Bitshifts and "And" vs Floor-division and Modular

[jimbo1qaz]

Is it faster to use bitshifts or floor division? And which is better, & or %?
All divisors and mods are power of 2, so are binary operations faster? And are they considered bad style?

 

[Mark Lawrence]

Is it faster to use bitshifts or floor division? And which is better, & or %?
All divisors and mods are power of 2, so are binary operations faster? And are they considered bad style?

Why don't you use the timeit module and find out for yourself?

 

[jimbo1qaz]

Why don't you use the timeit module and find out for yourself?



--

Cheers.



Mark Lawrence.

How do I use it? timeit.timer is not defined.

 

[jimbo1qaz]

Why don't you use the timeit module and find out for yourself?



--

Cheers.



Mark Lawrence.

How do I use it? timeit.timer is not defined.

 

[jimbo1qaz]

Is it faster to use bitshifts or floor division? And which is better, & or %?

All divisors and mods are power of 2, so are binary operations faster? And are they considered bad style?

OK, I decided to change my code. Which raises a similar question: Which oneis better for setting a bit of a byte: |= or +=, assuming each will only be run once? Intuitively, I think |=, but some timeits are inconclusive, mainly because I don't know how it works.

 

[Dave Angel]

Is it faster to use bitshifts or floor division?

Yes, and yes. Without doing any measurement, I'd expect that in
CPython, it makes negligible performance difference for ordinary ints
(under 2**31, more or less). Ordinary ints can be done with single
instructions, and any such instruction would be a tiny fraction of the
opcode overhead.

One place were there might be a difference would be for longs. The
implementation of those would have to be a loop, and eventually one
might be faster than the other. At that point, maybe you'd want to measure.

And which is better, & or %?
All divisors and mods are power of 2, so are binary operations faster? And are they considered bad style?

The better way is not the faster one, but rather is the one that more
clearly expresses the original problem. If the problem is a modulo one,
use % (or frequently divmod). If the problem is a bit shift/masking
one, then use such operators.

BTW, '/' on integers is redefined for Python 3.x to give float results,
and not to truncate.

 

[Terry Reedy]

Is it faster to use bitshifts or floor division? And which is better,
& or %? All divisors and mods are power of 2, so are binary
operations faster? And are they considered bad style?

Yes, meaningless, yes, and no.
I would do what seems sensible to you in the context.

 

[Steven D'Aprano]

Is it faster to use bitshifts or floor division?

Does it matter?

If you ever find yourself writing an application where the difference
between 0.0476 microseconds and 0.0473 microseconds matters to you,
Python is probably the wrong language.


py> from timeit import Timer
py> min(Timer('456789 // 8').repeat(repeat=35))
0.04760909080505371
py> min(Timer('456789 >> 3').repeat(repeat=35))
0.047319889068603516

And which is better, & or %?

Depends what you want to do. If you want to perform bitwise-and, then I
strongly recommend you use &, the bitwise-and operator. If you want to
perform modulus, then the modulus operator % is usually better.

All divisors and mods are power of 2, so are binary operations
faster?

As the MiddleMan says, "specificity is the soul of all good
communication". Python has many binary operations, e.g.:

+ - * / // % == is < <= > >= ** & ^ |

Some of them are faster than some other things, so would you like to be
more specific?

My *guess* is that you mean *bitwise* operators, compared to numeric
operators like * and // (integer division). The runtime cost is mostly
dominated by the object-oriented overhead -- Python is not C or assembly,
and the integers are rich objects, not low-level bitfields, so the
difference between division and bitshifting is much less than you might
expect from assembly language.

But, in principle at least, there *may* be some tiny advantage to the
bitwise operators. I say "may" because the difference is so small that it
is likely to be lost in the noise. I do not believe that there will be
any real world applications where the difference between the two is
significant enough to care about. But if you think different, feel free
to use the profile module to profile your code and demonstrate that
divisions are a significant bottleneck in your application.

And are they considered bad style?

Absolutely. Using & when you mean to take the remainder is a dirty
optimization hack only justified if you really, really, really need it.
I'm pretty confident that you will never notice a speed-up of the order
of 0.1 nanoseconds.


"More computing sins are committed in the name of efficiency (without
necessarily achieving it) than for any other single reason — including
blind stupidity." — W.A. Wulf

"We should forget about small efficiencies, say about 97% of the time:
premature optimization is the root of all evil. Yet we should not pass up
our opportunities in that critical 3%. A good programmer will not be
lulled into complacency by such reasoning, he will be wise to look
carefully at the critical code; but only after that code has been
identified" — Donald Knuth

"Bottlenecks occur in surprising places, so don't try to second guess and
put in a speed hack until you have proven that's where the bottleneck
is." — Rob Pike

"The First Rule of Program Optimization: Don't do it. The Second Rule of
Program Optimization (for experts only!): Don't do it yet." — Michael A.
Jackson

 

[Steven D'Aprano]

OK, I decided to change my code. Which raises a similar question: Which
one is better for setting a bit of a byte: |= or +=, assuming each will
only be run once? Intuitively, I think |=

Python (like most languages) doesn't have a "set this bit" operator, so
the closest match is a bitwise-or. So to set a bit of a byte, the
operation which most closely matches the programmer's intention is to use
the bitwise operator.

Even better would be to write a function called "setBit", and use that.

but some timeits are inconclusive,

Timing results are usually inconclusive because the difference between
the results are much smaller than that average random noise on any
particular result.

All modern computers, say for the last 20 or 30 years, have used
multitasking operating systems. This means that at any time you could
have dozens, even hundreds, of programs running at once, with the
operating system switching between them faster than you can blink.

In addition, the time taken by an operation can depend on dozens of
external factors, such as whether the data is already in a CPU cache,
whether CPU prediction has pre-fetched the instructions needed,
pipelines, memory usage, latency when reading from disks, and many
others.

Consequently, timing results are very *noisy* -- the *exact* same
operation can take different amount of time from one run to the next.
Sometimes *large* differences.

So any time you time a piece of code, what you are *actually* getting is
not the amount of time that code takes to execute, but something slightly
more. (And, occasionally, something a lot more.) Note that it is always
slightly more -- by definition, it will never be less.

So if you want a better estimate of the actual time taken to execute the
code, you should repeat the measurement as many times as you can bear,
and pick the smallest value.

*Not* the average, since the errors are always positive. An average just
gives you the "true" time plus some unknown average error, which may not
be small. The minimum gives you the "true" time plus some unknown but
hopefully small error.

The smaller the amount of time you measure, the more likely that it will
be disrupted by some external factor. So timeit takes a code snippet and
runs it many times (by default, one million times), and returns the total
time used. Even if one or two of those runs were blown out significantly,
the total probably won't be. (Unless of course your anti-virus decided to
start running, and *everything* slows down for 10 minutes, or something
like that.)

But even that total time returned by timeit is almost certainly wrong. So
you should call the repeat method, with as many iterations as you can
bear to wait for, and take the minimum, which will still be wrong but it
will be less wrong.

And remember, the result you get is only valid for *your* computer,
running the specific version of Python you have, under the specific
operating system. On another computer with a different CPU or a different
OS, the results may be *completely* different.

Are you still sure you care about shaving off every last nanosecond?

mainly because I don't know how it works.

The internal details of how timeit works are complicated, but it is worth
reading the comments and documentation, both in the Fine Manual and in
the source code:

http://docs.python.org/library/timeit.html
http://hg.python.org/cpython/file/2.7/Lib/timeit.py

 

[rusi]

Is it faster to use bitshifts or floor division? And which is better, & or %?
All divisors and mods are power of 2, so are binary operations faster? And are they considered bad style?

On an 8086/8088 a MUL (multiply) instruction was of the order of 100
clocks and a DIV nearly 200 compared to ADD, OR etc which were
something like 8 (IIRC -- this is decades-stale knowledge)
On most modern processors (after the pentium) the difference has
mostly vanished. I cant find a good data sheet to quote though -- one
of the sad things about modern processors is that the clocks which
were politely offered by intel earlier have now stopped presumably
because cache-(in)coherence, pipelining etc are more likely to
dominate the number of clocks than the specific instruction.

This question is interesting to a programmer but meaningless at the
python level (as others have pointed out). If it still interests you,
work at the C (or still better assembly) level and use a more
finegrained timer measure -- the finest being the RDTSC instruction.

 

[Paul Rubin]

On an 8086/8088 a MUL (multiply) instruction was of the order of 100
clocks ... On most modern processors (after the pentium) the
difference has mostly vanished. I cant find a good data sheet to
quote though

See http://www.agner.org/optimize/ :

4. Instruction tables: Lists of instruction latencies, throughputs
and micro-operation breakdowns for Intel, AMD and VIA CPUs

Multiplication is now fast but DIV is still generally much slower.
There are ways to make fast parallel dividers that I think nobody
bothers with, because of chip area and because one can often optimize
division out of algorithms, replacing most of it with multiplication.

Worrying about this sort of micro-optimization in CPython is almost
always misplaced, since the interpreter overhead generally swamps any
slowness of the machine arithmetic.

 

[Grant Edwards]

My *guess* is that you mean *bitwise* operators, compared to numeric
operators like * and // (integer division). The runtime cost is mostly
dominated by the object-oriented overhead -- Python is not C or assembly,
and the integers are rich objects, not low-level bitfields, so the
difference between division and bitshifting is much less than you might
expect from assembly language.

I don't suppose there's much of a chance that the OP is running Python
on a CPU that doesn't have an integer divide instruction? If that
_were_ the case, the difference would be more noticable, but would
still probably not worth worrying about unless a truely huge number of
operations were being done in a very tight loop with no intervening
I/O operations.

 

[rusi]

See http://www.agner.org/optimize/:

Hey Thanks! Seems like a nice resource! How on earth does he come up
with the data though, when Intel does not publish it?