overload 3-arg and 5-arg mul!()

Author: alyst

src/dual.jl

@@ -830,12 +830,15 @@ for MT in (StridedMatrix{<:LinearAlgebra.BlasFloat},
     @eval Base.:\(m::$MT, x::StridedMatrix{<:Dual}) =
         _map_dual_components!((y, x) -> ldiv!(y, m, x), (y, x, _) -> ldiv!(y, m, x), similar(x), x)
 
-    @eval function Base.:*(m::$MT, x::StridedVector{<:Dual})
-        T = valtype(eltype(x))
-        res = similar(x, (size(m, 1),))
-        mul!(reinterpret(reshape, T, res), reinterpret(reshape, T, x), m')
-        return res
-    end
+    @eval LinearAlgebra.mul!(C::StridedVector{T}, A::$MT, B::StridedVector{T}) where T <: Dual =
+        mul!(reinterpret(reshape, valtype(T), C), reinterpret(reshape, valtype(T), B), A')
+
+    @eval LinearAlgebra.mul!(C::StridedVector{T}, A::$MT, B::StridedVector{T},
+                             α::Union{LinearAlgebra.BlasFloat, Integer},
+                             β::Union{LinearAlgebra.BlasFloat, Integer}) where T <: Dual =
+        mul!(reinterpret(reshape, valtype(T), C), reinterpret(reshape, valtype(T), B), A', α, β)
+
+    @eval Base.:*(m::$MT, x::StridedVector{<:Dual}) = mul!(similar(x, (size(m, 1),)), m, x)
 
     @eval Base.:*(m::$MT, x::StridedMatrix{<:Dual}) =
         _map_dual_components!((y, x) -> mul!(y, m, x), (y, x, _) -> mul!(y, m, x),