diff --git a/Project.toml b/Project.toml
index 135695d..7b61f7f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "DistributionsAD"
 uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
-version = "0.6.52"
+version = "0.6.53"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
diff --git a/src/multivariate.jl b/src/multivariate.jl
index 31adf95..4c5c30d 100644
--- a/src/multivariate.jl
+++ b/src/multivariate.jl
@@ -154,40 +154,46 @@ end
 
 function Distributions._logpdf(d::TuringScalMvNormal, x::AbstractVector)
     σ2 = abs2(d.σ)
-    return -(length(x) * log(2π * σ2) + sum(abs2.(x .- d.m)) / σ2) / 2
+    return -(length(x) * log(twoπ * σ2) + sum(abs2.(x .- d.m)) / σ2) / 2
 end
 function Distributions.logpdf(d::TuringScalMvNormal, x::AbstractMatrix{<:Real})
     size(x, 1) == length(d) ||
         throw(DimensionMismatch("Inconsistent array dimensions."))
-    return -(size(x, 1) * log(2π * abs2(d.σ)) .+ vec(sum(abs2.((x .- d.m) ./ d.σ), dims=1))) ./ 2
+    return -(size(x, 1) * log(twoπ * abs2(d.σ)) .+ vec(sum(abs2.((x .- d.m) ./ d.σ), dims=1))) ./ 2
 end
 function Distributions.loglikelihood(d::TuringScalMvNormal, x::AbstractMatrix{<:Real})
     σ2 = abs2(d.σ)
-    return -(length(x) * log(2π * σ2) + sum(abs2.(x .- d.m)) / σ2) / 2
+    return -(length(x) * log(twoπ * σ2) + sum(abs2.(x .- d.m)) / σ2) / 2
 end
 
 function Distributions._logpdf(d::TuringDiagMvNormal, x::AbstractVector)
-    return -(length(x) * log(2π) + 2 * sum(log.(d.σ)) + sum(abs2.((x .- d.m) ./ d.σ))) / 2
+    z = 2 * sum(log.(d.σ)) + sum(abs2.((x .- d.m) ./ d.σ))
+    return -(length(x) * oftype(z, log2π) + z) / 2
 end
 function Distributions.logpdf(d::TuringDiagMvNormal, x::AbstractMatrix{<:Real})
     size(x, 1) == length(d) ||
         throw(DimensionMismatch("Inconsistent array dimensions."))
-    return -((size(x, 1) * log(2π) + 2 * sum(log.(d.σ))) .+ vec(sum(abs2.((x .- d.m) ./ d.σ), dims=1))) ./ 2
+    s = 2 * sum(log.(d.σ))
+    return -((size(x, 1) * oftype(s, log2π) + s) .+ vec(sum(abs2.((x .- d.m) ./ d.σ), dims=1))) ./ 2
 end
 function Distributions.loglikelihood(d::TuringDiagMvNormal, x::AbstractMatrix{<:Real})
-    return -(length(x) * log(2π) + 2 * size(x, 2) * sum(log.(d.σ)) + sum(abs2.((x .- d.m) ./ d.σ))) / 2
+    z = 2 * size(x, 2) * sum(log.(d.σ)) + sum(abs2.((x .- d.m) ./ d.σ))
+    return -(length(x) * oftype(z, log2π) + z) / 2
 end
 
 function Distributions._logpdf(d::TuringDenseMvNormal, x::AbstractVector)
-    return -(length(x) * log(2π) + logdet(d.C) + sum(abs2.(zygote_ldiv(d.C.U', x .- d.m)))) / 2
+    z = logdet(d.C) + sum(abs2.(zygote_ldiv(d.C.U', x .- d.m)))
+    return -(length(x) * oftype(z, log2π) + z) / 2
 end
 function Distributions.logpdf(d::TuringDenseMvNormal, x::AbstractMatrix{<:Real})
     size(x, 1) == length(d) ||
         throw(DimensionMismatch("Inconsistent array dimensions."))
-    return -((size(x, 1) * log(2π) + logdet(d.C)) .+ vec(sum(abs2.(zygote_ldiv(d.C.U', x .- d.m)), dims=1))) ./ 2
+    s = logdet(d.C)
+    return -((size(x, 1) * oftype(s, log2π) + s) .+ vec(sum(abs2.(zygote_ldiv(d.C.U', x .- d.m)), dims=1))) ./ 2
 end
 function Distributions.loglikelihood(d::TuringDenseMvNormal, x::AbstractMatrix{<:Real})
-    return -(length(x) * log(2π) + size(x, 2) * logdet(d.C) + sum(abs2.(zygote_ldiv(d.C.U', x .- d.m)))) / 2
+    z = size(x, 2) * logdet(d.C) + sum(abs2.(zygote_ldiv(d.C.U', x .- d.m)))
+    return -(length(x) * oftype(z, log2π) + z) / 2
 end
 
 function Distributions.entropy(d::TuringScalMvNormal)
diff --git a/test/others.jl b/test/others.jl
index 23549ae..66274c4 100644
--- a/test/others.jl
+++ b/test/others.jl
@@ -36,19 +36,19 @@
     end
 
     @testset "TuringMvNormal" begin
-        @testset "$TD" for TD in [TuringDenseMvNormal, TuringDiagMvNormal, TuringScalMvNormal]
-            m = rand(3)
+        @testset for TD in (TuringDenseMvNormal, TuringDiagMvNormal, TuringScalMvNormal), T in (Float64, Float32)
+            m = rand(T, 3)
             if TD <: TuringDenseMvNormal
-                A = rand(3, 3)
+                A = rand(T, 3, 3)
                 C = A' * A + I
                 d1 = TuringMvNormal(m, C)
                 d2 = MvNormal(m, C)
             elseif TD <: TuringDiagMvNormal
-                C = rand(3)
+                C = rand(T, 3)
                 d1 = TuringMvNormal(m, C)
                 d2 = MvNormal(m, Diagonal(C .^ 2))
             else
-                C = rand()
+                C = rand(T)
                 d1 = TuringMvNormal(m, C)
                 d2 = MvNormal(m, C^2 * I)
             end
@@ -56,13 +56,28 @@
             @testset "$F" for F in (length, size, mean)
                 @test F(d1) == F(d2)
             end
-            @test cov(d1) ≈ cov(d2)
-            @test var(d1) ≈ var(d2)
+            C1 = @inferred(cov(d1))
+            @test C1 isa AbstractMatrix{T}
+            @test C1 ≈ cov(d2)
+            V1 = @inferred(var(d1))
+            @test V1 isa AbstractVector{T}
+            @test V1 ≈ var(d2)
 
             x1 = rand(d1)
             x2 = rand(d1, 3)
-            @test isapprox(logpdf(d1, x1), logpdf(d2, x1), rtol = 1e-6)
-            @test isapprox(logpdf(d1, x2), logpdf(d2, x2), rtol = 1e-6)
+            for S in (Float64, Float32)
+                ST = promote_type(S, T)
+
+                z = map(S, x1)
+                logp = @inferred(logpdf(d1, z))
+                @test logp isa ST
+                @test logp ≈ logpdf(d2, z) rtol = 1e-6
+
+                zs = map(S, x2)
+                logps = @inferred(logpdf(d1, zs))
+                @test eltype(logps) === ST
+                @test logps ≈ logpdf(d2, zs) rtol = 1e-6
+            end
         end
     end