Pi Script?

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03-15-2013, 02:39 AM
Sawyer

Pi Script?
I am trying to make a script to calculate pi. I am having toubles, but i am trying to use Leibniz's formula to do it. I have barely started, yet I am already getting errors.. Here's my code so far:
Simba Code:
```
Program MathProblems;
var
Answer:Extended;

procedure PieMaker;
var
i:Integer;
x, d, e:Extended;
begin
i := 7;
x := ((2/3)+(1/5))-(1/i);
IncEx(i, 2);
d := (x) + (1/i);
Answer:= d;
Writeln(''+IntToStr(Answer)+'');
end;

begin
end.
```
03-15-2013, 02:42 AM
rj

there is a pi solver under competitions i cant link you to it atm though not on computer
03-15-2013, 02:43 AM
Neodymium

So, you are trying to convert answer, which is of type extended, as an integer to a string.
So, you need to find a function that will convert type extended to a string. I'm looking around.

EDIT: FloatToStr() is what you want to use in place of IntToStr().
03-15-2013, 02:45 AM
rj

Quote:

Originally Posted by Neodymium

So, you are trying to convert answer, which is of type extended, as an integer to a string.
So, you need to find a function that will convert type extended to a string. I'm looking around.

tostr(varhere)
03-15-2013, 02:46 AM
Sawyer

Ah. Yes I know there is already a script for it, but I am bored and wanted to make my own.
Ah Thanks :)
03-15-2013, 02:50 AM
Neodymium

Quote:

Originally Posted by RJJ95

tostr(varhere)

That works too I guess, I didn't know there was a generic string converter.
I always have to go though the trouble of typing inttostr(). ;|

Ah. Yes I know there is already a script for it, but I am bored and wanted to make my own.
How does this look? (Using Leibniz's formula) It still gives me
"Exception in Script: Operator expected at line 18, column 1' (Line 18 is the Answer := (y + 2/3))
Simba Code:
Program MathProblems;
var
Answer:Extended;

procedure PieMaker;
var
i:Integer;
x, d, e, y:Extended;
begin
  i := 7;
  x := 5;
  repeat
    e := (1/x) - (1/i);
    IncEx(i, 2);
    IncEx(x, 2);
    y := (1/x) + (1/i);
  until((x = 999))
Answer:= (y + (2/3));
ToStr(Answer);
Writeln(''+FloatToStr(Answer)+'');
end;

begin
PieMaker;
end.

03-15-2013, 02:58 AM
Neodymium
Quote:

Originally Posted by Sawyer

Ah. Yes I know there is already a script for it, but I am bored and wanted to make my own.
How does this look? (Using Leibniz's formula)
-snip-

Now you are trying to increment a float as an integer, I think you need to do something like
Simba Code:
```
x := x + 2;
```
instead. I've run it just to test it out, and I get: "0.001001001001", in case you wanted to know.
03-15-2013, 03:00 AM
Sawyer

1 Attachment(s)

GAh... The 2/3 is missing.. darnit.. I'll work on it.
Leibniz's formula:
Attachment 19925

Note: X and I should not be extended, but integers :\
03-15-2013, 03:14 AM
Neodymium

Quote:

Originally Posted by Sawyer

GAh... The 2/3 is missing.. darnit.. I'll work on it.
Leibniz's formula:
Attachment 19925

Note: X and I should not be extended, but integers :\

Oh, so this is a series? I wonder if Simba has anything for that. :P

So I changed x to an integer as well, and put back the IncEx() call, but now I'm getting "0".
Something else is amiss.

Simba Code:

Program MathProblems;
var
Answer:Extended;

procedure PieMaker;
var
i, x:Integer;
d, e, y:Extended;
begin
  i := 7;
  x := 5;
  repeat
    e := (1/x) - (1/i);
    IncEx(i, 2);
    y := e + (1/i);
    IncEx(i, 2);
    d := y - (1/i);
    Answer := ((d + 2/3)*4)
  until(i = 999);
  FloatToStr(Answer);
  Writeln(''+FloatToStr(Answer)+'');
end;

begin
PieMaker;
end.

EDIT: Got 3.46265459826847 with this,

03-15-2013, 03:20 AM
Neodymium

Quote:

Originally Posted by Sawyer

-snip-
This I think would do it, but I am not sure how to writeln the answer.

Are you sure? I know you assign a value to Answer before the repeat loop, but you don't do anything with it afterwards.

Also, for writing the answer, I just threw in WriteLn(FloatToStr(Answer)) at the end of the main loop.

Quote:

Originally Posted by Sawyer

Simba Code:

Program MathProblems;
var
Answer:Extended;

procedure PieMaker;
var
i, x:Integer;
d, e, y, k:Extended;
begin
  i := 7;
  x := 5;
  k := 1 - (1/3);
  e := (k) + (1/x) - (1/i);
    repeat
    IncEx(x, 2);
    IncEx(i, 2);
    y := e + (1/i);
    IncEx(i, 2);
    IncEx(x, 2);
    d := y - (1/i);
    Answer := ((d)*4)
  until(i = 999);
  FloatToStr(Answer);
  Writeln(''+FloatToStr(Answer)+'');
end;

begin
PieMaker;
end.

EDIT: Got 3.46265459826847 with this,

The formula is (1 - 1/3 + 1/5 - 1/7 + 1/9 ... = pi/4) ... it could be possible that this is impossible to do..

03-15-2013, 03:50 AM
Neodymium
Out of curiosity, I looked for Leibniz's formula on Wolfram. Didn't find it, but I did find another formula:
http://i.imgur.com/8G3IdbC.png
So, I just used that and came up with:
Simba Code:
```
Program MathProblems;
var
Answer:Extended;

procedure PieMaker;
var
  cycles, i: Integer;
begin
  cycles := 300;
  for i := 0 to cycles do
    Answer := Answer + (pow(-1, i) / ((2 * i) + 1));
  Answer := Answer * 4;
end;

begin
PieMaker;
Writeln(''+FloatToStr(Answer)+'');
end.
```
Just another way to do this I guess.

After changing the number of cycles to 10000, I get "3.14169264359054". Getting close. xD

Edit: Currently trying out 100 million cycles, its been about 3 minutes since the program started and my laptop is kicking into gear. :P

Edit 2: I'm fairly certain this is the same formula as your's, just in the form of a summation.

Edit 3: STILL GOING.

Edit 4: After 100 million cycles and almost 20 minutes, I got "3.14159266358979". :D
03-15-2013, 04:23 AM
Sawyer

Nice! :D I'm going to hit the sack :p but I'll work on mine tomorrow. Nice job!
03-16-2013, 12:46 AM
Sawyer

Interesting. It seems after my experiment with changing variables, I broke my simba :/ I redownloaded and copied most of my folders over though.
03-16-2013, 06:15 PM
Sawyer

Quote:

Originally Posted by core

I don't think that should happen... Did you manage to get it fixed?

I just redownloaded simba, copied various extensions/includes and my scripts over. I'm not sure what happened... After I was playing around with the math, I just kept getting "Exception in Script: Operator expected at line 453, column 93 in file "C:\Simba\Includes\SRL\SRL\core\gametab.simba" for ever single script. The scripts worked with the other simba however.
03-16-2013, 06:37 PM
Smidqe

Quote:

Originally Posted by Sawyer

I just redownloaded simba, copied various extensions/includes and my scripts over. I'm not sure what happened... After I was playing around with the math, I just kept getting "Exception in Script: Operator expected at line 453, column 93 in file "C:\Simba\Includes\SRL\SRL\core\gametab.simba" for ever single script. The scripts worked with the other simba however.

Make sure that interpreter is NOT set to Lape. Found under Script -> Interpreter.
03-16-2013, 10:17 PM
Sawyer

Oh Duh I feel dumb. *facepalm* Thanks :p
03-17-2013, 12:12 AM
Richard

No one has gone recursive? :(

I'll edit this post in a second with a recursive one for lols, shame that for loops can only increment by 1 or -1 in Pascal
03-17-2013, 12:30 PM
Richard

Quote:

Originally Posted by core

You can manually increment/decrement the variables using IncEx(variable,amount) and DecEx(variable, amount), or variable := variable +/- amt.

I tried to do a recursive implementation, but kept hitting out of memory errors on large numbers of cycles. Looking forward to your solution!

I know, but I enjoy using for loops, although not necessary for doing this recursively.

However, I seem to have run into a dead end, my code only ever seems to output 4.0, rather than the actual value of pi. I've even got to the point of using a pen and paper, and drawn out trace tables, and my algorithm should work. Makes me think I've done something wrong with types.

Sorry about the poor code, I haven't actually programmed in quite some time:

Code:

program new; var i: integer; pi: extended; const depth = 120; function pi2: extended; begin inc(i); if (i = depth) then result := 1 / ((2 * i) + 1) else if ((i mod 2) = 0) then result := (1 / ((2 * i) + 1)) + pi2 else result := (1 / ((2 * i) + 1)) - pi2; end; begin pi := (4 * (1 - pi2)); writeln(floattostr(pi)); end.
03-17-2013, 12:58 PM
Richard

Quote:

Originally Posted by core

One error is that you're losing precision in your expressions.
If you change all of your to you should get results of the correct type... but I think there might be some other issue I haven't found yet. I'll update this post if I do.

Edits:

That does seem to have fixed it, I have a feeling it would be a type issue. Now it just turns out my maths was off :p

You can all go home now:

source: http://www.mathpropress.com/stan/bib...phy/spigot.pdf
edited by me

Simba Code:

Program Pi_Spigot;

const
  n   = 1000;
  len = 10*n div 3;

var
  i, j, k, q, x, nines, predigit: integer;
  tm: integer;
  a: array[1..len] of longint;
  res: String;


begin
  tm := getSystemTime;
  for j := 1 to len do
    a[j] := 2;                 {Start with 2s}
  nines := 0;
  predigit := 0;               {First predigit is a 0}
  for j := 1 to n do
  begin
    q := 0;
    for i := len downto 1 do   {Work backwards}
    begin
      x    := 10*a[i] + q*i;
      a[i] := x mod (2*i - 1);
      q    := x div (2*i - 1);
    end;
    a[1] := q mod 10;
    q := q div 10;
    if q = 9 then
      nines := nines + 1
    else
      if q = 10 then
      begin
          res := res + ToStr(predigit+1);
          for k := 1 to nines do
            res := res + ToStr(0);            {zeros}
          predigit := 0;
          nines := 0
            end
            else
            begin
          res := res + ToStr(predigit);
          predigit := q;
          if nines <> 0 then
          begin
            for k := 1 to nines do
              res := res + ToStr(9);
            nines := 0
          end
      end
  end;
  res := res + ToStr(predigit);
  writeln('took ' + ToStr(getSystemTime- tm) + ' ms');
  writeln(res);
end.

03-17-2013, 04:36 PM
Sawyer

Eh... Does that use Leibniz's Formula?

No, let me write it one sec

e:

okay, here it is:

Simba Code:

function PiLeib(): Extended;
var
  I:Integer;
begin
  for I := 0 to 100000000 do
  begin
    Result := Result + (1.0 / ((I shl 2) + 1));
    Result := Result - (1.0 / ((I shl 2) + 3));
  end;

  Result := Result * 4;
end;

03-17-2013, 06:19 PM
masterBB

But that is no longer the formula which was given to us :D. If that counts, so does the spigot algorithm I posted. Also you are comparing different stuff. I don't see how x iterations of your formula equals x iterations of mine. I won't let you win that easy ^^

We need more clear rules!
03-17-2013, 08:35 PM
masterBB
Quote:

Originally Posted by core

Au contraire, cher ami!

That is indeed the same formula, it is just restructured. The steps to arrive at it are outlined in my post before. Just multiplied it out and factored out a 2.

Ah, I am an idiot ;). Anyhow, results on my pc are different then yours, I get faster times with method. Reason is that processors aren't a fast with uints as they are with signed integers. But after optimizing your code by taking out * 16, yours was faster.
Simba Code:
```
function corePi (m : uint32) : Extended;
  var n : uint32;
begin
  for n := 0 to m do
  begin
    result := result + 1.0 / (n * ((n shl 4) + 16) + 3)
  end;
  result := result * 8;
end;
```

Quote:

Originally Posted by core

I don't think its possible to go much faster with this formula

You thought wrong:

Simba Code:

program new;

function corePi(m : uint32) : Extended;
  var n : uint32;
begin
  for n := 0 to m do
  begin
    result := result + 1.0 / (n * ((n * 16) + 16) + 3)
  end;
  result := result * 8;
end;

function corePi2(m : uint32) : Extended;
  var n : uint32;
begin
  for n := 0 to m do
  begin
    result := result + 1.0 / (n * ((n shl 4) + 16) + 3)
  end;
  result := result * 8;
end;

function corePi3(m : uint32) : Extended;
  var n : Integer;
begin
  for n := 0 to m do
    result := result + 0.5 / ((n * (n + 1.0)) + 0.1875);
end

var
  timez, i, trials, m:longint;
begin
trials := 10;
m := 10000000;

writeln('corePi: ' + FloatToStr(corePi(m)));
writeln('corePi2: ' + FloatToStr(corePi2(m)));
writeln('corePi3: ' + FloatToStr(corePi3(m)));

timez := GetTickCount;
for i:= 0 to trials do corePi(m);
writeln('corePi: ' + FloatToStr((GetTickCount-timez)/trials) + 'ms');

timez := GetTickCount;
for i:= 0 to trials do corePi2(m);
writeln('corePi2: ' + FloatToStr((GetTickCount-timez)/trials) + 'ms');

timez := GetTickCount;
for i:= 0 to trials do corePi3(m);
writeln('corePi3: ' + FloatToStr((GetTickCount-timez)/trials) + 'ms');

end.

e:

Results:
corePi: 3.14159260358979
corePi2: 3.14159260358979
corePi3: 3.14159260358979
corePi: 1748.8ms
corePi2: 1483.5ms
corePi3: 993.7ms

03-17-2013, 10:36 PM
Richard

Please tell me I'm not the only one who panicked when they saw the bitwise shifting? :p

I'm starting to get concerned about my competence for starting this degree in September...
03-17-2013, 11:05 PM
masterBB

Quote:

Originally Posted by Richard

Please tell me I'm not the only one who panicked when they saw the bitwise shifting? :p

I'm starting to get concerned about my competence for starting this degree in September...

Bitwise shifting is just a very fast multiply/divide operator. The only con is that you can only divide/multiply with powers of 2 (2, 4, 8, etc etc). There is also a restriction that it can only be used on integers, not on an extended for example

example:

10 shl 4 == 10 * 2^4 == 10 * 16

10 shr 3 == 10 / 2^3 == 10 / 8
03-17-2013, 11:29 PM
Richard

Quote:

Originally Posted by masterBB

Bitwise shifting is just a very fast multiply/divide operator. The only con is that you can only divide/multiply with powers of 2 (2, 4, 8, etc etc). There is also a restriction that it can only be used on integers, not on an extended for example

example:

10 shl 4 == 10 * 2^4 == 10 * 16

10 shr 3 == 10 / 2^3 == 10 / 8

Ah, I remember now, thank you :) It has been far too long since I've programmed. It's all very stressful

EDIT: Finally fixed my function doing it recursively. I don't know how to edit the stack size in Simba, so I did it in java. (you might want to edit the VM stack size to get some reasonable degree of accuracy with this)

Code:

public class Pi2 { static int depth = 1000000; public static void main(String[] args) { double pi = 4.0 * pi2(-1); System.out.print(pi); } private static double pi2(int i) { i++; if (i == depth) return 1.0 / ((2.0 * i) + 1.0); else return Math.pow(-1, i) * (1.0 / ((2.0 * i) + 1.0)) + pi2(i); } }

Win.
03-18-2013, 11:00 AM
masterBB
Quote:

Originally Posted by Richard

Finally fixed my function doing it recursively.
Simba Code:
```
function corePi4(m : uint32; n:Integer = 0) : Extended;
begin
* if n > m then
* * result := 0
* else
* * result := 0.5 / ((n * (n + 1.0)) + 0.1875) + corePi4(m, n+1);
end;
```
*

Note however that lape got a maximum amount of recursive calls it can do. Therefor this one will never be exact-ish.*

Quote:

Originally Posted by core

Always a pleasure to get schooled by masterBB! :)

It was also a pleasure to win. I enjoyed our script fight ^^ I like these kind of challenges. Next time I will beat you with a bigger distance for sure (nah, I can't pull this of twice) ;)

Quote:
Originally Posted by core
Simba Code:
function corePi5(m : uint32) : Extended;
begin
  result := 0.5 / ((m * (m + 1.0)) + 0.1875);
  if m > 0 then
    result := result + corePi4(m - 1);
end;
*Dusts off shoulders*
Ignoring that the code you posted is actually using my code ;) (+ corePi4) I improved it slightly, not really significant though.
Simba Code:
function corePi6(m : Integer) : Extended;
begin
  result := 0.5 / ((m * (m + 1)) + 0.1875);
  if not(m = 0) then
    result := result + corePi6(m - 1);
end;
edit:
note that I improved it for m numbers not much higher then 10000.

edit2:
my results were:
7.208 ms
6.396 ms

with 10000 m and 1000 t

03-18-2013, 11:58 AM
masterBB

Quote:

Originally Posted by core

This code does not produce results identical to all of the others, and is therefore invalid :p

Hmm, how strange. Your results don't match any of mine:
3.14154265858932
3.14154265858932
3.14154265858932
03-18-2013, 12:09 PM
masterBB

Quote:

Originally Posted by core

See my edit. I used m := 275052, which I believe is the highest m possible to run.

But what precision can we live with? The highest m mine was able to run with was 46340, because you tested it with 10000, I wanted to nail that test. My first quick write up was able to go much higher btw.

e:
after some testing I realized I am not going to make this much faster
so the winner is:
Core for a 46340 < m < 275052
Me for 0 < m < 46340

Simba Code:

under construction

Result:

Simba Code:

Compiled successfully in 219 ms.
 An       = 3.6356761630528E-6
 S(n-1)   = 0.78539907231979
 Pi/4     = 0.78539816339744
 4*S(n-1) = 3.14159628927917
 Pi       = 3.14159265358979
Time:4.7ms
Successfully executed.

In LaPe.

03-18-2013, 12:38 PM
masterBB

Quote:

Originally Posted by core

(or someone significantly beats us here)

I am afraid another Russian joined this thread :S
03-18-2013, 01:18 PM
masterBB

Quote:

Originally Posted by core

is against all the rules!

The rules which have not been written, yet are so clear to us :P

Simba Code:

function GetPi(e: Extended; var Cnt : Integer): extended;
var
  i,sng : Integer;
  dx,res : Extended;
begin
  I := 1;
  Sng := 1;
  dx := 1;

  while Abs(dx) > Abs(e) Do
    begin
      Res := Res + dx;
      Cnt:=Cnt+1;
      i:=i+2;
      Sng := Sng * (-1);
      dx := Sng/I;
    end;
  Res := Res * 4;
  Result:=Res;
end;

Output:

Simba Code:

Compiled successfully in 234 ms.
 Pi       = 3.14159065358979
500000
Time:7.8ms
Successfully executed.

03-18-2013, 01:44 PM
CynicRus

Quote:

Originally Posted by core

We mingle with the unseen and dance with the ephemeral :)

I'm just curious as to why the super script is still "under construction"...

Because there is not considered to Leibniz. I've used a monte-carlo method:)

And you said that it is against the rules-)

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