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GEMM: Implementation of the Frame Algorithm                             [TOC]
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Finally we will put things together in the GEMM frame algorithm that computes

---- LATEX ---------------------------------------------------------------------
C   \leftarrow  \beta \cdot C + \alpha \cdot A \cdot B
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where $C$ is a $m \times n$ matrix, $A$ is a $m \times k$ matrix and $B$ a $k
\times n$ matrix.  The following special cases are treated:

- If $\beta = 0$ matrix $C$ can contain Nan (not a number) entries.
- If $\alpha = 0$ or $k = 0$ matrix $C$ just gets scaled by $\beta$ (or gets
  initialized with zero values if $\beta=0$).

Algorithm
=========
The frame algorithm uses the GEMM macro kernel and the packing functions as
building blocks.  With respect to the constants $M_c$, $N_c$ and $K_c$ matrices
$A$, $B$ and $C$ are considered as block matrices:

---- LATEX ---------------------------------------------------------------------
A = \left(\begin{array}{c|c|c}
                  &   \vdots                            &           \\
          \hline
          \dots   &   A_{i \cdot M_c,\, \ell \cdot K_c} &   \dots   \\
          \hline
                  &   \vdots                            &           \\
          \end{array}\right)
,\quad
 B = \left(\begin{array}{c|c|c}
                  &   \vdots                            &           \\
          \hline
          \dots   &   B_{\ell \cdot K_c,\, j \cdot N_c} &   \dots   \\
          \hline
                  &   \vdots                            &           \\
          \end{array}\right)
,\quad
 C = \left(\begin{array}{c|c|c}
                  &   \vdots                            &           \\
          \hline
          \dots   &   C_{i \cdot M_c,\, j \cdot N_c}    &   \dots   \\
          \hline
                  &   \vdots                            &           \\
          \end{array}\right)
--------------------------------------------------------------------------------

The complete algorithm then reads as:

---- BOX -----------------------------------------------------------------------

- if $\alpha = 0$ or $k = 0$
    - $C \leftarrow \beta C$
    - return
- Allocate buffers $\overline{A}$ and $\overline{B}$ for packing blocks of
  $A$ and $B$ respectively.

- For $j_b = 0, \dots, \left\lceil \frac{n}{N_c} \right\rceil - 1$
    - For $\ell_b = 0, \dots, \left\lceil \frac{k}{K_c} \right\rceil - 1$
        - Pack: $\overline{B} \leftarrow B_{\ell_b \cdot K_c,\, j_b \cdot N_c}$
        - $\overline{\beta} \leftarrow
          \begin{cases} 1, & \ell>0 \\ \beta, & \text{else.} \end{cases}$
        - For $i_b = 0, \dots, \left\lceil \frac{m}{M_c} \right\rceil - 1$
            - Pack: $\overline{A} \leftarrow A_{i_b \cdot M_c,\, \ell_b \cdot K_c}$
            - Macro Kernel:
              $C_{i_b \cdot M_c,\, j_b \cdot N_c}
              \leftarrow \overline{\beta} \cdot C_{i_b \cdot M_c,\, j_b \cdot N_c}
              + \alpha \cdot \overline{A} \cdot \overline{B}
              $

- Release buffers

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