Software architecture in C program

I need to find an efficient solution for matrix multiplication involving software architecture. 3 different types of multiplication The following matrix operation is done: C=A×B×BT+at×A where: • A and B are N x N size double-cell square array • A is a triangular top matrix • At is transposed to A and BT is transposed to B • × is the multiplication operation • + is the assembly operation The above operation is intended to be implemented in C/C++ in 3 modes: • Blas - a variant which uses one or more functions of BLAS Atlas for the performance of breeding and assembly operations. • neopt - a "hand" version without improvement. • eight_m - an improved version of the neeight. The improvement only aims at modifying the code in order to achieve better performance. Each of the 3 above implementations will take into account that A is a triangular top array.