On: Improving the fast inverse square root (2010)

[dnautics]

Even scientific calculation would be fine with 32 bit floats, but average floating point error due to representation creeps with ON (iirc) over N multiplications, so you have to use 64 bit for many scientific applications to get satisfactory results after a million or a trillion multiplications.

[llukas → dnautics]

Not really - https://en.wikipedia.org/wiki/Numerical_stability

If your algorithm is not stable then even 64-bit won't help you.

Compare Euler vs Verlet - https://en.wikipedia.org/wiki/Verlet_integration

[dnautics → llukas]

You're making a different argument.

[llukas → dnautics]

Which problem that has stable algorithm would require 64-bit then?

[toolslive → dnautics]

What they typically do in 3d gaming is update the matrix that holds the transformation by a left multiplication, every time the camera changes. So

Tn = U_{n-1} * U_{n-2} * .... * U_0 * T_0

After a while,your matrix accumulates errors, but it's easy to just start and take a fresh one.

[whyever → dnautics]

> Even scientific calculation would be fine with 32 bit floats

It really depends on the algorithms in question and the error tolerances.