Add VF64-specialized LinearCache for shorter stack traces

[ChrisRackauckas-Claude]

Summary

Implements the VF64 pattern for LinearCache and DefaultLinearSolverInit to reduce type string lengths in stack traces from ~1500 chars to ~500 chars per instance. This addresses the LinearSolve.jl component of SciML/DifferentialEquations.jl#1128.

Before: LinearCache had 12 type parameters and DefaultLinearSolverInit had 25 type parameters, producing ~1500 character type strings in stack traces.

After: LinearCacheVF64 has 4 type parameters and DefaultLinearSolverInitVF64 has 1 type parameter, producing ~500 character type strings. This is a 67% reduction.

New types

• LinearCacheVF64{Tp, Tc, Tlv, S} — hardcodes A::Matrix{Float64}, b/u::Vector{Float64}, Pl/Pr::IdentityOperator, abstol/reltol::Float64, assumptions::OperatorAssumptions{Bool}
• DefaultLinearSolverInitVF64{TA} — hardcodes all 24 factorization cache slot types for Matrix{Float64} at module load time via let/@eval
• LinearCacheType = Union{LinearCache, LinearCacheVF64} — for backward-compatible dispatch
• DefaultLinearSolverInitType = Union{DefaultLinearSolverInit, DefaultLinearSolverInitVF64}

How it works

• When init() detects Matrix{Float64} + Vector{Float64} + DefaultLinearSolver, it automatically constructs a LinearCacheVF64 instead of LinearCache
• All method signatures updated from cache::LinearCache to cache::LinearCacheType (Union-based dispatch)
• Field names are identical between the two structs, so all field access works unchanged
• Non-VF64 types (sparse matrices, non-Float64, custom solvers) still use the generic LinearCache

Files changed

• src/vf64_types.jl (new) — VF64 type definitions, conversion, and constructor
• src/common.jl — LinearCacheVF64 struct, Union type, VF64 branch in __init
• src/LinearSolve.jl — include, exports, moved defaultalg_symbol generic method earlier (fixes world age issue with @generated functions)
• src/factorization.jl — dispatch updates, moved specialized defaultalg_symbol overloads
• src/default.jl — dispatch updates
• All other src/*.jl solver files — dispatch updates
• All 16 extension files — dispatch updates

Test plan

• All existing Pkg.test() tests pass (no regressions)
• Basic solve correctness verified (A\b comparison)
• VF64 type construction verified (cache isa LinearCacheVF64)
• Cache mutation works (updating A and b)
• Type string length verified (492 chars vs ~1500 chars before)

🤖 Generated with Claude Code