65x penalty in performance for using float instead of RealNumber

[Pablo Angulo]

The function random() returns a "float", but 1.0*random() is a "RealNumber?". The following code:

%time
#1
N=5000
x=random()
for c in xrange(N):
    kk = exp(x)

takes 5.24 seconds, while

%time
#1
N=5000
x=random()*1.0
for c in xrange(N):
    kk = exp(x)

takes 0.08

[Pablo Angulo]

It's a bit worse:

x=random()
timeit('exp(x)')

125 loops, best of 3: 7.88 ms per loop

while

x=random()*1.0
timeit('exp(x)')

625 loops, best of 3: 48.3 µs per loop

so the ratio is rather around 150x.

[Nils Bruin]

note that "float" is the standard python float type, whereas RealNumber? is a preferred type for sage. Furthermore, "exp" is a general sage function that can do all kinds of "exponentiation" (symbolic, numeric etc.), and that incurs overhead. Apparently a particularly bad one for "float" types. Setting the base line:

sage: x=random()
sage: y=RealNumber(x)
sage: z=RDF(x)
sage: timeit('exp(x)')
625 loops, best of 3: 1.15 ms per loop
sage: timeit('exp(y)')
625 loops, best of 3: 10.3 µs per loop
sage: timeit('exp(z)')
625 loops, best of 3: 3.52 µs per loop

Using python's own "exp" is the fastest:

sage: timeit('math.exp(x)')
625 loops, best of 3: 373 ns per loop

You can shave off some time from the RealNumber? one too by calling a method specific for it. It's slower, but RealNumber? has much more functionality (also multiprecision)

sage: timeit('y.exp()')
625 loops, best of 3: 6.28 µs per loop

RDF is supposed to be Sage's version of "double precision floats" and is indeed comparable:

sage: timeit('z.exp()')
625 loops, best of 3: 704 ns per loop

If you don't mind a float, math.exp seems to receive a fairly efficiently coerced float from either RealNumber? or RDF

sage: timeit('math.exp(y)')
625 loops, best of 3: 510 ns per loop
sage: timeit('math.exp(z)')
625 loops, best of 3: 419 ns per loop

It would be nice if the generic "exp" would find a bit faster codepaths for some of these types, but I wouldn't consider the current behaviour a "defect".

[Marc Mezzarobba]

Fixed?

sage: sage: x=random()
sage: sage: y=RealNumber(x)
sage: sage: z=RDF(x)
sage: sage: timeit('exp(x)')
625 loops, best of 3: 17.7 µs per loop
sage: sage: timeit('exp(y)')
625 loops, best of 3: 5.9 µs per loop
sage: sage: timeit('exp(z)')
625 loops, best of 3: 2.29 µs per loop

[Vincent Delecroix]

Replying to mmezzarobba:

Fixed?

sage: sage: x=random()
sage: sage: y=RealNumber(x)
sage: sage: z=RDF(x)
sage: sage: timeit('exp(x)')
625 loops, best of 3: 17.7 µs per loop
sage: sage: timeit('exp(y)')
625 loops, best of 3: 5.9 µs per loop
sage: sage: timeit('exp(z)')
625 loops, best of 3: 2.29 µs per loop

Half

sage: x = random()
sage: timeit('exp(x)', number=50000)
50000 loops, best of 3: 8.15 µs per loop
sage: from math import exp as math_exp
sage: timeit('math_exp(x)', number=50000)
50000 loops, best of 3: 290 ns per loop

just 30x slower. Better than the 65x that was reported for the difference between float and RR.

[Jeroen Demeyer]

92x on my system:

sage: timeit('exp(x)', number=100000, repeat=10)
100000 loops, best of 10: 8.55 µs per loop
sage: timeit('math_exp(x)', number=100000, repeat=10)
100000 loops, best of 10: 92.1 ns per loop

[Marc Mezzarobba]

Wait, what exactly are we trying to measure? I thought this ticket was about the overhead of exp() (I mean sage.functions.log.exp) for some argument types. If we allow ourselves to call the “right” function or method for each type, then both RDF(x).exp() and math.exp(x) are fast when applicable.

[Vincent Delecroix]

Agreed that it is not exactly the same issue... but still there is a problem for exp being very slow. So we can either open a new ticket for that slightly similar issue or precise the issue here.

[Ralf Stephan]

I think there was progress from ​https://github.com/pynac/pynac/issues/108

I don't think you can get better than a few µs for symbolic exp(), there is too much overhead from symbolic/function.pyx even for GinacFunctions.

[Maarten Derickx]

I agree that the original problem is fixed.