GEMM stands for general matrix-matrix operation.
The first version
// create macros so that the matrices are stored in column-major order.
#define A(i,j) a[ (j) * lda + (i) ]
#define B(i,j) b[ (j) * ldb + (i) ]
#define C(i,j) c[ (j) * ldc + (i) ]
// C= A * B + C
void gemm(int m, int n, int k, double *a, int lda,
double *b, int ldb,
double *c, int ldc){
for(int i=0;i<m;++i){ // Loop over the rows of C
for(int j=0;j<n;++j){ // Loop over the columns of C
for(int p=0;p<k;++p){ // update C(i,j) with the inner
C(i,j) += A(i,p) * B(p,j); // product of the i-th row of A
} // and the j-th column of B.
}
}
}