834.

All seven bodies of the @define_ternary_dual_op for hypot delegated to a single helper that unwraps every argument with the one-argument value/partials, regardless of its tag:

@inline function calc_hypot(x, y, z, ::Type{T}) where T
    vx = value(x)
    vy = value(y)
    vz = value(z)
    h = hypot(vx, vy, vz)
    p = (vx / h) * partials(x) + (vy / h) * partials(y) + (vz / h) * partials(z)
    return Dual{T}(h, p)
end

When the arguments carry different tags, the ones with an inner tag are flattened as well and their partials are summed into whichever tag dispatch selected — their perturbations are annihilated, and the surviving tag's partials are polluted by their contributions:

julia> inner(x) = ForwardDiff.derivative(y -> hypot(x, y, 1.0), 2.0);

julia> ForwardDiff.derivative(inner, 3.0)   # correct: -0.11454053224818188
0.0

Each case now gets its own body that only unwraps the arguments known to carry the tag, as fma and muladd already do. Arguments with an inner tag are passed on unchanged; since Dual <: Real they are handled by the recursive hypot call, which keeps their perturbations nested inside the returned Dual. Because hypot is symmetric, two helpers plus permutations of their arguments cover all seven cases.

Since the tag is now read off the helpers' signatures instead of being passed as a ::Type{T} argument, this also makes ternary hypot work for non-Type tags, which previously threw a MethodError:

julia> hypot(Dual{:t}(1.0, 1.0), Dual{:t}(2.0, 1.0), Dual{:t}(3.0, 1.0))   # on master: MethodError
Dual{:t}(3.7416573867739413,1.6035674514745464)

Note that calc_hypot is not just arity plumbing and cannot simply be dropped in favour of composing binary operations: it calls Base's hypot on the values and applies the analytic ∂h/∂xᵢ = xᵢ/h, so no squares are formed and the partials do not overflow. There is a test for this.

Unchanged: the values and partials for single-tag arguments (including gradients and Hessians), and the NaN when differentiating at the origin, where hypot genuinely has no gradient. nansafe_mode does not help there because the NaN originates in the coefficient vx/h = 0/0 rather than in a zero partial, and the two-argument hypot from DiffRules behaves the same way.

Tests

Each of the seven bodies is now covered twice over — once with the non-tagged arguments as plain Reals, in the "Special Cases" block, and once with them carrying an inner tag, in the new testset. Both are needed: dispatch settles on one tag, and a different body runs depending on whether one or two of the arguments carry it, so a nested derivative with the differently-tagged argument in only one position reaches just five of the seven bodies.

The new tests fail on master in all three argument positions and for three distinct tags (0.0 instead of the correct derivative). Mis-permuting any of the six non-symmetric arguments of the @define_ternary_dual_op call also turns them into a MethodError, so the permutations are checked rather than merely written down.

Full test suite passes locally on Julia 1.12.6 with nansafe_mode disabled (9279/9279) and enabled (9361/9361).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.49%. Comparing base (f1bb430) to head (4600adb).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #835      +/-   ##
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+ Coverage   90.71%   91.49%   +0.78%     
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  Files          11       11              
  Lines        1055     1058       +3     
==========================================
+ Hits          957      968      +11     
+ Misses         98       90       -8     

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