Function atan 

pub const fn atan(x: Real) -> Real

Computes the arctangent of x (atan(x)).

Returns the principal value in the range [-π/2, π/2] radians.

Special cases

• atan(NaN) returns NaN
• atan(±0) returns ±0 (preserving the sign of zero)
• atan(±∞) returns ±π/2

Implementation notes

This is a const fn-compatible port of the FreeBSD libm implementation (s_atan.c). The algorithm reduces the argument based on the magnitude of |x| and evaluates it using either a polynomial approximation or an addition formula with precomputed constants (ATANHI/ATANLO).

Modifications for this crate:

• Adapted to the generic Real type (which is f64 under the hood)
• Made fully const fn compatible
• Removed force_eval! (subnormal underflow side-effect, not relevant in const context)
• Replaced the i! macro with direct array indexing
• Used the .abs() method instead of the fabs helper

Testing

This function is tested directly with:

• Sanity checks for standard angles (π/6, π/4, π/3 and their negatives)
• Special values: zero, ±infinity, NaN

It is also exercised by the full atan2 test suite (which calls atan internally). All tests pass and produce results matching the original libm implementation.