Wrong result while calculating big powers

[JK2Kgit]

Reporting a bug

• I have tried using the latest released version of Numba (most recent is
  visible in the change log (https://github.com/numba/numba/blob/master/CHANGE_LOG).
• I have included a self contained code sample to reproduce the problem.
  i.e. it's possible to run as 'python bug.py'.

While performing calculation on big powers function started to return diffrent result after adding @njit

Reproducabe with this code

from numba import njit

def calc(prime, i):
    return (2 ** (3 ** i) - i) % prime

@njit
def ncalc(prime, i):
    return (2 ** (3 ** i) - i) % prime

print(calc(3, 6))
print(ncalc(3, 6))

[JK2Kgit]

More Verbose example

from numba import njit

def calc(prime, i):
    print(prime, i)
    x = 3 ** i
    y = 2 ** x
    z = y - i
    w = z % prime
    print(x, "\n", y, "\n", z, "\n", w)
    return (2 ** (3 ** i) - i) % prime

@njit
def ncalc(prime, i):
    print(prime, i)
    x = 3 ** i
    y = 2 ** x
    z = y - i
    w = z % prime
    print(x, "\n", y, "\n", z, "\n", w)
    return (2 ** (3 ** i) - i) % prime

print(calc(3, 11))
print('\n\n')
print(ncalc(3, 11))

After analiazying that looks like buffer overflow

[stuartarchibald]

Thanks for the report. Unfortunately for the case presented, Numba does not support big integers. As a result the calculations overflow the 64bit int (which is the maximum size Numba supports). Closing as a duplicate of #5005, there are some suggestions there about calling into GMP as a potential workaround.