Speed up Python2 nested loops with XOR

Question

The answer of the question this is marked duplicate of is wrong and does not satisfy my needs.

My code aims to calculate a hash from a seri

Answer 1

I am afraid that, with the input you have in answer(2000000000,10**4) you'll never finish "in time".

You can get a pretty significant speed up by improving the inner loop, not updating the c variable every time and using xrange instead of range, like this:

def answer(start, length):
    val=0
    c=0
    for i in range(length):
        for j in range(length):
            if j < length-i:
                val^=start+c
            c+=1
    return val


def answer_fast(start, length):
    val = 0
    c = 0
    for i in xrange(length):
        for j in xrange(length - i):
            if j < length - i:
                val ^= start + c + j
        c += length
    return val


# print answer(10, 20000)
print answer_fast(10, 20000)

The profiler shows that answer_fast is about twice as fast:

> python -m cProfile script.py
366359392
        20004 function calls in 46.696 seconds

Ordered by: standard name

ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000   46.696   46.696 script.py:1()
        1   44.357   44.357   46.696   46.696 script.py:1(answer)
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
    20001    2.339    0.000    2.339    0.000 {range}

> python -m cProfile script.py
366359392
        3 function calls in 26.274 seconds

Ordered by: standard name

ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000   26.274   26.274 script.py:1()
        1   26.274   26.274   26.274   26.274 script.py:12(answer_fast)
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

But if you want major speed ups (orders of magnitute) you should consider rewriting your function in Cython.

Here is the "cythonized" version of it:

def answer(int start, int length):
    cdef int val = 0, c = 0, i, j
    for i in xrange(length):
        for j in xrange(length - i):
            if j < length - i:
                val ^= start + c + j
        c += length
    return val

With the same input parameters as above, it takes less than 200ms insted of 20+ seconds, which is a 100x speedup.

> ipython

In [1]: import pyximport; pyximport.install()
Out[1]: (None, )

In [2]: import script2

In [3]: timeit script2.answer(10, 20000)
10 loops, best of 3: 188 ms per loop

With your input parameters, it takes 58ms:

In [5]: timeit script2.answer(2000000000,10**4)
10 loops, best of 3: 58.2 ms per loop