"""
Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that
f(a) * f(b) < 0 and f(x) is continuous in [a, b].
Here f(x) represents algebraic or transcendental equation.
Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)

https://en.wikipedia.org/wiki/Bisection_method
"""


def equation(x: float) -> float:
 """
 >>> equation(5)
 -15
 >>> equation(0)
 10
 >>> equation(-5)
 -15
 >>> equation(0.1)
 9.99
 >>> equation(-0.1)
 9.99
 """
 return 10 - x * x


def bisection(a: float, b: float) -> float:
 """
 >>> bisection(-2, 5)
 3.1611328125
 >>> bisection(0, 6)
 3.158203125
 >>> bisection(2, 3)
 Traceback (most recent call last):
 ...
 ValueError: Wrong space!
 """
 # Bolzano theory in order to find if there is a root between a and b
 if equation(a) * equation(b) >= 0:
 raise ValueError("Wrong space!")

 c = a
 while (b - a) >= 0.01:
 # Find middle point
 c = (a + b) / 2
 # Check if middle point is root
 if equation(c) == 0.0:
 break
 # Decide the side to repeat the steps
 if equation(c) * equation(a) < 0:
 b = c
 else:
 a = c
 return c


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 print(bisection(-2, 5))
 print(bisection(0, 6))