comb: any value above 40 returns infinity? not sure why

Question

I'm completing a project euler problem, but this function returns infinity for any value over 40.

from scipy.special import comb
def B(x):
    product = 1
    for i in range(x + 1):
        product *= comb(x, i)
    return product

what I'm getting back

  problem_650.py:10: RuntimeWarning: overflow encountered in double_scalars
  product *= comb(x, i)
  inf

any help with fixing this would be appreciated.

You'll understand better if you remove the `int()` conversion. See here: https://stackoverflow.com/questions/7559595/python-runtimewarning-overflow-encountered-in-long-scalars — olinox14, Jul 04 '19 at 10:30
`1.7976931348623157e+308` is the largest possible float. Anything over it will be `inf`. Python's integers are only limited by memory; if you don't actually need floating point result, there's no benefit (except speed) in using floats for calculation. — Amadan, Jul 04 '19 at 10:31
I removed the integer conversion to make it clearer, still getting infinity — Edward S Logsdail, Jul 04 '19 at 10:35
@EdwardSLogsdail did you notice, that comb has a flag exact=False (false is the default and I am almost sure if you do numbertheoretic stuff, that you don't just want approximations to be caluclated) — jottbe, Jul 04 '19 at 10:38

jottbe · Answer 1 · 2019-07-04T10:40:23.130

4

Try this:

def B(x):
    product = 1
    for i in range(x + 1):
        product *= comb(x, i, exact=True)
    return int(product)

B(40)

It most likely is slower, but as you do stuff from project Euler I guess you don't want to approximate the comb values, but use the exact ones.

edited Jul 04 '19 at 10:40

answered Jul 04 '19 at 10:39

jottbe

Nicely spotted! – Amadan Jul 04 '19 at 10:39
1

If exact is False, then floating point precision is used, otherwise exact long integer is computed. – AnkushRasgon Jul 04 '19 at 10:48
AnkushRasgon: yes that's it. I guess with exact=False, they use the fact, that the binomial coefficients can be approximated by the normal distribution as a deep result of statistics. – jottbe Jul 04 '19 at 10:55

1 Answers1