Function ni_fast_atan2

pub const fn ni_fast_atan2(y: f32, x: f32) -> f32

Approximates the arctangent of y/x using a fast polynomial expansion.

• Special cases:
  • atan2(0, 0) → 0.0 rad
  • atan2(1, 0) → π/2 rad
  • atan2(0, -1) → π rad

Examples

// `atan2(1, 0)` -> `π/2`
assert!((ni_fast_atan2(1.0, 0.0) - core::f32::consts::FRAC_PI_2).abs() < 1e-6);
// `atan2(0, -1)` -> `π`
assert!((ni_fast_atan2(0.0, -1.0) - core::f32::consts::PI).abs() < 1e-6);

Explanation:

This function uses a polynomial approximation of atan(z):

atan(z) ≈ z × (0.9998660 + z² × (-0.3302995 + z² × (0.1801410 +
           z² × (-0.0851330 + z² × 0.0208351))))

The nested form (Horner's method) is used for faster computation:

• Reduces the number of multiplication operations.
• Avoids explicit power calculations (e.g., z^3, z^5) by reusing z².