Question

I’m trying to convert some C++ to Python.

The C++ can be found at

https://gist.github.com/1635288

from prime import prime
from fractions import gcd
from copy import copy
def phi(n, primes):
    if n < 2:
        return 0

    if n in primes:
        return n - 1

    if (n & 1) == 0:
        m = n >> 1
        #return ~(m & 1) ? phi(m, primes) << 1 : phi(m, primes)
        if ~(m & 1):
            return phi(m, primes) << 1
        else:
            return phi(m, primes)

    for i in primes:
        if i > n:
            break

        if n % i:
            continue

        m = copy(i)
        o = n / m
        d = gcd(m, o)
        #return d == 1 ? phi(m) * phi(o) : phi(m) * phi(o) * d / phi(d)
        if d == 1:
            return phi(m, primes) * phi(o, primes)
        else:
            return phi(m, primes) * phi(o, primes) * d / phi(d, primes)

primes = []
for i in range(3, 10000000, 2):
    if prime(i):
        primes.append(i)

for i in range(80, 90): # a test to see if I am getting correct results
    print phi(i, primes)
    # returns   64, 54, 80, 82, 48, 64, 84, 56, 80, 88
    # should be 32, 54, 40, 82, 24, 64, 42, 56, 40, 88

Basically, the function returns correct phi values for odd n, but returns double the correct value for even n. I suspect that where I am going wrong is at

m = copy(i)

whereas the C++ is

int m = *p; 

I have looked up Wikipedia and seen that this is defining m as the value p is pointing to. Is this the problem? If not, what is?

Answer 1

I think you should use if not (m & 1), rather that if ~(m & 1), since the former is a check for odd/even numbers, while the latter would only return false if you pass -1 to it.

Tilde (~) is the bitwise negation operator. For integer values it holds that ~x == -x-1, which in your case won’t happen at all.