Pi Script?

[Sawyer]

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:

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.

[rj]

there is a pi solver under competitions i cant link you to it atm though not on computer

[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().

[rj]

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)

[Sawyer]

Ah. Yes I know there is already a script for it, but I am bored and wanted to make my own.
Ah Thanks

[Neodymium]

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(). ;|

[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) It still gives me
"Exception in Script: Operator expected at line 18, column 1' (Line 18 is the Answer := (y + 2/3))

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.

[Neodymium]

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

x := x + 2;

instead. I've run it just to test it out, and I get: "0.001001001001", in case you wanted to know.

[Sawyer]

GAh... The 2/3 is missing.. darnit.. I'll work on it.
Leibniz's formula:
9e804b8a1a11e442be93fed1d52205a9.png

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

[Neodymium]

GAh... The 2/3 is missing.. darnit.. I'll work on it.
Leibniz's formula:
9e804b8a1a11e442be93fed1d52205a9.png

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.

[Sawyer]

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,

[Neodymium]

-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.

[Sawyer]

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..

[Neodymium]

Out of curiosity, I looked for Leibniz's formula on Wolfram. Didn't find it, but I did find another formula:

So, I just used that and came up with:

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".

[Sawyer]

Nice! I'm going to hit the sack but I'll work on mine tomorrow. Nice job!

[Sawyer]

Interesting. It seems after my experiment with changing variables, I broke my simba :/ I redownloaded and copied most of my folders over though.

[Sawyer]

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.

[Smidqe]

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.

[Sawyer]

Oh Duh I feel dumb. *facepalm* Thanks

[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

[Richard]

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:

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.

[Richard]

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

[masterBB]

You can all go home now:

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

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.

[Sawyer]

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

[masterBB]

No, let me write it one sec

e:

okay, here it is:

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;