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I counted thousand decimals of pi with this program:
- Code: Select all
program ThousandPi;
uses bigdecimalmath, sysutils,DateUtils;
const accuracy = 1000;
accuracyfactor = 2;
type strindeksi = 1..accuracy;
var pi, pihelp1, pihelp2,five,number239,four,one,ind,two,divider: BigDecimal;
str: array [1..accuracy] of char;
time1,time2:Double;
function potency(a,n: BigDecimal):BigDecimal; // a^n
var output,i: BigDecimal;
begin
output:=1;
i:=1;
while i<=n do begin
output:=output*a;
i:=i+1;
end;
potency:=output;
end;
begin
time1:=Now;
pi:= 0;
ind:= 1;
pihelp1:=0;
pihelp2:=0;
five:=5;
number239:=239;
four:=4;
one:=1;
two:=2;
while ind <= (accuracy*2) do
begin
divider:=ind*(potency(five,ind));
pihelp1:= pihelp1+(divide(four, divider,accuracyfactor*accuracy));
divider:=(ind*(potency(number239,ind)));
pihelp2:= pihelp2-(divide(one, divider,accuracyfactor*accuracy));
ind:=ind+two;
divider:=(ind*(potency(five,ind)));
pihelp1:=pihelp1-(divide(four, divider,accuracyfactor*accuracy));
divider:=(ind*(potency(number239,ind)));
pihelp2:=pihelp2+(divide(one, divider,accuracyfactor*accuracy));
pi:=four*(pihelp1+pihelp2);
ind:=ind+two;
end;
time2:=Now;
Writeln((time2-time1)*86400,' second.');
str:=BigDecimalToStr(pi);
writeln(str);
end.
It use quite effective John Mach's serie:
but my program is not so effective
It counts thousand decimals in minute, but it took too long to count ten thousand. I made a graph of time requirements, and the curve raises very fast:
If I try to count N decimals I count numbers in accuracy of 2*N and take 2*N number from John Mach's serie. Maybe it is too much?
Because my program was too slow I downloaded 1 billion decimals: [url]https://pi2e.ch/blog/2017/03/10/pi-digi … /#download[/url] and made experiments. First I wanted to know the longest chain of the same numbers. Among the first billion, there is only one chain of nine consecutive identical numbers.
Decimals from 386 980 425 to 386 980 433 are 6 so there are nine of them 666666666. I done my discovery with this program:
- Code: Select all
program DiscoveryPi;
uses Sysutils;
var file1 : File of Char;
digit: char;
trythis : char;
longest : word;
amount,indexi : LongInt;
begin
Assign (file1,'PI.txt'); //There is billion decimals in this file
Reset (file1);
longest:=0;
indexi:=1;
While not Eof(file1) do
begin
read(file1,digit);
indexi:=indexi+1;
trythis:=digit;
amount:=0;
while (trythis=digit) and (not Eof(file1)) do
begin
amount:=amount+1;
read(file1,digit);
indexi:=indexi+1;
end;
if amount>=longest then
begin
longest:=amount;
writeln(indexi,'-',indexi+amount-1,' ',trythis,' ',amount);
end;
end;
end.
Then I wanted to know what is the longest sequence of consecutive numbers. I found that decimals between 956753757-956753765 are 012345678.
And thirdly I wanted know how long pi there is inside the pi. I found that there is twelve places where are eight numbers 31415926 among first billion digits of pi.
And last I discoveried the stats of different numbers:
0 99993942
1 99997334
2 100002410
3 99986912
4 100011958
5 99998885
6 100010387
7 99996061
8 100001839
9 100000273
Number 4 is the 'winner' and 3 is the 'loser'.
Useless discoveries, but fun to program!
I'm even now downloading 100 billion decimals...So let's see what I will found