Skip to main content

ERR_COEFF_4

Constant ERR_COEFF_4 

Source
pub const ERR_COEFF_4: f64 = _; // 2.664535259100382E-15f64
Expand 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, yielding the 12·EPS + 128·EPS² bound. See REFERENCES.md [8] for the Shewchuk framework these bounds follow.

Prefer Matrix::det_direct_with_errbound over this constant for typical use; see ERR_COEFF_2 for a worked example.