Use promote_op in broadcasting and matrix multiplication

This makes it easier to support these operations on AbstractArrays with generic eltypes

(cherry picked from commit 82f9a21)
ref #13803
remove _pure_meta for backport
also qualify Base.MulFun

Author: timholy

base/abstractarray.jl

@@ -1273,6 +1273,15 @@ function map_promote(f, A::AbstractArray)
     return promote_to!(f, 2, dest, A)
 end
 
+# These are needed because map(eltype, As) is not inferrable
+promote_eltype_op(::Any) = Bottom
+promote_eltype_op{T}(op, ::AbstractArray{T}) = promote_op(op, T)
+promote_eltype_op{T}(op, ::T               ) = promote_op(op, T)
+promote_eltype_op{R,S}(op, ::AbstractArray{R}, ::AbstractArray{S}) = promote_op(op, R, S)
+promote_eltype_op{R,S}(op, ::AbstractArray{R}, ::S) = promote_op(op, R, S)
+promote_eltype_op{R,S}(op, ::R, ::AbstractArray{S}) = promote_op(op, R, S)
+promote_eltype_op(op, A, B, C, D...) = promote_op(op, eltype(A), promote_eltype_op(op, B, C, D...))
+
 ## 1 argument
 map!{F}(f::F, A::AbstractArray) = map!(f, A, A)
 function map!{F}(f::F, dest::AbstractArray, A::AbstractArray)

base/bool.jl

@@ -59,3 +59,5 @@ fld(x::Bool, y::Bool) = div(x,y)
 cld(x::Bool, y::Bool) = div(x,y)
 rem(x::Bool, y::Bool) = y ? false : throw(DivideError())
 mod(x::Bool, y::Bool) = rem(x,y)
+
+promote_op(op, ::Type{Bool}, ::Type{Bool}) = typeof(op(true, true))

base/broadcast.jl

@@ -3,9 +3,8 @@
 module Broadcast
 
 using ..Cartesian
-import Base.promote_eltype
-import Base.@get!
-import Base.num_bit_chunks, Base._msk_end, Base.unsafe_bitgetindex
+using Base: promote_op, promote_eltype, promote_eltype_op, @get!, _msk_end, unsafe_bitgetindex
+using Base: AddFun, SubFun, MulFun, LDivFun, RDivFun, PowFun
 import Base: .+, .-, .*, ./, .\, .//, .==, .<, .!=, .<=, .%, .<<, .>>, .^
 export broadcast, broadcast!, broadcast_function, broadcast!_function, bitbroadcast
 export broadcast_getindex, broadcast_setindex!
@@ -232,7 +231,7 @@ for (Bsig, Asig, gbf, gbb) in
 end
 
 
-broadcast(f, As...) = broadcast!(f, Array(promote_eltype(As...), broadcast_shape(As...)), As...)
+broadcast(f, As...) = broadcast!(f, Array(promote_eltype_op(f, As...), broadcast_shape(As...)), As...)
 
 bitbroadcast(f, As...) = broadcast!(f, BitArray(broadcast_shape(As...)), As...)
 
@@ -286,35 +285,28 @@ end
 
 ## elementwise operators ##
 
-.*(As::AbstractArray...) = broadcast(*, As...)
 .%(A::AbstractArray, B::AbstractArray) = broadcast(%, A, B)
 .<<(A::AbstractArray, B::AbstractArray) = broadcast(<<, A, B)
 .>>(A::AbstractArray, B::AbstractArray) = broadcast(>>, A, B)
 
-eltype_plus(As::AbstractArray...) = promote_eltype(As...)
-eltype_plus(As::AbstractArray{Bool}...) = typeof(true+true)
+eltype_plus(As::AbstractArray...) = promote_eltype_op(AddFun(), As...)
 
 .+(As::AbstractArray...) = broadcast!(+, Array(eltype_plus(As...), broadcast_shape(As...)), As...)
 
-type_minus(T, S) = promote_type(T, S)
-type_minus(::Type{Bool}, ::Type{Bool}) = typeof(true-true)
-
 function .-(A::AbstractArray, B::AbstractArray)
-    broadcast!(-, Array(type_minus(eltype(A), eltype(B)), broadcast_shape(A,B)), A, B)
+    broadcast!(-, Array(promote_op(SubFun(), eltype(A), eltype(B)), broadcast_shape(A,B)), A, B)
 end
 
-type_div(T,S) = promote_type(T,S)
-type_div{T<:Integer,S<:Integer}(::Type{T},::Type{S}) = typeof(one(T)/one(S))
-type_div{T,S}(::Type{Complex{T}},::Type{Complex{S}}) = Complex{type_div(T,S)}
-type_div{T,S}(::Type{Complex{T}},::Type{S})          = Complex{type_div(T,S)}
-type_div{T,S}(::Type{T},::Type{Complex{S}})          = Complex{type_div(T,S)}
+eltype_mul(As::AbstractArray...) = promote_eltype_op(MulFun(), As...)
+
+.*(As::AbstractArray...) = broadcast!(*, Array(eltype_mul(As...), broadcast_shape(As...)), As...)
 
 function ./(A::AbstractArray, B::AbstractArray)
-    broadcast!(/, Array(type_div(eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
+    broadcast!(/, Array(promote_op(RDivFun(), eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
 end
 
 function .\(A::AbstractArray, B::AbstractArray)
-    broadcast!(\, Array(type_div(eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
+    broadcast!(\, Array(promote_op(LDivFun(), eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
 end
 
 typealias RatIntT{T<:Integer} Union{Type{Rational{T}},Type{T}}
@@ -327,12 +319,8 @@ function .//(A::AbstractArray, B::AbstractArray)
     broadcast!(//, Array(type_rdiv(eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
 end
 
-type_pow(T,S) = promote_type(T,S)
-type_pow{S<:Integer}(::Type{Bool},::Type{S}) = Bool
-type_pow{S}(T,::Type{Rational{S}}) = type_pow(T, type_div(S, S))
-
 function .^(A::AbstractArray, B::AbstractArray)
-    broadcast!(^, Array(type_pow(eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
+    broadcast!(^, Array(promote_op(PowFun(), eltype(A), eltype(B)), broadcast_shape(A, B)), A, B)
 end
 
 ## element-wise comparison operators returning BitArray ##

base/complex.jl

@@ -26,6 +26,13 @@ promote_rule{T<:Real,S<:Real}(::Type{Complex{T}}, ::Type{S}) =
 promote_rule{T<:Real,S<:Real}(::Type{Complex{T}}, ::Type{Complex{S}}) =
     Complex{promote_type(T,S)}
 
+promote_op{T<:Real,S<:Real}(op, ::Type{Complex{T}}, ::Type{Complex{S}}) =
+    Complex{promote_op(op,T,S)}
+promote_op{T<:Real,S<:Real}(op, ::Type{Complex{T}}, ::Type{S}) =
+    Complex{promote_op(op,T,S)}
+promote_op{T<:Real,S<:Real}(op, ::Type{T}, ::Type{Complex{S}}) =
+    Complex{promote_op(op,T,S)}
+
 widen{T}(::Type{Complex{T}}) = Complex{widen(T)}
 
 real(z::Complex) = z.re

base/functors.jl

@@ -120,6 +120,10 @@ EqX{T}(x::T) = EqX{T}(x)
 
 call(f::EqX, y) = f.x == y
 
+# More promote_op rules
+
+promote_op{T<:Integer}(::PowFun, ::Type{Bool}, ::Type{T}) = Bool
+
 #### Bitwise operators ####
 
 # BitFunctors are functions that behave in the same bit-wise manner when applied

base/int.jl

@@ -340,6 +340,8 @@ promote_rule(::Type{UInt128}, ::Type{Int32} ) = UInt128
 promote_rule(::Type{UInt128}, ::Type{Int64} ) = UInt128
 promote_rule(::Type{UInt128}, ::Type{Int128}) = UInt128
 
+promote_op{R<:Integer,S<:Integer}(op, ::Type{R}, ::Type{S}) = typeof(op(one(R), one(S)))
+
 ## traits ##
 
 typemin(::Type{Int8  }) = Int8(-128)

base/linalg.jl

@@ -7,6 +7,7 @@ importall ..Base.Operators
 import Base: USE_BLAS64, size, copy, copy_transpose!, power_by_squaring,
              print_matrix, transpose!, unsafe_getindex, unsafe_setindex!,
              isapprox
+using Base: promote_op, MulFun
 
 export
 # Modules

base/linalg/matmul.jl

@@ -38,8 +38,8 @@ function scale!(C::AbstractMatrix, b::AbstractVector, A::AbstractMatrix)
     end
     C
 end
-scale(A::Matrix, b::Vector) = scale!(similar(A, promote_type(eltype(A),eltype(b))), A, b)
-scale(b::Vector, A::Matrix) = scale!(similar(b, promote_type(eltype(A),eltype(b)), size(A)), b, A)
+scale(A::Matrix, b::Vector) = scale!(similar(A, promote_op(MulFun(),eltype(A),eltype(b))), A, b)
+scale(b::Vector, A::Matrix) = scale!(similar(b, promote_op(MulFun(),eltype(b),eltype(A)), size(A)), b, A)
 
 # Dot products
 
@@ -78,11 +78,11 @@ At_mul_B{T<:BlasComplex}(x::StridedVector{T}, y::StridedVector{T}) = [BLAS.dotu(
 
 # Matrix-vector multiplication
 function (*){T<:BlasFloat,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     A_mul_B!(similar(x, TS, size(A,1)), A, convert(AbstractVector{TS}, x))
 end
 function (*){T,S}(A::AbstractMatrix{T}, x::AbstractVector{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     A_mul_B!(similar(x,TS,size(A,1)),A,x)
 end
 (*)(A::AbstractVector, B::AbstractMatrix) = reshape(A,length(A),1)*B
@@ -101,22 +101,22 @@ end
 A_mul_B!(y::StridedVector, A::StridedVecOrMat, x::StridedVector) = generic_matvecmul!(y, 'N', A, x)
 
 function At_mul_B{T<:BlasFloat,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     At_mul_B!(similar(x,TS,size(A,2)), A, convert(AbstractVector{TS}, x))
 end
 function At_mul_B{T,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     At_mul_B!(similar(x,TS,size(A,2)), A, x)
 end
 At_mul_B!{T<:BlasFloat}(y::StridedVector{T}, A::StridedVecOrMat{T}, x::StridedVector{T}) = gemv!(y, 'T', A, x)
 At_mul_B!(y::StridedVector, A::StridedVecOrMat, x::StridedVector) = generic_matvecmul!(y, 'T', A, x)
 
 function Ac_mul_B{T<:BlasFloat,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     Ac_mul_B!(similar(x,TS,size(A,2)),A,convert(AbstractVector{TS},x))
 end
 function Ac_mul_B{T,S}(A::StridedMatrix{T}, x::StridedVector{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     Ac_mul_B!(similar(x,TS,size(A,2)), A, x)
 end
 
@@ -127,7 +127,7 @@ Ac_mul_B!(y::StridedVector, A::StridedVecOrMat, x::StridedVector) = generic_matv
 # Matrix-matrix multiplication
 
 function (*){T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S})
-    TS = promote_type(arithtype(T), arithtype(S))
+    TS = promote_op(MulFun(), arithtype(T), arithtype(S))
     A_mul_B!(similar(B, TS, (size(A,1), size(B,2))), A, B)
 end
 A_mul_B!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = gemm_wrapper!(C, 'N', 'N', A, B)
@@ -144,14 +144,14 @@ end
 A_mul_B!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_matmatmul!(C, 'N', 'N', A, B)
 
 function At_mul_B{T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S})
-    TS = promote_type(arithtype(T), arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T), arithtype(S))
     At_mul_B!(similar(B, TS, (size(A,2), size(B,2))), A, B)
 end
 At_mul_B!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = is(A,B) ? syrk_wrapper!(C, 'T', A) : gemm_wrapper!(C, 'T', 'N', A, B)
 At_mul_B!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_matmatmul!(C, 'T', 'N', A, B)
 
 function A_mul_Bt{T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S})
-    TS = promote_type(arithtype(T), arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T), arithtype(S))
     A_mul_Bt!(similar(B, TS, (size(A,1), size(B,1))), A, B)
 end
 A_mul_Bt!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = is(A,B) ? syrk_wrapper!(C, 'N', A) : gemm_wrapper!(C, 'N', 'T', A, B)
@@ -168,7 +168,7 @@ end
 A_mul_Bt!(C::StridedVecOrMat, A::StridedVecOrMat, B::StridedVecOrMat) = generic_matmatmul!(C, 'N', 'T', A, B)
 
 function At_mul_Bt{T,S}(A::AbstractMatrix{T}, B::StridedVecOrMat{S})
-    TS = promote_type(arithtype(T), arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T), arithtype(S))
     At_mul_Bt!(similar(B, TS, (size(A,2), size(B,1))), A, B)
 end
 At_mul_Bt!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = gemm_wrapper!(C, 'T', 'T', A, B)
@@ -177,7 +177,7 @@ At_mul_Bt!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_m
 Ac_mul_B{T<:BlasReal}(A::StridedMatrix{T}, B::StridedMatrix{T}) = At_mul_B(A, B)
 Ac_mul_B!{T<:BlasReal}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = At_mul_B!(C, A, B)
 function Ac_mul_B{T,S}(A::StridedMatrix{T}, B::StridedMatrix{S})
-    TS = promote_type(arithtype(T), arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T), arithtype(S))
     Ac_mul_B!(similar(B, TS, (size(A,2), size(B,2))), A, B)
 end
 Ac_mul_B!{T<:BlasComplex}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = is(A,B) ? herk_wrapper!(C,'C',A) : gemm_wrapper!(C,'C', 'N', A, B)
@@ -186,16 +186,16 @@ Ac_mul_B!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_ma
 A_mul_Bc{T<:BlasFloat,S<:BlasReal}(A::StridedMatrix{T}, B::StridedMatrix{S}) = A_mul_Bt(A, B)
 A_mul_Bc!{T<:BlasFloat,S<:BlasReal}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{S}) = A_mul_Bt!(C, A, B)
 function A_mul_Bc{T,S}(A::StridedMatrix{T}, B::StridedMatrix{S})
-    TS = promote_type(arithtype(T),arithtype(S))
+    TS = promote_op(MulFun(),arithtype(T),arithtype(S))
     A_mul_Bc!(similar(B,TS,(size(A,1),size(B,1))),A,B)
 end
 A_mul_Bc!{T<:BlasComplex}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = is(A,B) ? herk_wrapper!(C, 'N', A) : gemm_wrapper!(C, 'N', 'C', A, B)
 A_mul_Bc!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_matmatmul!(C, 'N', 'C', A, B)
 
-Ac_mul_Bc{T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S}) = Ac_mul_Bc!(similar(B, promote_type(arithtype(T), arithtype(S)), (size(A,2), size(B,1))), A, B)
+Ac_mul_Bc{T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S}) = Ac_mul_Bc!(similar(B, promote_op(MulFun(),arithtype(T), arithtype(S)), (size(A,2), size(B,1))), A, B)
 Ac_mul_Bc!{T<:BlasFloat}(C::StridedMatrix{T}, A::StridedVecOrMat{T}, B::StridedVecOrMat{T}) = gemm_wrapper!(C, 'C', 'C', A, B)
 Ac_mul_Bc!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_matmatmul!(C, 'C', 'C', A, B)
-Ac_mul_Bt{T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S}) = Ac_mul_Bt(similar(B, promote_type(arithtype(A), arithtype(B)), (size(A,2), size(B,1))), A, B)
+Ac_mul_Bt{T,S}(A::AbstractMatrix{T}, B::StridedMatrix{S}) = Ac_mul_Bt(similar(B, promote_op(MulFun(),arithtype(A), arithtype(B)), (size(A,2), size(B,1))), A, B)
 Ac_mul_Bt!(C::StridedMatrix, A::StridedVecOrMat, B::StridedVecOrMat) = generic_matmatmul!(C, 'C', 'T', A, B)
 
 # Supporting functions for matrix multiplication
@@ -420,7 +420,7 @@ end
 function generic_matmatmul{T,S}(tA, tB, A::AbstractVecOrMat{T}, B::AbstractMatrix{S})
     mA, nA = lapack_size(tA, A)
     mB, nB = lapack_size(tB, B)
-    C = similar(B, promote_type(arithtype(T),arithtype(S)), mA, nB)
+    C = similar(B, promote_op(MulFun(),arithtype(T),arithtype(S)), mA, nB)
     generic_matmatmul!(C, tA, tB, A, B)
 end
 
@@ -625,7 +625,7 @@ end
 
 # multiply 2x2 matrices
 function matmul2x2{T,S}(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    matmul2x2!(similar(B, promote_type(T,S), 2, 2), tA, tB, A, B)
+    matmul2x2!(similar(B, promote_op(MulFun(),T,S), 2, 2), tA, tB, A, B)
 end
 
 function matmul2x2!{T,S,R}(C::AbstractMatrix{R}, tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
@@ -654,7 +654,7 @@ end
 
 # Multiply 3x3 matrices
 function matmul3x3{T,S}(tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})
-    matmul3x3!(similar(B, promote_type(T,S), 3, 3), tA, tB, A, B)
+    matmul3x3!(similar(B, promote_op(MulFun(),T,S), 3, 3), tA, tB, A, B)
 end
 
 function matmul3x3!{T,S,R}(C::AbstractMatrix{R}, tA, tB, A::AbstractMatrix{T}, B::AbstractMatrix{S})

base/promotion.jl

@@ -203,7 +203,10 @@ checked_mul(x::Integer, y::Integer) = checked_mul(promote(x,y)...)
 # as needed. For example, if you need to provide a custom result type
 # for the multiplication of two types,
 #   promote_op{R<:MyType,S<:MyType}(::MulFun, ::Type{R}, ::Type{S}) = MyType{multype(R,S)}
+promote_op(::Any)    = Bottom
+promote_op(::Any, T) = T
 promote_op{R,S}(::Any, ::Type{R}, ::Type{S}) = promote_type(R, S)
+promote_op(op, T, S, U, V...) = promote_op(op, T, promote_op(op, S, U, V...))
 
 ## catch-alls to prevent infinite recursion when definitions are missing ##
 

base/sparse/sparsematrix.jl

@@ -1023,7 +1023,7 @@ end # macro
 (.-)(A::Number, B::SparseMatrixCSC) = A .- full(B)
 ( -)(A::Array , B::SparseMatrixCSC) = A  - full(B)
 
-(.*)(A::AbstractArray, B::AbstractArray) = broadcast_zpreserving(*, A, B)
+(.*)(A::AbstractArray, B::AbstractArray) = broadcast_zpreserving(Base.MulFun(), A, B)
 (.*)(A::SparseMatrixCSC, B::Number) = SparseMatrixCSC(A.m, A.n, copy(A.colptr), copy(A.rowval), A.nzval .* B)
 (.*)(A::Number, B::SparseMatrixCSC) = SparseMatrixCSC(B.m, B.n, copy(B.colptr), copy(B.rowval), A .* B.nzval)
 

test/arrayops.jl

@@ -1233,7 +1233,7 @@ b = rand(6,7)
 # return type declarations (promote_op)
 module RetTypeDecl
     using Base.Test
-    import Base: +, *, .*
+    import Base: +, *, .*, zero
 
     immutable MeterUnits{T,P} <: Number
         val::T
@@ -1243,9 +1243,11 @@ module RetTypeDecl
     m  = MeterUnits(1.0, 1)   # 1.0 meter, i.e. units of length
     m2 = MeterUnits(1.0, 2)   # 1.0 meter^2, i.e. units of area
 
-    (+){T}(x::MeterUnits{T,1}, y::MeterUnits{T,1}) = MeterUnits{T,1}(x.val+y.val)
+    (+){T,pow}(x::MeterUnits{T,pow}, y::MeterUnits{T,pow}) = MeterUnits{T,pow}(x.val+y.val)
+    (*){T,pow}(x::Int, y::MeterUnits{T,pow}) = MeterUnits{typeof(x*one(T)),pow}(x*y.val)
     (*){T}(x::MeterUnits{T,1}, y::MeterUnits{T,1}) = MeterUnits{T,2}(x.val*y.val)
     (.*){T}(x::MeterUnits{T,1}, y::MeterUnits{T,1}) = MeterUnits{T,2}(x.val*y.val)
+    zero{T,pow}(x::MeterUnits{T,pow}) = MeterUnits{T,pow}(zero(T))
 
     Base.promote_op{R,S}(::Base.AddFun, ::Type{MeterUnits{R,1}}, ::Type{MeterUnits{S,1}}) = MeterUnits{promote_type(R,S),1}
     Base.promote_op{R,S}(::Base.MulFun, ::Type{MeterUnits{R,1}}, ::Type{MeterUnits{S,1}}) = MeterUnits{promote_type(R,S),2}
@@ -1255,6 +1257,8 @@ module RetTypeDecl
     @test @inferred([m,m]+m) == [m+m,m+m]
     @test @inferred(m.*[m,m]) == [m2,m2]
     @test @inferred([m,m].*m) == [m2,m2]
+    @test @inferred([m 2m; m m]*[m,m]) == [3m2,2m2]
+    @test @inferred([m m].*[m,m]) == [m2 m2; m2 m2]
 end
 
 # range, range ops