[thegeomaster]

What do you mean by "taking the square root"? sqrtps has exactly the same problem, it's not standardized, so you need a custom algorithm.

[dooglius]

Sqrt is standardized by IEEE, it is required to be the correctly rounded value.

[stephencanon]

square root is an IEEE 754 basic operation, correctly rounded (and therefore bitwise reproducible) on all compliant systems. What made you think that it isn't?