Does GMPY2 (or GMP) have a pow() function?

Question

GMPY2 (or GMP) has a powmod function but I can't find anything for regular exponentiation aside from python's native pow. Does a function like this exist for mpz integers?

Answer 1

Just use Python's standard pow() function or the exponentiation ** operator. GMPY2's mpz type overloads all the standard special methods so you should just be able to use standard Python commands.

For example:

>>> from gmpy2 import mpz
>>> pow(mpz(3),7)
mpz(2187)
>>> pow(mpz(3),7,13)
mpz(3)
>>> mpz(3)**7
mpz(2187)
>>> 

The same holds true for divmod(), etc.

Answer 2

Some performance information:

gmpy2 pow is twice as fast as python's pow, even when factoring in construction:

>>> timeit.timeit('pow(98765, 10)', number=100000)
0.048412954514788
>>> timeit.timeit('pow(gmpy2.mpz(98765), 10)', number=100000, setup='import gmpy2')
0.024286470230094892

You can use the built-in pow(x,y,modulus) on an mpz, but using powmod instead is a about 10% faster.

>>> timeit.timeit('pow(gmpy2.mpz(987654321),1000,100003)', 
number=100000, setup='import gmpy2')
0.057212181510976734
>>> timeit.timeit('gmpy2.powmod(987654321,1000,100003)', 
number=100000, setup='import gmpy2')
0.04513445007546579
>>> timeit.timeit('pow(987654321,1000,100003)', 
number=100000, setup='import gmpy2')
0.15511784474188062

The gmpy2 version is much faster than the native python with a modulus (sometimes as much as 10 times faster). Using powmod is only marginally faster than using pow/mpz, because of the construction time of the mpz.

If you already have an mpz, powmod and pow are aboslutely equivalent.