Add bigfloat tests

test/misc/exotic_type_tests.jl

@@ -0,0 +1,30 @@
+# File for different types of exotic types
+@testsetup module NonlinearSolveExoticTypeTests
+using NonlinearSolve
+
+fn_iip = NonlinearFunction{true}((du, u, p) -> du .= u .* u .- p)
+fn_oop = NonlinearFunction{false}((u, p) -> u .* u .- p)
+
+u0 = BigFloat[1.0, 1.0, 1.0]
+prob_iip_bf = NonlinearProblem{true}(fn_iip, u0, BigFloat(2))
+prob_oop_bf = NonlinearProblem{false}(fn_oop, u0, BigFloat(2))
+
+export fn_iip, fn_oop, u0, prob_iip_bf, prob_oop_bf
+end
+
+@testitem "BigFloat Support" tags=[:misc] setup=[NonlinearSolveExoticTypeTests] begin
+    using NonlinearSolve, LinearAlgebra
+
+    for alg in [NewtonRaphson(), Broyden(), Klement(), DFSane(), TrustRegion(),
+        LimitedMemoryBroyden(; threshold = 2)]
+        sol = solve(prob_oop_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+
+        alg isa Halley && continue
+
+        sol = solve(prob_iip_bf, alg)
+        @test norm(sol.resid, Inf) < 1e-6
+        @test SciMLBase.successful_retcode(sol.retcode)
+    end
+end