Which is faster in Python: x**.5 or math.sqrt(x)?
I've been wondering this for some time. As the title say, which is faster, the actual function or simply raising to the half power?
UPDATE
This is not a matter of premature optimization. This is simply a question of how the underlying code actually works. What is the theory of how Python code works?
I sent Guido van Rossum an email cause I really wanted to know the differences in these methods.
My email:
There are at least 3 ways to do a square root in Python: math.sqrt, the '**' operator and pow(x,.5). I'm just curious as to the differences in the implementation of each of these. When it comes to efficiency which is better?
His response:
pow and ** are equivalent; math.sqrt doesn't work for complex numbers, and links to the C sqrt() function. As to which one is faster, I have no idea...
As per comments, I've updated the code:
import time
import math
def timeit1():
s = time.time()
for i in xrange(750000):
z=i**.5
print "Took %f seconds" % (time.time() - s)
def timeit2(arg=math.sqrt):
s = time.time()
for i in xrange(750000):
z=arg(i)
print "Took %f seconds" % (time.time() - s)
timeit1()
timeit2()
Now the math.sqrt function is directly in a local argument, meaning it has the fastest lookup possible.
UPDATE: The python version seems to matter here. I used to think that timeit1 would be faster, since when python parses "i**.5" it knows, syntactically, which method to call ( __pow__ or some variant), so it doesn't have to go through the overhead of lookup that the math.sqrt variant does. But I might be wrong:
Python 2.5: 0.191000 vs. 0.224000
Python 2.6: 0.195000 vs. 0.139000
Also psyco seems to deal with math.sqrt better:
Python 2.5 + Psyco 2.0: 0.109000 vs. 0.043000
Python 2.6 + Psyco 2.0: 0.128000 vs. 0.067000
| Interpreter | x**.5, | sqrt, | sqrt faster, % |
| | seconds | seconds | |
|----------------+---------+---------+----------------|
| Python 3.2rc1+ | 0.32 | 0.27 | 19 |
| Python 3.1.2 | 0.136 | 0.088 | 55 |
| Python 3.0.1 | 0.155 | 0.102 | 52 |
| Python 2.7 | 0.132 | 0.079 | 67 |
| Python 2.6.6 | 0.121 | 0.075 | 61 |
| PyPy 1.4.1 | 0.083 | 0.0159 | 422 |
| Jython 2.5.1 | 0.132 | 0.22 | -40 |
| Python 2.5.5 | 0.129 | 0.125 | 3 |
| Python 2.4.6 | 0.131 | 0.123 | 7 |
#+TBLFM: $4=100*($2-$3)/$3;%.0f
Table results produced on machine:
$ uname -vms
Linux #42-Ubuntu SMP Thu Dec 2 02:41:37 UTC 2010 x86_64
$ cat /proc/cpuinfo | grep 'model name' | head -1
model name : Intel(R) Core(TM) i7 CPU 920 @ 2.67GHz
To reproduce results:
git clone git://gist.github.com/783011.git gist-783011 tox : pip install tox tox from the directory with tox.ini file. Here's some timings (Python 2.5.2, Windows):
$ python -mtimeit -s"from math import sqrt; x = 123" "x**.5"
1000000 loops, best of 3: 0.445 usec per loop
$ python -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
1000000 loops, best of 3: 0.574 usec per loop
$ python -mtimeit -s"import math; x = 123" "math.sqrt(x)"
1000000 loops, best of 3: 0.727 usec per loop
This test shows that x**.5 is slightly faster than sqrt(x) .
For the Python 3.0 the result is the opposite:
$ Python30python -mtimeit -s"from math import sqrt; x = 123" "x**.5"
1000000 loops, best of 3: 0.803 usec per loop
$ Python30python -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
1000000 loops, best of 3: 0.695 usec per loop
$ Python30python -mtimeit -s"import math; x = 123" "math.sqrt(x)"
1000000 loops, best of 3: 0.761 usec per loop
math.sqrt(x) is always faster than x**.5 on another machine (Ubuntu, Python 2.6 and 3.1):
$ python -mtimeit -s"from math import sqrt; x = 123" "x**.5"
10000000 loops, best of 3: 0.173 usec per loop
$ python -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
10000000 loops, best of 3: 0.115 usec per loop
$ python -mtimeit -s"import math; x = 123" "math.sqrt(x)"
10000000 loops, best of 3: 0.158 usec per loop
$ python3.1 -mtimeit -s"from math import sqrt; x = 123" "x**.5"
10000000 loops, best of 3: 0.194 usec per loop
$ python3.1 -mtimeit -s"from math import sqrt; x = 123" "sqrt(x)"
10000000 loops, best of 3: 0.123 usec per loop
$ python3.1 -mtimeit -s"import math; x = 123" "math.sqrt(x)"
10000000 loops, best of 3: 0.157 usec per loop
How many square roots are you really performing? Are you trying to write some 3D graphics engine in Python? If not, then why go with code which is cryptic over code that is easy to read? The time difference is would be less than anybody could notice in just about any application I could forsee. I really don't mean to put down your question, but it seems that you're going a little too far with premature optimization.
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