import math
from dataclasses import dataclass


@dataclass
class Approximate:

    ai: float;  af: float
    da: float;  n : int

    # Default values
    aa: float = 0
    ei: float = -1
    a : float = 0
    e : float = 0
    i : int   = 0

    done: bool = False
    stop: bool = False

    def step(self):

        if (self.ei < 0) or (self.ei > self.e):

            self.ei = self.e
            self.aa = self.a

        if (self.stop):

            self.i += 1

            if (self.i >= self.n):

                self.done = True
                self.a = self.aa

                return  # Max iter

            # Restrict to window around 'solution'
            self.ai = self.aa - self.da
            self.af = self.aa + self.da

            self.a = self.ai

            # Increase accuracy
            self.da *= 0.1
            self.ai += self.da
            self.af -= self.da

            self.stop = False

        else:

            # Probe some points in [ai,af] with step da
            self.a = self.a + self.da

            if (self.a > self.af):

                self.a = self.af
                self.stop = True