The implementation of every BLAS implementation I'm aware of basically looks like this: if (dims in range A) gemm_implA else if (dims in range B) g

The implementation of every BLAS implementation I'm aware of basically looks like this: if (dims in range A) gemm_implA else if (dims in range B) gemm_implB else if (dims in range C) gemm_implC // several more implementations... The immediate call function is invariably a switch over several implementations, and by the time you reach that call, you have actual knowledge of dimensions.