===================
Packing Blocks of B
===================

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
$B_{l,j}$ of $B$ gets packed into row-major vertical panels with $N_r$ columns.

Exercise
========
Assume that $p$ is a buffer for $K_c \cdot N_c$ elements and $X$ a matrix block
with dimension $k \times n$ where $k \leq K_c$ and $n \leq N_c$.

*Be honest for your own sake and derive the following algorithm (or any equivalent
algorithm) for packing blocks of $B$:*


---- BOX -----------------------------------------------------------------------
`dgepack_B(X, p)`
~~~~~~~~~~~~~~~~~
+------------------------------------------------------------------------------+
|- Input:                                                                      |
|   - matrix $X = \left(x_{l,j}\right)$ with dimension $k \times n$            |
|     (assume $k \leq K_c$, $n \leq N_c$)                                      |
|   - array $p$ with length $K_c \cdot N_c$                                    |
|- On Return:                                                                  |
|   - $p$ contains $X$ packed in vertical row-major panels with $N_r$ columns  |
+------------------------------------------------------------------------------+
| - for $j_1$ with $0 \leq j_1 < \left\lceil \frac{n}{N_r} \right\rceil$       |
|    - for $j_0$ with $0 \leq j_0 < N_r$                                       |
|       - for $l$ with $0 \leq l < k$                                          |
|             - $j \leftarrow j_1 \cdot N_r + j_0$                             |
|             - $\nu \leftarrow j_1 \cdot N_r \cdot k + l \cdot N_r + j_0$     |
|             - if $j < n$                                                     |
|                 - $p_\nu \leftarrow x_{l,j}$                                 |
|             - 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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