Hue shifting code snippet (with trivia)

Recently, to add variety to instances of a crowd system, I experimented with cheap methods to do hue shifting (as the pixel shader is very cheap at the moment and has a few ALU cycles to spare, as they are hidden by color texture access latency)... After 3 mostly-failed attempts I ended up with the following (actually, it's a test I did in the weekend, I'm not 100% sure it's error-free as I didn't test it much yet... LOL!):

float2 sc;

sincos(IN.random_recolor, sc.x, sc.y);

sc.y = 1.f - sc.y;

sc /= float2(sqrt(3.f), 3.f);

float3 xVec = float3(1.f, sc.xx * float2(-1,1)) + (sc.yyy * float3(-2,1,1));

float3x3 recolorMatrix = float3x3(xVec.xyz, xVec.zxy, xVec.yzx);

float3 recolored = mul(tex2D(colorTexture, IN.UV), recolorMatrix);

Have you figured out what it does? Try, even if the code is kinda cryptic, you should be able to understand the underlying idea... I've changed the names of variables to make is less obvious and protect the innocent (in my real code, I don't waste an interpolator only for the recoloring random float for example)... (hint: start from the bottom...)

Done? Well, if your guess was along the lines of "a rotation on the 45° positive axis in RGB space" then you're right! Mhm if it was not, then either you're wrong, or I did a mistake in the code :)

Bonus question: what kind of errors does it make (compared to a real hue-shift i.e. the one that photoshop implements)? Hints follow... What kind of errors could it make? Being a hue shift, it's wrong if it changes the other two components of the HSL space instead of the hue (we could argue that is an error even if it's non-linear in the hue, but as we want to encode a random shift we don't care much, even if a strong non-linearity if feed with an uniform random variable leads to a preference towards some colors). So we have to see if it changes the saturation or the luminosity... Which of the two is more a probably going to be a problem? Which of the two that code gets more wrong?

Second bonus question: how many ALU cycles does that technique take?