use core::scalar
use core::functions
use core::error

fn _fixed_point<X: Dim>(f: Fn[(X) -> X], x0: X, ε: X, max_iter: Scalar) =
  if abs(x1 - x0) < ε
    then x1
    else
      if max_iter > 0
        then _fixed_point(f, x1, ε, max_iter - 1)
        else error("fixed_point: Exceeded max. number of iterations")
  where
    x1 = f(x0)

@name("Fixed-point iteration")
@url("https://en.wikipedia.org/wiki/Fixed-point_iteration")
@description("Compute the approximate fixed point of a function $f: X \\rightarrow X$ starting from $x_0$, until $|f(x) - x| < ε$.")
@example("fn function(x) = x/2 - 1\nfixed_point(function, 0, 0.01)", "Compute the fixed poin of $f(x) = x/2 -1$.")
fn fixed_point<X: Dim>(f: Fn[(X) -> X], x0: X, ε: X) =
  _fixed_point(f, x0, ε, 100)