diff --git a/lib/OrdinaryDiffEqBDF/src/algorithms.jl b/lib/OrdinaryDiffEqBDF/src/algorithms.jl
index 387a9d6a72..1a4c960c7b 100644
--- a/lib/OrdinaryDiffEqBDF/src/algorithms.jl
+++ b/lib/OrdinaryDiffEqBDF/src/algorithms.jl
@@ -150,7 +150,7 @@ end
 function QNDF1(; chunk_size = Val{0}(), autodiff = Val{true}(), standardtag = Val{true}(),
         concrete_jac = nothing, diff_type = Val{:forward},
         linsolve = nothing, precs = DEFAULT_PRECS, nlsolve = NLNewton(),
-        extrapolant = :linear, kappa = -0.1850,
+        extrapolant = :linear, kappa = -37//200,
         controller = :Standard, step_limiter! = trivial_limiter!)
     QNDF1{
         _unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve), typeof(nlsolve),
@@ -233,7 +233,7 @@ function QNDF(; max_order::Val{MO} = Val{5}(), chunk_size = Val{0}(),
         diff_type = Val{:forward},
         linsolve = nothing, precs = DEFAULT_PRECS, nlsolve = NLNewton(), κ = nothing,
         tol = nothing,
-        extrapolant = :linear, kappa = promote(-0.1850, -1 // 9, -0.0823, -0.0415, 0),
+        extrapolant = :linear, kappa = (-37//200, -1//9, -823//10000, -83//2000, 0//1),
         controller = :Standard, step_limiter! = trivial_limiter!) where {MO}
     QNDF{MO, _unwrap_val(chunk_size), _unwrap_val(autodiff), typeof(linsolve),
         typeof(nlsolve), typeof(precs), diff_type, _unwrap_val(standardtag),
diff --git a/lib/OrdinaryDiffEqBDF/src/bdf_caches.jl b/lib/OrdinaryDiffEqBDF/src/bdf_caches.jl
index 7cdc4b580f..9d60023c13 100644
--- a/lib/OrdinaryDiffEqBDF/src/bdf_caches.jl
+++ b/lib/OrdinaryDiffEqBDF/src/bdf_caches.jl
@@ -358,7 +358,7 @@ function alg_cache(alg::QNDF{MO}, u, rate_prototype, ::Type{uEltypeNoUnits},
         ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits
 } where {MO}
     max_order = MO
-    γ, c = one(eltype(alg.kappa)), 1
+    γ, c = one(uEltypeNoUnits), 1
     nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits,
         uBottomEltypeNoUnits, tTypeNoUnits, γ, c, Val(false))
     dtprev = one(dt)
@@ -539,7 +539,7 @@ function alg_cache(alg::FBDF{MO}, u, rate_prototype, ::Type{uEltypeNoUnits},
         dt, reltol, p, calck,
         ::Val{false}) where {uEltypeNoUnits, uBottomEltypeNoUnits, tTypeNoUnits
 } where {MO}
-    γ, c = 1.0, 1.0
+    γ, c = one(uEltypeNoUnits), 1
     max_order = MO
     nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits,
         uBottomEltypeNoUnits, tTypeNoUnits, γ, c, Val(false))
@@ -614,7 +614,7 @@ function alg_cache(alg::FBDF{MO}, u, rate_prototype, ::Type{uEltypeNoUnits},
         dt, reltol, p, calck,
         ::Val{true}) where {MO, uEltypeNoUnits, uBottomEltypeNoUnits,
         tTypeNoUnits}
-    γ, c = 1.0, 1.0
+    γ, c = one(uEltypeNoUnits), 1
     fsalfirst = zero(rate_prototype)
     max_order = MO
     nlsolver = build_nlsolver(alg, u, uprev, p, t, dt, f, rate_prototype, uEltypeNoUnits,
diff --git a/lib/OrdinaryDiffEqBDF/src/controllers.jl b/lib/OrdinaryDiffEqBDF/src/controllers.jl
index f3cbdf2d03..c001e6a586 100644
--- a/lib/OrdinaryDiffEqBDF/src/controllers.jl
+++ b/lib/OrdinaryDiffEqBDF/src/controllers.jl
@@ -172,7 +172,7 @@ function choose_order!(alg::FBDF, integrator,
             terk_tmp = @.. broadcast=false fd_weights[k - 2, 1]*u
             vc = _vec(terk_tmp)
             for i in 2:(k - 2)
-                @.. broadcast=false @views vc += fd_weights[i, k - 2] * u_history[:, i - 1]
+                @.. @views vc += fd_weights[i, k - 2] * u_history[:, i - 1]
             end
             @.. broadcast=false terk_tmp*=abs(dt^(k - 2))
             calculate_residuals!(atmp, _vec(terk_tmp), _vec(uprev), _vec(u),
@@ -204,22 +204,24 @@ function choose_order!(alg::FBDF, integrator,
             terkm1 = terkm2
             fd_weights = calc_finite_difference_weights(ts_tmp, t + dt, k - 2,
                 Val(max_order))
-            terk_tmp = @.. broadcast=false fd_weights[k - 2, 1]*u
+            local terk_tmp
             if u isa Number
+                terk_tmp = fd_weights[k - 2, 1]*u
                 for i in 2:(k - 2)
                     terk_tmp += fd_weights[i, k - 2] * u_history[i - 1]
                 end
                 terk_tmp *= abs(dt^(k - 2))
             else
-                vc = _vec(terk_tmp)
+                # we need terk_tmp to be mutable.
+                # so it can be updated
+                terk_tmp = similar(u)
+                @.. terk_tmp = fd_weights[k - 2, 1]*_vec(u)
                 for i in 2:(k - 2)
-                    @.. broadcast=false @views vc += fd_weights[i, k - 2] *
-                                                     u_history[:, i - 1]
+                    @.. @views terk_tmp += fd_weights[i, k - 2] * u_history[:, i - 1]
                 end
-                terk_tmp = reshape(vc, size(terk_tmp))
-                terk_tmp *= @.. broadcast=false abs(dt^(k - 2))
+                @.. terk_tmp *= abs(dt^(k - 2))
             end
-            atmp = calculate_residuals(_vec(terk_tmp), _vec(uprev), _vec(u),
+            atmp = calculate_residuals(terk_tmp, _vec(uprev), _vec(u),
                 integrator.opts.abstol, integrator.opts.reltol,
                 integrator.opts.internalnorm, t)
             terkm2 = integrator.opts.internalnorm(atmp, t)
diff --git a/test/interface/linear_solver_test.jl b/test/interface/linear_solver_test.jl
index 515fbd3459..12a449d603 100644
--- a/test/interface/linear_solver_test.jl
+++ b/test/interface/linear_solver_test.jl
@@ -161,14 +161,14 @@ end
 using OrdinaryDiffEq, StaticArrays, LinearSolve, ParameterizedFunctions
 
 hires = @ode_def Hires begin
-    dy1 = -1.71 * y1 + 0.43 * y2 + 8.32 * y3 + 0.0007
-    dy2 = 1.71 * y1 - 8.75 * y2
-    dy3 = -10.03 * y3 + 0.43 * y4 + 0.035 * y5
-    dy4 = 8.32 * y2 + 1.71 * y3 - 1.12 * y4
-    dy5 = -1.745 * y5 + 0.43 * y6 + 0.43 * y7
-    dy6 = -280.0 * y6 * y8 + 0.69 * y4 + 1.71 * y5 - 0.43 * y6 + 0.69 * y7
-    dy7 = 280.0 * y6 * y8 - 1.81 * y7
-    dy8 = -280.0 * y6 * y8 + 1.81 * y7
+    dy1 = -1.71f0 * y1 + 0.43f0 * y2 + 8.32f0 * y3 + 0.0007f0 + 1f-18*t
+    dy2 = 1.71f0 * y1 - 8.75f0 * y2
+    dy3 = -10.03f0 * y3 + 0.43f0 * y4 + 0.035f0 * y5
+    dy4 = 8.32f0 * y2 + 1.71f0 * y3 - 1.12f0 * y4
+    dy5 = -1.745f0 * y5 + 0.43f0 * y6 + 0.43f0 * y7
+    dy6 = -280.0f0 * y6 * y8 + 0.69f0 * y4 + 1.71f0 * y5 - 0.43f0 * y6 + 0.69f0 * y7
+    dy7 = 280.0f0 * y6 * y8 - 1.81f0 * y7
+    dy8 = -280.0f0 * y6 * y8 + 1.81f0 * y7
 end
 
 u0 = zeros(8)
@@ -178,7 +178,11 @@ u0[8] = 0.0057
 probiip = ODEProblem{true}(hires, u0, (0.0, 10.0))
 proboop = ODEProblem{false}(hires, u0, (0.0, 10.0))
 probstatic = ODEProblem{false}(hires, SVector{8}(u0), (0.0, 10.0))
+probiipf32 = ODEProblem{true}(hires, Float32.(u0), (0f0, 10f0))
+proboopf32 = ODEProblem{false}(hires, Float32.(u0), (0f0, 10f0))
+probstaticf32 = ODEProblem{false}(hires, SVector{8}(Float32.(u0)), (0f0, 10f0))
 probs = (; probiip, proboop, probstatic)
+probsf32 = (;probiipf32, proboopf32, probstaticf32)
 qndf = QNDF()
 krylov_qndf = QNDF(linsolve = KrylovJL_GMRES())
 fbdf = FBDF()
@@ -197,3 +201,13 @@ refsol = solve(probiip, FBDF(), abstol = 1e-12, reltol = 1e-12)
         end
     end
 end
+
+@testset "Hires Float32 calc_W tests" begin
+    @testset "$probname" for (probname, prob) in pairs(probsf32)
+        @testset "$solname" for (solname, solver) in pairs(solvers)
+            sol = solve(prob, solver, maxiters = 2e4)
+            @test sol.retcode == ReturnCode.Success
+            @test isapprox(sol.u[end], refsol.u[end], rtol = 2e-3, atol = 1e-6)
+        end
+    end
+end