find_best_x.py

'''
given a function and a value y, find the bext x for which |f(x) - y| is minimal
'''

def get_boundaries(func, y):

    # x * x > max_value #overflow
    # sqrt(max_value) < x # next x will be overflow
    # in python this is not an issue but it could be in some other languages
    
    x = 1
    prev = 0
    while func(x) < y
        prev = x
        x = x * x

    return prev, x

def get_best_value(func, y):

    left, right = get_boundaries(func, y)
    sol = left
    while left <= right:
        mid = left + (right - left) / 2
        if func(mid) <= y:
            left = mid + 1
        else func(mid) > y:
            right = mid - 1
        
        if math.abs(func(mid) - y) < math.abs(func(sol) - y):
            sol = mid
    
    return sol