"""
Ex 2.20 from "A primer on...
Reduce a number eps until the expression
1 + eps == 1 is True
The last value of eps is the smallest
number that can be represented on the
computer.
"""


eps = 1.0

while 1.0 != 1.0 + eps:
    print("...............", eps)
    eps = eps / 2.0
print("final eps:", eps)

"""
Terminal> python machine_zero.py 
............... 1.0
............... 0.5
............... 0.25
............... 0.125
............... 0.0625
............... 0.03125
............... 0.015625
............... 0.0078125
............... 0.00390625
............... 0.001953125
............... 0.0009765625
............... 0.00048828125
............... 0.000244140625
............... 0.0001220703125
...
............... 5.684341886080802e-14
............... 2.842170943040401e-14
............... 1.4210854715202004e-14
............... 7.105427357601002e-15
............... 3.552713678800501e-15
............... 1.7763568394002505e-15
............... 8.881784197001252e-16
............... 4.440892098500626e-16
............... 2.220446049250313e-16
final eps: 1.1102230246251565e-16
"""