Programming Challenge
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 level1
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As their has been a lot of programming related discussion of late I thought I would suggest a programming challenge.
Estimate Pi, to as many decimal places as you can in 20,000 iterations. There are several ways of estimating Pi so it would be interesting to see which one is better (I have no idea).
CC.
Estimate Pi, to as many decimal places as you can in 20,000 iterations. There are several ways of estimating Pi so it would be interesting to see which one is better (I have no idea).
CC.
Make something idiot proof, and someone will invent a better idiot.

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

 level5
 Posts: 2725
 Joined: Sun Mar 17, 2002 4:40 pm
 Location: W. Australia
Yeah, I'd probably be up for that.
Would you want us to submit the source, or just an exe, or what?
Any preference as to language used?
Any other "rules" I should be aware of?
Would you want us to submit the source, or just an exe, or what?
Any preference as to language used?
Any other "rules" I should be aware of?
ME!
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**

 level1
 Posts: 55
 Joined: Tue Apr 22, 2003 2:51 pm
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As their is no prize (excepting our undying admiration)and cheating would be kind of pointless as it is merely a test for yourself, simply describe/name the method used , and the accuracy of your result.
So any language you like really!
CC
So any language you like really!
CC
Make something idiot proof, and someone will invent a better idiot.

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

 level5
 Posts: 2725
 Joined: Sun Mar 17, 2002 4:40 pm
 Location: W. Australia
Cool. I'll get on to it right away 20,000 iterations, yeah?
ME!
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**

 level1
 Posts: 55
 Joined: Tue Apr 22, 2003 2:51 pm
 Location: Uk
 Contact:
Yep.
Make something idiot proof, and someone will invent a better idiot.

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants
Code: Select all
[size=17]pi# = 4
FOR i& = 3 TO 40000 STEP 2
Â pi# = (pi# * 1) + (4 / i&)
NEXT i&
PRINT ABS(pi#)[/size]
I did that in qbasic.
it's just
4  4/3 + 4/9  4/11 ...
which gives 3.141542653589821 (as deep as QBASIC will go)
with (just under) 20000 itterations it's accurate to 4dp
but looping 1,073,741,823* times gives a more accurate number but takes ages.
there is probably a better way to code this in QB but i'm rushing
* because of the nature of my code the value of i& cannot excede 2,147,483,647, as i'm going in steps of 2 1,073,741,823 is the number of loops
Just usin' Ramanujan's algorithm.
Can only do 49 iterations before breaking the max value of a double with a pow operation.
In order to do more iterations, I would need to set up my own math funcs to do math with arrays, and arrays to be able to store large values.
Gives 3.1415926535897931, a very accurate approximation of pi.
Edit:
Bleh, tabs not displaying. I'm certainly not converting them to spaces.
(Edited by Jackmn at 8:44 pm on May 21, 2003)
Can only do 49 iterations before breaking the max value of a double with a pow operation.
In order to do more iterations, I would need to set up my own math funcs to do math with arrays, and arrays to be able to store large values.
Gives 3.1415926535897931, a very accurate approximation of pi.
Code: Select all
#include <math.h>
#include <stdio.h>
double fact(double num) {
double result=1;
for(double i=2;i<=num;i++)
result*=i;
return result;
}
int main(int ARGC, char* ARGV) {
double xrec=0;
for(double i=0; i<42; i++)
xrec += (fact(4*i)*(1103+26390*i))/(pow(fact(i),4)*pow(396, 4*i));
xrec *= sqrt(8)/9801;
xrec = 1/xrec;
printf("%.20f", xrec);
return 0;
}
Edit:
Bleh, tabs not displaying. I'm certainly not converting them to spaces.
(Edited by Jackmn at 8:44 pm on May 21, 2003)

 level5
 Posts: 2725
 Joined: Sun Mar 17, 2002 4:40 pm
 Location: W. Australia
I can so as accurate as you like in one iteration, using Machin's fomula. This is accurate to 16 dp, the most you can get with type double.

//PI.CPP  Calculating pi
#include <math.h>
#include <stdio.h>
//double one = 1;
//double twothreenine = 239;
double X = 0.2;
double Y = one/twothreenine;
double arctanX;
double arctanY;
double pi;
void main()
{
arctanX = atan(X);
arctanY = atan(Y);
pi = 4*((4*arctanX)  arctanY);
printf("%.16f", pi);
}


//PI.CPP  Calculating pi
#include <math.h>
#include <stdio.h>
//double one = 1;
//double twothreenine = 239;
double X = 0.2;
double Y = one/twothreenine;
double arctanX;
double arctanY;
double pi;
void main()
{
arctanX = atan(X);
arctanY = atan(Y);
pi = 4*((4*arctanX)  arctanY);
printf("%.16f", pi);
}

ME!
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**

 level1
 Posts: 55
 Joined: Tue Apr 22, 2003 2:51 pm
 Location: Uk
 Contact:
Hehe, well as everyone else seemed to be using series I thought I would give the montecarlo method a go. I suspected it would be quite pants, and it was.
The accuracy varies each run as a different seed is used, but the best I saw out of it was 3.146 which you can beat with the good old 22/7. The accuracy does not seem to improve much either if you increase the iterations.
Nice range of solutions so far
CC
Code: Select all
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <time.h>
int main(int argc, char* argv)
{
double x,y;
double pi;
int n;
int hits=0;
srand( (unsigned)time( NULL ) );
for(n=0;n<20000;n++)
{
x=((2.0*rand()/RAND_MAX)  1);
y=((2.0*rand()/RAND_MAX)  1);
if( ((x*x)+(y*y)) < 1.0 )
hits++;
}
pi=4.0*hits/20000.0;
printf("%f\n",pi);
return 0;
}
The accuracy varies each run as a different seed is used, but the best I saw out of it was 3.146 which you can beat with the good old 22/7. The accuracy does not seem to improve much either if you increase the iterations.
Nice range of solutions so far
CC
Make something idiot proof, and someone will invent a better idiot.

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants
Actually, in school I had to write the same program, using the random numbers. I found if you have a VERY fast comp (2Ghz+) and are running nothing but your compiler, you can do around 500,000 iterations, and get 3.14159 pretty consistenly. Took ages though
"Had I succeeded, The Germans would claim me a German citizen, and the French would claim me a citizen of the world. Had I failed, the French would claim me a German, and the Germans would claim me a jew." Albert Einstein

 level1
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 Joined: Tue Apr 22, 2003 2:51 pm
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With 50000 iterations it is better, 3.1416 but still not as accurate as using one of the other non probabilistic algorithms.
I think you could produce a far more accurate answer if you made it completly non random and simply tried all the numbers from 1,1 to 1,1 with a step size which would give you x number of iterations.
I have just this week upgraded my machine to 2.4Ghz :0 I am a happy chappy!
I think you could produce a far more accurate answer if you made it completly non random and simply tried all the numbers from 1,1 to 1,1 with a step size which would give you x number of iterations.
I have just this week upgraded my machine to 2.4Ghz :0 I am a happy chappy!
Make something idiot proof, and someone will invent a better idiot.

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants

http://uplink.stewsburntmonkey.com/profile.php?Captain%20Chickenpants
 The GoldFish
 level5
 Posts: 3961
 Joined: Fri Mar 01, 2002 9:01 pm
 Location: Bowl / South UK
 Contact:
well, for a start trignometry is cheating, at least in my books. It's a theorum basically based on Pi. 4 arctan 1 = pi, after all
Anyway, I used VB (dont laugh ) and used the trapezium rule to estimate the area under a quarter circle of radius 1. given the total area = Pi r^2, r = 1 so the total area is just Pi. Times the output by 4 and you get Pi, or rather a decent approximation of it. Basically I got:
3.14159223790874
Which is alright, I think
I'm refining it now, so I reckon I can get even closer... hehe
Anyway, I used VB (dont laugh ) and used the trapezium rule to estimate the area under a quarter circle of radius 1. given the total area = Pi r^2, r = 1 so the total area is just Pi. Times the output by 4 and you get Pi, or rather a decent approximation of it. Basically I got:
3.14159223790874
Which is alright, I think
I'm refining it now, so I reckon I can get even closer... hehe
 The GoldFish  member of former GIT and commander in chief of GALLAHAD. You could have done something, but it's been fixed. The end. Also, play bestgameever!

 level5
 Posts: 2725
 Joined: Sun Mar 17, 2002 4:40 pm
 Location: W. Australia
How DARE you call me a cheat
It wasn't said we could use trig to get pi, and therefore mine is not only legal, but also the best as it get pi exactly in one iteration.
You just can't take losing
Oh, and I wrote a "Monte Carlo" one for my maths teacher. They are utter shite....
It wasn't said we could use trig to get pi, and therefore mine is not only legal, but also the best as it get pi exactly in one iteration.
You just can't take losing
Oh, and I wrote a "Monte Carlo" one for my maths teacher. They are utter shite....
ME!
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**
Procrastination  Hard work often pays of after time, but laziness always pays off now!
**Bibo ergo sum!**
 The GoldFish
 level5
 Posts: 3961
 Joined: Fri Mar 01, 2002 9:01 pm
 Location: Bowl / South UK
 Contact:
Actually your method of getting pi using trig is shite.
4 * arctan 1
is just a tad less complicated
4 * arctan 1
is just a tad less complicated
 The GoldFish  member of former GIT and commander in chief of GALLAHAD. You could have done something, but it's been fixed. The end. Also, play bestgameever!

 level1
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