Rational reduction and enclosures for the complex argument

The input order is (x, y) for arg (x + i*y). A rational slope and an integer multiple of π/4 describe the principal branch (-π, π]. The negative real axis selects +π. At the origin this numerical helper uses the totalized mathematical value zero; format wrappers whose contract rejects the origin must do so before rounding.

def FloatLib.Numerics.TrigonometricComparison.atan2Reduction (x y : ℚ) : ℚ × ℚ

Return a slope and a multiple of π/4 whose shifted arctangent is the principal argument. The second component is rational to support exact boundary shifts in comparisons of arg / π.

def FloatLib.Numerics.TrigonometricComparison.atan2Interval (x y : ℚ) (degree : ℕ) : RationalInterval

Enclose the principal argument using exact rational arctangent and Machin π/4 enclosures. All series arguments are reduced by the existing arctangent kernel.