normalize implementation is not numerically stable

[jordanwalker98]

I found that the current implementation of normalize:
return v * inversesqrt(dot(v, v));
is less numerically stable than:
return v / sqrt(dot(v, v));
even for double precision vectors.

By this I mean that if you repeatedly call the original implementation, the result will perpetually oscillate between two values. The division version will converge and is very stable with double precision. A simple test is to generate a series of random vectors, normalize, then normalize again and compare the first and second results. This can cause (in my case) hard-to-diagnose issues when using glm to solve computational geometry problems that require high precision.

EDIT: there are still rare cases where normalizing double precision vectors doesn't converge but division does appear to be more stable

I also found this link that points out the same issue:
https://stackoverflow.com/questions/23303598/3d-vector-normalization-issue