Custom math functions vs. supplied Math functions?

Question

I am basically making a Java program that will have to run a lot of calculations pretty quickly(each frame, aiming for at least 30 f/s). These will mostly be trigonometric and p

Answer 1

The built-in Math functions will be extremely difficult to beat, given that most of them have special JVM magic that makes them use hardware intrinsics. You could conceivably beat some of them by trading away accuracy with a lot of work, but you're very unlikely to beat the Math utilities otherwise.