[Haskell-cafe] The maths behind the Fastest Fibb In The West.

I've been working on a project that needs a good fibonacci generator, and I'm to the point where can now improve upon this one: https://wiki.haskell.org/The_Fibonacci_sequence#Fastest_Fib_in_the_West thanks to this guy: https://groups.google.com/forum/#!topic/haskell-cafe/HUgbAUCvCp4 He suggested breaking up a guard into two diffeent functions, which I can do, but I don't know what to call them because I don't know why the operations are different. I'm referring to this section: fib' (f, g) p | p = (f*(f+2*g), f^2 + g^2) | otherwise = (f^2+g^2, g*(2*f-g)) I'd like to know the reason why each guard does two entirely different things, so I know what to call the functions when I seperate them out.