In the current implementation, computing the argument of a complex number depends on the system math library's implementation of atan2, which is not guaranteed to produce exactly rounded (or otherwise portably reproducible) results. However, the principal complex square root can be computed using only the usual correctly rounded operations (+, -, *, /, sqrt), which are reproducible on all IEEE 754 systems.
In the current implementation, computing the argument of a complex number depends on the system math library's implementation of
atan2, which is not guaranteed to produce exactly rounded (or otherwise portably reproducible) results. However, the principal complex square root can be computed using only the usual correctly rounded operations (+, -, *, /, sqrt), which are reproducible on all IEEE 754 systems.