Finding the value of pi=3.141592653589793238...

[AtoZ]

This program find the value of pi to some number of digits using the method to find an accurate value. Unfortunately, household computers are not very powerful and neither is the turing environment, therefore, it only calculates to 6 digits quickly. For my computer, with a speed of around 1.3mil loops/sec, it takes 25 seconds to get 7 digits, but only 3 seconds to get 6 digits.

Also, it calculates pi to 49 digits (which is the max in turing i think), but the correct digits are only limited to maybe 5-7.

If you have time or a very fast and powerful computer, run it for maybe 8-10 digits, and let me know if it works properly.

This program also finds your computer speed and your processor number and operating system.

If you post about the run time of the program, plz also post ur computer speed with it.

Oh btw, i copied the method to find the computer speed from a turing submission by Zren from this link:http://compsci.ca/v3/viewtopic.php?t=19986. So, sorry for copying, but it is not a major part of the program.

Turing:

% 4(1-1/3+1/5-1/7+...)= pi /*  Running time in ms     Number of digits (after the decimal) of pi you want.  12                     0  12                     1  12                     2  13                     3  35                     4  265                    5  2550                   6  25600                  7    These times are for a computer with a speed of  around 1.3 million loops/second. */ var correctdigits : int := 0 locate (20, 1) put "~~~ Note: Any value higher than 6 will take very long to process.~~~" locate (21, 1) put "For 6 digits, it takes approximately 2500 ms." put "After which the processing time increases by 10 times." locate (1, 1) put "Hello!" put "To how many correct digits of pi would you like to see: " .. get correctdigits const CONST := (10 ** correctdigits) const digits := 49 var x : array 1 .. CONST of real var y : array 1 .. CONST of real var answer1 : real var answer2 : real var total : real var pi : real for i : 1 .. CONST     x (i) := 1 / (-1 * (i * 4 - 1)) end for for i : 1 .. CONST     y (i) := 1 / (i * 4 - 3) end for answer1 := 0 for i : 1 .. CONST     answer1 := answer1 + x (i) end for answer2 := 0 for i : 1 .. CONST     answer2 := answer2 + y (i) end for total := answer2 + answer1 pi := 4 * total put "" put "The value of pi to the calculated digits: " put pi : 0 : digits put "" put "The value of pi to the correct digits: " .. put pi : 0 : correctdigits var speed : int := 0 function compSpeed : int     var tstart : int := Time.Sec     var t, cycle : int := 0     loop         t := Time.Sec         exit when t > tstart + 1         cycle += 1     end loop     result cycle end compSpeed speed := compSpeed put "" put "" put "Your compter speed: " .. put speed, " (loops/sec)" put "" put "Operating System: ", Config.Machine (cmOS) put "Processor Number: ", Config.Machine (cmProcessor)

MOD EDIT: Remember the code tags!

[Ultrahex]

Using your code:

code:

1 digits - 3.1 - Time: 0.019 seconds 2 digits - 3.14 - Time: 0.025 seconds 3 digits - 3.141 - Time: 0.100 seconds 4 digits - 3.1415 - Time: 0.152 seconds 5 digits - 3.14159 - Time: 0.628 seconds 6 digits - 3.141592 - Time: 4.794 seconds 7 digits - 3.1415926 - Time: 44.842 seconds 8 digits - failed (due to limit of dynamic allocation of an array)

Using my modification of your code (same algorithm):
(slower due to printing of statements, cause of other processes plus allocation of memory)

code:

1 digits - 3.1 - Time: 0.019 seconds 2 digits - 3.14 - Time: 0.346 seconds 3 digits - 3.141 - Time: 0.357 seconds 4 digits - 3.1415 - Time: 0.431 seconds 5 digits - 3.14159 - Time: 0.879 seconds 6 digits - 3.141592 - Time: 4.622 seconds 7 digits - 3.1415926 - Time: 52.552 seconds 8 digits - 3.14159265 - Time: 430.287 seconds 9 digits - Integer Overflow

1.4GHZ amd thunderbird
emulated using wine on linux

similar program written in C

code:

1 digits - 3.1 - Time: 0.000 seconds 2 digits - 3.14 - Time: 0.000 seconds 3 digits - 3.141 - Time: 0.000 seconds 4 digits - 3.1415 - Time: 0.000 seconds 5 digits - 3.14159 Time: 0.000 seconds 6 digits - 3.141592 - Time: 0.020 seconds 7 digits - 3.1415926 - Time: 0.310 seconds 8 digits - 3.14159265 - Time: 3.100 seconds 9 digits - 3.14159265(8?3) - Time: 31.750 seconds - INCORRECT (due to overflow)

Or if you want even better (14 digits, 0.179 seconds):

Turing:

var a :=1.0 var a2:=a var b:=1.0/sqrt(2.0) var t:=1.0/4 var p:=1 for i : 1 .. 3     a2 := (a+b)/2     b := sqrt(a*b)     t := t-p*(a-a2)**2     p := 2*p     a := a2; end for var pi := (a+b)**2/(4*t) put pi:0:14 put "Time: ", Time.Elapsed () / 1000, " seconds"

[The_Bean]

I would have to say memorizing the number of digits you want is a lot faster. Sure it might take 2 months for 155 decimal places, but then it only takes roughly 30 seconds to type it in. You can also use random sections from it for passwords.

Turing:

View.Set ("graphics:500,500,nobuttonbar,position:center,center") var pi : string := "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111" var timeStart : int var input : char Text.Colour (42) Text.ColourBack (7) cls put "Enter Pi to 155 decimal places!" loop     exit when hasch end loop timeStart := Time.Elapsed for i : 1 .. 157     input := getchar     if input = pi (i) then         put input ..     else         put "E"         put "You messed up at the number: ", i - 2, " decimal place."         exit     end if end for put "" put "That took: ", (Time.Elapsed - timeStart) / 1000

[michaelp]

http://www.gamedev.net/community/forums/topic.asp?topic_id=418236