The GameCube GPU is a complex, tight-knit piece of hardware with impressive features for its time. It is so powerful and so flexible, it was used unmodified within the Wii architecture. For a comparison, just imagine a SNES running with an NES’s graphics system. This is completely unheard of, before or since. The GameCube is a remarkable achievement of hardware engineering! With its impressive capabilities, emulating the GameCube’s GPU has been one of the most challenging tasks Dolphin has ever faced.
Fantastic in-depth look at specific parts of the GameCube/Wii GPU, written by the developers of the Dolphin emulator.
Don’t try to do integer math with floating point. It works for normal math, but as soon as anything like bitwise operations or integer overflow is expected (and it always is in pixel handling), it just won’t work.