Cherry-pick changes from jishnub/bidigamul_empty

stdlib/LinearAlgebra/src/bidiag.jl

@@ -535,12 +535,18 @@ function rmul!(B::Bidiagonal, D::Diagonal)
 end
 
 @noinline function check_A_mul_B!_sizes((mC, nC)::NTuple{2,Integer}, (mA, nA)::NTuple{2,Integer}, (mB, nB)::NTuple{2,Integer})
+    # check for matching sizes in one column of B and C
+    check_A_mul_B!_sizes((mC,), (mA, nA), (mB,))
+    # ensure that the number of columns in B and C match
+    if nB != nC
+        throw(DimensionMismatch(lazy"second dimension of output C, $nC, and second dimension of B, $nB, must match"))
+    end
+end
+@noinline function check_A_mul_B!_sizes((mC,)::Tuple{Integer}, (mA, nA)::NTuple{2,Integer}, (mB,)::Tuple{Integer})
     if mA != mC
         throw(DimensionMismatch(lazy"first dimension of A, $mA, and first dimension of output C, $mC, must match"))
     elseif nA != mB
         throw(DimensionMismatch(lazy"second dimension of A, $nA, and first dimension of B, $mB, must match"))
-    elseif nB != nC
-        throw(DimensionMismatch(lazy"second dimension of output C, $nC, and second dimension of B, $nB, must match"))
     end
 end
 
@@ -563,6 +569,7 @@ _mul!(C::AbstractMatrix, A::BiTriSym, B::TriSym, _add::MulAddMul) =
 _mul!(C::AbstractMatrix, A::BiTriSym, B::Bidiagonal, _add::MulAddMul) =
     _bibimul!(C, A, B, _add)
 function _bibimul!(C, A, B, _add)
+    require_one_based_indexing(C)
     check_A_mul_B!_sizes(size(C), size(A), size(B))
     n = size(A,1)
     if n <= 3
@@ -733,14 +740,9 @@ end
 
 function _mul!(C::AbstractVecOrMat, A::BiTriSym, B::AbstractVecOrMat, _add::MulAddMul)
     require_one_based_indexing(C, B)
+    check_A_mul_B!_sizes(size(C), size(A), size(B))
     nA = size(A,1)
     nB = size(B,2)
-    if !(size(C,1) == size(B,1) == nA)
-        throw(DimensionMismatch(lazy"A has first dimension $nA, B has $(size(B,1)), C has $(size(C,1)) but all must match"))
-    end
-    if size(C,2) != nB
-        throw(DimensionMismatch(lazy"A has second dimension $nA, B has $(size(B,2)), C has $(size(C,2)) but all must match"))
-    end
     iszero(nA) && return C
     iszero(_add.alpha) && return _rmul_or_fill!(C, _add.beta)
     if nA <= 3