Restoring the exact angle from std::cos(angle) using std::acos

Question

Is it guaranteed by the C++ standard that angle == std::acos(std::cos(angle)) if angle is in the range [0, Pi], or in other words is it possible to restore the exact original value of angle from the result of std::cos using std::acos given the mentioned range limit?

The marginal cases when angle is infinity or NaN are omitted.

Answer 1

Answer by StoryTeller:

The standard cannot make that guarantee, simply because the result of std::cos may not be representable exactly by a double, so you get a truncation error, which will affect the result of std::acos.