Parallel program to calculate PI

**Prime Mover** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Let me just be a bit more specific:

My (understading) problem starts in the line 5 of the pseudo-code:
5. find out if I am MASTER or WORKER

How would I specificy a "worker"? Would that be another computer?
If yes, how can I access this remote computer in the calculations, in
C language?
If yes, it means that I have to have a LAN or something to perform
tests?

I have found that there are some libraries such as OMP or MPI that
could be
used, but I'd like to know if there is a more "raw" way of doing this
first.

Again, thank you all.

**Spiros Bousbouras** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On 13 May, 15:20, Prime Mover <eple...@hotmai l.comwrote:

Hello all,
>
I have got the pseudo-code below that I would like to convert to c
language. The algorithm calculates Pi value. I am somewhat familiar
with C language, but I am just starting to learn parallel programming.
In this specific example, the idea seems to be simple: one must
subdivide the main loop into pieces that can be executed by
independent "tasks" (computers??).
>
Then, each "worker task" executes a part of the loop a certain number
of times, independently of the other worker tasks. One specific task
plays the role of "master task", which will collect and sum the
results of the worker tasks:
>
% descriptive algorithm:
1. Inscribe a circle inside a square
2. Generate random points inside the square
3. Determine the number of points that fell inside the circle
4. Let r be the number of points inside the circle divided by the
total number of points
5. Pi is approximately equal to 4*r
6. The more points are generated, the more is the precision in P value
>
% pseudo-code (parallel):
1. npoints = 10000
2. circle_count = 0
3. p = number of tasks
4. num = npoints/p
5. find out if I am MASTER or WORKER
6. do j = 1,num
7. generate 2 random numbers between 0 and 1
8. xcoordinate = random1
9. ycoordinate = random2
10. if (xcoordinate, ycoordinate) inside circle then
circle_count = circle_count + 1
11. end do
12. if I am MASTER
13. receive from WORKERS their circle_counts
14. compute PI (use MASTER and WORKER calculations)
15. else if I am WORKER
16. send to MASTER circle_count
17. endif

On 13 May, 15:28, Prime Mover <eple...@hotmai l.comwrote:

Let me just be a bit more specific:
>
My (understading) problem starts in the line 5 of the pseudo-code:
5. find out if I am MASTER or WORKER
>
How would I specificy a "worker"? Would that be another computer?
If yes, how can I access this remote computer in the calculations, in
C language?
If yes, it means that I have to have a LAN or something to perform
tests?
>
I have found that there are some libraries such as OMP or MPI that
could be
used, but I'd like to know if there is a more "raw" way of doing this
first.

Standard C has no built-in support for parallel processing so an
answer
to the question "find out if I am MASTER or WORKER" falls outside
standard C which is what's topical here. I have no idea what kind of
hardware set-up and extensions to C can be used to tackle numerically
intensive parallel algorithms. Perhaps others here have the relevant
experience. Searching Google groups for *parallel* I found
comp.parallel.m pi and comp.parallel.p vm where I'm guessing you might
get more useful advice than here.

Out of curiosity for what value of npoints are you aiming for ? In
your example it's only 100000 and you can get that on a modern desktop
in a few seconds.

**Spiros Bousbouras** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On 13 May, 15:28, Prime Mover <eple...@hotmai l.comwrote:

>

Let me just be a bit more specific:

>

My (understading) problem starts in the line 5 of the pseudo-code:
5. find out if I am MASTER or WORKER

>

How would I specificy a "worker"? Would that be another computer?
If yes, how can I access this remote computer in the calculations, in
C language?
If yes, it means that I have to have a LAN or something to perform
tests?

>

I have found that there are some libraries such as OMP or MPI that
could be
used, but I'd like to know if there is a more "raw" way of doing this
first.

>
Standard C has no built-in support for parallel processing so an
answer
to the question "find out if I am MASTER or WORKER" falls outside
standard C which is what's topical here. I have no idea what kind of
hardware set-up and extensions to C can be used to tackle numerically
intensive parallel algorithms. Perhaps others here have the relevant
experience. Searching Google groups for *parallel* I found
comp.parallel.m pi and comp.parallel.p vm where I'm guessing you might
get more useful advice than here.

There's also comp.parallel

**Pietro Cerutti** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Prime Mover wrote:

% descriptive algorithm:
1. Inscribe a circle inside a square
2. Generate random points inside the square
3. Determine the number of points that fell inside the circle

How can you determine it without knowing PI a priori?

Pietro Cerutti

**Bart** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On May 13, 3:55 pm, Spiros Bousbouras <spi...@gmail.c omwrote:

On 13 May, 15:20, Prime Mover <eple...@hotmai l.comwrote:

I have got the pseudo-code below that I would like to convert to c
language. The algorithm calculates Pi value. I am somewhat familiar

Out of curiosity for what value of npoints are you aiming for ? In
your example it's only 100000 and you can get that on a modern desktop
in a few seconds.- Hide quoted text -

I got 3.1415 using a billion points. Looks like it will converge very
slowly.

Also the granularity of the x,y points may affect the maximum accuracy
(because it introduces errors near the circular edge). Tried a sphere
too but not any better.

--
Bartc

**Richard Heathfield** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Pietro Cerutti said:

Prime Mover wrote:

>% descriptive algorithm:
>1. Inscribe a circle inside a square
>2. Generate random points inside the square
>3. Determine the number of points that fell inside the circle

>
How can you determine it without knowing PI a priori?

There's nothing in the above description that requires a knowledge of pi.

For example, you can draw a circle of radius r easily enough just by
applying the equation x^2 + y^2 = r^2 (no, that is not C code!) for all y
in the range -r to +r, taking the positive result and its negative
analogue for your x points. (Actually, it's even easier than that, because
there are other symmetries to exploit.)

Determining whether you're in the circle can be done either by tedious
inspection (a process not unlike floodfill) or (much faster) by
determining whether x^2 + y^2 <= r^2.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

**Spiros Bousbouras** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On 13 May, 16:02, Pietro Cerutti <gahr@localhost wrote:

Prime Mover wrote:

% descriptive algorithm:
1. Inscribe a circle inside a square
2. Generate random points inside the square
3. Determine the number of points that fell inside the circle

>
How can you determine it without knowing PI a priori?

Imagine a circle with radius is 1 and its center has coordinates
(0 , 0).
A random point with coordinates (x,y) will be inside the square
if -1 <= x <= 1 and -1 <= y <= 1
if ( x*x + y*y < 1) /* inside the circle */

**Spiros Bousbouras** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On 13 May, 16:15, Bart <b...@freeuk.co mwrote:

On May 13, 3:55 pm, Spiros Bousbouras <spi...@gmail.c omwrote:
>

On 13 May, 15:20, Prime Mover <eple...@hotmai l.comwrote:

I have got the pseudo-code below that I would like to convert to c
language. The algorithm calculates Pi value. I am somewhat familiar

Out of curiosity for what value of npoints are you aiming for ? In
your example it's only 100000 and you can get that on a modern desktop
in a few seconds.- Hide quoted text -

>
I got 3.1415 using a billion points. Looks like it will converge very
slowly.
>
Also the granularity of the x,y points may affect the maximum accuracy
(because it introduces errors near the circular edge). Tried a sphere
too but not any better.

And of course you must know that your random numbers
will be uniformly distributed within the square.

**CBFalconer** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Pietro Cerutti wrote:

Prime Mover wrote:
>

>% descriptive algorithm:
>1. Inscribe a circle inside a square
>2. Generate random points inside the square
>3. Determine the number of points that fell inside the circle

>
How can you determine it without knowing PI a priori?

Write the expression for the area of a circle. Do the same for the
area of the superscribed square. Take the ratio of areas. It
contains PI.

--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home .att.net>
Try the download section.

** Posted from http://www.teranews.com **

**Richard Heathfield** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Spiros Bousbouras said:

<snip>

And of course you must know that your random numbers
will be uniformly distributed within the square.

That's easy. Use the following random point generator:

#include <assert.h>

void rndpt(unsigned long int *x,
unsigned long int *y,
unsigned long int max) /* max = side of square */
{
static unsigned long int n = 0;
assert(x != NULL && y != NULL);
*x = n % max;
*y = n++ / max;
n %= max;
return;
}

If you call this i * max times, where max is a constant and i is an
integer, the distribution of the random points will be uniform.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

**Spiros Bousbouras** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On 13 May, 17:00, Richard Heathfield <r...@see.sig.i nvalidwrote:

Spiros Bousbouras said:
>
<snip>
>

And of course you must know that your random numbers
will be uniformly distributed within the square.

>
That's easy. Use the following random point generator:
>
#include <assert.h>
>
void rndpt(unsigned long int *x,
unsigned long int *y,
unsigned long int max) /* max = side of square */
{
static unsigned long int n = 0;
assert(x != NULL && y != NULL);
*x = n % max;
*y = n++ / max;
n %= max;
return;
>
}
>
If you call this i * max times, where max is a constant and i is an
integer, the distribution of the random points will be uniform.

Since *y will always get the value 0 I don't think
so.

**Richard Heathfield** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Spiros Bousbouras said:

On 13 May, 17:00, Richard Heathfield <r...@see.sig.i nvalidwrote:

>Spiros Bousbouras said:
>>
><snip>
>>

And of course you must know that your random numbers
will be uniformly distributed within the square.

>>
>That's easy. Use the following random point generator:
>>
>#include <assert.h>
>>
>void rndpt(unsigned long int *x,
> unsigned long int *y,
> unsigned long int max) /* max = side of square */
>{
> static unsigned long int n = 0;
> assert(x != NULL && y != NULL);
> *x = n % max;
> *y = n++ / max;
> n %= max;
> return;
>>
>}
>>
>If you call this i * max times, where max is a constant and i is an
>integer, the distribution of the random points will be uniform.

>
Since *y will always get the value 0 I don't think
so.

Since it won't, I do.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

**Eric Sosman** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

Richard Heathfield wrote:

Spiros Bousbouras said:
>

>On 13 May, 17:00, Richard Heathfield <r...@see.sig.i nvalidwrote:

>>Spiros Bousbouras said:
>>>
>><snip>
>>>
>>>And of course you must know that your random numbers
>>>will be uniformly distributed within the square.
>>That's easy. Use the following random point generator:
>>>
>>#include <assert.h>
>>>
>>void rndpt(unsigned long int *x,
>> unsigned long int *y,
>> unsigned long int max) /* max = side of square */
>>{
>> static unsigned long int n = 0;
>> assert(x != NULL && y != NULL);
>> *x = n % max;
>> *y = n++ / max;
>> n %= max;
>> return;
>>>
>>}
>>>
>>If you call this i * max times, where max is a constant and i is an
>>integer, the distribution of the random points will be uniform.

>Since *y will always get the value 0 I don't think
>so.

>
Since it won't, I do.

Try running it for a while and making a histogram of
the y outputs.

(The bug is in the line preceding the return.)

--
Eric.Sosman@sun .com

**Bart** · Jun 27 '08, 07:37 PM

Re: Parallel program to calculate PI

On May 13, 5:00 pm, Richard Heathfield <r...@see.sig.i nvalidwrote:

Spiros Bousbouras said:
>
<snip>
>

And of course you must know that your random numbers
will be uniformly distributed within the square.

>
That's easy. Use the following random point generator:
>
#include <assert.h>
>
void rndpt(unsigned long int *x,
unsigned long int *y,
unsigned long int max) /* max = side of square */
{
static unsigned long int n = 0;
assert(x != NULL && y != NULL);
*x = n % max;
*y = n++ / max;
n %= max;
return;
>
}
>
If you call this i * max times, where max is a constant and i is an
integer, the distribution of the random points will be uniform.

You mean max*max?

This looks to be simply filling in a square sequentially. You are then
effectively calculating the area of a circle in a square by counting
the all dots. That's not really in the spirit of the original method.
(I think it also converges more slowly compared with the same number
of points picked randomly.)

--
Bartc

Parallel program to calculate PI

Parallel program to calculate PI

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