Comparing floating-point numbers for equality
Comparing floating-point numbers for absolute equality with == is often
inappropriate because of the risk of rounding errors, particularly when doing
parallel summation using strictly speaking non-associative floating-point
addition. A common solution is to use a function that checks approximate
equality, using both a relative and an absolute tolerance:
def approx_eql (rel_tol: f64) (a: f64) (b: f64) : bool =
let diff = f64.abs (a - b)
let scale = f64.max (f64.abs a) (f64.abs b)
let abs_tol = 100.0 * f64.epsilon * scale
in diff <= f64.max abs_tol (rel_tol * scale)> approx_eql 1e-9 1.0 1.0000000005true