Dispatch more cases to BLAS.gemm! (#33229)

* Dispatch more cases to BLAS.gemm!

* Use α and β instead of alpha′ and beta′

(cherry picked from commit 51b3227)

stdlib/LinearAlgebra/src/matmul.jl

@@ -152,15 +152,23 @@ function (*)(A::AbstractMatrix, B::AbstractMatrix)
  TS = promote_op(matprod, eltype(A), eltype(B))
  mul!(similar(B, TS, (size(A,1), size(B,2))), A, B)
 end
-@inline mul!(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
- alpha::Union{T, Bool}, beta::Union{T, Bool}) where {T<:BlasFloat} =
- gemm_wrapper!(C, 'N', 'N', A, B, MulAddMul(alpha, beta))
+
+@inline function mul!(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T},
+ α::Number, β::Number) where {T<:BlasFloat}
+ alpha, beta = promote(α, β, zero(T))
+ if alpha isa T && beta isa T
+ return gemm_wrapper!(C, 'N', 'N', A, B, MulAddMul(alpha, beta))
+ else
+ return generic_matmatmul!(C, 'N', 'N', A, B, MulAddMul(α, β))
+ end
+end
+
 # Complex Matrix times real matrix: We use that it is generally faster to reinterpret the
 # first matrix as a real matrix and carry out real matrix matrix multiply
 for elty in (Float32,Float64)
  @eval begin
  @inline function mul!(C::StridedMatrix{Complex{$elty}}, A::StridedVecOrMat{Complex{$elty}}, B::StridedVecOrMat{$elty},
- alpha::Union{$elty, Bool}, beta::Union{$elty, Bool})
+  alpha::Real, beta::Real)
  Afl = reinterpret($elty, A)
  Cfl = reinterpret($elty, C)
  mul!(Cfl, Afl, B, alpha, beta)

stdlib/LinearAlgebra/test/matmul.jl

@@ -586,7 +586,7 @@ end
  A = rand(n, n)
  B = rand(n, n)
  C = zeros(n, n)
- mul!(C, A, B, -1, 0)
+ mul!(C, A, B, -1 + 0im, 0)
  D = -A * B
  @test D ≈ C