pub const ERR_COEFF_3: f64 = _; // 1.7763568394002536E-15f64Expand description
Absolute error coefficient for Matrix::<3>::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 3×3 determinant formula.
For a 3×3 matrix A whose closed-form determinant intermediates do not
undergo gradual underflow,
|A.det_direct() - det_exact(A)| ≤ ERR_COEFF_3 · p(|A|)where p(|A|) is the absolute Leibniz sum (the same cofactor
expansion as det_direct but with |·| at every leaf).
det_direct for D=3 uses three 2×2 FMA minors combined by a nested
FMA. The determinant and permanent each have at most five rounding events
per monomial; 8·EPS + 64·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.