Module compile_time 

Compile-time determinants and dimension dispatch.

det_direct() is a const fn providing closed-form determinants for D=0–4, using fused multiply-add where applicable. It returns Ok(Some(det)) for those dimensions and Ok(None) for D ≥ 5. Matrix::<0>::zero().det_direct() returns Ok(Some(1.0)) (the empty-product convention). For D=1–4, direct formulas bypass LU factorization entirely. This enables compile-time evaluation when inputs are known:

use la_stack::prelude::*;

// Evaluated entirely at compile time — no runtime cost.
const DET: Result<Option<f64>, LaError> = match Matrix::<4>::try_from_rows([
    [2.0, 0.0, 0.0, 0.0],
    [0.0, 3.0, 0.0, 0.0],
    [0.0, 0.0, 5.0, 0.0],
    [0.0, 0.0, 0.0, 7.0],
]) {
    Ok(matrix) => matrix.det_direct(),
    Err(err) => Err(err),
};

fn main() -> Result<(), LaError> {
    assert_eq!(DET?, Some(210.0));
    Ok(())
}

The public det() method automatically dispatches through the closed-form path for D ≤ 4 and falls back to zero-tolerance LU for D ≥ 5. Tiny nonzero determinants are not flattened by a configured pivot tolerance. The LU fallback returns LaError::Singular when floating-point elimination cannot produce a non-zero pivot; it does not misreport that numerical failure as an exact zero. Use lu() directly when you need a different tolerance policy, and use the exact determinant APIs when exact singularity classification matters.