floating point inaccuracy in Processing

animation_nerd

Here is a simple bouncing ball.

The ball seems to lose energy until its peak reaches about 2/3 of the original height. Is this simply a floating point inaccuracy problem?

Changing the values to type double or rounding values fixes the behavior.

Changing the value of gravity to .981 (or a different value) fixes the behavior.

Also, curiously, this problem doesn't occur in Javascript Mode.

Can someone tell me why the ball's height settles at 2/3 of the height? And, why this problem doesn't occur in Javascript Mode?

EDIT: Oops. Initially had .98 commented out...

float ballY=0;
float ballVelocityY=0;

// float gravity=0.981;
float gravity=0.98;

void setup ()
{
  size (400, 400);
  noStroke();
  fill (255, 152, 49);
}

void draw ()
{
  ballVelocityY=ballVelocityY+gravity;
  ballY=ballY+ballVelocityY;

  if (ballY>height)
  {
    println(ballVelocityY);
    ballY=height;
    ballVelocityY=-ballVelocityY;
  }

  background (255);
  ellipse (width/2, ballY, 40, 40);
}

quark

It is due to rounding errors caused by the float data type in these 2 lines

ballVelocityY=ballVelocityY+gravity;
ballY=ballY+ballVelocityY;

The double fixes it because the rounding errors are too small to be noticed.

Rounding values removes the least significant digits from the number where the errors occur.

Javascript treats all decimal numbers as doubles

animation_nerd

Thanks quark! I should have googled float in Javascript....

animation_nerd

Have you observed the behavior? Doesn't it seem strange that the ball descends every second bounce and then ceases to descend any further?

quark

When gravity is 0.98 then the output is

28.41999
27.439993
27.439991
26.459993
26.459991
25.479994
25.479992
24.499994
24.499992
24.499994

notice that it doesn't always go down or up because rounding errors can be plus or minus.

When 0.982 the velocity is rock steady!