diff --git a/test/testsuite/ad_utils.jl b/test/testsuite/ad_utils.jl
index def762889..1ab76e2d1 100644
--- a/test/testsuite/ad_utils.jl
+++ b/test/testsuite/ad_utils.jl
@@ -59,6 +59,27 @@ test in-place Hermitian eigendecomposition rules via Mooncake's non-primitive AD
 """
 eigh!_wrapper(f!, A, alg) = (F = f!(project_hermitian!(A), alg); MatrixAlgebraKit.zero!(A); F)
 
+"""
+    eig_vals_wrapper(f, A, alg)
+
+Wrapper that sorts the eigenvalues returned by `f(A, alg)` by modulus and then by imaginary part.
+LAPACK's ordering of the eigenvalues can change discontinuously under small perturbations of
+`A`, which breaks finite-difference checks. The ordering imposed here is smooth for matrices
+built with `make_eig_matrix`, whose eigenvalues have distinct moduli up to conjugate pairs.
+"""
+eig_vals_wrapper(f, A, alg) = sort_eigvals(f(A, alg))
+
+"""
+    eig_vals!_wrapper(f!, A, alg)
+
+In-place variant of [`eig_vals_wrapper`](@ref), which zeros `A` after calling `f!`.
+"""
+eig_vals!_wrapper(f!, A, alg) = sort_eigvals(call_and_zero!(f!, A, alg))
+
+# sortperm is used here because Mooncake CAN differentiate that on CUDA,
+# but CANNOT differentiate sort
+sort_eigvals(D) = D[sortperm(collect(D); by = λ -> (abs(λ), imag(λ)))]
+
 """
     qr_gauge_invariant_wrapper(f, A, alg, r)
 
@@ -149,11 +170,27 @@ function stabilize_eigvals!(D::AbstractVector)
     n = maximum(p)
     # rescale eigenvalues so that they lie on distinct radii in the complex plane
     # that are chosen randomly in non-overlapping intervals [10 * k/n, 10 * (k+0.5)/n)] for k=1,...,n
-    radii = 10 .* ((1:n) .+ rand(real(eltype(D)), n) ./ 2) ./ n
+    radii = 10 .* ((1:n) .+ rand(rng, real(eltype(D)), n) ./ 2) ./ n
     hD = sign.(collect(D)) .* radii[p]
     copyto!(D, hD)
     return D
 end
+"""
+    midgap_tol(vals)
+
+Return a truncation tolerance halfway across the widest gap between consecutive values of
+`abs.(vals)`, restricted to the middle half so that truncation keeps a nontrivial subset.
+This keeps the number of retained values fixed under the perturbations used by
+finite-difference checks.
+"""
+function midgap_tol(vals)
+    s = sort!(collect(abs.(vals)))
+    n = length(s)
+    gaps = (max(1, n ÷ 4)):(min(n - 1, (3n) ÷ 4))
+    _, i = findmax(i -> s[i + 1] - s[i], gaps)
+    return (s[gaps[i]] + s[gaps[i] + 1]) / 2
+end
+
 function make_eig_matrix(T, sz)
     A = instantiate_matrix(T, sz)
     D, V = eig_full(A)
diff --git a/test/testsuite/chainrules.jl b/test/testsuite/chainrules.jl
index 631d95576..df95e7026 100755
--- a/test/testsuite/chainrules.jl
+++ b/test/testsuite/chainrules.jl
@@ -442,7 +442,7 @@ function test_chainrules_eigh(
                 @test isequal(ΔDVtrunc, ΔDVtrunc_copy)
             end
             D, ΔD = ad_eigh_vals_setup(A / 2)
-            truncalg = TruncatedAlgorithm(alg, trunctol(; atol = maximum(abs, D) / 2))
+            truncalg = TruncatedAlgorithm(alg, trunctol(; atol = midgap_tol(eigh_vals(A))))
             DV, DVtrunc, ΔDV, ΔDVtrunc = ad_eigh_trunc_setup(A, truncalg)
             ind = MatrixAlgebraKit.findtruncated(diagview(DV[1]), truncalg.trunc)
             ot = (ΔDVtrunc..., zero(real(T)))
@@ -601,7 +601,7 @@ function test_chainrules_svd(
                 @test isequal(ΔUSVᴴtrunc, ΔUSVᴴtrunc_copy)
             end
             S, ΔS = ad_svd_vals_setup(A)
-            truncalg = TruncatedAlgorithm(alg, trunctol(atol = S[1, 1] / 2))
+            truncalg = TruncatedAlgorithm(alg, trunctol(atol = midgap_tol(S)))
             USVᴴ, _, ΔUSVᴴ, ΔUSVᴴtrunc = ad_svd_trunc_setup(A, truncalg)
             ot = (ΔUSVᴴtrunc..., zero(real(T)))
             ot_copy = deepcopy(ot)
@@ -625,7 +625,7 @@ function test_chainrules_svd(
             dA1 = MatrixAlgebraKit.svd_pullback!(zero(A), A, USVᴴ, ΔUSVᴴtrunc, ind)
             dA2 = MatrixAlgebraKit.svd_trunc_pullback!(zero(A), A, (Utrunc, Strunc, Vᴴtrunc), ΔUSVᴴtrunc)
             @test isapprox(dA1, dA2; atol = atol, rtol = rtol)
-            trunc = trunctol(; atol = S[1, 1] / 2)
+            trunc = truncalg.trunc
             ind = MatrixAlgebraKit.findtruncated(diagview(S), trunc)
             ot = (ΔUSVᴴtrunc..., zero(real(T)))
             ot_copy = deepcopy(ot)
diff --git a/test/testsuite/enzyme/eig.jl b/test/testsuite/enzyme/eig.jl
index 4eaf878f3..b9e609d81 100644
--- a/test/testsuite/enzyme/eig.jl
+++ b/test/testsuite/enzyme/eig.jl
@@ -19,7 +19,7 @@ Test the Enzyme foward- and reverse-mode AD rule for `eig_full` and its in-place
 """
 function test_enzyme_eig_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "eig_full: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -40,17 +40,17 @@ Test the Enzyme forward- and reverse-mode AD rule for `eig_vals` and its in-plac
 """
 function test_enzyme_eig_vals(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "eig_vals: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = make_eig_matrix(T, sz)
         alg = MatrixAlgebraKit.select_algorithm(eig_vals, A)
         D, ΔD = ad_eig_vals_setup(A)
-        test_reverse(eig_vals, RT, (A, TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
-        test_reverse(call_and_zero!, RT, (eig_vals!, Const), (copy(A), TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
-        test_forward(eig_vals, RT, (A, TA), (alg, Const); atol, rtol, fdm)
-        test_forward(call_and_zero!, RT, (eig_vals!, Const), (copy(A), TA), (alg, Const); atol, rtol, fdm)
+        test_reverse(eig_vals_wrapper, RT, (eig_vals, Const), (A, TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
+        test_reverse(eig_vals!_wrapper, RT, (eig_vals!, Const), (copy(A), TA), (alg, Const); atol, rtol, output_tangent = ΔD, fdm)
+        test_forward(eig_vals_wrapper, RT, (eig_vals, Const), (A, TA), (alg, Const); atol, rtol, fdm)
+        test_forward(eig_vals!_wrapper, RT, (eig_vals!, Const), (copy(A), TA), (alg, Const); atol, rtol, fdm)
     end
 end
 
@@ -62,7 +62,7 @@ in-place variants, over a range of truncation ranks and a tolerance-based trunca
 """
 function test_enzyme_eig_trunc(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "eig_trunc reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -83,7 +83,7 @@ function test_enzyme_eig_trunc(
         @testset "trunctol" begin
             A = make_eig_matrix(T, sz)
             D = eig_vals(A)
-            trunc = trunctol(atol = maximum(abs, D) / 2; by = abs)
+            trunc = trunctol(atol = midgap_tol(D); by = abs)
             truncalg = TruncatedAlgorithm(alg, trunc)
             DV, _, ΔDV, ΔDVtrunc = ad_eig_trunc_setup(A, truncalg)
             test_reverse(eig_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
diff --git a/test/testsuite/enzyme/eigh.jl b/test/testsuite/enzyme/eigh.jl
index 8143678ec..84cf41842 100644
--- a/test/testsuite/enzyme/eigh.jl
+++ b/test/testsuite/enzyme/eigh.jl
@@ -19,7 +19,7 @@ Test the Enzyme forward- and reverse-mode AD rule for `eigh_full` and its in-pla
 """
 function test_enzyme_eigh_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "eigh_full: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -40,7 +40,7 @@ Test the Enzyme forward- and reverse-mode AD rule for `eigh_vals` and its in-pla
 """
 function test_enzyme_eigh_vals(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "eigh_vals: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -62,7 +62,7 @@ in-place variants, over a range of truncation ranks.
 """
 function test_enzyme_eigh_trunc(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "eigh_trunc reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -82,8 +82,8 @@ function test_enzyme_eigh_trunc(
         end
         @testset "trunctol" begin
             A = make_eigh_matrix(T, sz)
-            D = eigh_vals(A / 2, alg)
-            trunc = trunctol(; atol = maximum(abs, D) / 2)
+            D = eigh_vals(A, alg)
+            trunc = trunctol(; atol = midgap_tol(D))
             truncalg = TruncatedAlgorithm(alg, trunc)
             DV, _, ΔDV, ΔDVtrunc = ad_eigh_trunc_setup(A, truncalg)
             test_reverse(eigh_wrapper, RT, (eigh_trunc_no_error, Const), (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔDVtrunc, fdm)
diff --git a/test/testsuite/enzyme/lq.jl b/test/testsuite/enzyme/lq.jl
index 9b56ce110..2e35b3d56 100644
--- a/test/testsuite/enzyme/lq.jl
+++ b/test/testsuite/enzyme/lq.jl
@@ -15,7 +15,7 @@ end
 
 function test_enzyme_lq_compact(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "lq_compact: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -31,7 +31,7 @@ end
 
 function test_enzyme_lq_compact_rank_deficient(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "lq_compact rank deficient A: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -52,7 +52,7 @@ end
 
 function test_enzyme_lq_full(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "lq_full reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -70,7 +70,7 @@ end
 
 function test_enzyme_lq_null(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "lq_null reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
diff --git a/test/testsuite/enzyme/orthnull.jl b/test/testsuite/enzyme/orthnull.jl
index 05a1640ea..dec6969f1 100644
--- a/test/testsuite/enzyme/orthnull.jl
+++ b/test/testsuite/enzyme/orthnull.jl
@@ -22,7 +22,7 @@ algorithms, and their in-place variants.
 """
 function test_enzyme_left_orth(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "left_orth reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -61,7 +61,7 @@ algorithms, and their in-place variants.
 """
 function test_enzyme_right_orth(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "right_orth reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -99,7 +99,7 @@ in-place variant.
 """
 function test_enzyme_left_null(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "left_null: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -124,7 +124,7 @@ in-place variant.
 """
 function test_enzyme_right_null(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "right_null: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
diff --git a/test/testsuite/enzyme/polar.jl b/test/testsuite/enzyme/polar.jl
index e342f416d..21cf54f67 100644
--- a/test/testsuite/enzyme/polar.jl
+++ b/test/testsuite/enzyme/polar.jl
@@ -19,7 +19,7 @@ Only runs for tall or square matrices (`m >= n`).
 """
 function test_enzyme_left_polar(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "left_polar: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = instantiate_matrix(T, sz)
@@ -44,7 +44,7 @@ Only runs for wide or square matrices (`m <= n`).
 """
 function test_enzyme_right_polar(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "right_polar: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
         A = instantiate_matrix(T, sz)
diff --git a/test/testsuite/enzyme/projections.jl b/test/testsuite/enzyme/projections.jl
index 2c5240a2f..c40c0006c 100644
--- a/test/testsuite/enzyme/projections.jl
+++ b/test/testsuite/enzyme/projections.jl
@@ -19,7 +19,7 @@ Test the Enzyme forward- and reverse-mode AD rule for `project_hermitian` and it
 """
 function test_enzyme_project_hermitian(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "project_hermitian: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -42,7 +42,7 @@ Test the Enzyme forward- and reverse-mode AD rule for `project_antihermitian` an
 """
 function test_enzyme_project_antihermitian(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "project_antihermitian: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
diff --git a/test/testsuite/enzyme/qr.jl b/test/testsuite/enzyme/qr.jl
index f3b8f0901..f7caaa2f5 100644
--- a/test/testsuite/enzyme/qr.jl
+++ b/test/testsuite/enzyme/qr.jl
@@ -15,7 +15,7 @@ end
 
 function test_enzyme_qr_compact(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "qr_compact reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -31,7 +31,7 @@ end
 
 function test_enzyme_qr_compact_rank_deficient(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "qr_compact rank deficient A reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -52,7 +52,7 @@ end
 
 function test_enzyme_qr_full(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "qr_full reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -70,7 +70,7 @@ end
 
 function test_enzyme_qr_null(
         T::Type, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "qr_null reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
diff --git a/test/testsuite/enzyme/svd.jl b/test/testsuite/enzyme/svd.jl
index cddd1b8ee..9155021f1 100644
--- a/test/testsuite/enzyme/svd.jl
+++ b/test/testsuite/enzyme/svd.jl
@@ -15,7 +15,7 @@ Test the Enzyme forward- and reverse-mode AD rule for `svd_compact` and its in-p
 """
 function test_enzyme_svd_compact(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "svd_compact: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -37,7 +37,7 @@ gauge-dependent extra columns of `U` and rows of `Vᴴ` are zeroed out in the co
 """
 function test_enzyme_svd_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "svd_full: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -60,7 +60,7 @@ Test the Enzyme forward- and reverse-mode AD rule for `svd_vals` and its in-plac
 """
 function test_enzyme_svd_vals(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "svd_vals: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -82,7 +82,7 @@ in-place variants, over a range of truncation ranks and a tolerance-based trunca
 """
 function test_enzyme_svd_trunc(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T),
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T),
         fdm = enzyme_fdm(T)
     )
     return @testset "svd_trunc reverse: RT $RT, TA $TA" for RT in (Duplicated,), TA in (Duplicated,)
@@ -101,7 +101,7 @@ function test_enzyme_svd_trunc(
         end
         @testset "trunctol" begin
             S = svd_vals(A, alg)
-            trunc = trunctol(atol = maximum(S) / 2)
+            trunc = trunctol(atol = midgap_tol(S))
             truncalg = TruncatedAlgorithm(alg, trunc)
             USVᴴ, _, ΔUSVᴴ, ΔUSVᴴtrunc = ad_svd_trunc_setup(A, truncalg)
             test_reverse(svd_trunc_no_error, RT, (A, TA), (truncalg, Const); atol, rtol, output_tangent = ΔUSVᴴtrunc, fdm)
diff --git a/test/testsuite/mooncake/eig.jl b/test/testsuite/mooncake/eig.jl
index 8c9c29199..51a1049f8 100644
--- a/test/testsuite/mooncake/eig.jl
+++ b/test/testsuite/mooncake/eig.jl
@@ -19,7 +19,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `eig_full` and its in-pl
 """
 function test_mooncake_eig_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "eig_full" begin
         A = make_eig_matrix(T, sz)
@@ -65,7 +65,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `eig_vals` and its in-pl
 """
 function test_mooncake_eig_vals(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "eig_vals" begin
         A = make_eig_matrix(T, sz)
@@ -74,8 +74,8 @@ function test_mooncake_eig_vals(
         output_tangent = Mooncake.randn_tangent(rng, D)
 
         Mooncake.TestUtils.test_rule(
-            rng, eig_vals, A, alg;
-            output_tangent, atol, rtol
+            rng, eig_vals_wrapper, eig_vals, A, alg;
+            output_tangent, atol, rtol, is_primitive = false
         )
         if A isa Diagonal{<:Complex}
             A2 = copy(A)
@@ -90,7 +90,7 @@ function test_mooncake_eig_vals(
             )
         end
         Mooncake.TestUtils.test_rule(
-            rng, call_and_zero!, eig_vals!, A, alg;
+            rng, eig_vals!_wrapper, eig_vals!, A, alg;
             output_tangent, atol, rtol, is_primitive = false
         )
     end
@@ -104,7 +104,7 @@ in-place variants, over a range of truncation ranks and a tolerance-based trunca
 """
 function test_mooncake_eig_trunc(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "eig_trunc" begin
         A = make_eig_matrix(T, sz)
@@ -144,7 +144,7 @@ function test_mooncake_eig_trunc(
 
         @testset "trunctol" begin
             D = eig_vals(A)
-            trunc = trunctol(atol = maximum(abs, D) / 2; by = abs)
+            trunc = trunctol(atol = midgap_tol(D); by = abs)
             alg_trunc = TruncatedAlgorithm(alg, trunc)
 
             DV, DVtrunc, ΔDV_arrays, ΔDVtrunc_arrays = ad_eig_trunc_setup(A, alg_trunc)
diff --git a/test/testsuite/mooncake/eigh.jl b/test/testsuite/mooncake/eigh.jl
index 481c4ea54..81c5bd16b 100644
--- a/test/testsuite/mooncake/eigh.jl
+++ b/test/testsuite/mooncake/eigh.jl
@@ -19,7 +19,7 @@ Test the Mooncake reverse-mode AD rule for `eigh_full` and its in-place variant.
 """
 function test_mooncake_eigh_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "eigh_full" begin
         A = make_eigh_matrix(T, sz)
@@ -55,7 +55,7 @@ Test the Mooncake reverse-mode AD rule for `eigh_vals` and its in-place variant.
 """
 function test_mooncake_eigh_vals(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "eigh_vals" begin
         A = make_eigh_matrix(T, sz)
@@ -94,7 +94,7 @@ in-place variants, over a range of truncation ranks and a tolerance-based trunca
 """
 function test_mooncake_eigh_trunc(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "eigh_trunc" begin
         A = make_eigh_matrix(T, sz)
@@ -134,7 +134,7 @@ function test_mooncake_eigh_trunc(
 
         @testset "trunctol" begin
             D = eigh_vals(A)
-            trunc = trunctol(atol = maximum(abs, D) / 2; by = abs)
+            trunc = trunctol(atol = midgap_tol(D); by = abs)
             alg_trunc = TruncatedAlgorithm(alg, trunc)
 
             DV, DVtrunc, ΔDV_arrays, ΔDVtrunc_arrays = ad_eigh_trunc_setup(A, alg_trunc)
diff --git a/test/testsuite/mooncake/lq.jl b/test/testsuite/mooncake/lq.jl
index f947095fc..3de9dac4c 100644
--- a/test/testsuite/mooncake/lq.jl
+++ b/test/testsuite/mooncake/lq.jl
@@ -19,7 +19,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `lq_compact` and its in-
 """
 function test_mooncake_lq_compact(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "lq_compact" begin
         A = instantiate_matrix(T, sz)
@@ -71,7 +71,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `lq_full` and its in-pla
 """
 function test_mooncake_lq_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "lq_full" begin
         A = instantiate_matrix(T, sz)
@@ -107,7 +107,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `lq_null` and its in-pla
 """
 function test_mooncake_lq_null(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "lq_null" begin
         A = instantiate_matrix(T, sz)
diff --git a/test/testsuite/mooncake/orthnull.jl b/test/testsuite/mooncake/orthnull.jl
index f0285634a..d3bc5b84f 100644
--- a/test/testsuite/mooncake/orthnull.jl
+++ b/test/testsuite/mooncake/orthnull.jl
@@ -22,7 +22,7 @@ algorithms, and their in-place variants.
 """
 function test_mooncake_left_orth(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "left_orth" begin
         A = instantiate_matrix(T, sz)
@@ -70,7 +70,7 @@ algorithms, and their in-place variants.
 """
 function test_mooncake_right_orth(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "right_orth" begin
         A = instantiate_matrix(T, sz)
@@ -118,7 +118,7 @@ in-place variant.
 """
 function test_mooncake_left_null(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "left_null" begin
         A = instantiate_matrix(T, sz)
@@ -157,7 +157,7 @@ in-place variant.
 """
 function test_mooncake_right_null(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "right_null" begin
         A = instantiate_matrix(T, sz)
diff --git a/test/testsuite/mooncake/polar.jl b/test/testsuite/mooncake/polar.jl
index fee32e71e..5170b5d57 100644
--- a/test/testsuite/mooncake/polar.jl
+++ b/test/testsuite/mooncake/polar.jl
@@ -19,7 +19,7 @@ Only runs for tall or square matrices (`m >= n`).
 """
 function test_mooncake_left_polar(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "left_polar" begin
         A = instantiate_matrix(T, sz)
@@ -48,7 +48,7 @@ Only runs for wide or square matrices (`m <= n`).
 """
 function test_mooncake_right_polar(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "right_polar" begin
         A = instantiate_matrix(T, sz)
diff --git a/test/testsuite/mooncake/projections.jl b/test/testsuite/mooncake/projections.jl
index 359c9cbe9..f6baf91ec 100644
--- a/test/testsuite/mooncake/projections.jl
+++ b/test/testsuite/mooncake/projections.jl
@@ -19,7 +19,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `project_hermitian` and
 """
 function test_mooncake_project_hermitian(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "project_hermitian" begin
         A = instantiate_matrix(T, sz)
@@ -47,7 +47,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `project_antihermitian`
 """
 function test_mooncake_project_antihermitian(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "project_antihermitian" begin
         A = instantiate_matrix(T, sz)
diff --git a/test/testsuite/mooncake/qr.jl b/test/testsuite/mooncake/qr.jl
index 830e3472b..96a35e309 100644
--- a/test/testsuite/mooncake/qr.jl
+++ b/test/testsuite/mooncake/qr.jl
@@ -19,7 +19,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `qr_compact` and its in-
 """
 function test_mooncake_qr_compact(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "qr_compact" begin
         A = instantiate_matrix(T, sz)
@@ -71,7 +71,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `qr_full` and its in-pla
 """
 function test_mooncake_qr_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "qr_full" begin
         A = instantiate_matrix(T, sz)
@@ -107,7 +107,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `qr_null` and its in-pla
 """
 function test_mooncake_qr_null(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "qr_null" begin
         A = instantiate_matrix(T, sz)
diff --git a/test/testsuite/mooncake/svd.jl b/test/testsuite/mooncake/svd.jl
index de9dbc543..f13faa874 100644
--- a/test/testsuite/mooncake/svd.jl
+++ b/test/testsuite/mooncake/svd.jl
@@ -20,7 +20,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `svd_compact` and its in
 """
 function test_mooncake_svd_compact(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "svd_compact" begin
         A = instantiate_matrix(T, sz)
@@ -47,7 +47,7 @@ gauge-dependent extra columns of `U` and rows of `Vᴴ` are zeroed out in the co
 """
 function test_mooncake_svd_full(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "svd_full" begin
         A = instantiate_matrix(T, sz)
@@ -75,7 +75,7 @@ Test the Mooncake forward- and reverse-mode AD rule for `svd_vals` and its in-pl
 """
 function test_mooncake_svd_vals(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "svd_vals" begin
         A = instantiate_matrix(T, sz)
@@ -102,7 +102,7 @@ in-place variants, over a range of truncation ranks and a tolerance-based trunca
 """
 function test_mooncake_svd_trunc(
         T, sz;
-        rng = Random.default_rng(), atol::Real = 0, rtol::Real = precision(T)
+        rng = TestSuite.rng, atol::Real = 0, rtol::Real = precision(T)
     )
     return @testset "svd_trunc" begin
         A = instantiate_matrix(T, sz)
@@ -143,7 +143,7 @@ function test_mooncake_svd_trunc(
 
         @testset "trunctol" begin
             S = svd_vals(A)
-            trunc = trunctol(atol = maximum(S) / 2)
+            trunc = trunctol(atol = midgap_tol(S))
             alg_trunc = TruncatedAlgorithm(alg, trunc)
 
             USVᴴ, USVᴴtrunc, ΔUSVᴴ_arrays, ΔUSVᴴtrunc_arrays = ad_svd_trunc_setup(A, alg_trunc)