Unit 5 Solution Computer Science Students

Sample Answer for Programming Assignment Unit 5

 

Python Program

import math def mysqrt(a):

x = a

while True:

y = (x + a/x) / 2.0 if y == x:

break x = y

return x

 

def test_square_root(): a = 1

while a < 26:

mine = mysqrt(a) maths = math.sqrt(a)

print("a =", a, "| mysqrt(a) =", mine, "| math.sqrt(a) =", maths, "| diff =", abs(mine-maths))

a = a + 1 test_square_root()

 

Output for Python 3

 

a = 1 | mysqrt(a) = 1 | math.sqrt(a) = 1.0 | diff = 0.0 a = 2 | mysqrt(a) = 1.414213562373095 | math.sqrt(a) = 1.4142135623730951 | diff = 2.220446049250313e-16

a = 3 | mysqrt(a) = 1.7320508075688772 | math.sqrt(a) = 1.7320508075688772 | diff = 0.0

a = 4 | mysqrt(a) = 2.0 | math.sqrt(a) = 2.0 | diff = 0.0 a = 5 | mysqrt(a) = 2.23606797749979 | math.sqrt(a) = 2.23606797749979 | diff = 0.0

a = 6 | mysqrt(a) = 2.449489742783178 | math.sqrt(a) = 2.449489742783178 | diff = 0.0

a = 7 | mysqrt(a) = 2.6457513110645907 | math.sqrt(a) = 2.6457513110645907 | diff = 0.0

a = 8 | mysqrt(a) = 2.82842712474619 | math.sqrt(a) = 2.8284271247461903 | diff = 4.440892098500626e-16

a = 9 | mysqrt(a) = 3.0 | math.sqrt(a) = 3.0 | diff = 0.0


a = 10 | mysqrt(a) = 3.162277660168379 | math.sqrt(a) = 3.1622776601683795 | diff = 4.440892098500626e-16

a = 11 | mysqrt(a) = 3.3166247903554 | math.sqrt(a) = 3.3166247903554 | diff = 0.0

a = 12 | mysqrt(a) = 3.4641016151377544 | math.sqrt(a) = 3.4641016151377544 | diff = 0.0

a = 13 | mysqrt(a) = 3.6055512754639896 | math.sqrt(a) = 3.605551275463989 | diff = 4.440892098500626e-16

a = 14 | mysqrt(a) = 3.7416573867739413 | math.sqrt(a) = 3.7416573867739413 | diff = 0.0

a = 15 | mysqrt(a) = 3.872983346207417 | math.sqrt(a) = 3.872983346207417 | diff = 0.0

a = 16 | mysqrt(a) = 4.0 | math.sqrt(a) = 4.0 | diff = 0.0 a = 17 | mysqrt(a) = 4.123105625617661 | math.sqrt(a) = 4.123105625617661 | diff = 0.0

a = 18 | mysqrt(a) = 4.242640687119286 | math.sqrt(a) = 4.242640687119285 | diff = 8.881784197001252e-16

a = 19 | mysqrt(a) = 4.358898943540673 | math.sqrt(a) = 4.358898943540674 | diff = 8.881784197001252e-16

a = 20 | mysqrt(a) = 4.47213595499958 | math.sqrt(a) = 4.47213595499958 | diff = 0.0

a = 21 | mysqrt(a) = 4.58257569495584 | math.sqrt(a) = 4.58257569495584 | diff = 0.0

a = 22 | mysqrt(a) = 4.69041575982343 | math.sqrt(a) = 4.69041575982343 | diff = 0.0

a = 23 | mysqrt(a) = 4.795831523312719 | math.sqrt(a) = 4.795831523312719 | diff = 0.0

a = 24 | mysqrt(a) = 4.898979485566356 | math.sqrt(a) = 4.898979485566356 | diff = 0.0

a = 25 | mysqrt(a) = 5.0 | math.sqrt(a) = 5.0 | diff = 0.0

 

 

Output for Python 2

 

('a =', 1, '| mysqrt(a) =', 1, '| math.sqrt(a) =', 1.0, '| diff =', 0.0)

('a =', 2, '| mysqrt(a) =', 1.414213562373095, '|

math.sqrt(a) =', 1.4142135623730951, '| diff =', 2.220446049250313e-16)

('a =', 3, '| mysqrt(a) =', 1.7320508075688772, '| math.sqrt(a) =', 1.7320508075688772, '| diff =', 0.0)

('a =', 4, '| mysqrt(a) =', 2.0, '| math.sqrt(a) =', 2.0, '| diff =', 0.0)

('a =', 5, '| mysqrt(a) =', 2.23606797749979, '|

math.sqrt(a) =', 2.23606797749979, '| diff =', 0.0) ('a =', 6, '| mysqrt(a) =', 2.449489742783178, '|

math.sqrt(a) =', 2.449489742783178, '| diff =', 0.0)


('a =', 7, '| mysqrt(a) =', 2.6457513110645907, '| math.sqrt(a) =', 2.6457513110645907, '| diff =', 0.0) ('a =', 8, '| mysqrt(a) =', 2.82842712474619, '|

math.sqrt(a) =', 2.8284271247461903, '| diff =', 4.440892098500626e-16)

('a =', 9, '| mysqrt(a) =', 3.0, '| math.sqrt(a) =', 3.0, '| diff =', 0.0)

('a =', 10, '| mysqrt(a) =', 3.162277660168379, '|

math.sqrt(a) =', 3.1622776601683795, '| diff =', 4.440892098500626e-16)

('a =', 11, '| mysqrt(a) =', 3.3166247903554, '|

math.sqrt(a) =', 3.3166247903554, '| diff =', 0.0) ('a =', 12, '| mysqrt(a) =', 3.4641016151377544, '| math.sqrt(a) =', 3.4641016151377544, '| diff =', 0.0) ('a =', 13, '| mysqrt(a) =', 3.6055512754639896, '|

math.sqrt(a) =', 3.605551275463989, '| diff =', 4.440892098500626e-16)

('a =', 14, '| mysqrt(a) =', 3.7416573867739413, '| math.sqrt(a) =', 3.7416573867739413, '| diff =', 0.0) ('a =', 15, '| mysqrt(a) =', 3.872983346207417, '|

math.sqrt(a) =', 3.872983346207417, '| diff =', 0.0)

('a =', 16, '| mysqrt(a) =', 4.0, '| math.sqrt(a) =', 4.0, '| diff =', 0.0)

('a =', 17, '| mysqrt(a) =', 4.123105625617661, '|

math.sqrt(a) =', 4.123105625617661, '| diff =', 0.0) ('a =', 18, '| mysqrt(a) =', 4.242640687119286, '|

math.sqrt(a) =', 4.242640687119285, '| diff =', 8.881784197001252e-16)

('a =', 19, '| mysqrt(a) =', 4.358898943540673, '|

math.sqrt(a) =', 4.358898943540674, '| diff =', 8.881784197001252e-16)

('a =', 20, '| mysqrt(a) =', 4.47213595499958, '|

math.sqrt(a) =', 4.47213595499958, '| diff =', 0.0) ('a =', 21, '| mysqrt(a) =', 4.58257569495584, '|

math.sqrt(a) =', 4.58257569495584, '| diff =', 0.0) ('a =', 22, '| mysqrt(a) =', 4.69041575982343, '|

math.sqrt(a) =', 4.69041575982343, '| diff =', 0.0) ('a =', 23, '| mysqrt(a) =', 4.795831523312719, '|

math.sqrt(a) =', 4.795831523312719, '| diff =', 0.0) ('a =', 24, '| mysqrt(a) =', 4.898979485566356, '|

math.sqrt(a) =', 4.898979485566356, '| diff =', 0.0)

('a =', 25, '| mysqrt(a) =', 5.0, '| math.sqrt(a) =', 5.0, '| diff =', 0.0)


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