sqrt.py

# Given r, real number in [0, inf)
# Return the sqrt of r without sqrt function

def _mid(left, right):
    # Avoiding possible overflow that
    # l + r / 2 could cause
    return (right - left)/2 + left

def sqrt(r):
    # Assumption: r is real and >= 0
    if r < 1:
        left = r
        right = 1
    else:
        left = 1
        right = r

    max_iterations = 1000
    i = 0
    tol = 1e-9
    while True:
        i+=1
        if i == max_iterations:
            break
        mid = _mid(left, right)
        est = mid**2
        if abs(r - est) <= tol:
            return mid
        elif est > r:
            right = mid
        else:
            left = mid
    raise ValueError(f"Solution not found after {max_iterations}. Current estimate is {est}")

x = sqrt(.5)
print(x)
print(sqrt(100))
print(sqrt(509))