Fix data race in BSpline and QuadraticSpline evaluation (rebase of #533)

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Rebased version of #533 (original by @alecloudenback) onto current master. That PR was 18 commits behind and conflicting; this branch resolves the conflicts and updates it for the new test layout. Opened from the bot fork because I lacked push access to update #533's head branch directly. Supersedes #533 — close whichever is not merged.

Original change (#532 fix)

BSplineInterpolation, BSplineApprox, and uncached QuadraticSpline kept a scratch buffer in their sc field and overwrote it in place on every evaluation, so a "read" mutated shared state — evaluating one shared interpolant from multiple threads raced and silently returned wrong values.

• BSpline{Interpolation,Approx}: allocate the spline-coefficient scratch per call instead of reusing A.sc, making evaluation reentrant.
• QuadraticSpline: compute the three nonzero degree-2 B-spline basis values in local variables instead of writing to the shared buffer.
• Thread-safety regression tests: a deterministic no-mutation-on-eval guard plus a concurrent stress test (now also covering degree-1 BSpline).

Rebase conflict resolution

• src/parameter_caches.jl: master's Fix QuadraticSpline edge-case crashes: n=2 BoundsError, Rational t starting at 0, duplicate knots #543 added a length(t) == 2 edge-case guard while still using the shared sc buffer; Fix data race in BSpline and QuadraticSpline evaluation #533 removed that buffer for thread safety. Merged both — kept the 2-point edge case and the reentrant local-variable basis evaluation.
• test/runtests.jl: master migrated to SciMLTesting's folder-based run_tests() (Use SciMLTesting v1.2 (folder-based run_tests) #547), so the manual @safetestset list is gone. Took master's version and moved the new test to test/Methods/thread_safety_tests.jl so it's auto-discovered under the Methods group.

Verification (run locally)

• All 28 thread-safety tests pass with julia -t4 (concurrent stress path exercised, not skipped).
• 2-point QuadraticSpline edge case works; cached vs uncached agree across the range.
• Runic-formatted.

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[ChrisRackauckas-Claude]

Added a follow-up commit: Make BSpline evaluation allocation-free as well as thread-safe.

The original #532 fix made BSpline eval reentrant by allocating a per-call scratch buffer (zeros(eltype(t), n)), which removed the data race but added a heap allocation per call (848 B for a length-99 scalar spline). QuadraticSpline was already allocation-free via its local-variable rewrite; this brings BSpline to parity.

Approach: a degree-d B-spline has only d + 1 nonzero basis functions at any point, so the new bspline_nonzero_coefficients computes them into a stack-allocated MVector (StaticArrays) and returns an SVector window + control-point offset. Allocation-free and reentrant — no shared or heap state per call. All four _interpolate and four _derivative BSpline methods use it.

To keep a single statically-allocation-free path (AllocCheck sees every branch reachable from the call operator, including extrapolation paths into _derivative), the heap fallback is removed and degree is bounded at construction (d < 16). Max degree used anywhere in this repo is 3; degree ≥16 global B-splines are numerically degenerate.

StaticArrays moves from a test-only dep to a hard dep.

Allocations/call (length-99 scalar spline):

	before	after
BSpline value	848 B	0 B
BSpline derivative	848 B	0 B
BSplineApprox	128 B	0 B
BSpline array value	1888 B	1040 B (output array only)

Verification (all run locally):

• New bspline_nonzero_coefficients matches the reference spline_coefficients! exactly (max diff 0.0) over degrees 1–7 incl. both endpoints
• Derivatives match finite differences (~1e-10) and ForwardDiff (~1e-16)
• AllocCheck.check_allocs: 0 allocation sites for value and derivative
• test/qa/alloc_tests.jl (with new BSpline value+derivative cases): 16/16
• test/Methods/thread_safety_tests.jl with -t4: 28/28 (concurrent stress path exercised)
• interpolation_tests.jl: 17412 pass, 0 fail; derivative_tests.jl: 34479 pass, 0 fail

🤖 Generated with Claude Code