Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

[jwrweatherley@gmail.com]

I'm pretty new to python, but am very happy with it. As well as using
it at work I've been using it to solve various puzzles on the Project
Euler site - http://projecteuler.net. So far it has not let me down,
but it has proved surprisingly slow on one puzzle.

The puzzle is: p is the perimeter of a right angle triangle with
integral length sides, {a,b,c}. which value of p < 1000, is the
number of solutions {a,b,c} maximised?

Here's my python code:

#!/usr/local/bin/python

solutions = [0] * 1001
p = 0

for a in xrange(1, 1000):
for b in xrange(1, 1000 - a):
for c in xrange(1, 1000 - a - b):
p = a + b + c
if p < 1000:
if a ** 2 + b ** 2 == c ** 2:
solutions[p] += 1

max = 0
maxIndex = 0
index = 0
for solution in solutions:
if solution max:
max = solution
maxIndex = index
index += 1

print maxIndex


It takes 2 minutes and twelve seconds on a 2.4GHz Core2Duo MacBook
Pro. Surprised at how slow it was I implemented the same algorithm in
C:

#include <stdio.h>
#include <stdlib.h>

int main() {
int* solutions = calloc(1000, sizeof(int));

int p;
for(int a = 1; a < 1000; ++a) {
for(int b = 1; b < 1000 - a; ++b) {
for(int c = 1; c < 1000 - a - b; ++c) {
p = a + b + c;
if(p < 1000) {
if(a * a + b * b == c * c) {
solutions[p] += 1;
}
}
}
}
}

int max = 0;
int maxIndex = 0;

for(int i = 0; i < 1000; ++i) {
if(solutions[i] max) {
max = solutions[i];
maxIndex = i;
}
}
printf("%d\n", maxIndex);
return 0;
}


gcc -o 39 -std=c99 -O3 39.c

The resulting executable takes 0.24 seconds to run. I'm not expecting
a scripting language to run faster than native code, but I was
surprised at how much slower it was in this case. Any ideas as to what
is causing python so much trouble in the above code?

[Arnaud Delobelle]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

On Sep 2, 12:51 pm, jwrweather...@g mail.com wrote:

I'm pretty new to python, but am very happy with it. As well as using
it at work I've been using it to solve various puzzles on the Project
Euler site -http://projecteuler.ne t. So far it has not let me down,
but it has proved surprisingly slow on one puzzle.
>
The puzzle is: p is the perimeter of a right angle triangle with
integral length sides, {a,b,c}. which value of p < 1000, is the
number of solutions {a,b,c} maximised?
>
Here's my python code:
>
#!/usr/local/bin/python
>
solutions = [0] * 1001
p = 0
>
for a in xrange(1, 1000):
for b in xrange(1, 1000 - a):
for c in xrange(1, 1000 - a - b):
p = a + b + c
if p < 1000:
if a ** 2 + b ** 2 == c ** 2:
solutions[p] += 1
>
max = 0
maxIndex = 0
index = 0
for solution in solutions:
if solution max:
max = solution
maxIndex = index
index += 1
>
print maxIndex
>
It takes 2 minutes and twelve seconds on a 2.4GHz Core2Duo MacBook
Pro. Surprised at how slow it was I implemented the same algorithm in
C:
>
#include <stdio.h>
#include <stdlib.h>
>
int main() {
int* solutions = calloc(1000, sizeof(int));
>
int p;
for(int a = 1; a < 1000; ++a) {
for(int b = 1; b < 1000 - a; ++b) {
for(int c = 1; c < 1000 - a - b; ++c) {
p = a + b + c;
if(p < 1000) {
if(a * a + b * b == c * c) {
solutions[p] += 1;
}
}
}
}
}
>
int max = 0;
int maxIndex = 0;
>
for(int i = 0; i < 1000; ++i) {
if(solutions[i] max) {
max = solutions[i];
maxIndex = i;
}
}
printf("%d\n", maxIndex);
return 0;
>
}
>
gcc -o 39 -std=c99 -O3 39.c
>
The resulting executable takes 0.24 seconds to run. I'm not expecting
a scripting language to run faster than native code, but I was
surprised at how much slower it was in this case. Any ideas as to what
is causing python so much trouble in the above code?

from math import sqrt

solutions = [0] * 1001
p = 0

for a in xrange(1, 1000):
a2 = a*a
for b in xrange(1, 1000 - a):
c = sqrt(a2 + b*b)
if c == int(c) and a+b+c < 1000:
solutions[a+b+int(c)] += 1

max = 0
maxIndex = 0
index = 0
for solution in solutions:
if solution max:
max = solution
maxIndex = index
index += 1

print maxIndex

--
Arnaud

[Greg Copeland]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

On Sep 2, 7:20 am, Arnaud Delobelle <arno...@google mail.comwrote:

On Sep 2, 12:51 pm, jwrweather...@g mail.com wrote:
>
>
>

I'm pretty new to python, but am very happy with it. As well as using
it at work I've been using it to solve various puzzles on the Project
Euler site -http://projecteuler.ne t. So far it has not let me down,
but it has proved surprisingly slow on one puzzle.

>

The puzzle is: p is the perimeter of a right angle triangle with
integral length sides, {a,b,c}. which value of p < 1000, is the
number of solutions {a,b,c} maximised?

>

Here's my python code:

>

#!/usr/local/bin/python

>

solutions = [0] * 1001
p = 0

>

for a in xrange(1, 1000):
for b in xrange(1, 1000 - a):
for c in xrange(1, 1000 - a - b):
p = a + b + c
if p < 1000:
if a ** 2 + b ** 2 == c ** 2:
solutions[p] += 1

>

max = 0
maxIndex = 0
index = 0
for solution in solutions:
if solution max:
max = solution
maxIndex = index
index += 1

>

print maxIndex

>

It takes 2 minutes and twelve seconds on a 2.4GHz Core2Duo MacBook
Pro. Surprised at how slow it was I implemented the same algorithm in
C:

>

#include <stdio.h>
#include <stdlib.h>

>

int main() {
int* solutions = calloc(1000, sizeof(int));

>

int p;
for(int a = 1; a < 1000; ++a) {
for(int b = 1; b < 1000 - a; ++b) {
for(int c = 1; c < 1000 - a - b; ++c) {
p = a + b + c;
if(p < 1000) {
if(a * a + b * b == c * c) {
solutions[p] += 1;
}
}
}
}
}

>

int max = 0;
int maxIndex = 0;

>

for(int i = 0; i < 1000; ++i) {
if(solutions[i] max) {
max = solutions[i];
maxIndex = i;
}
}
printf("%d\n", maxIndex);
return 0;

>

}

>

gcc -o 39 -std=c99 -O3 39.c

>

The resulting executable takes 0.24 seconds to run. I'm not expecting
a scripting language to run faster than native code, but I was
surprised at how much slower it was in this case. Any ideas as to what
is causing python so much trouble in the above code?

>
from math import sqrt
>
solutions = [0] * 1001
p = 0
>
for a in xrange(1, 1000):
a2 = a*a
for b in xrange(1, 1000 - a):
c = sqrt(a2 + b*b)
if c == int(c) and a+b+c < 1000:
solutions[a+b+int(c)] += 1
>
max = 0
maxIndex = 0
index = 0
for solution in solutions:
if solution max:
max = solution
maxIndex = index
index += 1
>
print maxIndex
>
--
Arnaud

For the curious:

O O + P A A + P
======= ======= ======= =======
2:22.56 0:25.65 0:00.75 0:00.20

O = Original Implementation
P = Psyco (psyco.full())
A = Arnaud's Revised Implementation

[rzed]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

jwrweatherley@g mail.com wrote in
news:1188733902 .513512.87510@r 34g2000hsd.goog legroups.com:

The puzzle is: p is the perimeter of a right angle triangle with
integral length sides, {a,b,c}. which value of p < 1000, is the
number of solutions {a,b,c} maximised?
>
Here's my python code:
>
#!/usr/local/bin/python
>
solutions = [0] * 1001
p = 0
>
for a in xrange(1, 1000):
for b in xrange(1, 1000 - a):
for c in xrange(1, 1000 - a - b):
p = a + b + c
if p < 1000:
if a ** 2 + b ** 2 == c ** 2:
solutions[p] += 1
>

Once p >= 1000, it ain't goin' back. If you break out of the
innermost loop here after that happens, you'll save a bunch of
time.

max = 0
maxIndex = 0
index = 0
for solution in solutions:
if solution max:
max = solution
maxIndex = index
index += 1
>
print maxIndex
>
>
It takes 2 minutes and twelve seconds on a 2.4GHz Core2Duo
MacBook Pro.
>

[...]

The resulting executable takes 0.24 seconds to run. I'm not
expecting a scripting language to run faster than native code,
but I was surprised at how much slower it was in this case. Any
ideas as to what is causing python so much trouble in the above
code?
>

[jwrweatherley@gmail.com]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

[snip code]

Thanks for that. I realise that improving the algorithm will speed
things up. I wanted to know why my less than perfect algorithm was so
much slower in python than exactly the same algorithm in C. Even when
turning off gcc's optimiser with the -O0 flag, the C version is still

100 times quicker.

[Mark Dickinson]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

On Sep 2, 9:45 am, jwrweather...@g mail.com wrote:

[snip code]
>
Thanks for that. I realise that improving the algorithm will speed
things up. I wanted to know why my less than perfect algorithm was so
much slower in python than exactly the same algorithm in C. Even when
turning off gcc's optimiser with the -O0 flag, the C version is still
>

100 times quicker.

Well, for one thing, you're creating half a million xrange objects in
the course of the search. All the C code has
to do is increment a few integers.

Mark

[Ivan Wang]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

On Sep 2, 9:45 pm, jwrweather...@g mail.com wrote:

[snip code]
>
Thanks for that. I realise that improving the algorithm will speed
things up. I wanted to know why my less than perfect algorithm was so
much slower in python than exactly the same algorithm in C. Even when
turning off gcc's optimiser with the -O0 flag, the C version is still
>
>
>

100 times quicker.- Hide quoted text -

>
- Show quoted text -

Maybe Python is the slowest programming language in the world.
So there is a joke: some python hater said that "python" can only
crawl rather than run. :)

Python is slow because:
(1) dynamic binding
(2) it is a interpretation language
For example, in C code, an interger expression "a+b" will directly
generate an assembly code "add" for x86 processors.
A python interpreter, on the other side, need detect the type of a and
b first, then choose the right "+" operation for them and use a
evaluation stack to get the result.

Psyco is a JIT compiler with just in time specialization which can
somehow solve these two problems

[Arnaud Delobelle]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

On Sep 2, 12:51 pm, jwrweather...@g mail.com wrote:
[...]

The resulting executable takes 0.24 seconds to run. I'm not expecting
a scripting language to run faster than native code, but I was
surprised at how much slower it was in this case. Any ideas as to what
is causing python so much trouble in the above code?

Sorry I didn't answer your question at all in my previous post
(although my modified method gets the answer in about 6s on a measly
PB G4 1GHz :).
Your little code snippet is just about the worst bit of code for
python to be compared to C. Three loops, only integer arithmetic:
that's not going to make Python shine!

Nevertheless as you optimise your C snippet (-O3), there are probably
a few things that the compiler does for you:

* as in the inner loop, a*a + b*b always remain the same, it is
probably stored in a register once and for all
* in the second loop, a*a remains the same so it might be calculated
once and for all as well.

It gives this:

M = 1000
solutions = [0] * M

def f1():
"Your original implementation"
for a in xrange(1, M):
for b in xrange(1, M - a):
for c in xrange(1, M - a - b):
if a**2 + b**2 == c**2:
solutions[a+b+c] += 1

def f2():
"a*a + b*b precalculated"
for a in xrange(1, M):
a2 = a*a
for b in xrange(1, M - a):
s = a2 + b*b
for c in xrange(1, M - a - b):
if s == c*c:
solutions[a+b+c] += 1

It doesn't make it as quick as C of course, but more than halves the
execution time.

--
Arnaud

[Cameron Laird]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

In article <1188742231.470 668.29910@g4g20 00hsf.googlegro ups.com>,
Mark Dickinson <dickinsm@gmail .comwrote:

>On Sep 2, 9:45 am, jwrweather...@g mail.com wrote:

>[snip code]
>>
>Thanks for that. I realise that improving the algorithm will speed
>things up. I wanted to know why my less than perfect algorithm was so
>much slower in python than exactly the same algorithm in C. Even when
>turning off gcc's optimiser with the -O0 flag, the C version is still
>>

100 times quicker.

>
>Well, for one thing, you're creating half a million xrange objects in
>the course of the search. All the C code has
>to do is increment a few integers.
>
>Mark
>

Right: Mr. Dickinson's original question is entirely
legitimate, and it's not adequate to respond, as some
follow-ups did, with ways to improve the Python-coded
algorithm.

The correct answer, which I want to reinforce, is that
the exhibited Python and C versions are NOT "exactly
the same algorithm", at least not without more quali-
fication. Part of Python expertise is to recognize
that creation of xrange objects, mentioned above, is
far from free. Also, -O3 gives C the opportunity,
also remarked in a follow-up, to factor calculations
outside their loops.

[Bruno Desthuilliers]

Re: Why is this loop heavy code so slow in Python? Possible ProjectEuler spoilers

Ivan Wang a écrit :

On Sep 2, 9:45 pm, jwrweather...@g mail.com wrote:
>

>>[snip code]
>>
>>Thanks for that. I realise that improving the algorithm will speed
>>things up. I wanted to know why my less than perfect algorithm was so
>>much slower in python than exactly the same algorithm in C. Even when
>>turning off gcc's optimiser with the -O0 flag, the C version is still
>>
>>
>>
>>

>>>100 times quicker.- Hide quoted text -

>>
>>- Show quoted text -

>
Maybe Python is the slowest programming language in the world.
So there is a joke: some python hater said that "python" can only
crawl rather than run. :)
>
Python is slow because:
(1) dynamic binding

Yes.

(2) it is a interpretation language

Not quite. It's compiled to byte-code - just like Java (would you call
Java an 'interpreted language' ?)

[Paul Rubin]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

aleax@mac.com (Alex Martelli) writes:

...which suggests that creating an xrange object is _cheaper_ than
indexing a list...

Why not re-use the xrange instead of keeping a list around?

Python 2.4.4 (#1, Oct 23 2006, 13:58:00)

>>a = xrange(3)
>>print list(a)

[0, 1, 2]

>>print list(a)

[0, 1, 2]

[Alex Martelli]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

Paul Rubin <http://phr.cx@NOSPAM.i nvalidwrote:

aleax@mac.com (Alex Martelli) writes:

...which suggests that creating an xrange object is _cheaper_ than
indexing a list...

>
Why not re-use the xrange instead of keeping a list around?
>
Python 2.4.4 (#1, Oct 23 2006, 13:58:00)

>>a = xrange(3)
>>print list(a)

[0, 1, 2]

>>print list(a)

[0, 1, 2]

Reusing xranges is exactly what my code was doing -- at each for loop
you need an xrange(1, k) for a different value of k, which is why you
need some container to keep them around (and a list of xrange objects is
the simplest applicable container).

Your suggestion doesn't appear to make any sense in the context of the
optimization problem at hand -- what list(...) calls are you thinking
of?! Please indicate how your suggestion would apply in the context of:

def f3(M=M, solutions=solut ions):
"pull out all the stops"
xrs = [xrange(1, k) for k in xrange(0, M+1)]
for a in xrs[M]:
a2 = a*a
for b in xrs[M-a]:
s = a2 + b*b
for c in xrs[M-a-b]:
if s == c*c:
solutions[a+b+c] += 1


Alex

[Paul Rubin]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

aleax@mac.com (Alex Martelli) writes:

Reusing xranges is exactly what my code was doing

Oh cool, I missed that, I was just going by the text description.
Looking at the code, yes, it's re-using the xranges. Thanks.

[Mark Dickinson]

Re: Why is this loop heavy code so slow in Python? Possible Project Euler spoilers

On Sep 2, 12:55 pm, al...@mac.com (Alex Martelli) wrote:

Mark Dickinson <dicki...@gmail .comwrote:

Well, for one thing, you're creating half a million xrange objects in
the course of the search. All the C code has
to do is increment a few integers.

>
I don't think the creation of xrange objects is a meaningful part of
Python's execution time here. Consider:
[...]

Agreed---I just came to the same conclusion after doing some tests.
So maybe it's the billion or so integer objects being created that
dominate the running time? (Not sure how many integer objects
actually are created here: doesn't Python cache *some* small
integers?)

Mark

[=?ISO-8859-1?Q?=22Martin_v=2E_L=F6wis=22?=]

Re: Why is this loop heavy code so slow in Python? Possible ProjectEuler spoilers

>(2) it is a interpretation language

Not quite. It's compiled to byte-code - just like Java (would you call
Java an 'interpreted language' ?)

Python is not implemented like Java. In Java (at least in HotSpot),
the byte code is further compiled to machine code before execution;
in Python, the byte code is interpreted.

Whether this makes Python an interpreter or a compiler,
I don't know.

Regards,
Martin