def eps(base, n): # n = Anzahl Stellen der Mantisse
    return 0.5 * (base ** (1-n))


def bitsMantiss(base):
    last_x = 0
    x = 1.5
    n = 0
    while x > 1:
        last_x = x
        x = x - (x - 1) / base
        n = n + 1
    return n, last_x

def largestNumber(bitsMantiss):
    x = 0.0
    for i in range(bitsMantiss):
        x = x + 2 ** i
    return x

def largestNumber_eps(eps, n):
    return eps * 2**(2*n) - 1


bitsMan = bitsMantiss(2)
epsVal = eps(2, bitsMan[0])
largest = largestNumber(bitsMan[0])
largest_eps = largestNumber_eps(epsVal, bitsMan[0])


print(f'eps: {epsVal}')
print(f'Bits Mantiss: {bitsMan[0]}')
print(f'Smallest Number 1 + eps > 1: {bitsMan[1]}')
print(f'largest Number 1 + qmax > qmax: {largest}')
print(f'largest Number 1 + qmax > qmax (calculated by eps: {largest_eps}')