To find out, I turned to the famous Stack Overflow question Why is processing a sorted array faster than an unsorted array? That question has a simple C++ test case where the code runs ~6x as fast on x86 and x86_64 platforms with most compilers, and it's been verified to be similar in other compiled languages like Java, C#, and go.
So, what about Python?
The code
The original question takes a 32K array of bytes, and sums the bytes that are >= 128: long long sum = 0;
/* ... */
for (unsigned c = 0; c < arraySize; ++c)
{
if (data[c] >= 128)
sum += data[c];
}
In Python terms: total = 0
for i in data:
if i >= 128:
total += i
When run with a random array of bytes, this usually takes about 6x as long as when run with the same array pre-sorted. (Your mileage may vary, because there's a way the compiler can optimize away the loop for you, at least on x86 and x86_64, and some compilers will, depending on your optimization settings, figure that out for you. If you want to know more, read the linked question.)So, here's a simple test driver:
import functools
import random
import timeit
def sumbig(data):
total = 0
for i in data:
if i >= 128:
total += i
return total
def test(asize, reps):
data = bytearray(random.randrange(256) for _ in range(asize)
t0 = timeit.timeit(functools.partial(sumbig, data), number=reps)
t1 = timeit.timeit(functools.partial(sumbig, bytearray(sorted(data))), number=reps)
print(t0, t1)
if __name__ == '__main__':
import sys
asize = int(sys.argv[1]) if len(sys.argv) > 1 else 32768
reps = int(sys.argv[2]) if len(sys.argv) > 2 else 1000
test(asize, reps)
I tested this on a few different computers, using Apple pre-installed CPython 2.7.6, Python.org CPython 2.7.8 and 3.4.1, Homebrew CPython 3.4.0, and a custom build off trunk, and it pretty consistently saves about 12% to pre-sort the array. Nothing like the 84% savings in C++, but still, a lot more than you'd expect. After all, we're doing roughly 65x as much work in the CPython ceval loop than we were doing in the C++ loop, so you'd think the difference would be lost in the noise, and we're also doing much larger loops, so you'd think branch prediction wouldn't be helping as much in the first place. But if you watch the BR_MISP counters in Instruments, or do the equivalent with cachegrind, you'll see that it's mispredicting a lot more branches for the unsorted case than the sorted case—as in 1.9% of the total conditional branches in the ceval loop instead of 0.1%. Presumably, even though this is still pretty small, and nothing like what you see in C, the cost of the misprediction is also higher? It's hard to be sure…You'd expect a much bigger benefit in the other Python implementations. Jython and IronPython compile to JVM and ILR code, which then gets the same kind of JIT recompilation as Java and C#, so if those JITs aren't smart enough to optimize away the branch with a conditional move instruction for Java and C#, they won't be for Python code either. PyPy is JIT-compiling directly from Python—plus, its JIT is itself driven by tracing, which can be hurt by the equivalent of branch misprediction at a higher level. And in fact I found a difference of 54% in Jython 2.5.1, 68% in PyPy 2.3.1 (both the 2.7 and 3.2 versions), and 72% in PyPy 2.4.0 (2.7 only).
C++ optimizations
There are a number of ways to optimize this in C, but they all amount to the same thing: find some way to do a bit of extra work to avoid the conditional branch—bit-twiddling arithmetic, a lookup table, etc. The lookup table seems like the most likely version to help in Python, so here it is:
table = bytearray(i if i >= 128 else 0 for i in range(256))
total = 0
for i in a:
total + table[i]
To put this inside a function, you'd want to build the table globally instead of once per call, then copy it to a local inside the function to avoid the slow name lookup inside the inner loop: _table = bytearray(i if i >= 128 else 0 for i in range(256))
def sumbig_t(data):
table = _table
total = 0
for i in a:
total + table[i]
The sorted and unsorted arrays are now about the same speed. And for PyPy, that's about 13% faster than with the sorted data in the original version. For CPython, on the other hand, it's 33% slower. I also tried the various bit-twiddling optimizations; they're slightly slower than the lookup table in PyPy, and at least 250% slower in CPython.So, what have we learned? Python, even CPython, can be affected by the same kinds of low-level performance problems as compiled languages. The alternative implementations can also handle those problems the same way. CPython can't… but then if this code were a bottleneck in your problem, you'd almost certainly be switching to PyPy or writing a C extension anyway, right?
Python optimizations
There's an obvious Python-specific optimization here—which I wouldn't even really call an optimization, since it's also a more Pythonic way of writing the code:total = sum(i for i in data if i >= 128)This does in fact speed things up by about 13% in CPython, although it slows things down by 217% in PyPy. It leaves us with the same original difference between random and sorted arrays, and the same basic effects for applying the table or bit twiddling.
You'd think that taking two passes, applying the table to the data and then summing the result, would obviously be slower, right? And normally you'd be right; a quick test shows a 31% slowdown. But if you think about it, when we're dealing with bytes, applying the table can be done with bytes.translate. And of course the sum is now just summing a builtin sequence, not a generator. So we effectively have two C loops instead of one Python loop, which may be a win:
def sumbig_s(data):
return sum(data.translate(bytearray(_table)))
For CPython, this saves about 83% of the time vs. the original sumbig's speed on unsorted data. And the difference between sorted and unsorted data is very small, so it's still an 81% savings on sorted data. However, for PyPy, it's 4% slower for unsorted data, and you lose the gain for sorted data.If you think about it, while we're doing that pass, we might as well just remove the small values instead of mapping them to 0:
def sumbig_s2(data):
return sum(data.translate(bytearray(_table), bytearray(range(128))))
That ought to make the first loop a little slower, and affected by branch misprediction, while making the second loop twice as fast, right? And that's exactly what we see, in CPython. For unsorted data, it cuts 90% off the original code, and now sorting it gives us another 36% improvement. That's near PyPy speeds. On the other hand, in PyPy, it's just as slow for sorted data as the previous fix, and twice as slow for unsorted data, so it's even more of a pessimization.What about using numpy? The obvious implementation is:
def sumbig_n(data):
data = np.array(data)
return data[data>=128].sum()
In CPython, this cuts 90% of the speed off the original code for unsorted data, and for sorted data it cuts off another 48%. Either way, it's the fastest solution so far, even faster than using PyPy. But we can do the equivalent of translating the if to arithmetic or bit-twiddling too. I tried tricks like ~((data-128)>>31)&data, but the fastest turned out to be the simplest: def sumbig_n2(data):
data = np.array(data)
return (data&(data>=128)).sum()
Now just as fast for unsorted data as for sorted, cutting 94% of the time off the original.Conclusions
So, what does this mean for you?Well, most of the time, nothing. If your code is too slow, and it's doing arithmetic inside a loop, and the algorithm itself can't be improved, the first step should almost always be converting to numpy, PyPy, or C, and often that'll be the last step as well.
But it's good to know that the same issues that apply to low-level code still affect Python, and in some cases (especially if you're already using numpy or PyPy) the same solutions may help.
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