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Is “x < y < z” faster than “x < y and y < z”?

Posted by: admin November 1, 2017 Leave a comment

Questions:

From this page, we know that:

Chained comparisons are faster than using the and operator.
Write x < y < z instead of x < y and y < z.

However, I got a different result testing the following code snippets:

$ python -m timeit "x = 1.2" "y = 1.3" "z = 1.8" "x < y < z"
1000000 loops, best of 3: 0.322 usec per loop
$ python -m timeit "x = 1.2" "y = 1.3" "z = 1.8" "x < y and y < z"
1000000 loops, best of 3: 0.22 usec per loop
$ python -m timeit "x = 1.2" "y = 1.3" "z = 1.1" "x < y < z"
1000000 loops, best of 3: 0.279 usec per loop
$ python -m timeit "x = 1.2" "y = 1.3" "z = 1.1" "x < y and y < z"
1000000 loops, best of 3: 0.215 usec per loop

It seems that x < y and y < z is faster than x < y < z. Why?

After searching some posts in this site (like this one) I know that “evaluated only once” is the key for x < y < z, however I’m still confused. To do further study, I disassembled these two functions using dis.dis:

import dis

def chained_compare():
        x = 1.2
        y = 1.3
        z = 1.1
        x < y < z

def and_compare():
        x = 1.2
        y = 1.3
        z = 1.1
        x < y and y < z

dis.dis(chained_compare)
dis.dis(and_compare)

And the output is:

## chained_compare ##

  4           0 LOAD_CONST               1 (1.2)
              3 STORE_FAST               0 (x)

  5           6 LOAD_CONST               2 (1.3)
              9 STORE_FAST               1 (y)

  6          12 LOAD_CONST               3 (1.1)
             15 STORE_FAST               2 (z)

  7          18 LOAD_FAST                0 (x)
             21 LOAD_FAST                1 (y)
             24 DUP_TOP
             25 ROT_THREE
             26 COMPARE_OP               0 (<)
             29 JUMP_IF_FALSE_OR_POP    41
             32 LOAD_FAST                2 (z)
             35 COMPARE_OP               0 (<)
             38 JUMP_FORWARD             2 (to 43)
        >>   41 ROT_TWO
             42 POP_TOP
        >>   43 POP_TOP
             44 LOAD_CONST               0 (None)
             47 RETURN_VALUE

## and_compare ##

 10           0 LOAD_CONST               1 (1.2)
              3 STORE_FAST               0 (x)

 11           6 LOAD_CONST               2 (1.3)
              9 STORE_FAST               1 (y)

 12          12 LOAD_CONST               3 (1.1)
             15 STORE_FAST               2 (z)

 13          18 LOAD_FAST                0 (x)
             21 LOAD_FAST                1 (y)
             24 COMPARE_OP               0 (<)
             27 JUMP_IF_FALSE_OR_POP    39
             30 LOAD_FAST                1 (y)
             33 LOAD_FAST                2 (z)
             36 COMPARE_OP               0 (<)
        >>   39 POP_TOP
             40 LOAD_CONST               0 (None)

It seems that the x < y and y < z has less dissembled commands than x < y < z. Should I consider x < y and y < z faster than x < y < z?

Tested with Python 2.7.6 on an Intel(R) Xeon(R) CPU E5640 @ 2.67GHz.

Answers:

The difference is that in x < y < z y is only evaluated once. This does not make a large difference if y is a variable, but it does when it is a function call, which takes some time to compute.

from time import sleep
def y():
    sleep(.2)
    return 1.3
%timeit 1.2 < y() < 1.8
10 loops, best of 3: 203 ms per loop
%timeit 1.2 < y() and y() < 1.8
1 loops, best of 3: 405 ms per loop

Questions:
Answers:

Optimal bytecode for both of the functions you defined would be

          0 LOAD_CONST               0 (None)
          3 RETURN_VALUE

because the result of the comparison is not used. Let’s make the situation more interesting by returning the result of the comparison. Let’s also have the result not be knowable at compile time.

def interesting_compare(y):
    x = 1.1
    z = 1.3
    return x < y < z  # or: x < y and y < z

Again, the two versions of the comparison are semantically identical, so the optimal bytecode is the same for both constructs. As best I can work it out, it would look like this. I’ve annotated each line with the stack contents before and after each opcode, in Forth notation (top of stack at right, -- divides before and after, trailing ? indicates something that might or might not be there). Note that RETURN_VALUE discards everything that happens to be left on the stack underneath the value returned.

          0 LOAD_FAST                0 (y)    ;          -- y
          3 DUP_TOP                           ; y        -- y y
          4 LOAD_CONST               0 (1.1)  ; y y      -- y y 1.1
          7 COMPARE_OP               4 (>)    ; y y 1.1  -- y pred
         10 JUMP_IF_FALSE_OR_POP     19       ; y pred   -- y
         13 LOAD_CONST               1 (1.3)  ; y        -- y 1.3
         16 COMPARE_OP               0 (<)    ; y 1.3    -- pred
     >>  19 RETURN_VALUE                      ; y? pred  --

If an implementation of the language, CPython, PyPy, whatever, does not generate this bytecode (or its own equivalent sequence of operations) for both variations, that demonstrates the poor quality of that bytecode compiler. Getting from the bytecode sequences you posted to the above is a solved problem (I think all you need for this case is constant folding, dead code elimination, and better modeling of the contents of the stack; common subexpression elimination would also be cheap and valuable), and there’s really no excuse for not doing it in a modern language implementation.

Now, it happens that all current implementations of the language have poor-quality bytecode compilers. But you should ignore that while coding! Pretend the bytecode compiler is good, and write the most readable code. It will probably be plenty fast enough anyway. If it isn’t, look for algorithmic improvements first, and give Cython a try second — that will provide far more improvement for the same effort than any expression-level tweaks you might apply.

Questions:
Answers:

Since the difference in the output seem to be due to lack of optimization I think you should ignore that difference for most cases – it could be that the difference will go away. The difference is because y only should be evaluated once and that is solved by duplicating it on the stack which requires an extra POP_TOP – the solution to use LOAD_FAST might be possible though.

The important difference though is that in x<y and y<z the second y should be evaluated twice if x<y evaluates to true, this has implications if the evaluation of y takes considerable time or have side effects.

In most scenarios you should use x<y<z despite the fact it’s somewhat slower.

Questions:
Answers:

First of all, your comparison is pretty much meaningless because the two different constructs were not introduced to provide a performance improvement, so you shouldn’t decide whether to use one in place of the other based on that.

The x < y < z construct:

  1. Is clearer and more direct in its meaning.
  2. Its semantics is what you’d expect from the “mathematical meaning” of the comparison: evalute x, y and z once and check if the whole condition holds. Using and changes the semantics by evaluating y multiple times, which can change the result.

So choose one in place of the other depending on the semantics you want and, if they are equivalent, whether one is more readable than the other.

This said: more disassembled code does does not imply slower code.
However executing more bytecode operations means that each operation is simpler and yet it requires an iteration of the main loop.
This means that if the operations you are performing are extremely fast (e.g. local variable lookup as you are doing there), then the overhead of executing more bytecode operations can matter.

But note that this result does not hold in the more generic situation, only to the “worst case” that you happen to profile.
As others have noted, if you change y to something that takes even a bit more time you’ll see that the results change, because the chained notation evaluates it only once.

Summarizing:

  • Consider semantics before performance.
  • Take into account readability.
  • Don’t trust micro benchmarks. Always profile with different kind of parameters to see how a function/expression timing behave in relation to said parameters and consider how you plan to use it.