Add mul!!(C, A, B, α, β)

src/NoBang/linearalgebra.jl

@@ -1 +1,2 @@
 mul(::Any, x, y) = x * y
+mul(C, A, B, α, β) = A * B * α + C * β

src/linearalgebra.jl

@@ -1,18 +1,24 @@
 """
-    mul!!(C, A, B) -> C′
+    mul!!(C, A, B, [α, β]) -> C′
 """
 mul!!(C, A, B) = may(mul!, C, A, B)
+mul!!(C, A, B, α, β) = may(mul!, C, A, B, α, β)
 
 pure(::typeof(mul!)) = NoBang.mul
 _asbb(::typeof(mul!)) = mul!!
 possible(::typeof(mul!), C, A, B) =
     ismutable(C) && _matmuleltype(A, B) <: eltype(C)
+possible(::typeof(mul!), C, A, B, α, β) =
+    ismutable(C) && _matmuleltype(C, A, B, α, β) <: eltype(C)
 
 # Estimate `eltype` of `C`.  This is how it's done in LinearAlgebra.jl
 # but maybe it's better to use the approach of
 # https://github.com/tpapp/AlgebraResultTypes.jl ?
 _matprod(x, y) = x * y + x * y
+_matprod(c, a, b, α, β) = a * b * α + a * b * α + c * β
 _matmuleltype(A, B) = Base.promote_op(_matprod, eltype(A), eltype(B))
+_matmuleltype(C, A, B, α, β) =
+    Base.promote_op(_matprod, eltype(C), eltype(A), eltype(B), typeof(α), typeof(β))
 
 """
     lmul!!(A, B) -> B′

test/test_mul.jl

@@ -19,4 +19,21 @@ include("preamble.jl")
     @test_inferred mul!!(C, A, B)
 end
 
+if VERSION >= v"1.3"
+    @testset "mul!(C, A, B, α, β)" begin
+        C = zeros(2, 2)
+        A = reshape(1:4, 2, 2)
+        B = ones(2, 2)
+
+        desired = A * B * 3 + C * 4
+        @test mul!!(C, A, B, 3, 4) === C
+        @test C == desired
+        @test_inferred mul!!(C, A, B, 3, 4)
+
+        desired = A * B * 3 + C * 4
+        @test mul!!(C, A, B, 3, 4) :: Matrix{Float64} == desired
+        @test_inferred mul!!(C, A, B, 3, 4)
+    end
+end
+
 end  # module