pub const ERR_COEFF_4: f64 = _; // 2.664535259100382E-15f64Expand description
Absolute error coefficient for Matrix::<4>::det_direct.
This constant is not a caller-tuned tolerance. It is the dimension-specific multiplier that turns the matrix’s absolute Leibniz sum into a conservative bound on floating-point roundoff in the closed-form 4×4 determinant formula.
For a 4×4 matrix A whose closed-form determinant intermediates do not
undergo gradual underflow,
|A.det_direct() - det_exact(A)| ≤ ERR_COEFF_4 · p(|A|)where p(|A|) is the absolute Leibniz sum. det_direct for D=4
evaluates four nested 3×3 cofactors, sharing their six 2×2 minors when
every coefficient in the first two rows is non-zero, and reduces them with
an FMA row combination. Dense and sparse trees each have at most nine
rounding events per monomial, as does the permanent tree. The coefficient
12·EPS + 128·EPS² also covers rounding the permanent and final bound
product. See ERR_COEFF_2 for the derivation link and REFERENCES.md
[8-11] for the analysis framework.
Prefer
Matrix::det_direct_with_errbound
over this constant for typical use; see ERR_COEFF_2 for a worked
example.