I looked up the Inverse Square Root method that Traer Physics uses because I'm developing a physics engine of my own for use at work.

I converted it to Java and for a moment I thought it was slower until I realised why having the inverse square root is useful. It means you can calculate normals by multiplication instead of division.

So here is the speed proof:

Code:

float dx = 0;
float dy = 0;
int timer = 0;
void setup(){  
}
void draw(){
  timer = millis();
  for(int i = 0; i < 10000000; i++){
    float d = myDist1();
    dx = mouseX / d;
    dy = mouseY / d;
  }
  println("dx:"+dx+" dy:"+dy+" 1:"+(millis()-timer));
  timer = millis();
  for(int i = 0; i < 10000000; i++){
    float d = myDist2();
    dx = mouseX * d;
    dy = mouseY * d;
  }
  println("dx:"+dx+" dy:"+dy+" 2:"+(millis()-timer));
}

float myDist1(){
  return (float)Math.sqrt((mouseX - 0) * (mouseX - 0) + (mouseY - 0) * (mouseY - 0));
}
float myDist2(){
  return invSqrt((mouseX - 0) * (mouseX - 0) + (mouseY - 0) * (mouseY - 0));
}

static float invSqrt(float x){
  float xhalf = 0.5f*x;
  int i = Float.floatToIntBits(x); // get bits for floating value
  i = 0x5f375a86- (i>>1); // gives initial guess y0
  x = Float.intBitsToFloat(i); // convert bits back to float
  x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
  return x;
}

/*
// Original C code by Chris Lomont <http://www.lomont.org/Math/Papers/2003/InvSqrt.pdf>
static float InvSqrt(float x){
  float xhalf = 0.5f*x;
  int i = (int)&x; // get bits for floating value
  i = 0x5f375a86- (i>>1); // gives initial guess y0
  x = (float)&i; // convert bits back to float
  x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
  return x;
}
*/
 

I'd like to port this to Flash though, does anyone know how the float to ints and back is done? Seeing as the speed boost is so slight with inverse square root I'm thinking it might also help this example to inline that method.