perf(BMT): recover the primal tendency from the Rosenbrock Jacobian pass

[haakon-e]

Summary

In the Rosenbrock micro substep the primal tendency f = g(x) and the Jacobian ForwardDiff.jacobian(g, x) were computed separately, but ForwardDiff's Jacobian pass already evaluates f as the dual .value and discards it. Recover it with DiffResults/jacobian!, eliminating one full (quadrature-dominated) tendency evaluation per substep.

What changed (src/BMT_rosenbrock.jl, Project.toml, BulkMicrophysicsTendencies.jl)

• Both the 2M+P3 and the 1M ExactJacobian substep paths now go through a shared _tendency_and_jacobian(jacobian, g, x) method: r = ForwardDiff.jacobian!(DiffResults.JacobianResult(x), g, x), then f = typeof(x)(DiffResults.value(r)), J = DiffResults.jacobian(r). The method reconstructs the same FieldVector species type as x (MicroState1M or MicroState2MP3), removing the duplicated DiffResults code that previously lived inline in the 2M+P3 loop.
• The analytic Donor / CoupledDonor 1M Jacobians have no f by-product, so their _tendency_and_jacobian methods keep the separate f = g(x). The non-finite euler fallback also keeps f = g(x).
• Add DiffResults to [deps] + [compat]; import DiffResults in BulkMicrophysicsTendencies.jl.

Mechanism / why

ForwardDiff.jacobian(g, x::StaticArray) runs one dual evaluation and extracts the Jacobian, throwing away the dual .value (= f). jacobian! into an immutable JacobianResult does the identical single pass and additionally records the value, so f is recovered for free. JacobianResult is immutable for a StaticArray, so the jacobian! return value must be captured (it is not mutated in place). Two opaque call sites otherwise prevent common-subexpression elimination, so the saving is real.

Validation

• f and J bit-identical to the separate computation (verified === on the reconstructed MicroState1M and MicroState2MP3 and on J); no extra allocations (@allocated == 0 for both helper paths and the full 2M+P3 bulk_microphysics_tendencies); type-stable (@inferred).
• ~27% faster per substep (order-independent since J ≈ 2.68× f).
• rosenbrock_1m / mode / framework / verbose tests pass (F32 + F64), including the allocation and "vs fine explicit reference" checks.

Caveats

• ExactJacobian paths only (by design). DiffResults becomes a direct dep (it was transitive via ForwardDiff).

[haakon-e]

This change is part of the following stack:

• feat(P3): Gauss-Legendre quadrature, integrand breakpoints -> GL(6) default #741
  • feat(Rosenbrock): unified RosenbrockAverage substepping framework + 2M+P3 exact-AD mode #726
    • feat(Rosenbrock): 1M donor / coupled / exact modes on the unified framework #731
      • feat(Rosenbrock): post-solve per-process verbose diagnostics #732
        • fix(Rosenbrock): saturation adjustment on max(S_ice, S_liq) #737
          • perf(BMT): recover the primal tendency from the Rosenbrock Jacobian pass #742 ◀
            • feat(BMT): analytic ManualJacobian for the 2M+P3 Rosenbrock substep #743
              • feat(BMT): coupled Tier-3 donor linearization for the 2M+P3 ManualJacobian #744

_{Change managed by git-spice.}

[codecov]

Codecov Report

❌ Patch coverage is 88.23529% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 92.99%. Comparing base (10acc85) to head (4a53652).

Additional details and impacted files

@@                   Coverage Diff                   @@
##           he/rosenbrock-modes     #742      +/-   ##
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- Coverage                93.11%   92.99%   -0.13%     
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  Files                       57       57              
  Lines                     3298     3310      +12     
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+ Hits                      3071     3078       +7     
- Misses                     227      232       +5     

Components	Coverage Δ
src	93.68% <88.23%> (-0.14%)	⬇️
ext	69.47% <ø> (ø)

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