Question

I’m using floats to represent a position in my game:

struct Position
{
    float x;
    float y;
};

I’m wondering if this is the best choice and what the consequences will be as the position values continue to grow larger. I took some time to brush up on how floats are stored and realized that I am a little confused.

(I’m using Microsoft Visual C++ compiler.)

In float.h, FLT_MAX is defined as follows:

#define FLT_MAX         3.402823466e+38F        /* max value */

which is 340282346600000000000000000000000000000.

That value is much greater than UINT_MAX which is defined as:

#define UINT_MAX        0xffffffff

and corresponds to the value 4294967295.

Based on this, it seems like a float would be a good choice to store a very large number like a position. Even though FLT_MAX is very large, I’m wondering how the precision issues will come into play.

Based on my understanding, a float uses 1 bit to store the sign, 8 bits to store the exponent, and 23 bits to store the mantissa (a leading 1 is assumed):

    S EEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM

That means FLT_MAX might look like:

    0 11111111 11111111111111111111111

which would be the equivalent of:

1.11111111111111111111111 x 2^128

or

111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Even knowing this, I have trouble visualizing the loss of precision and I’m getting confused thinking about what will happen as the values continue to increase.

Is there any easier way to think about this? Are floats or doubles generally used to store very large numbers over something like an unsigned int?

Answer 1

A way of thinking about the precision of a float, is to consider that they have roughly 5 digits of accuracy. So if your units are meters, and you have something 1km away, thats 1000m – attempting to deal with that object at a resolution of 10cm (0.1m) or less may be problematic.

The usual approach in a game would be to use floats, but to divide the world up such that positions are relative to local co-ordinate systems (for example, divide the world into a grid, and for each grid square have a translation value). Everything will have enough precision until it gets transformed relative to the camera for rendering, at which point the imprecision for far away things is not a problem.

As an example, imagine a game set in the solar system. If the origin of your co-ordinate system is in the heart of the sun, then co-ordinates on the surface of planets will be impossible to represent accurately in a float. However if you instead have a co-ordinate system relative to the planet’s surface, which in turn is relative to the center of the planet, and then you know where the planet is relative to the sun, you can operate on things in a local space with accuracy, and then transform into whatever space you want for rendering.