Precision in a logarithmic function with Python

Question

I am trying to plot the logarithmic function: x*log(1+1/x) for very large values of x. I have checked for few terms since the overall plot was not good and the problem seems to be that although this function should never be higher than 1, for some points it becomes larger than 1. I believe it has something to do with accuracy of the log function.

for the following values of x:

[ 5.4380181e+11  3.1688845e+12  4.5195668e+13  7.4634268e+14  1.2442192e+16
  2.0754228e+17  3.4624427e+18  5.787843e+19  9.9925409e+20  2.6069079e+22]

I get for x*np.log(1+1/x):

[ 0.99999999  0.99999989  0.99999774  0.9999925  0.99959801  0.99007829
  1.1261964  0.0  0.0  0.0]

As you can see the 7th term is bigger than 1.

I have tried using log1p instead but that gives non-sensical answers.

I have also tried using np.float128() but I get exactly the same results as above.

Any ideas?

Thanks a lot!

What have you tried with log1p? It should be able to give the correct result. — kennytm
– kennytm, Commented Jan 28, 2017 at 11:42

Torkel Bjørnson-Langen · Accepted Answer · 2017-01-28 12:00:53Z

1

Read the manual page for log1p. It does not take the same argument as log. I guess that explains the "non-sensical answers".

It works for me:

l = [5.4380181e+11, 3.1688845e+12, 4.5195668e+13, 7.4634268e+14, 1.2442192e+16, 2.0754228e+17, 3.4624427e+18, 5.787843e+19, 9.9925409e+20, 2.6069079e+22]

[n*log1p(1/n) for n in l]

Output:

[0.9999999999990805,
0.9999999999998422,
0.9999999999999888,
0.9999999999999992,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0]

answered Jan 28, 2017 at 12:00

Torkel Bjørnson-Langen

1,02413 silver badges17 bronze badges

Sign up to request clarification or add additional context in comments.

3 Comments

Andrés Over a year ago

Hi, thanks a lot! Yes that seems to work now, I feel so stupid. However, I get all 1.0, even using np.float128. Do you know why?

Torkel Bjørnson-Langen Over a year ago

@Andrés Glad to help. No need to feel stupid; all programmers do these kinds of mistakes from time to time. Numpy defaults to 8 digit of precision for floating point output, so what you see is not whats actually there :) The numbers are rounded up to 1.0. Try changing Numpy's default with np.set_printoptions (precision=20) or print them an other way.

Andrés Over a year ago

Awesome! Thanks a lot!

Collectives™ on Stack Overflow

Precision in a logarithmic function with Python

1 Answer 1

3 Comments

Your Answer

Hot Network Questions

Collectives™ on Stack Overflow

1 Answer 1

3 Comments

Your Answer

Sign up or log in

Post as a guest

Related