View source for Pre-calculated cycles for 8x3 matrix transpose

When [[driving 8 WS2811 strips in parallel with an 8Mhz AVR]] we need to transpose arrays of rgb-values into groups of red-, green- and blue values (rgbrgbrgb... to rrrrrrrrggggggggbbbbbbbb). This boils down to an [https://en.wikipedia.org/wiki/In-place_matrix_transposition in-place 8*3 matrix transpose]. This again boils down to going through cycles like this:

* pick up the value at position '''1'''
* place the saved value from the previous step at position '''8''', but first save the value at that location
* place the saved value from the previous step at position '''18''', but first save the value at that location
* place the saved value from the previous step at position '''6''', but first save the value at that location
* etc, etc...

Obviously, when doing this, you'd need a description of the cycles, i.e. which values need to be moved where. For 24 values, finding the cycles could be done with a set of numbered cards. But of course, in about the same time, you could whip up a program that does this. The program looks like this:

<code lang="cpp">
/**
 * calculate cycles along which values should be rotated in the array. See:
 * https://en.wikipedia.org/wiki/In-place_matrix_transposition#Non-square_matrices:_Following_the_cycles
 *
 */
void findCycles()
{
    // this array describes for each cell in the array
    // where its value should go to.
    // e.g. positions[2] == 16 means that the value at
    // position 2 needs to move to position 16
    int positions[] = {
             0,  8, 16,
             1,  9, 17,
             2, 10, 18,
             3, 11, 19,
             4, 12, 20,
             5, 13, 21,
             6, 14, 22,
             7, 15, 23
    };

    while (true)
    {
        // find the starting point of the cycle
        int seed = 0;
        for (;seed<24;++seed)
        {
            if (positions[seed] != seed) break;
        }
        if (seed == 24) break; // everything in order

        // now walk the cycle
        std::cout << seed << ": ";
        int transfer = positions[seed];
        positions[seed] = -1;

        while (transfer != -1)
        {
            std::cout << transfer << " ";
            std::swap( positions[transfer], transfer);
        }
        std::cout << '\n';
    }
}
</code>