sign(integer) is horribly slow

[Paul Zimmermann]

Noticed in Sage 4.8:

sage: a=-17
sage: %timeit s = sign(a)  
125 loops, best of 3: 757 µs per loop
sage: %timeit s = a//abs(a) 
625 loops, best of 3: 246 ns per loop

thus computing sign(a) with a//abs(a) is 3000 faster!!!

[D.S. McNeil]

The fall-through into constructing a ComplexIntervalField? is expensive. Maybe it makes sense to give the obvious suspects (ZZ, QQ, RR, etc.) a .sign() method.

[Karl-Dieter Crisman]

Try it out and see what the speedup is. I'd be happy to review something like that.

[D.S. McNeil]

Hmmm. Well, it helps, but you still lose a lot going from something(sign) to sign(something):

# unpatched
sage: %timeit s = sign(2)
5 loops, best of 3: 427 µs per loop

# with .sign() using mpz_sgn
sage: %timeit s = sign(2)
625 loops, best of 3: 47.4 µs per loop
sage: %timeit s = 2.sign()
625 loops, best of 3: 352 ns per loop

Function calls are slow. :-/

[D.S. McNeil]

Well, to be clear, it's not function call overhead itself, it's BuiltinFunction?-related.

[Paul Zimmermann]

regarding comment 4, I don't understand since for abs we get similar timings, and even abs(something) is faster:

sage: %timeit s = abs(2)
625 loops, best of 3: 201 ns per loop
sage: %timeit s = 2.abs() 
625 loops, best of 3: 456 ns per loop

Paul

[Paul Zimmermann]

Robert, do you have a hint to solve this?

Paul

[Robert Bradshaw]

Attached a patch to add sign() methods to QQ and ZZ. The sign(x) function is still really slow because

sage: sign.__call__??
    def __call__(self, *args, coerce=True, hold=False):
        """
        Evaluates this function at the given arguments.
        
        We coerce the arguments into symbolic expressions if coerce=True, then
        call the Pynac evaluation method, which in turn passes the arguments to
        a custom automatic evaluation method if ``_eval_()`` is defined.

in other words, it creates SR(x) and a ginac representation of the call before finally calling x.sign(). Ugh, I've filed #13933.

[Paul Zimmermann]

Robert, thanks, I see a speedup of a factor of more than 10 on my example:

sage: a=-17
sage: %timeit s = sign(a)  
625 loops, best of 3: 41 µs per loop
sage: %timeit s = a//abs(a) 
625 loops, best of 3: 257 ns per loop

However I wonder about the need of the "pool" cache for integers in [-5,100], since the speedup is "only" about 20%:

sage: a=100                 
sage: %timeit s = sign(a)   
625 loops, best of 3: 34.7 µs per loop
sage: a=101                 
sage: %timeit s = sign(a)   
625 loops, best of 3: 41.5 µs per loop

Paul

[Robert Bradshaw]

Oops, there was an error in this patch. Yeah, the pool doesn't make a big difference here, but it can be used more genrally as well so I think it's worth including.

[Robert Bradshaw]

I don't think that sign(x) can be made much faster than in #13933 (vs. abs, which is a builtin function), but a.sign() is *much* faster now. It also scales better :)

sage: a = 3^2^20       
sage: %timeit a//abs(a)
 625 loops, best of 3: 129 µs per loop

[Paul Zimmermann]

good work, thanks Robert!

Paul

[Jeroen Demeyer]

Replying to robertwb:

Yeah, the pool doesn't make a big difference here, but it can be used more genrally as well so I think it's worth including.

Sorry, but allocating 103 integers just because somebody might possibly write a patch in the future to use them is silly. For this patch, could we stick just with the integers that we actually use? Your hypothetical futute patch can still enlarge the pool.

[Robert Bradshaw]

apply only this patch

[Robert Bradshaw]

Replying to jdemeyer:

Replying to robertwb:

Yeah, the pool doesn't make a big difference here, but it can be used more genrally as well so I think it's worth including.

Sorry, but allocating 103 integers just because somebody might possibly write a patch in the future to use them is silly. For this patch, could we stick just with the integers that we actually use? Your hypothetical futute patch can still enlarge the pool.

Done.

[Robert Bradshaw]

See also #13981

[Paul Zimmermann]

thank you Robert for the new patch.

Paul