"""
Exercise 2.19 from "A primer on..."
Demonstrate the impact of roundoff
error by taking n repeated square roots
followed by n squares. This should bring back
the same number, but for large values of
n the result is destroyed by roundoff error. 
"""


from numpy import sqrt
for n in range(1, 60):
    r = 2.0
    for i in range(n):
        r = sqrt(r)
    for i in range(n):
        r = r**2
    print(f'{n} times sqrt and **2: {r:.16f}')

"""
Terminal> python repeated_sqrt.py 
1 times sqrt and **2: 2.0000000000000004
2 times sqrt and **2: 1.9999999999999996
3 times sqrt and **2: 1.9999999999999996
4 times sqrt and **2: 1.9999999999999964
...
45 times sqrt and **2: 1.9887374575497223
46 times sqrt and **2: 1.9887374575497223
47 times sqrt and **2: 1.9887374575497223
48 times sqrt and **2: 1.9887374575497223
49 times sqrt and **2: 1.8682459487159784
50 times sqrt and **2: 1.6487212645509468
51 times sqrt and **2: 1.6487212645509468
52 times sqrt and **2: 1.0000000000000000
53 times sqrt and **2: 1.0000000000000000
54 times sqrt and **2: 1.0000000000000000
55 times sqrt and **2: 1.0000000000000000
56 times sqrt and **2: 1.0000000000000000
57 times sqrt and **2: 1.0000000000000000
58 times sqrt and **2: 1.0000000000000000
59 times sqrt and **2: 1.0000000000000000
"""