diff --git a/src/triangular.jl b/src/triangular.jl
index 10925565..e1267ee3 100644
--- a/src/triangular.jl
+++ b/src/triangular.jl
@@ -256,16 +256,15 @@ Base.@constprop :aggressive @propagate_inbounds function getindex(A::Union{Lower
     _shouldforwardindex(A, b) ? A.data[b] : diagzero(A.data, b)
 end
 
-_zero_triangular_half_str(::Type{<:UpperOrUnitUpperTriangular}) = "lower"
-_zero_triangular_half_str(::Type{<:LowerOrUnitLowerTriangular}) = "upper"
+_zero_triangular_half_str(T::Type) = T <: UpperOrUnitUpperTriangular ? "lower" : "upper"
 
-@noinline function throw_nonzeroerror(T, @nospecialize(x), i, j)
+@noinline function throw_nonzeroerror(T::DataType, @nospecialize(x), i, j)
     Ts = _zero_triangular_half_str(T)
     Tn = nameof(T)
     throw(ArgumentError(
         lazy"cannot set index in the $Ts triangular part ($i, $j) of an $Tn matrix to a nonzero value ($x)"))
 end
-@noinline function throw_nononeerror(T, @nospecialize(x), i, j)
+@noinline function throw_nononeerror(T::DataType, @nospecialize(x), i, j)
     Tn = nameof(T)
     throw(ArgumentError(
         lazy"cannot set index on the diagonal ($i, $j) of an $Tn matrix to a non-unit value ($x)"))
@@ -311,7 +310,7 @@ end
     return A
 end
 
-@noinline function throw_setindex_structuralzero_error(T, @nospecialize(x))
+@noinline function throw_setindex_structuralzero_error(T::DataType, @nospecialize(x))
     Ts = _zero_triangular_half_str(T)
     Tn = nameof(T)
     throw(ArgumentError(