Equation solver

module utils
implicit none

  interface
    function f_if(x)
      real :: f_if, x
    end function f_if
  end interface

contains

  !Custom equation: f = ...
  function f(x)
    real :: f, x

    f = x**3 + (1.1 * x**2) + 0.9 * x - 1.4
  end function f

  function next_x(x, x_1, fn)
    real :: next_x, x, x_1
    procedure(f_if), pointer :: fn

    next_x = x_1 - (fn(x_1) * (x - x_1))/(fn(x) - fn(x_1))
  end function next_x

  function solve(x, x_1, fn, eps)
    real :: solve, root, root_1, delta, eps_
    real, intent(inout) :: x, x_1
    real, optional :: eps
    integer :: i = 0
    procedure(f_if), pointer :: fn

    if (.not. present(eps)) then
      eps_ = 0.001
    else
      eps_ = eps
    end if
    do
      root = next_x(x, x_1, fn)
      if (i /= 0 ) then
        delta = abs(root - root_1)
        if (delta <= eps_) then
          exit
        end if
      end if
      i = i + 1
      x_1 = x
      x = root
      root_1 = root
    end do
    solve = root
  end function solve

end module utils

program eqsolver
  use utils
  implicit none
  real :: x=1., x_1=0.
  procedure(f_if), pointer :: fn => f
  !write(*,*) next_x(1., 0., fn)
  write(*,*) solve(x, x_1, fn)
end program eqsolver