===================
Packing Blocks of A
===================

In the cache optimized GEMM-Operation $\beta C + \alpha A B \to C$ the matrix $A$
gets partitioned into blocks of maximal dimension $M_c \times K_c$.  Each block
$A_{i,l}$ of $A$ gets packed into col-major horizontal panels with $M_r$ rows.

Assume that $p$ is a buffer for $M_c \cdot K_c$ elements and $X$ a matrix block
with dimension $m \times k$ where $m \leq M_c$ and $k \leq K_c$.  Then the
following algorithm (which is using zero-based indices) can be used for packing:

---- BOX -----------------------------------------------------------------------
`dgepack_A(X, p)`
~~~~~~~~~~~~~~~~~
+------------------------------------------------------------------------------+
|- Input:                                                                      |
|   - matrix $X = \left(x_{i,l}\right)$ with dimension $m \times k$            |
|     (assume $m \leq M_c$, $k \leq K_c$)                                      |
|   - array $p$ with length $M_c \cdot K_c$                                    |
|- On Return:                                                                  |
|   - $p$ contains $X$ packed in horizontal col-major panels with $M_r$ rows   |
+------------------------------------------------------------------------------+
| - for $l$ with $0 \leq l < k$                                                |
|     - for $i_1$ with $0 \leq i_1 < \left\lceil \frac{m}{M_r} \right\rceil$   |
|         - for $i_0$ with $0 \leq i_0 < M_r$                                  |
|             - $i \leftarrow i_1 \cdot M_r + i_0$                             |
|             - $\nu \leftarrow i_1 \cdot M_r \cdot k + l \cdot M_r + i_0$     |
|             - if $i < m$                                                     |
|                 - $p_\nu \leftarrow x_{i,l}$                                 |
|             - else                                                           |
|                 - $p_\nu \leftarrow 0$                                       |
+------------------------------------------------------------------------------+
--------------------------------------------------------------------------------


Exercise
========
- Implement and *test* the following algorithm for packing blocks of $A$
- Start with an empty source file!

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