Iterating over np.arange gives incorrect results starting from i = 10

Question


import numpy as np
from math import pi, sqrt, exp, factorial

def pyas(x, sred):
    return sred**x*exp(-sred)/factorial(x)

for i, j in zip(np.arange(20), range(20)):
    print(i, j, pyas(i,10), pyas(j,10))

The question is, why do the values of the pyas() function start to differ?
The output:

0 0 4.5399929762484854e-05 4.5399929762484854e-05
1 1 0.00045399929762484856 0.00045399929762484856
2 2 0.0022699964881242427 0.0022699964881242427
3 3 0.007566654960414142 0.007566654960414142
4 4 0.018916637401035354 0.018916637401035354
5 5 0.03783327480207071 0.03783327480207071
6 6 0.06305545800345118 0.06305545800345118
7 7 0.09007922571921599 0.09007922571921599
8 8 0.11259903214901998 0.11259903214901998
9 9 0.1251100357211333 0.1251100357211333
10 10 0.01764133335640144 0.1251100357211333
11 11 0.001382752728810601 0.11373639611012118
12 12 -6.89413134691794e-05 0.09478033009176766
13 13 9.595669338819968e-06 0.07290794622443666
14 14 1.4396571374678832e-07 0.05207710444602619
15 15 -5.313583114618023e-08 0.03471806963068413
16 16 4.0683489446471356e-09 0.021698793519177577
17 17 2.0030859032126935e-10 0.012763996187751515
18 18 -1.0541774694098002e-11 0.007091108993195286
19 19 -7.394475413970681e-13 0.0037321626279975192

Asked By: Александр Евстратенко

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Source

Answer 1

The difference is that np.arange is iterating fixed size np.int64 values while range is iterating python’s unbounded int. We can see this by choosing the highest value in your range: 19.

>>> foo=10**np.int64(19)
>>> bar=10**19
>>> type(foo), type(bar)
(<class 'numpy.int64'>, <class 'int'>)
>>> foo, bar
(-8446744073709551616, 10000000000000000000)

The numpy version overflowed and wrapped to a negative number with a smaller absolute value. The python int is not limited to 64 bits and can expand indefinately.

Answered By: tdelaney

Iterating over np.arange gives incorrect results starting from i = 10

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