import math

def function(beta):
    L = 1.0
    H2 = 50.0
    return (beta * math.tan(beta * L)) - H2
    
def testFunction(x):
    L = 1.0
    return math.cos(2 * L * x)

def expectedNumberIterations(upperBound, lowerBound, threshold):
    return ((math.log10(upperBound - lowerBound)) - (math.log10(threshold))) \
                                                              / (math.log10(2))
                                                              
def findRoots():
    lowerBound = 0.0
    upperBound = 18.0
    rangeThreshold = math.pow(10, -3)
    
    root = None
    roots = []
    
    stepSize = upperBound - lowerBound
    k = 1.0
    
    while(stepSize >= rangeThreshold):
        rangeLowerBound = lowerBound
        rangeUpperBound = rangeLowerBound + stepSize
        while (rangeUpperBound <= upperBound):
            root = bisectionMethod(rangeLowerBound, rangeUpperBound)
            if((root is not None) and ((root in roots) != True) and \
                                                   (testFunction(root) != -1)):
                roots.insert(len(roots), root)
            root = None
            rangeLowerBound = rangeUpperBound
            rangeUpperBound = rangeUpperBound + stepSize
        stepSize = ((lowerBound + upperBound) / math.pow(2, k)) - lowerBound
        k = k + 1
        
    return roots
            
def bisectionMethod(lowerBound, upperBound):
    threshold = math.pow(10, -30)
    absoluteError = 1

    k = 0.0
    maxNumberIter = round(expectedNumberIterations(upperBound, lowerBound, \
                                                                    threshold))

    if ((function(lowerBound) * function(upperBound)) < 0):
        while ((absoluteError >= threshold) or (k <= maxNumberIter)):
            midPoint = (upperBound + lowerBound) / 2.0
    
            if ((function(lowerBound) * function(midPoint)) < 0.0):
                upperBound = midPoint
            elif ((function(lowerBound) * function(midPoint)) > 0.0):
                lowerBound = midPoint
            else:
                return midPoint
    
            absoluteError = math.fabs((((upperBound + lowerBound) / 2.0) - \
                               (midPoint)) / ((upperBound + lowerBound) / 2.0))
            k = k + 1.0
    
        return midPoint
    else:
        return None