Distributions integration tests

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diff --git a/test/integration/Distributions/runtests.jl b/test/integration/Distributions/runtests.jl
index b8eb219..bf2c67a 100644
--- a/test/integration/Distributions/runtests.jl
+++ b/test/integration/Distributions/runtests.jl
@@ -42,29 +42,29 @@ end
 
 # Turn a distribution into a call to logpdf.
 function TestCase(d::Distribution, value, name, runtime_activity, broken, splat)
-    TestCase(x -> logpdf(d, x), value, name, runtime_activity, broken, splat)
+    return TestCase(x -> logpdf(d, x), value, name, runtime_activity, broken, splat)
 end
 
 # Defaults for name, runtime_activity and broken.
 function TestCase(
-    f, value;
-    name=nothing, runtime_activity=Neither, broken=Neither, splat=false
-)
+        f, value;
+        name = nothing, runtime_activity = Neither, broken = Neither, splat = false
+    )
     return TestCase(f, value, name, runtime_activity, broken, splat)
 end
 
 # Default name for a Distribution.
 function TestCase(
-    d::Distribution, value;
-    name=string(nameof(typeof(d))), runtime_activity=Neither, broken=Neither, splat=false
-)
+        d::Distribution, value;
+        name = string(nameof(typeof(d))), runtime_activity = Neither, broken = Neither, splat = false
+    )
     return TestCase(d, value, name, runtime_activity, broken, splat)
 end
 
 """
 Test Enzyme.gradient, both Forward and Reverse mode, against FiniteDifferences.grad.
 """
-function test_grad(case::TestCase; rtol=1e-6, atol=1e-6)
+function test_grad(case::TestCase; rtol = 1.0e-6, atol = 1.0e-6)
     @nospecialize
     f = case.func
     # We'll call the function as f(x...), so wrap in a singleton tuple if need be.
@@ -209,10 +209,10 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
         TestCase(LogUniform(0.15, 7.8), 7.1),
         TestCase(LogUniform(2.0, 3.0), 2.1),
         # TODO Broken tests, see https://github.com/EnzymeAD/Enzyme.jl/issues/1620
-        TestCase(NoncentralBeta(1.1, 1.1, 1.2), 0.8; broken=Both), # foreigncall (Rmath.dnbeta).
-        TestCase(NoncentralChisq(2, 3.0), 10.0; broken=Both), # foreigncall (Rmath.dnchisq).
-        TestCase(NoncentralF(2, 3, 1.1), 4.1; broken=Both), # foreigncall (Rmath.dnf).
-        TestCase(NoncentralT(1.3, 1.1), 0.1; broken=Both), # foreigncall (Rmath.dnt).
+        TestCase(NoncentralBeta(1.1, 1.1, 1.2), 0.8; broken = Both), # foreigncall (Rmath.dnbeta).
+        TestCase(NoncentralChisq(2, 3.0), 10.0; broken = Both), # foreigncall (Rmath.dnchisq).
+        TestCase(NoncentralF(2, 3, 1.1), 4.1; broken = Both), # foreigncall (Rmath.dnf).
+        TestCase(NoncentralT(1.3, 1.1), 0.1; broken = Both), # foreigncall (Rmath.dnt).
         TestCase(Normal(), 0.1),
         TestCase(Normal(0.0, 1.0), 1.0),
         TestCase(Normal(0.5, 1.0), 0.05),
@@ -220,7 +220,7 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
         TestCase(Normal(-0.1, 0.9), -0.3),
         # TODO Broken test, see https://github.com/EnzymeAD/Enzyme.jl/issues/1603
         # foreigncall -- https://github.com/JuliaMath/SpecialFunctions.jl/blob/be1fa06fee58ec019a28fb0cd2b847ca83a5af9a/src/bessel.jl#L265
-        TestCase(NormalInverseGaussian(0.0, 1.0, 0.2, 0.1), 0.1; broken=Both),
+        TestCase(NormalInverseGaussian(0.0, 1.0, 0.2, 0.1), 0.1; broken = Both),
         TestCase(Pareto(1.0, 1.0), 3.5),
         TestCase(Pareto(1.1, 0.9), 3.1),
         TestCase(Pareto(1.0, 1.0), 1.4),
@@ -231,7 +231,7 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
         TestCase(Rayleigh(0.9), 1.1),
         TestCase(Rayleigh(0.55), 0.63),
         # TODO Broken test, see https://github.com/EnzymeAD/Enzyme.jl/issues/1620
-        TestCase(Rician(0.5, 1.0), 2.1; broken=Both),  # foreigncall (Rmath.dnchisq).
+        TestCase(Rician(0.5, 1.0), 2.1; broken = Both),  # foreigncall (Rmath.dnchisq).
         TestCase(Semicircle(1.0), 0.9),
         TestCase(Semicircle(5.1), 5.05),
         TestCase(Semicircle(0.5), -0.1),
@@ -281,24 +281,26 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
         TestCase(MvNormal([0.2, 0.3], Symmetric(Diagonal([0.5, 0.4]))), [-0.1, 0.05]),
         TestCase(MvNormal([0.2, 0.3], Diagonal([0.5, 0.4])), [-0.1, 0.05]),
         # TODO Broken tests, see https://github.com/EnzymeAD/Enzyme.jl/issues/1991
-        TestCase(MvNormal([-0.15], _pdmat([1.1]')), [-0.05]; broken=Forward),
+        TestCase(MvNormal([-0.15], _pdmat([1.1]')), [-0.05]; broken = Forward),
         TestCase(
             MvNormal([0.2, -0.15], _pdmat([1.0 0.9; 0.7 1.1])), [0.05, -0.05];
-            broken=Forward
+            broken = Forward
         ),
         TestCase(MvNormal([0.2, -0.3], [0.5, 0.6]), [0.4, -0.3]),
         # TODO https://github.com/EnzymeAD/Enzyme.jl/issues/2618, trmv error
-        TestCase(MvNormalCanon([0.1, -0.1], _pdmat([0.5 0.4; 0.45 1.0])), [0.2, -0.25]; 
-            broken=(VERSION >= v"1.11" ? Forward : Neither)),
+        TestCase(
+            MvNormalCanon([0.1, -0.1], _pdmat([0.5 0.4; 0.45 1.0])), [0.2, -0.25];
+            broken = (VERSION >= v"1.11" ? Forward : Neither)
+        ),
         # TODO Broken tests, see https://github.com/EnzymeAD/Enzyme.jl/issues/1991
         TestCase(
             MvLogNormal(MvNormal([0.2, -0.1], _pdmat([1.0 0.9; 0.7 1.1]))), [0.5, 0.1];
-            broken=Forward
+            broken = Forward
         ),
         TestCase(product_distribution([Normal()]), [0.3]),
         TestCase(
             product_distribution([Normal(), Uniform()]), [-0.4, 0.3];
-            runtime_activity=Both
+            runtime_activity = Both
         ),
 
         #
@@ -315,12 +317,12 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
         TestCase(
             Wishart(5, _pdmat(randn(rng, 3, 3))),
             Symmetric(collect(_pdmat(randn(rng, 3, 3))));
-            broken=Forward
+            broken = Forward
         ),
         TestCase(
             InverseWishart(5, _pdmat(randn(rng, 3, 3))),
             Symmetric(collect(_pdmat(randn(rng, 3, 3))));
-            broken=Forward
+            broken = Forward
         ),
         # TODO Broken tests, see https://github.com/EnzymeAD/Enzyme.jl/issues/1820
         # getrf derivative needed
@@ -332,15 +334,15 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
                 _pdmat(randn(rng, 3, 3)),
             ),
             randn(rng, 2, 3);
-            broken=Both
+            broken = Both
         ),
-        TestCase(MatrixBeta(5, 6.0, 7.0), rand(rng, MatrixBeta(5, 6.0, 6.0)); broken=Both),
+        TestCase(MatrixBeta(5, 6.0, 7.0), rand(rng, MatrixBeta(5, 6.0, 6.0)); broken = Both),
         TestCase(
             MatrixFDist(6.0, 7.0, _pdmat(randn(rng, 5, 5))),
             rand(rng, MatrixFDist(6.0, 7.0, _pdmat(randn(rng, 5, 5))));
-            broken=Both
+            broken = Both
         ),
-        TestCase(LKJ(5, 1.1), rand(rng, LKJ(5, 1.1)); broken=Both),
+        TestCase(LKJ(5, 1.1), rand(rng, LKJ(5, 1.1)); broken = Both),
 
         #
         # Miscellaneous others
@@ -348,50 +350,50 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
 
         TestCase(
             (a, b, x) -> logpdf(InverseGamma(a, b), x), (1.5, 1.4, 0.4);
-            name="InverseGamma", splat=true
+            name = "InverseGamma", splat = true
         ),
         TestCase(
             (m, s, x) -> logpdf(NormalCanon(m, s), x), (0.1, 1.0, -0.5);
-            name="NormalCanon", splat=true
+            name = "NormalCanon", splat = true
         ),
-        TestCase(x -> logpdf(Categorical(x, 1 - x), 1), 0.3; name="Categorical"),
+        TestCase(x -> logpdf(Categorical(x, 1 - x), 1), 0.3; name = "Categorical"),
 
         # TODO Broken test, see https://github.com/EnzymeAD/Enzyme.jl/issues/1995
         # Forward mode runtime needed
         TestCase(
             (m, S, x) -> logpdf(MvLogitNormal(m, S), vcat(x, 1 - sum(x))),
             ([0.4, 0.6], _pdmat([0.9 0.4; 0.5 1.1]), [0.27, 0.24]);
-            name="MvLogitNormal", runtime_activity=Forward, broken=Forward, splat=true,
+            name = "MvLogitNormal", runtime_activity = Forward, broken = Forward, splat = true,
         ),
         TestCase(
             (a, b, α, β, x) -> logpdf(truncated(Beta(α, β), a, b), x),
             (0.1, 0.9, 1.1, 1.3, 0.4);
-            name="truncated Beta", splat=true
+            name = "truncated Beta", splat = true
         ),
         TestCase(
             (a, b, x) -> logpdf(truncated(Normal(), a, b), x),
             (-0.3, 0.3, 0.1);
-            name="allocs Normal", splat=true
+            name = "allocs Normal", splat = true
         ),
         TestCase(
             (a, b, α, β, x) -> logpdf(truncated(Uniform(α, β), a, b), x),
             (0.1, 0.9, -0.1, 1.1, 0.4);
-            name="allocs Uniform", splat=true
+            name = "allocs Uniform", splat = true
         ),
         TestCase(
             (a, x) -> logpdf(Dirichlet(a), [x, 1 - x]), ([1.5, 1.1], 0.6);
-            name="Dirichlet", splat=true, runtime_activity=Forward
+            name = "Dirichlet", splat = true, runtime_activity = Forward
         ),
         TestCase(
             x -> logpdf(reshape(product_distribution([Normal(), Uniform()]), 1, 2), x),
             [2.1 0.7];
-            name="reshape"
+            name = "reshape"
         ),
         # TODO Broken test, see https://github.com/EnzymeAD/Enzyme.jl/issues/1820
         # needs getrf derivative
         TestCase(
             x -> logpdf(vec(LKJ(2, 1.1)), x), [1.0, 0.489, 0.489, 1.0];
-            name="vec", broken=Both
+            name = "vec", broken = Both
         ),
         TestCase(
             function (X, v)
@@ -403,7 +405,7 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
                 return logpdf(LKJCholesky(2, v), C)
             end,
             (randn(rng, 2, 2), 1.1);
-            name="LKJCholesky", splat=true
+            name = "LKJCholesky", splat = true
         ),
     ]
 
@@ -412,4 +414,4 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
     end
 end
 
-end
\ No newline at end of file
+end