Comment #8 on issue 1946 by asmeurer: Recursion error with
SYMPY_GROUND_TYPES=sympy (caching problem)
http://code.google.com/p/sympy/issues/detail?id=1946
I can confirm your results:
In [11]: %timeit type(a) in (int, long)
1000000 loops, best of 3: 473 ns per loop
In [12]: %timeit type(b) in (int, long)
1000000 loops, best of 3: 477 ns per loop
In [13]: %timeit type(c) in (int, long)
100000 loops, best of 3: 3.03 us per loop
In [14]: %timeit type(d) in (int, long)
100000 loops, best of 3: 3.05 us per loop
In [15]: %timeit isinstance(a, (int, long))
1000000 loops, best of 3: 384 ns per loop
In [16]: %timeit isinstance(b, (int, long))
1000000 loops, best of 3: 727 ns per loop
In [17]: %timeit isinstance(c, (int, long))
1000000 loops, best of 3: 992 ns per loop
In [18]: %timeit isinstance(d, (int, long))
1000000 loops, best of 3: 988 ns per loop
It looks like isinstance just takes longer to short-circuit (according to
the docstring, it's equivalent to
isinstance(a, int) or isinstance(b, long)):
In [22]: %timeit isinstance(a, (long, int))
1000000 loops, best of 3: 699 ns per loop
In [23]: %timeit isinstance(b, (long, int))
1000000 loops, best of 3: 402 ns per loop
In [24]: %timeit type(a) in (long, int)
1000000 loops, best of 3: 506 ns per loop
In [25]: %timeit type(b) in (long, int)
1000000 loops, best of 3: 415 ns per loop
As for mpz, in master I get:
In [9]: Integer(123) == mpz(123)
Out[9]: True
which is basically because sympify(mpz(123)) works (though it returns a
Real!).
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